Essays on Asset Allocation Strategies for Defined Contribution Plans
Anup Kumar Basu MBA QUT, BSc (Hons) Cal
Submitted in partial fulfilment of the requirements of the degree of Doctor of Philosophy The School of Economics and Finance Queensland University of Technology
Brisbane, Australia
January 2008
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Keywords and Abbreviations
• Asset Allocation
• Bootstrap Resampling
• Defined Contribution (DC) Plan
• Downside Risk
• Dynamic Lifecycle Strategy
• Expected Tail Loss (ETL)
• Lifecycle Fund
• Lower Partial Moment (LPM)
• Monte Carlo Simulation (MCS)
• Stochastic Dominance (SD)
• Tail Risk
• Terminal Wealth
• Value at Risk (VaR)
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Abstract
Asset allocation is the most influential factor driving investment performance.
While researchers have made substantial progress in the field of asset allocation
since the introduction of mean-variance framework by Markowitz, there is little
agreement about appropriate portfolio choice for multi-period long horizon
investors. Nowhere this is more evident than trustees of retirement plans
choosing different asset allocation strategies as default investment options for
their members. This doctoral dissertation consists of four essays each of which
explores either a novel or an unresolved issue in the area of asset allocation for
individual retirement plan participants. The goal of the thesis is to provide
greater insight into the subject of portfolio choice in retirement plans and
advance scholarship in this field.
The first study evaluates different constant mix or fixed weight asset allocation
strategies and comments on their relative appeal as default investment options.
In contrast to past research which deals mostly with theoretical or hypothetical
models of asset allocation, we investigate asset allocation strategies that are
actually used as default investment options by superannuation funds in
Australia. We find that strategies with moderate allocation to stocks are
consistently outperformed in terms of upside potential of exceeding the
participant’s wealth accumulation target as well as downside risk of falling
below that target by very aggressive strategies whose allocation to stocks
approach 100%. The risk of extremely adverse wealth outcomes for plan
participants does not appear to be very sensitive to asset allocation.
Drawing on the evidence of the previous study, the second essay explores
possible solutions to the well known problem of gender inequality in retirement
investment outcomes. Using non-parametric stochastic simulation, we simulate
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and compare the retirement wealth outcomes for a hypothetical female and male
worker under different assumptions about breaks in employment,
superannuation contribution rates, and asset allocation strategies. We argue that
modest changes in contribution and asset allocation strategy for the female plan
participant are necessary to ensure an equitable wealth outcome in retirement.
The findings provide strong evidence against gender-neutral default contribution
and asset allocation policy currently institutionalized in Australia and other
countries.
In the third study we examine the efficacy of lifecycle asset allocation models
which allocate aggressively to risky asset classes when the employee
participants are young and gradually switch to more conservative asset classes
as they approach retirement. We show that the conventional lifecycle strategies
make a costly mistake by ignoring the change in portfolio size over time as a
critical input in the asset allocation decision. Due to this portfolio size effect,
which has hitherto remained unexplored in literature, the terminal value of
accumulation in retirement account is critically dependent on the asset allocation
strategy adopted by the participant in later years relative to early years.
The final essay extends the findings of the previous chapter by proposing an
alternative approach to lifecycle asset allocation which incorporates
performance feedback. We demonstrate that strategies that dynamically alter
allocation between growth and conservative asset classes at different points on
the investment horizon based on cumulative portfolio performance relative to a
set target generally result in superior wealth outcomes compared to those of
conventional lifecycle strategies. The dynamic allocation strategy exhibits clear
second-degree stochastic dominance over conventional strategies which switch
assets in a deterministic manner as well as balanced diversified strategies.
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Contents
1. INTRODUCTION................................................................................................. 1
1.1 Background ...................................................................................................................... 1
1.2 Motivation ........................................................................................................................ 3
1.3 Research Objectives ......................................................................................................... 6
1.4 Thesis Structure and Research Description................................................................... 10
2. LITERATURE REVIEW ............................... ..................................................... 14
2.1 Behavioural Biases Influencing Portfolio Choice........................................................... 15
2.2 Default Investment Options in Retirement Plans .......................................................... 18
2.3 Modern Portfolio Theory and Asset Allocation............................................................. 25
2.4 Lifecycle Asset Allocation Strategies.............................................................................. 32
2.5 Optimal Asset Allocation Strategy for DC plans ........................................................... 45
2.6 Strategic Asset Allocation: Role of Equity Premium.....................................................52
2.7 Measures of Risk ............................................................................................................ 56
2.8 Measures of Investment Performance............................................................................ 62
3. METHODOLOGY AND DATA ............................ .............................................. 68
3.1 Model Description .......................................................................................................... 68 3.1.1 General Structure................................................................................................... 68 3.1.2 Control Variables.................................................................................................... 70 3.1.3 Other Variables....................................................................................................... 71
3.2 Asset Class Return Generating Process ......................................................................... 72 3.2.1 Monte Carlo Simulation......................................................................................... 74 3.2.2 Bootstrap Resampling............................................................................................. 77
3.3 Data ................................................................................................................................ 80 3.3.1 Asset Class Returns................................................................................................. 80 3.3.2Asset Allocation of Default Strategies...................................................................... 83 3.3.3 Earnings Data......................................................................................................... 83
4. EVALUATION OF FIXED WEIGHT STRATEGIES AS DEFAULT OPTIONS... 84
4.1 Introduction.................................................................................................................... 84
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4.1.1 Background............................................................................................................. 84 4.1.2 Research Description.............................................................................................. 86 4.1.3 Summary of Findings.............................................................................................. 89
4.2 Metrics for Evaluating Retirement Wealth Outcomes .................................................. 90
4.3 Methodology ................................................................................................................... 96
4.4 Data ................................................................................................................................ 98
4.4 Results and Discussion ..................................................................................................104 4.4.1 RWR Distribution..................................................................................................105 4.4.2 Downside Risk and Risk-Adjusted Performance Estimates..................................111 4.4.3 Tail-Related Risk Estimates...................................................................................117
4.5 Conclusion .....................................................................................................................124
5. GENDER-SENSITIVE CONTRIBUTION AND ASSET ALLOCATI ON STRATEGIES IN SUPERANNUATION PLANS ................. .................................142
5.1 Introduction...................................................................................................................142 5.1.1 Background............................................................................................................142 5.1.2 Research Description.............................................................................................143 5.1.3 Summary of Findings.............................................................................................144
5.2 Methodology ..................................................................................................................144
5.3 Data ...............................................................................................................................148 5.3.1 Earnings Data........................................................................................................148 5.3.2 Asset Class Returns................................................................................................153
5.4 Results and Discussion ..................................................................................................153 5.4.1 Contribution Rate..................................................................................................153 5.4.2 Asset Allocation......................................................................................................157 5.4.3 Combination...........................................................................................................163
5.5 Conclusion .....................................................................................................................167
6. PORTFOLIO SIZE EFFECT AND LIFECYCLE ASSET ALLOCA TION ..........169
6.1 Introduction...................................................................................................................169 6.1.1 Background............................................................................................................169 6.1.2 Research Description.............................................................................................172 6.1.3 Summary of Findings.............................................................................................173
6.2 Methodology ..................................................................................................................174 6.2.1 Lifecycle and Contrarian Strategy Pairs...............................................................175 6.2.2 Bootstrap Resampling............................................................................................180 6.2.3 Data........................................................................................................................181
6.3 Results and Discussion ..................................................................................................182 6.3.1 Terminal Wealth Estimates...................................................................................182
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6.3.2 Accumulation Paths over Horizon.........................................................................185 6.3.3 Adverse Outcomes and Tail Risk...........................................................................190
6.4 Conclusion .....................................................................................................................193
7. A DYNAMIC ASSET ALLOCATION FRAMEWORK FOR LIFECYC LE INVESTING IN RETIREMENT PLANS ...................... ......................................... 200
7.1 Introduction...................................................................................................................200 7.1.1 Background............................................................................................................200 7.1.2 Research Description.............................................................................................201 7.1.3 Summary of Findings.............................................................................................205
7.2 Methodology ..................................................................................................................205 7.2.1 Conventional Versus Dynamic Lifecycle Strategy.................................................205 7.2.2 Bootstrap Resampling............................................................................................208 7.2.3 Stochastic Dominance............................................................................................210 7.2.4 Shortfall Measures for Dynamic Strategy.............................................................211
7.3 Results and Discussion ..................................................................................................212 7.3.1 Terminal Wealth Estimates...................................................................................212 7.3.2 CDF and Stochastic Dominance Test.....................................................................214 7.3.3 Shortfall Estimates for Dynamic Strategy.............................................................218 7.3.4 Extreme Adverse Outcomes...................................................................................221
7.4 Conclusion .....................................................................................................................223
8. CONCLUSION................................................................................................ 226
8.1 Scholarly Contributions ................................................................................................226
8.2 Relevance.......................................................................................................................229
8.3 Limitations & Avenues for Future Research................................................................230
REFERENCES.................................................................................................... 233
APPENDIX A: REAL RETURN DATA FOR AUSTRALIAN AND US ASSET CLASSES............................................ ............................................................... 253
APPENDIX B: NOMINAL RETURNS DATA FOR AUSTRALIAN ASS ET CLASSES (1900-2004)................................ ....................................................... 256
APPENDIX C: NOMINAL RETURNS DATA FOR US ASSET CLASS ES (1900-2004) ........................................................................................................ 257
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List of Tables
TABLE 4.1: ASSET ALLOCATION OF DEFAULT INVESTMENT OPTIONS..................102
TABLE 4.2: DISTRIBUTION PARAMETERS OF RETIREMENT WEALTH RATIO (RWR)
....................................................................................................................................105
TABLE 4.3: ESTIMATES FOR DOWNSIDE RISK AND PERFORMANCE MEASURES..113
TABLE 4. 4: TAIL RISK ESTIMATES FOR RWR DISTRIBUTION...................................119
TABLE 4B.1 DISTRIBUTION PARAMETERS FOR RWR .................................................129
TABLE 4B.2 ESTIMATES FOR DOWNSIDE RISK & PERFORMANCE MEASURES......130
TABLE 4B.3 TAIL RISK ESTIMATES................................................................................131
TABLE 4C.1 ASSET ALLOCATION FOR DEFAULT INVESTMENT OPTIONS..............132
TABLE 4C.2 DISTRIBUTION PARAMETERS OF RETIREMENT WEALTH RATIO (RWR)
....................................................................................................................................133
TABLE 4C.3 ESTIMATES FOR DOWNSIDE RISK AND PERFORMANCE MEASURES 136
TABLE 4C.4 TAIL RISK ESTIMATES FOR RWR DISTRIBUTION ..................................139
TABLE 5.1: WEEKLY INDIVIDUAL INCOME OF AUSTRALIAN MEN AND WOMEN BY
AGE............................................................................................................................149
TABLE 5.2 ACCUMULATION OUTCOMES FOR DIFFERENT FEMALE CONTRIBUTION
RATES........................................................................................................................155
TABLE 5.3: ACCUMULATION OUTCOMES FOR DIFFERENT FEMALE ASSET
ALLOCATION STRATEGIES....................................................................................159
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TABLE 5.4: EXTREME ADVERSE OUTCOMES FOR DIFFERENT FEMALE ASSET
ALLOCATION STRATEGIES....................................................................................162
TABLE 5.5: ACCUMULATION OUTCOMES FOR DIFFERENT FEMALE
CONTRIBUTION RATES AND ASSET ALLOCATION STRATEGIES....................165
TABLE 6.1: TERMINAL VALUE OF RETIREMENT PORTFOLIO IN NOMINAL
DOLLARS ..................................................................................................................183
TABLE 6.2: VAR ESTIMATES FOR LIFECYCLE & CONTRARIAN STRATEGIES ........191
TABLE 7.1: TERMINAL VALUE OF RETIREMENT PORTFOLIO IN NOMINAL
DOLLARS ..................................................................................................................213
TABLE 7.2: SHORTFALL MEASURES OF DYNAMIC STRATEGIES RELATIVE TO
OTHER ASSET ALLOCATION STRATEGIES..........................................................219
TABLE 7.3: VAR ESTIMATES FOR DIFFERENT ASSET ALLOCATION STRATEGIES222
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List of Figures FIGURE 4.1 RWR DISTRIBUTION PARAMETERS OF ASSET ALLOCATION
STRATEGIES.............................................................................................................109 FIGURE 4.2 DOWNSIDE RISK ESTIMATES OF ASSET ALLOCATION STRATEGIES..112 FIGURE 4.3 TAIL RISK ESTIMATES OF ASSET ALLOCATION STRATEGIES .............122
FIGURE 4A.1: SIMULATED RWR DISTRIBUTION..........................................................127
FIGURE 5.1: INCOME DISTRIBUTION OF AUSTRALIAN POPULATION......................151 FIGURE 5.2: EARNINGS PROFILE OF AUSTRALIAN POPULATION BY AGE .............152
FIGURE 6.1: ASSET ALLOCATION OVER INVESTMENT HORIZON (PAIR A) ............176
FIGURE 6.2: ASSET ALLOCATION OVER INVESTMENT HORIZON (PAIR B).............177
FIGURE 6.3: ASSET ALLOCATION OVER INVESTMENT HORIZON (PAIR C).............178
FIGURE 6.4: ASSET ALLOCATION OVER INVESTMENT HORIZON (PAIR D) ............179
FIGURE 6.5: SIMULATED ACCUMULATION PATHS OVER INVESTMENT HORIZON
(PAIR A) .....................................................................................................................186
FIGURE 6.6: SIMULATED ACCUMULATION PATHS OVER INVESTMENT HORIZON
(PAIR B) .....................................................................................................................187
FIGURE 6.7: SIMULATED ACCUMULATION PATHS OVER INVESTMENT HORIZON
(PAIR C) .....................................................................................................................188
FIGURE 6.8: SIMULATED ACCUMULATION PATHS OVER INVESTMENT HORIZON
(PAIR D) .....................................................................................................................189
FIGURE 6A.1: TWO-DIMENSIONAL VIEW OF ACCUMULATION PATHS OVER
HORIZON (PAIR A) ...................................................................................................196 FIGURE 6A.2: TWO-DIMENSIONAL VIEW OF ACCUMULATION PATHS OVER
HORIZON (PAIR B) ...................................................................................................197
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FIGURE 6A.3: TWO-DIMENSIONAL VIEW OF ACCUMULATION PATHS OVER HORIZON (PAIR C) ...................................................................................................198
FIGURE 6A.4 TWO-DIMENSIONAL VIEW OF ACCUMULATION PATHS OVER
HORIZON (PAIR D) ...................................................................................................199
FIGURE 7.1: CUMULATIVE DISTRIBUTION PLOTS FOR FIRST PAIR OF LIFECYCLE
AND DYNAMIC STRATEGIES ( 20,20LC AND )20,20DLC ....................................215
FIGURE 7. 2: CUMULATIVE DISTRIBUTION PLOTS FOR SECOND PAIR OF
LIFECYCLE AND DYNAMIC STRATEGIES ( 10,30LC AND )10,30DLC ...............217
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Statement of Original Authorship
The work contained in this thesis has not been previously submitted to meet
requirements for an award at this or any other higher education institution. To
the best of my knowledge and belief, the thesis contains no material previously
published or written by another person except where due reference is made.
Signature: Date:
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Acknowledgements
This thesis is the outcome of an amazing voyage during which I have been supported by many people. I wish to acknowledge the efforts of these remarkable individuals who have enriched my journey in several ways. Professor Michael Drew, the principal supervisor of my thesis, was instrumental in my relocating to Australia and joining the doctoral research program three years back. Whatever progress has been achieved since then, academic and otherwise, is largely because of Mike’s constant support and guidance for which I would remain ever indebted. I would also like to express great appreciation for the efforts of Peter Whelan who, as my associate supervisor, has provided valuable feedback on many aspects of the research. Apart from the supervisory team, several other members within the school have extended helpful support throughout the program. Special thanks go to Professor Stan Hurn and Associate Professor Adam Clements for being extremely generous with their time whenever approached. Such collegial relationships are essential for nurturing early career researchers and I consider myself very fortunate to have colleagues like Stan and Adam around. I would like to thank Dr. Robert Bianchi, Evan Reedman, and John Polichronis for their friendship which lightened up many afternoons that were often quite ordinary in terms of research output. Being a recent recipient of the doctorate degree, Rob has also been helpful in passing on some of the ‘tricks of the trade’. The research has benefited from ongoing discussions with several prominent scholars from different academic institutions around the world. Those who deserve special mentioning include Martin Gruber and Stephen Brown from New York University, Christopher James from University of Florida, and Alistair Byrne from University of Edinburgh. Finally, I express deepest gratitude to my family members. To my parents, Piyush and Sipra, who have always reposed their trust on my abilities and provided unwavering support to all my endeavours. To my sister, Mousumi, her prayers and good wishes have been with me all the time. To my uncle, Debesh, for taking keen interest in my career at all times. To my wife, Swati, for her constant love, care, encouragement, not to forget outstanding proofreading skills, which have all contributed to smooth completion of the thesis. Her patience in bearing with my absence over numerous weekends, withstanding the relentless clatter of the keyboard into the wee hours of many a morning, and compensating for my general lack of attention to household affairs has left me with no excuse for not completing the task on time. Our newborn son, Siddharth, has also been very cooperative (perhaps knowingly) by sleeping quietly through most evenings while finishing touches were being applied to this document.
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1. Introduction
1.1 Background
In most developed countries, the rapidly aging population, with a rising
proportion of retirees, have started placing considerable pressure on current
social security programs. This demographic trend is likely to continue rendering
benefits from social security uncertain for future retirees, unless there is a sharp
increase in productivity. In light of this situation, many governments are
attempting to limit their social security related commitments by moving out of a
pay-as-you-go social security framework towards a funded system where
individuals build up their retirement savings during their working life through
investment of mandatory or voluntary contributions into retirement plans
(generally set up by their employers or other private providers). These
retirement savings, they feel, would promote better income security and standard
of living for retirees while rationalizing the burden of running costly social
security programs.
Currently retirement plans mainly belong to two broad categories – defined
benefit (DB) and defined contribution (DC) – which differ in terms of
distribution of risk between the plan sponsor and the participants. In the former,
the sponsor undertakes to pay the employee participants (members) on their
retirement a fixed benefit proportionate to their final or average salary, with the
proportion generally determined by the length of their tenure in the plan. In
doing so, the sponsor assumes the investment risk because the benefits have to
be paid even if the plan assets decline in value. In contrast to this, investment
risk in a DC plan is borne by the participants because retirement benefits are
2
entirely dependent on their contributions to the plan and accumulated investment
returns.
DC plans are fast becoming the principal foundation of private sector retirement
system around the world.1 These plans are typically self-directed or self-
managed in nature where the participant makes investment decision of their plan
contributions by selecting from a range of investment options provided by the
plan provider. This is in line with the worldwide trend of giving the individual
participants more control over the decision of how their retirement plan assets
are invested. However, whether such choice is actually exercised also remains a
matter of choice i.e. in most plans the participants are free to decide whether or
not to exercise control over the investment of their plan contributions.
The idea of providing employees more autonomy and choice over investments
in DC plans is underpinned by an implicit assumption – the employee-
participants are well-informed economic agents who are capable of maximizing
their self interests by making rational investment decisions and implementing
them. The investment decision for the participants in a DC plan, typically,
involves selecting an asset allocation strategy for investing the plan
contributions i.e. how to allocate capital between available asset classes like
stocks, bonds, cash, and other alternative assets. But there is now sufficient
global evidence to suggest that majority of plan participants refrain from
selecting the investment strategies for their own retirement accounts (for
example, Choi, Laibson, Madrian & Metrick, 2002; Cronqvist & Thaler, 2004).
For all participants who do not choose an investment strategy for their plan
assets, most retirement plans provide a default investment strategy to direct their
plan contributions. The asset allocation decision, irrespective of whether it is
made by the plan sponsors or the participants themselves, has a significant
1 For instance, in Australia, which has a more well-established private retirement system than most countries, the majority of retirement plans belong to the DC category.
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impact on the final wealth outcome and, therefore, on their financial well being
of the participants in retirement. The asset allocation strategies that are currently
offered by DC plan providers and those suggested in literature constitute the
focal point of our investigation in this doctoral dissertation.
1.2 Motivation
The value of the retirement portfolio at the end of an employee’s working life
determines the amount of annuity that he or she is able to purchase at retirement
and how much of the pre-retirement income he or she is able to replace after
retirement.2 Ignoring transaction costs and taxes, the value of retirement
portfolio of an individual during the accumulation phase (normally the
employment tenure of the individual) depends on two factors: (i) contribution
rate and (ii) investment returns on the accumulated contributions. If
contributions are only those made by the employers at the mandatory rate
prescribed by the government, investment returns solely determine the variation
in retirement wealth accumulated by an individual at the end of his or her
working life.3 Following the seminal work of Brinson, Hood, and Beebower
(1986), most academics and practitioners accept that asset allocation is the
dominant driver of a portfolio’s investment returns over long horizons. Since
retirement plan assets of individuals in DC plans are invested over a span of
several decades, it is reasonable to identify asset allocation as the key
determinant of their final retirement wealth.
2For example, Vittas (1992) show that with 40 years of contribution at the rate of 10%, real wage growth of 2%, and life expectancy of 20 years after retirement, real return of 3% would obtain an indexed pension of 33% of final salary while a real return of 5% would obtain an indexed pension to replace 60% of final salary. 3 This applies to much of the working population in Australia.
4
Given such important role of asset allocation in influencing the wealth outcome
at retirement, one would expect that the investment choices within DC plans and
their asset allocation structures are designed with utmost care by the plan
sponsors or the trustees. The nomination of the default option among available
investment choices in a plan is even more important considering that there is
enough evidence (for instance, Beshears, Choi, Laibson & Madrian, 2006) to
suggest that many individuals perceive the default choices offered to them as
recommendation or endorsement of a particular course of action by the provider.
Not only do most participants adopt the default choice, but they are also likely to
persist with it for much of their working life. Given the very long horizon of
retirement plan investments, a sub-optimal default asset allocation strategy runs
enormous risk for the participants. A mistake committed at the outset is unlikely
to be reversed at a later date and the compounding effect over the long horizon
can lead to very adverse outcomes, even potentially ruinous in some cases.
Whether the failure of participants to exercise choice is due to perceived lack of
relevant investment knowledge and skills, inadequacy of the available options,
or common biases in human behaviour is a topic that has been widely debated
and researched in recent times. Much less attention has been devoted towards
the appropriateness of the default and other investment options made available
to the participants. This is surprising considering that there is wide disparity in
asset allocation of the default fund which indicates a complete lack of consensus
among retirement plan providers on the subject. The range of asset allocation
strategies and lifecycle profiles used as default choices by different plans is so
wide that it leads Blake, Byrne, Cairns, and Dowd (2006) to comment that the
concerned members face a virtual lottery in terms of retirement outcomes. In
Australia, the problem of members across different superannuation funds facing
significantly different end benefits due to difference in their default choices is
highlighted by Gallery, Gallery, and Brown (2004). The difference is even more
5
acute when one compares retirement plans across different countries.4 Although
there is general agreement about the objective of these investment vehicles -
generating adequate retirement wealth for the participants - it seems plan
sponsors in different countries have very different ideas about the ‘right’ asset
allocation strategy needed to achieve this goal.
While the reasons for retirement plan participants’ apparent reluctance to take
charge of their own financial destiny is a topic worthy of debate in its own right,
we feel the question of appropriateness of the asset allocation strategy is more
important from a practical standpoint and deserves serious attention from the
academic community. Retirement plans with their long investment horizons
provide fertile testing ground for examining the desirability of alternative asset
allocation strategies for long term investors. The researcher has good
opportunity to study their outcomes over many periods and comment on their
appropriateness.
The issue of default choice is particularly important from policy perspective.
Although public policy is neutral regarding setting the default investment option
(or even the menu of investment choices) offered to participants in DC plans i.e.
individual plan sponsors are free to choose the asset allocation structure for
default options as they deem fit, as Beshears et al. (2006) point out the defaults
themselves are not neutral since they either facilitate or hinder the desired
retirement outcome. One of the foremost goals of public policy associated with
retirement savings is to promote institutions that provide sufficient income to
retired individuals in order to reduce the government’s burden in running costly
social welfare programs. As asset allocation choices can significantly affect the
retirement outcome for participants in DC plans, it is important to find out
whether policy intervention is necessary to encourage any particular type of
4 Although no study to our knowledge has documented the issue of inter-country differences in selection of default options in retirement plans, we present evidence for four countries in 2.2.
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asset allocation approach as default investment strategy for investment of
retirement assets. This is the key motivation behind this doctoral dissertation.
1.3 Research Objectives
Empirical research on asset allocation for DC plan investors is still in the
developing stage. Therefore researchers are presented with opportunities to
examine a number of interesting issues and add to the existing body of
knowledge. Although studies like Gallery et al. (2003) and Blake et al. (2006)
have highlighted the vast range of asset allocation strategies used by trustees as
default investment strategies in retirement plans, little progress has been made
by researchers in evaluating these strategies and commenting on their
appropriateness as default arrangements. This investigation is necessary to
adjudge the best course of action given our experience with return
characteristics from different asset classes over past several decades. Also,
gender inequality in the labour market outcomes is a serious problem and
several authors have expressed concern that this overflows to the retirement
system and tends to create major disparity in wealth accumulation between the
typical male and female employee. Yet most studies of default options in DC
plans have universally considered the case of a male worker with uninterrupted
career profile. No suggestion has been made in the literature to put up an
alternative investment strategy for the female worker which would alleviate this
problem.
Although academic research on asset allocation strategies in DC plans is a
relatively new area of interest, asset allocation per se is not a new topic in
investment; the basic concept is known to be prevalent from the days of the
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Talmud almost 2000 years ago.5 But as with practitioners, there is a glaring lack
of agreement among scholars in this field on the issue of appropriateness of
asset allocation decisions over long horizons. Siegel (2003) recommends
investors to allocate heavily to equities over long horizons. Kim and Wong
(1997) also find 100% equity strategy dominant over all other strategies for long
horizon investors. This is supported by Vigna and Haberman (2002) but only in
case of a risk neutral investor. Other studies like Booth and Yakoubov (2002)
and Blake, Cairns, and Dowd (2001) do not support such strong conclusions.
They suggest that DC plan participants should pursue a well diversified strategy
till retirement.
There is also considerable debate about adoption of lifecycle strategies, which
has gained substantial popularity among retirement planners in recent years.6
Lifecycle funds in USA and UK have enjoyed phenomenal growth in recent
years so much so that they are the most commonly used default investment
options in the latter. Yet, most Australian superannuation funds do not offer
lifecycle investment options to their members. Typically lifecycle models
recommend investing heavily in the stock market when the plan participants are
young and have a long investment horizon but systematically switch towards
less volatile assets like bonds and cash in the last few years before retirement.
The belief that stocks are less risky over long horizons than over short horizons
has been theoretically challenged by Samuelson (1963, 1989). Bodie (1995)
lends support to this using option pricing theory. Among empirical research,
Hibbert and Mowbray (2002) as well as Blake, Byrne, Cairns, and Dowd (2006)
5 ‘Let every man divide his money into three parts, and invest a third in land, a third in business, and a third let him keep in reserve’ says the Talmud, Circa 1200 B.C.- 500 A.D (Gibson, 2000) 6 Sometimes the term ‘lifestyle’ is used interchangeably with ‘lifecycle’ by some authors in the popular press. But these two are distinct investment strategies. The former allocates a constant proportion of assets to risky investments according to investor’s risk tolerance whereas the latter gradually changes allocation to risky assets according to the investor’s age or length of the investment horizon. Viciera (2007) provides a good exposition on the subject.
8
find that lifecycle strategies can be effective in reducing investment risk, but at
the cost of lowering the expected terminal wealth for the plan participant.
However, recent research like Poterba, Roth, Venti, and Wise (2006) indicate
that the retirement wealth distribution in case of lifecycle strategies do not differ
from those of other strategies in many cases. Shiller (2005a) does not find
evidence to support of the lifecycle asset allocation model.
The lifecycle model of asset allocation has remained a controversial area for
academic researchers. While the model has been popular among practitioners in
many countries, its claim of superiority especially over constant mix strategies
has received mixed support from scholars in this field. Even among the
proponents of lifecycle strategy, there is little agreement about the precise point
of time when the asset switching should commence as well as the switching
mechanism itself.7 Moreover, the current literature in DC plan investments has
largely ignored the fact that the size of contributions of DC plan investors are
likely to grow over the years (Shiller, 2005b), which along with compounding of
investment returns, would contribute to a growing portfolio size as one
approaches retirement. The significance of the interplay between this increasing
portfolio size and asset allocation strategy in determining the final wealth
outcome of the retirement plan investor has never been examined. This has
resulted in lack of proper understanding about what precisely leads to success or
failure of lifecycle strategies (relative to other strategies) in generating desired
wealth outcomes for participants in DC plans. A number of studies in recent
years do not find any evidence to justify the popularity of lifecycle strategies
among plan sponsors and investors. But since this body of work barely
investigates the reason behind this apparently inferior performance of the
lifecycle strategy, there is noticeable reluctance among scholars to propose an
7 For example, linear versus non-linear.
9
alternative model of lifecycle asset allocation that would yield superior
outcomes.8
In terms of methodology and research design, a review of the current literature
on DC plans reveals three shortcomings. Firstly, most of these studies seem to
examine only a small number of asset allocation strategies compared to the vast
number of possible alternatives. Also, very few of these directly investigate the
actual strategies offered by DC plan providers. Secondly, researchers have
focussed on conventional measures of risk and rewards in ranking alternative
approaches to asset allocation. A few studies are exclusively based on risk
measures like value-at risk (VaR), whose validity has been questioned in recent
times. Important downside risk measures like lower partial moments (Bawa,
1975; Fishburn, 1977), which can be extremely useful in evaluating investment
outcomes, have remained largely ignored. Finally, almost all research on DC
plans has used asset class return data from either the United States (US) or the
United Kingdom (UK). There is a growing body of evidence (Dimson, Marsh &
Staunton, 2002)) that the experiences of these markets over the last century have
not been necessarily similar to that of every other nation. Since evaluation of
asset allocation strategies is largely dependent on the data used by the
researchers, the relevance of their findings for DC plan participants in other
markets remains questionable to some extent.
This doctoral research seeks to address some of the above inadequacies and
advance academic research on asset allocation decisions of DC plans. We test
asset allocation strategies with the specific aim to evaluate their appeal as
default investment options in DC plans. The study then further examines the
case for instituting a gender-specific default investment option to reduce the
disparity in wealth outcomes between male and female participants. In our study
8 Blake et al. (2001) is one of the exceptions in testing novel allocation strategies for DC plan participants. However, it does not pose these models as alternatives to lifecycle model and therefore, does not attempt to address the latter’s shortcomings.
10
of lifecycle and other asset allocation strategies, we not only consider the final
investment outcomes in terms of their risk-return characteristics but also explore
the accumulation process over the entire investment horizon. This leads to a
better understanding of the interplay of asset allocation with the portfolio size at
different points on the horizon and how this influences the final outcome.
In contrast to most researchers who have tested theoretical or hypothetical
models of asset allocation, a part of this doctoral dissertation examines many
asset allocation strategies that are actually used as default options within DC
plans. In addition, we investigate asset allocation models that are suggested in
literature but which are not currently used by practitioners. We adopt a
fundamentally different approach than many of the past studies in using
alternative measures of risk based on wealth accumulation target. The robust
measures of downside risk and related performance metrics exploited in this
research have been suggested earlier in economics literature but rarely employed
in evaluation of competing asset allocation models. A part of the novelty of this
research lies in the fact that it employs long run return data (over one hundred
years) for Australian asset classes for the first time to evaluate asset allocation
decisions in DC plans.
1.4 Thesis Structure and Research Description
The essays in this dissertation share the common theme of asset allocation in DC
plan investments. Each of these examines a distinct, well defined research
problem related to the main topic and occupies a separate chapter. In addition,
the thesis contains chapters on literature review, and methodology and data,
which apply commonly to all the research problems within this doctoral study.
Brief outline of each chapter is provided below.
11
The following chapter reviews the literature relevant to all the essays in this
dissertation. It initially covers the behavioural foundations of investment choice
and default options in DC plan. Next, we review the pioneering work of
researchers in the field of modern portfolio theory and how it relates to asset
allocation decision over long horizon. Further, the theoretical and empirical
research conducted so far in the area of asset allocation within DC plans is
discussed. The role of equity premium in asset allocation and related research is
also covered in this context. Finally, we look into the existing literature for
proposed measures of downside risk and investment performance as these play a
significant role in evaluation of asset allocation strategies in this thesis.
In Chapter 3, we put forward the stochastic simulation model used to generate
terminal wealth outcomes for DC plan participants. This general model is used
in all the four essays with minor variations that are discussed within each
chapter. We also explain two methods that have been employed to generate
returns every period for individual asset classes. The bootstrap resampling
method is used in all the chapters in generating portfolio returns over the
investment horizon while the Monte Carlo method is additionally employed in
the research taken up in chapter 4. Finally, we discuss the data used in this
dissertation. This mainly comprises of historical returns on different asset
classes in the Australian (used in chapters 4 and 5) and the US (used in chapters
6 and 7) market. In addition, chapter 4 uses data on default asset allocation for
several Australian superannuation funds and chapter 5 makes use of earnings
data for different age categories of Australian male and female workers.
Chapter 4 investigates the first research problem that focuses on fixed weight or
constant mix asset allocation strategies as most plan superannuation funds in
Australia currently offer this type of pre-mixed options to the employee
participants. Trustees of different funds choose different asset allocation mixes
as their default option ranging from ‘capital stable’ strategies whose allocation
12
to stocks is well below 50% to extremely aggressive strategies that invest the
entire portfolio in equities. We examine which of the ‘constant mix’ asset
allocation strategies result in best outcome for participants and therefore is the
most suitable candidate for selection as default strategy. We investigate whether
lifecycle investment strategies offered by a few Australian superannuation funds
are more likely to result in superior outcomes for plan participants as compared
to fixed weight asset allocation strategies.
The second research study, taken up in chapter 5, examines the well known
problem of inequity of wealth outcomes between male and female participants
in DC plans. Typically female participants accumulate far less in their retirement
accounts than their male counterparts mainly due to lower career wage profile
and broken patterns in employment. We investigate whether gender-specific
default investment options to mitigate this problem. We consider different
combination rates and asset allocation strategies and find out to what extent they
can reduce the gender gap in wealth accumulation under different assumptions
regarding employment pattern for the female worker.
In Chapter 6 we investigate the ‘lifecycle’ investment approach which is widely
used in DC plans in USA and UK (but rarely used in Australia). Here the funds
gradually reduce their allocation to equities in the participants’ accounts and
increase that to bonds (and cash) as they approach retirement. However
empirical research has not always been supportive of this concept. Shiller
(2005b) specifically questions the rationale of switching from growth to
conservative assets later in the lifecycle when the participants’ contribution
amounts grow larger. This essay examines different switching strategies from
equities to bonds (and cash) at different points of time on the investment horizon
in testing Shiller’s contention that the growing size of contributions would
warrant a reversal of the direction of switching as proposed by conventional
lifecycle strategy. In this context, we study the interplay between growing
13
portfolio size and asset allocation strategies resulting in different wealth
outcomes and their associated riskiness.
In chapter 7, we examine an alternative to conventional lifecycle strategy in
light of the latter’s apparent shortcomings. The fixed weight and lifecycle asset
allocation strategies discussed in previous chapters are static in nature since the
allocation rule for the entire horizon is set right at the beginning i.e. when the
participant joins the plan. Based on suggestions made by a few earlier studies,
we model and test a dynamic asset allocation strategy which uses past
performance feedback in order to determine the direction and extent of asset
switching. The wealth outcomes for the plan participant under the dynamic
allocation rule are then compared to those under lifecycle and fixed weight
allocation strategies.
Chapter 8 concludes the thesis. In addition to enumerating several scholarly
contributions made by this study, we discuss the relevance of the research
findings for pension plan sponsors, trustees, investors, and policymakers.
Finally, we point out the limitations of the current dissertation and suggest a few
areas that deserve the attention from future research in this field.
14
2. Literature Review
This chapter consists of eight sections. In section 2.1, we review research on
behavioural anomalies which influence investment choices of individuals since
this underlines the importance of default investment choices offered to DC plan
participants. Next, we present evidence on default investment choices offered by
plan sponsors in four countries – Australia, Sweden, UK, and USA – and
highlight the differences in asset allocation structures of these default funds in
section 2.2. The tenets of modern portfolio theory and their implications on asset
allocation are discussed in section 2.3. The desirability of ‘lifecycle’ strategies
over ‘constant mix’ asset allocation strategies is a key research topic in this
dissertation. Section 2.4 reviews the theoretical issues concerning lifecycle
models of investment as well as the empirical evidence in this area. Past
research on optimal asset allocation strategies for DC plans is presented in
section 2.5 as the current dissertation draws on this body of work to make
further advancement. Since the role of equity premium is considered to be
critical in determining asset allocation strategies for long term investors like DC
plan participants, section 2.6 analyses the research evidence in this area. The
concept of risk and its various measures are discussed in section 2.7 as asset
allocation strategies are heavily influenced by how individuals view risk and its
trade-off with investment return objective. Finally, section 2.8 reviews
investment performance measures used in academic and practitioner literature as
some of these would be employed in this dissertation to evaluate the outcomes
of alternative asset allocation strategies.
15
2.1 Behavioural Biases Influencing Portfolio Choice
The assumption of classical microeconomic theories regarding rational human
behaviour in making optimal decisions was questioned by Keynes (1936) who
argued that human decisions are a result of ‘animal spirits - a spontaneous urge
to action rather than inaction’ and not of ‘a weighted average of quantitative
benefits multiplied by quantitative probabilities’. Later, Simon (1955), among
others, highlighted the ‘bounded rationality’ problem where decisions made by
human beings are limited by knowledge and cognitive ability and therefore, can
be sub-optimal in maximising expected utility. This perspective has gained
considerable clout in recent times primarily due to influential work of
researchers working at the confluence of psychology, economics, finance, and
even sociology. The growing discipline of behavioural economics and finance
not only questions the validity of standard assumptions like rational behaviour
but importantly, cites evidence on several common biases in human decision-
making process caused by cognitive limitations, emotional constraints, and the
presence of certain external factors.
Contrary to the view held by market economists, researchers in psychology have
often argued that an expansion in choice does not always make the consumer
better off. According to them, too much choice can be confusing for most
consumers, a problem they term as choice overload. This often leads to inaction
on their part as they are overwhelmed and less confident about the soundness of
their decisions. The problem with excessive choice has been demonstrated in a
well-known experiment documented by Iyengar and Lepper (2000). In their
experiment, these researchers set up two booths outside an upscale grocery store
offering to sell jams to shoppers who passed by. While one booth offered 6
varieties of jams, the other had 24 varieties for shoppers to select from. They
found that although more shoppers were attracted to the booth offering wider
selection of jams, only 3 percent of them made any purchase. On the other hand,
16
30 percent of visitors to the booth offering a limited choice of 6 varieties bought
a jar of jam. It seems to indicate that having more choice actually inhibited their
motivation to make a purchase decision.
According to psychologists, the problem people face in making decisions when
faced with alternatives may be caused by their desire to avoid regret and self-
recrimination. While human beings dislike bad outcomes, they feel even worse
when such outcomes are perceived as fallout of their own decisions i.e. different
decisions could have resulted in better consequences (Sugden, 1985). While the
actual regret is caused only after the consequence of a decision becomes known,
people can experience anxiety at the time of making a decision fearing the
possibility of future regret in case of an unfavourable outcome. According to
decision researchers, the anxiety is particularly heightened in two situations: (i)
when decision makers feel that they lack proficiency in the concerned field
(Heath & Tversky, 1991) and (ii) when decisions involve difficult tradeoffs e.g.
when choosing between a high risk, high expected return investment option and
a low risk, low return one (Loewenstein, 2000).
Whether individuals have necessary willpower and self control to exercise
investment choice, as normally assumed by advocates of more investment
choice, is highly debatable. According to some researchers, inertia and
procrastination bias seem to play a major role in investment decisions. Madrian
and Shea (2001) finds evidence of high level of inertia among retirement plan
participants in their retaining both the default contribution rate and asset
allocation. In their study of 2.3 million participants at the Vanguard Group,
Mitchell and Utkus (2004) find that less than 10 percent of plan participants
actually change their contribution allocations each year. They also find that new
participants are sensitive to market conditions in allocating contributions during
enrolment but later display inertia by not reallocating their retirement plan
assets to reflect changes in market conditions. The initial portfolio choice,
17
therefore serves as an anchor which influences subsequent portfolio changes,
and therefore serves as evidence of anchoring effect under which final outcome
is strongly influenced by the starting allocations. In Australia, Fry, Heaney, and
Mckewon (2007) find evidence of inertia among superannuation fund members
with respect to exercising choice of funds.
Even where investors make their own investment decisions, it does not
necessarily follow that such decisions are optimal. In recent times, researchers in
the field of behavioural finance have questioned how good investors actually
understand and act on the predictions of rational models like mean-variance
optimisation.9 If investors are rational, as assumed in standard finance theories,
there should be substantial evidence of individual investors demonstrating
reasonable competence in constructing portfolios that are indeed mean-variance
efficient. However, several studies on human behaviour show that individuals
often make decisions based on heuristics or rules-of thumb when confronted
with complicated problems or when the outcomes are uncertain. Simonson
(1990) and Read and Loewenstein (1995) documents a diversification heuristic
where human beings tend to choose ‘a bit of everything’ when uncertain.
Benartzi and Thaler (2001) finds evidence of diversification heuristic or its
extreme form, the 1/n heuristic (where investors divide their investments equally
among the n options offered to them) , among participants in DC plans in United
States. If investors are rational in a mean-variance sense, one can also expect
them to have well-defined risk attitudes and demonstrate firm preferences in
constructing their portfolios. However, results of an experiment carried out by
Benartzi and Thaler (2002) among employees of University of California and
Swedish American Health Systems indicated that retirement plan participants
ranked the median portfolio higher than the portfolios they chose for themselves
and therefore demonstrated relatively weak preference for their own portfolios.
9 This is the cornerstone of modern portfolio theory and is described in section 2.3.
18
The above behavioural research findings have very important implications for
this research. They not only motivate the research by highlighting the problem
with choices (and therefore the need for appropriate default options) but also
suggest that the use of conventional utility based measures used by economists
in modelling investor preferences may have inherent deficiencies. The latter in
turn warrants the use of robust performance measures that are independent of
specific utility functions and therefore can be used to develop an appropriate
default investment strategy for any plan participant who do not make a choice.
2.2 Default Investment Options in Retirement Plans
A substantial body of recent empirical work demonstrates that although
members of retirement plans have the option to exercise choice, most accept the
default arrangements in the plans. Choi et al. (2002) find that in USA,
employees tend to accept default arrangements in their plans even for critical
features like contribution rate and investment choice. In their study, between
42% and 71% of employees accept the default contribution rate and between
48% and 81% plan assets are invested in the default fund. In another study
conducted by Beshears et al. (2006), 86% of existing employees who were
subject to automatic enrolment in the company retirement plan had some of their
assets invested in default fund, with 61% having all their assets in the default
fund. They conclude that automatic enrolment tends to anchor employees
towards default asset allocation just as it anchors them towards default
contribution rate. According to consulting firm Hewitt Bacon and Woodrow,
about 80% of group personal pension scheme members in UK accept the default
option (Bridgeland, 2002). Also consistent with the US evidence, Byrne (2004)
finds that many members in UK retirement plans lack the knowledge and
interest to exercise active choice and therefore opt for default options. Cronqvist
19
and Thaler (2004) find that in Sweden, about two-thirds of the participants
actively chose their retirement funds in 2000, when mandatory individual
accounts were introduced by the government and fund choice was offered to the
participants. However, fund choice dramatically dropped off in the subsequent
years and between 2003 and 2005, only 10% of the new participants who were
eligible to choose their funds actually made any choice.
The situation is not much different in Australia. In December 2002, the
Association of Superannuation Funds of Australia (ASFA), the apex body of
superannuation industry, conducted a survey of industry superannuation funds to
find that between 1% and 25% of members exercised active choice in selecting
from various investment options offered to them (Duffield & Burke, 2003). Also
as per ASFA, only 10% of the Australian superannuation fund members who are
offered investment choices actually make a choice (Bowman, 2003). According
to statistics of Australian Prudential Regulatory Authority (APRA), as of June
2004, about 60% of all assets held by all superannuation entities with more than
four members are in default investment strategies (APRA Annual
Superannuation Bulletin, 2005).
While the issue of whether people are better off with more choice is vigorously
debated among academics and policymakers, there is strong evidence to suggest
that majority of members in retirement plans do not make active decisions in
selecting their investment choice. Contributions for these members end up in the
default investment options offered by their respective plans. Therefore, the role
of the default investment option, the asset allocation structure of which is
normally decided by the fund trustees, becomes critical in determining the value
of superannuation accumulated by a vast majority of members at the end of their
working lives. There is also a growing body of evidence that suggests trustees of
retirement plans make better asset allocation choices than the participants
(Benartzi & Thaler 2001, Cronqvist & Thaler, 2004). This makes selecting the
20
default investment option a significant responsibility for trustees which deserves
serious consideration and analysis.
So what determines selection of asset allocation structure for default options?
For retirement plans, it is generally the plan sponsors or trustees who assume
fiduciary responsibility for investment of assets when a participant does not
make an active investment choice. In discharging such responsibility, sponsors
are expected to diligently formulate investment strategies that benefit the
members enrolled to the default option. Bateman (2003) observes that in
countries with established principles of trust law there is little investment
regulation and asset allocation is only subject to the prudent person standard.
For example, the Employee Retirement Income Security Act (ERISA) of 1974
in USA specifies ‘prudent investor’ principle as a standard for plan fiduciary
decisions. Thus, the plan sponsors are expected to possess a level of investment
knowledge and expertise at par with prudent investors and superior to prudent
layperson (Utkus, 2005).
The ERISA does not prescribe any list of approved investments and put no
obligation on plan sponsors to allocate assets exclusively to conservative form
of investments like money market funds. To ensure better compliance with the
requirements of Pensions Act 2004, the Pension Regulator (2004) in UK
specifies that the trustees have a duty to exercise reasonable care and act
prudently, particularly in dealing with investments ‘as it is a way of coping with
risk’. The guideline also asks trustees to decide on investment strategies by
aiming to get the best financial returns achievable at the desired level of risk.
Although stakeholder schemes are required to offer a default fund, the
regulations do not prescribe the nature of any default fund and various
providers, as we discuss below, choose very different investment strategies. In
Australia, the guidelines for trustees provided by the regulatory authority
emphasises the benefits of diversification as, according to them, it would ‘result
21
in a lower overall level of risk to achieve desired return’ (APRA, 1999). The
regulator also makes it necessary for trustees to identify a default strategy where
investment choice is offered to standard employer-sponsored members.10
In USA, a cash or stable value option is typically used as default choice for all
members. Choi et al. (2003) note that 66% of plans in their study have
nominated a stable value fund as the default investment option. The authors
question whether this automatic enrolment to such conservative investment
choice actually makes the participants better off. In December 2004, out of a
sample of nearly 1,889 DC plans administered by Vanguard, one of largest
investment mangers in USA, 81% were found to have chosen a money market or
an investment contract fund as their default options while only 16% used
balanced funds and 3% selected equity funds as their default investment choices
(Utkus, 2005). However, Feinberg (2004) indicates that there is a growing trend
among American retirement plans in selecting balanced or lifecycle funds as
default investment options in recent years.
Blake et al. (2004) examine stakeholder pension schemes in UK, which were
introduced in UK in April 2001 to improve pensions for low to middle income
earners. These schemes share features that are common to most DC pension
arrangements as well as some extra features like no penalties for ceasing,
reducing or transferring contributions and charges capped to 1% per annum. In
addition, these schemes have to compulsorily offer a default fund so that no
member is compelled to make an explicit investment choice. Among the 35 non-
trivially distinct schemes studied by them, 19 offered a ‘balanced’ fund as
default investment option (typically invested 70-80% in equities, 10-20% in
bonds, and up to 5% in cash) while a further 13 schemes had a 100% equity
fund as default choice. The remaining 3 funds had an average asset allocation of
60% equities and 40% fixed interest.
10 Exception can be made where active choice is a pre-condition for membership.
22
Sweden uses a government-operated universal default fund known as the
Premium Savings Fund for those employees who do not choose a fund for their
individual investment account or prefer the government to manage their
investment. The objective of the fund is stated as ‘People who do not have a
fund manager, for whatever reason, should receive the same pension as others-
that is our goal’ (Weaver, 2004). The default fund follows a static asset
allocation strategy with investment in equities between 80% and 90% with a cap
of 75% on international stock holdings (Palme, Sunden & Soderlind, 2005). The
remaining portion (10-20%) is invested in bonds. Of late the target asset
allocation is slightly modified to include 4% investment in private equity and
another 4% in hedge funds (Weaver, 2004).
In Australia, most superannuation funds offer a balanced diversified investment
strategy as the default choice (Duffield & Burke, 2005). An examination of
current top 50 default investment options (in terms of investment performance
as of 31 October 2005) offered by Australian superannuation funds reveals that
majority are called ‘balanced’ investment option while a few are categorised as
‘growth’ options. None of the default options in the list belongs to the ‘cash’ or
the ‘capital stable’ category. At the end of June 2004, the majority of default
strategy assets were held in equities: 33 % in Australian shares and 21 % in
international shares. A further 15 % was in Australian fixed interest, 6 % in
international fixed interest, 7 % in cash, 6 % in property, and 12 % was in other
assets (APRA, 2005).
From the above evidence it seems clear that although a majority of plan
participants passively direct their contributions to the default fund chosen by the
providers, the default options themselves differ substantially in their strategic
asset allocation with strategies ranging from very conservative capital stable
options with investments mostly in money market instruments to extremely
23
aggressive high growth options allocating 100% (or nearly 100%) of their assets
to equities. Since behavioural researchers have shown that the majority of the
members passively accept the default investment option in their plan, such
variation in asset allocation profiles is bound to result in significant differences
in retirement wealth for employees belonging to the same cohort. This virtually
renders the pension plan, as Blake et al. (2004) points out, a lottery for the
participants in terms of subsequent retirement income. Drew and Stanford
(2003) observe the existence of agency problems among Australian
superannuation funds which often leads to sub-optimal investment decisions to
the detriment of the members.
Even among retirement plans in UK and Australia, where balanced diversified
funds are more commonly selected as default investment options for members
who do not exercise choice, a fair degree of heterogeneity exists between the
balanced funds in terms of their benchmark asset allocation. Blake et al. (2004)
finds evidence of wide dispersion in characteristics across default options
offered by occupational pension schemes in UK. According to their study, the
allocation to equity within balanced funds range between 70% and 80%. This is
remarkably different from balanced funds offered as default choice by plan
providers in Australia where the average allocation of default options to equities
is about 56% (APRA, 2005). However, Australian superannuation plans tend to
make significant investments in property and alternative asset classes like
private equities and hedge funds. If one includes average allocations to these
asset classes, the total allocation to risky assets excluding bonds rises to 74%.
Apparently the above data on asset allocation of balanced diversified funds
chosen as default options in Australia and UK indicates that there is very little
difference in risk-return profile between these funds. Yet there is a marked
difference in their asset allocation strategies when one considers the entire
investment horizon of the plan member. In UK, a majority of the default funds
24
(including the balanced funds) are lifecycle funds which gradually decrease their
allocation to equities in favour of less risky asset classes like bonds and bills as
the member approaches retirement. In other words, the equity exposure of the
plan portfolio declines with the age of the member. Out of 35 stakeholder
schemes examined by Blake et al. (2005), 24 offered some form of switching of
assets with lifecycle either as default or as a choice the members could opt for.
Expectedly, this was more common where the initial asset allocation to equity
was high. For example, they found that 6 of the 7 funds with 100% equity
allocation used a lifecycle strategy as a default arrangement. In contrast, most
Australian plans have employed static asset allocation strategy which allows for
diversification among various asset categories but does not change with the age
of the member. This is despite the regulator’s explicit guideline that default
strategies may vary with the age of the members. However, lifecycle funds with
target retirement dates have recently been introduced in Australia but offered by
only a handful of providers (Drury, 2005).
Use of lifecycle funds as default options in 401(k) plans have also been growing
in popularity in United States (Feinberg, 2004). Mottola and Utkus (2005)
observe that participant adoption of static asset allocation funds is on the decline
in recent years while there is an upward trend for funds with target maturity
dates which are gradually rebalanced to achieve a more conservative asset
allocation as the members approach retirement. The life-cycle portfolio is also
the centrepiece of the US President’s proposed plan to reform the social security
system (Shiller, 2005a). According to this, investing in life-cycle fund would be
optional for younger workers but all personal accounts would be invested in a
life-cycle portfolio by default once an employee reaches the age of 47, unless he
or she specifically desires to opt out of it. In Sweden, only 4% of the available
retirement funds belong to the life-cycle category (Sundén, 2004). The universal
default fund is also not a life-cycle fund.
25
The above review of the literature on default funds clearly reveals the lack of
agreement among pension plan providers in different countries about the
appropriateness of asset allocation strategies used as default investment options.
Academic researchers, so far, have barely addressed the issue, let alone propose
any resolution to the conundrum. The current thesis aims to investigate the
suitability of different asset allocation strategies as default options and, thereby,
provide valuable insight on the subject.
2.3 Modern Portfolio Theory and Asset Allocation
Modern portfolio theory provides the theoretical foundation to the asset
allocation decisions in finance. Markowitz (1952) formally describes mean-
variance optimisation framework where expected return (mean) and volatility
(variance) are the only portfolio characteristics which influence investors’
utility. 11 With knowledge about expected returns, standard deviation of returns,
and the correlation between different asset classes, an optimal set of portfolios
can be constructed which lie on the mean-variance efficient frontier. One of the
key prescriptions of portfolio theory is that investors should hold well-
diversified portfolios. Although the mean-variance framework has been widely
accepted as a standard model in finance literature, questions have been raised on
whether investors and financial advisors actually follow its recommendations as
well as on its assumptions and implementation.
In mean variance optimisation model, investor behaviour is assumed to be
consistent with a utility which increases with mean (return) and decreases with
return variance (risk) and is given by
11 If the return distributions are normal i.e. can be defined by the two parameters of mean and variance only, the optimisation rule would obviously hold irrespective of whether investors’ utility function is quadratic or not.
26
1( ) * ( )
2U E r A V r= − (1)
where A is a risk-aversion parameter. The return r is a combination of returns
on investment at risk-free rate fr and that on risky asset with returnRr . If α is
the proportion of funds invested in risk asset, then
(1 ) f Rr r rα α= − + (2)
Maximization of the utility function U in (1) using (2) results in mean-variance
optimal allocation as given by
( )
* ( )R f
R
E r r
A V rα
−= (3)
While the mean-variance optimization model of Markowitz was originally
intended to construct efficient stock portfolios, it has been mostly employed in
deciding how investors should allocate their funds among major asset classes
such as stocks, bonds, property, and cash (Haugen, 2001).12 Radcliffe (1997)
defines this as strategic asset allocation (SAA) which represents the optimal
combination of various asset classes where investors believe that the aggregate
asset classes are efficiently priced.13 As opposed to this, if the investors believe
certain asset classes are mispriced, they would employ tactical asset allocation
(TAA). Haugen (2001) differentiates the two types of asset allocation from the
investment horizon perspective. According to him, SAA decisions relate to
relative amounts invested in different asset classes over long horizons i.e.
horizon periods for estimates of volatilities, correlations, and expected returns
are typically decades long while those for TAA are much shorter – a year or
less.
12 According to some authors like Jahnke(1997) and Nawrocki (1997) the Wells Fargo Bank was the first to apply portfolio theory to asset allocation decisions in the late 1970s. 13 The term ‘strategic asset allocation’ was coined by Brennan, Schwartz, and Lagnado (1997).
27
To employ modern portfolio theory to formulate strategic asset allocation
requires obtaining estimates of expected returns on asset classes under
consideration, the volatility of these returns, and the correlation among them.
These estimates, then, can be used to approach asset allocation formally through
mean-variance optimization which solves for asset class weights that maximizes
returns at each level of risk or minimizes risk at each level of return.
Traditionally, researchers have used historical record of asset class returns to
derive the estimates of expected return, volatility, and correlations which are
used as inputs to the mean-variance optimisation model. However, many authors
like Michaud (1998) have advised users to exercise extreme caution about the
reliability of these estimates, since small changes in the inputs can result in
dramatic changes in suggested asset class weights.
For mean-variance efficiency to be consistent with expected utility
maximization, which most financial economists consider as the basis for rational
decision making, either of the two conditions – normally distributed asset
returns or quadratic utility function - must hold (Michaud, 1998). Although the
limitations of these assumptions are well known to most investment analysts,
mean-variance efficiency is a reasonable approximation of expected utility
maximization in many situations and therefore, provides a practical framework
for portfolio optimization (Levy & Markowitz, 1979; Kroll, Levy & Markowitz,
1984).
However, as a framework for portfolio choice for long horizon investors, the
mean-variance paradigm has been severely criticised because of its myopic
nature being essentially a single period model.14 For the DC plan participant,
this single period can be as large as 40 years. Therefore, to employ mean
variance optimisation to the portfolio choice in this case one has to accurately
14 However, some scholars show this model to be applicable in a multi-period setting under certain restrictive assumptions. Elton and Gruber (1974) offers an excellent synthesis of the arguments.
28
estimate expected returns for available asset classes over this period as well as
their standard deviations and correlation coefficients. Campbell and Viceira
(2002) show that such myopic portfolio selection can be optimal for long term
investors only under extremely restrictive conditions which are likely to be
violated in practice. They argue that in reality long horizon investors are free to
periodically rebalance their portfolios, a possibility that the single period model
fails to recognise.
The two sets of conditions under which such myopic portfolio choice prescribed
by mean-variance paradigm would be valid for long horizon investor is given by
Samuelson (1969) and Merton (1969, 1971). First, investors live in world of
constant risk and return and second, investors treat financial wealth independent
of income. Although these assumptions were considered good approximations of
reality by scholars and practitioners for past several decades, recent research has
argued that they fail to hold in several ways. Campbell and Viciera (2002) show
time varying investment opportunities to be an important consideration for
portfolio choice over long horizons. Similarly, they argue that most investors
use their income stream along with their financial wealth to support their
lifestyle thus violating the second condition.
The conundrum of asset allocation gets deeper when we consider the issue of
investors advised to hold a different proportion of stocks and bonds in their
portfolio according to their level of risk tolerance. Tobin (1958) and several
other analyses of financial markets have shown that the portfolio allocation
decision can be reduced to a two stage decision process: first decision involving
the relative allocation of wealth across the risky assets, and second decision on
how to divide total wealth between the risky assets and the safe asset. In
particular, the mutual fund separation theorem (Cass & Stiglitz, 1970), which is
based on portfolio theory, shows that investors should hold a portfolio of
riskless and risky assets in a proportion determined by their risk preferences
29
(higher the degree of risk aversion, higher the proportion of riskless asset in
portfolio and vice versa). The composition of risky assets, however, is
independent of the investors’ risk attitudes. However, Canner, Mankiw, and
Weil (1997) observe systematic violation of this basic finance theory by
professional investment advisors leading to what they describe as ‘asset
allocation puzzle’. Among the portfolios recommended by the financial
advisors, those with a higher proportion of stocks have a smaller ratio of bonds
to stocks and vice versa. This is in contradiction to the prediction of the textbook
mutual fund separation theorem.15 According to the authors this puzzle can only
be solved under the assumption that human capital has similar risk-return
characteristics to stock. However they are sceptical of the validity of such
restrictive assumption. Also, if human capital indeed shared a similar risk-return
profile to stock, it would lead to investors holding a smaller fraction of stock in
their portfolio when they are young (and hold more human capital) than when
they are old. This is exactly opposite of what is observed in practice and also
goes against the conventional asset allocation advice imparted by financial
advisors.
There have been other attempts made by researchers to reconcile academic
theory with practitioners’ view on portfolio choice. Notable among them is the
work of Campbell and Viceira (2002) who argue that the asset allocation advice
of financial advisors can be consistent with theory if one considers the
limitations of the single period mean-variance analysis which treats cash as
riskless asset and bonds as another risky asset like stock. According to them,
long horizon analysis lends a different view as cash (money market instruments)
is no longer riskless due to inherent reinvestment risk. For long horizon
investors, an inflation-indexed long term bond may be less risky than cash and
conservative investors would actually shift from equities to these inflation-
15 The rationality of asset allocation decisions has also been examined by Elton and Gruber (2000) but with different conclusions.
30
indexed bonds if available. In case the inflation risk is low, even nominal bonds
can be favoured by these investors. Their conclusion indicates that asset
allocation over long term is not just dependent on conditional means and
variances that drive myopic portfolio choice but also on relevant state variables
like inflation and real interest rates.
Due to the seminal work of Brinson, Hood, and Beebower (1986), [hereafter
BHB], it is now well accepted that a portfolio’s SAA is by far the major
determinant of its investment performance. Analysing data from 91 large US
pension plans over the period 1974-83, they observe that asset allocation policy,
which select asset classes for investments and their relative weights in the
portfolio, explains on average 93.6% of the variation in total returns. Two other
factors, security selection and market timing (akin to TAA), are found to
contribute much less to returns. An update of this study by the same authors
(Brinson, Hood, & Beebower, 1991) reached similar conclusions. Blake,
Lehmann, and Timbermann (1999) also find that asset allocation is responsible
for most of the variation in pension fund returns in UK.
But the conclusions of BHB study have come under attack from some authors.
Hensel, Ezra, and Ilkiw (1991) observe that BHB’s findings are largely
dependent on the choice of the benchmark portfolio. They show that while asset
allocation policy largely explains variations in returns when comparing an
average portfolio to a T-bill portfolio, it plays a less dominant role in
determining returns when a diversified portfolio, even a naively diversified one,
is used as a benchmark. Jahnke (1997) uses holding period returns (rather than
return variability used in BHB study) to show that less than 15% of the holding
period returns in BHB sample accounts can be attributed to asset allocation. In
spite of these criticisms, the importance of strategic asset allocation on portfolio
performance has been well accepted by the academic community although there
is some disagreement on the extent of its dominance as indicated by BHB.
31
Asset allocation strategies can not only differ from one another in terms of their
distribution of funds to different asset categories. Several other factors like
frequency of rebalancing and horizon dependence (or independence) can cause
considerable variation between strategies. Perold and Sharpe (1988), among
others, point out that the fluctuations in the market value of assets held within a
portfolio may result in its drifting from its strategic asset allocation over time
and discuss methods to deal with the problem, two of which are most commonly
used by investors. The first of these is a static buy-and-hold strategy where
assets are purchased after deciding on an initial mix and then held during the
entire investment horizon without doing anything. The effect of fluctuations in
market value of assets on their allocations is, therefore, ignored. In contrast,
constant mix strategy aims to maintain the initial allocation among asset classes
through periodic rebalancing – whenever actual asset allocations move away
from the target range. Hence, unlike buy-and-hold, it is considered to be a
dynamic strategy. Baker, Logue, and Rader (2005) argue that the relative
performance of the two strategies depends on the nature of the relative
performance of the asset classes. For example, in a two asset class scenario, if
the relative performance of stocks to bills makes a sustained move (either up or
down), the buy-and-hold strategy would outperform the rebalancing approach.
However, if asset class returns are mean reverting i.e. relative performance of
stocks to bills is not sustained, the constant mix strategy is likely to produce a
superior outcome.
Given the importance accorded to strategic asset allocation and the amount of
resource spent in developing strategic target weights, Buetow, Sellers, Trotter,
Hunt, and Whipple Jr. (2002) argue that plan sponsors would deliberately not
allow any portfolio’s asset mix deviate significantly from its established targets.
Yet they find current practice among sponsors range from disciplined to random
rebalancing. Using actual return data from 1968 to 1991 to investigate various
32
rebalancing strategies for two asset class portfolios, Arnott and Lovell (1993)
find that more frequent rebalancing produces better results than less frequent
rebalancing. They also find the periodic rebalancing is superior to non-periodic
rebalancing based on drift intervals from target allocation. Their findings receive
support from Plaxco and Arnott (2002) whose study encompasses a global
portfolio as well as from Buetow et al. (2002) who use simulation approach to
evaluate different rebalancing strategies for a four asset class portfolio.
2.4 Lifecycle Asset Allocation Strategies
As we have discussed in 2.2, most superannuation funds in Australia currently
use constant mix or fixed weight asset allocation strategies as default investment
option i.e. the relative weights of different asset classes in the default strategy
remain constant irrespective of the plan participant’s age or time to retirement.
However in addition to such strategies, this dissertation investigates the
suitability of lifecycle strategies as default investment options for DC plan
participants in comparison with fixed weight asset allocation strategies. Like
fixed weight strategies, lifecycle strategies automatically rebalance the
investments to keep the overall portfolio mix of the fund in line with a pre-
specified target asset allocation. Unlike fixed weight strategies, however,
lifecycle funds do not keep the asset weightings constant over time; instead, they
change their target asset mix according to a predefined schedule until they reach
target maturity date of the fund. Typically, the target asset allocation for
lifecycle funds becomes increasingly conservative over time i.e. investments are
switched away from risky assets like equities towards less volatile assets like
bonds and cash.
An important investment principle anchoring most participant education
programs in USA is the belief that younger individuals can assume greater risk
33
than older individuals and therefore invest more in risky assets like equities
(Utkus, 2005). This, therefore, could qualify as a rationale for choice of default
options by plan sponsors. Malkiel (1996) asserts that risk tolerance is a function
of both risk attitude of the investor as well as his or her risk capacity. While risk
attitude is subjective, according to Malkiel, risk capacity depends on his position
in the lifecycle. This implies the portfolio of an older investor would be different
from that of a younger investor i.e. optimal portfolio structure depends on the
age of the investor. This is the centrepiece of all lifecycle models of investment.
As explained in the previous paragraph, lifecycle strategies would follow
aggressive allocation to risky asset classes earlier and gradually move towards a
more conservative asset allocation later. In the context of retirement plan
investments, the lifecycle portfolio would be one that is heavily concentrated in
stocks at the beginning of worklife when the investor is young, and then
gradually shifting towards bonds and cash as retirement nears. Malkiel’s
reference portfolios move from an allocation of 70% to stocks for investors in
their mid-twenties to 30% when they are in their mid-fifties. The allocation to
bonds increases from 25% to 60% during the same period while that to cash
increases from 5% to 10%. Although lifecycle models differ from one another in
respect to how and when the switching from equities to bonds/bills occurs, there
is almost total consensus about the direction of the switch with most
commentators favouring higher allocation to equities (70%-90%) during early
years of employment with gradual shift to conservative asset classes
encompassing bonds and cash as the investor approaches retirement (Baker et
al., 2005).
One theoretical justification for adopting the lifecycle asset allocation strategy
rests on the concept of time diversification, according to which risk of investing
decreases with time or length of horizons and therefore, investors should be
more inclined to hold risky assets with higher expected returns over long
34
horizons than over shorter periods of time.16 It is usual advice given by financial
planners to their clients, especially to those who save for retirement. This advice
is underpinned by the argument put forward by academics like Siegel (2003) and
practitioners (for example, Greer, 2003). The risk of a portfolio containing risky
assets like stocks decreases with the increase in investment horizon. Direct
fallout of this logic is investors with long horizon should allocate higher
proportions of their portfolios to equities and reduce the proportions as they age.
The belief that time reduces risk has been forcefully challenged by academics
like Samuelson (1963, 1969) and Bodie (1995). Samuelson (1963) points out
that the reasoning behind time diversification is a fallacious interpretation of law
of large numbers. Using repeated lotteries, Samuelson demonstrates that if an
agent rejects a lottery at all wealth levels, he will also reject any sequence of that
lottery with same distribution. Therefore, if at each income or wealth level
within a range, the expected utility of a certain investment or bet is worse than
abstention, then no sequence of such independent ventures can have a
favourable expected utility. The result implies that although the probability of
loss on an investment reduces with the length of investment horizon, it is offset
by an increase in the magnitude of potential loss.
Bodie (1995) uses option-pricing theory to demonstrate the fallacy with the
notion of time diversification. According to him, if stocks are actually less risky
in the long run, the cost of insurance against any shortfall in stock return over
risk-free rate would decrease. However, using the Black-Scholes option pricing
model in computing cost of such insurance (which is essentially a European put
option), he shows that the value of the put option actually increases with time
approaching 100% of the investment at infinite horizon. However, Bodie’s using
a constant annualised standard deviation of 20% in stock returns as a key input
in the option pricing model to get his results has been challenged by Taylor and
16 See Kritzman (2000) among others.
35
Brown (1996) since variation in standard deviation of risky assets like stocks is
most critical to the argument for time diversification.
A careful analysis of the arguments reveals the following key assumptions made
by financial theorists like Samuelson while refuting time diversification.
1. Stock returns are serially uncorrelated i.e. follow a random walk
2. Investors have a constant relative risk aversion (CRRA)
3. Investors’ future wealth depends only on their investment portfolio
Although the mathematical correctness behind the ‘irrelevance of time’
argument is well accepted, the abovementioned assumptions under which the
proof of irrelevance is derived are open to challenge.17 While the second and
the third assumption have been discussed in the literature, it is the validity of the
first assumption that has drawn the most attention from researchers. If asset
prices truly follow a random walk, tp is the logarithm of assetj ’s price in time
t, tj ,ε is a white noise with mean 0 and variance 2jσ then:
ttjtj pp εα ++= −1,, (4)
or in the return form:
ttjr εα +=, (5)
If tjR , is the mean return over τ periods, then:
17 A few researchers have tried to explore time diversification or its irrelevance from the perspective of traditional mean-variance framework. In the previous section, it was shown that
mean-variance optimal allocation is given by ( )
* ( )R f
R
E r r
A V rα
−= , where ( )RE r and ( )RV r denotes
expected return and variance respectively. Thorley (1995) shows mathematically that with increase in time horizon ( )RV r increases at a faster rate than ( )RE r under any distribution
assumption, including lognormality. This results in decrease in mean-variance optimal risky asset allocation,α , with increase in investment horizon. Therefore, unlike Samuelson (1963) mean variance optimisation model does not predict investment horizon indifference but rather takes the other extreme and counterintuitive position to imply that longer horizon investors should be less inclined to invest in risky assets.
36
∑−
=−=
1
0,,
1 τ
τ iitjtj rR (6)
This gives the following expected returns and variance for tR .
α=)( ,tjRE (7)
τσ 2
, )( jtjRVar = (8)
The above equations imply that if asset returns follow a random walk, the
expected return over long horizon (tjR , ) is the same as that of the short horizon
( tr ). However the variance decreases with the length of the investment
horizonτ . The volatility, given by standard deviation oftjR , , decays by a factor
of τ over long horizon. But if returns from stocks, bonds, and bills all follow
random walk, then standard deviations of all these asset classes would shrink by
the same factor i.e. the risk of stocks would not decline faster relative to the risk
of bonds and bills. In such a case, there is no reason why risk averse investors
would prefer to hold higher proportion of stocks over long horizon than what
they are willing to hold over short horizon. Therefore, investment horizon
should not have any impact on asset allocation.
However the assumption of random walk of asset class returns is not well
supported by empirical evidence. It is possible for asset class return generation
to be a stationary autoregressive process with either negative or positive serial
autocorrelation observed in the return series. If we assume asset returns to
follow a simple stationary autoregressive process, then:
tjtjtj rr ,1,, εβα ++= − (9)
The mean and the variance in this case would be given by18
18 For derivation, see Guo and Darnell (2005).
37
βα−
=1
)( ,tjRE (10)
( )
−+−
= ∑−
=
1
12
2
,
21
)1()(
τ
βττβτ
σk
ktj kRVar (11)
If 0<β , the process is commonly known as mean-reversion. In that case, the
standard deviation of tjR , would decay by a factor greater thanτ . On the other
hand, when 0>β , the process is standard positively autocorrelated. The
volatility in this case also decreases with the length of the investment horizon
but at a slower rate, the rate of decay being less than τ . Therefore, if returns
from an asset class follow mean reversion while returns from another asset class
is positively correlated over time or follow a random walk, the riskiness of
investing the former (relative to the latter) would decline with increase in
investment horizon.
Historical data of asset class returns in the US market has not been supportive of
the random walk hypothesis. Using real returns data from 1802 to 2001, Siegel
(2003) reports that the risk of investing in stocks diminishes over long holding
periods at a rate that is faster than what is predicted under the random walk
assumption. However the risk of investing in bonds and bills seem to decline at
a slower rate than the prediction of random walk model over long horizons. This
evidence suggests that stock returns show mean reversion while returns from
fixed income securities show mean aversion. Earlier work like Poterba and
Summers (1988), and Fama and French (1988) had also observed mean-
reversion in stock prices. Dimson, Marsh, and Staunton (2002) provide
corroborating evidence from other countries.
38
The above findings have provided support for the argument that investing in
stocks is indeed less risky over a long horizon. Thus the conventional wisdom of
lifecycle model which recommends holding a higher proportion of stocks in
one’s portfolio when the horizon is longer seems to be justified. However such a
claim is strongly refuted by researchers like McEnally (1985) who contends that
the appropriate measure for investment risk is the variability of the terminal
wealth outcomes that arise by holding an asset for the intended investment
horizon and not the variability of periodic returns of the asset around its average
return. The underlying argument here is that although the standard deviation of
asset returns becomes smaller as the holding period increases, the dispersion in
terminal wealth for all asset classes actually increases. This implies that if
investors emphasize on total returns over the investment horizon, risk uniformly
increases with horizon length (Samuelson, 1969).
In measuring the risk associated with the cumulative wealth, we can again
examine the expected mean and variance under random walk or stationary
models. If investors only aim to maximize cumulative wealth ( τttj RW += 1, ),
we have under the random walk assumption:
τα jtjWE += 1)( , (12)
τσ 2, )( jtjWVar = (13)
The expected wealth as well as its variance rise at the rate given by the length of
the investment horizonτ . The standard deviation, therefore, increases at the rate
of τ . However this is again true for all asset classes (stocks, bonds, bills) and
therefore, stocks would not appear to be less risky relative to bonds and bills
over long horizons. Thus, as with the case for returns, the wealth maximisation
39
objective under the random walk model does not prescribe changing asset
allocation over different horizons.
Under the stationarity assumption, however, asset allocation does not remain
time invariant. The expected cumulative wealth and its variance in this case is
given by
τα jtjWE += 1)( , (14)
ij
ijjtj iWVar βτστσ
τ
)(2)(1
1
22, ∑
−
=−+= (15)
Although the expected wealth is still increasing at a rate τ the variance of tjW , is
dependent on the magnitude of jβ and its sign. If jβ is negative for stocks and
positive for bonds and bills as indicated by empirical evidence, the variance of
wealth for stocks rises at a slower rate than τ while the variance for bills and
bonds rises at a rate faster than τ . The asset allocation should thus be more
tilted towards stocks over longer holding periods.
Although mean reversion in stock market returns can cause relative riskiness of
stocks to decline over longer holding periods relative to bonds and bills, the
literature is divided over whether that makes stocks a safe bet over long
horizons. McEnally (1985) reports that investment in stocks results in highest
dispersion in terminal wealth outcomes while investment in T-Bills shows the
lowest. According to him, this indicates that stocks are riskier than other asset
classes over longer investment horizons. But several other researchers argue that
the uncertainty is not about whether stocks would outperform T-bills over long
holding periods but about to what degree the former would outperform the latter.
Their contention is that the greater risk of investing in stocks over safe assets for
40
long holding periods as shown by McEnally is more about upside uncertainty
than any risk of underperformance, which the investors seem to be more
concerned about. For example, Butler and Domian (1991) estimate that the
chance of equities underperforming bonds over 20 year holding periods is about
5%, assuming that future returns would be drawn randomly from past history of
returns (US. data for 1926-1988 period in their study). If one believes in mean
reversion of stock prices over the long run, the risk of underperformance would
be even lower (Thaler and Williamson, 1994). Siegel (1992) finds that between
1871 and 1990, over horizons of 20 years and longer, stocks in US
underperformed short-term bonds on only one occasion and outperformed long-
term bonds 95% of the time. For 5 year holding periods, stocks outperformed
long-term and short term bonds, but only by about a three-to-one margin i.e.
about 75% of the times.
Empirical evidence overwhelmingly suggests that probability of stocks
underperforming less risky assets like bills and bonds (shortfall) over longer
holding periods is very low. Yet many researchers are unwilling to accept this as
a proof that the risk of investments in stocks reduces with time. According to
them, although the probability of shortfall declines with the length of the
investment horizon, it is an imperfect measure of risk since it does not say
anything about how large the potential shortfall can be. To do so one has to
focus on the magnitude of potential negative returns. Bodie (1995) makes this
point by showing that the worst possible outcomes from investing in stocks
actually increase with the investment horizon.
Now we take up the Samuelson’s second assumption of CRRA in describing
investors’ utility function. If we accept Samuelson’s argument that the ratio of
risky assets to total wealth remains unchanged, we automatically assume CRRA.
This issue is most important in resolving the time diversification debate since
decreasing, increasing, or constant RRA will have positive, negative, or nil
41
impact respectively on time diversification strategies. One popular functional
form of utility used by economists (for example, Arrow, 1971) in describing
investor’s relative risk aversion (RRA) is given by
1( ) 1( ) ,
1
WU W
γηγ
−− −=−
(16)
where η and γ are investor-specific risk aversion parameters.
Pratt (1964) and Arrow (1971) show that RRA is mathematically given by
( )R W WU U′′ ′= − (17)
This when applied to the above form of utility function gives
( )1 ( )
R WW
γη
=−
(18)
If η =0, ( )R W =γ i.e. a constant at all levels of wealth. But when η >0, then
relative risk aversion ( )R W decreases with increase in wealth level (W ).
Several techniques have been used to estimate RRA of investors. The
measurement seems to be sensitive to what measure of wealth is used by the
particular researcher. There has been conflicting evidence with findings of
increasing (Siegel and Hoban, 1982), constant (Szpiro, 1986) and decreasing
(Levy, 1994) risk aversion, which implies that the debate on time diversification
remains wide open.
The detractors of time diversification, nevertheless, admit that there can be a
different rationale for investors to reduce exposure to risky assets as they age.
The total wealth of an individual is a summation of investment and human
capital and with age both of these undergo changes. It is quite plausible that
young investors with long investment horizons may be induced to invest more in
risky assets because if the investments perform poorly they can compensate by
42
postponing consumption or working harder to generate more labour income
(Bodie & Samuelson, 1989). On the other hand, as investors get older, their
stock of human capital declines and so does their ability to alter labour income.
Although this violates the third assumption in the mathematical derivation of
time diversification irrelevance, Samuelson (1989) points out that this does not
validate the notion that time diversifies risk but only provides a rational basis for
investors being more risk tolerant when young than when old. Samuelson (1994)
argues that with age human capital gets converted into liquid capital resulting in
a fractional holding of stocks appearing to decrease when compared to liquid
capital, whereas the fraction actually remains unchanged when compared to total
wealth. Viceira (2001) shows that even with a random future income, time
diversification is optimal as long as there is low correlation between labour
income and stock returns.19 Cocco, Gomes, and Maenhout (2005) also find that
a lifecycle investment strategy that reduces equity exposure with age may be
optimal depending on the shape of labour income profile.
The Markowitz mean-variance optimisation model assumes that investors are
‘myopic’ in a sense that they make decisions in a static, single-period
framework. Among contemporary theoretical works in finance which aims to
address this problem, the most widely accepted framework is Merton’s (1992)
continuous-time model of optimal consumption and portfolio choice. In its most
developed version (Bodie, Merton & Samuelson, 1992), this model includes
human capital as a choice variable. In this model, individuals decide on their
consumption, proportion of financial wealth to invest in risky assets and fraction
of their labour income to be spent on leisure to maximise their expected lifetime
utility at any point of time. This implies that the fraction of an individual’s
wealth invested in equities would normally decline with age due to several
reasons like difference in riskiness between equity and human capital, decline of
19 More sophisticated models are reviewed in Campbell and Viciera (2002). The conclusions, however, are the same.
43
human capital as a proportion of wealth as a person ages, and varying degree of
flexibility to alter labour income at different stages of life.
The Bodie-Merton-Samuelson model has received some empirical support in
United States and elsewhere. Other life-cycle theories like Jagannathan and
Kocherlachota (1996) suggest that as individuals age, their stream of future
income shortens, which diminishes the value of their human capital. According
to them, individuals should offset this decline in the value of their human capital
by reducing the risk of their financial portfolio. While many studies conducted
among retirement plan participants confirm the inverse relationship between
stocks and age (Bodie & Crane, 1997; Agnew, Balduzzi & Sunden, 2003),
Ameriks and Zeldes (2001) find that the relationship follows a hump-shaped
pattern with the proportion of stocks first increasing with age and then declining.
They observe that the relationship is very much sensitive to the choice of sample
period and do not rule out the possibility of a cohort effect influencing the
results. According to them, earlier-born cohorts are less likely to hold stocks in
their portfolio compared to later-born cohorts and they also find evidence of
individuals making few changes in their portfolios as they age. Other empirical
studies on actual age-specific investment patterns of households find weak
evidence of decline in equity exposure with age (Poterba & Samwick, 2001;
Gomes & Michaelides, 2005).
It is important to note that age (or length of the investor’s time horizon) is not
the only determinant of riskiness of a portfolio in the life-cycle model of Bodie,
Merton, and Samuelson (1992). Their model emphasises the value of human
capital and degree of labour flexibility which may be influenced by factors other
than age like occupational categories (opportunities for working extra hours,
taking extra jobs, delaying retirement) or family status (number of workers or
potential workers in a family). Poterba and Wise (1996) find evidence of age-
related and income-related patterns of asset allocation where younger
44
participants in retirement plans and high income households tend to hold
significantly higher proportion stocks in their portfolios while Agnew, Balduzzi,
and Sundén (2003) find that equity allocations are higher for males, married
investors, and for those with higher earnings and more seniority on the job.
Exley, Mehta, Smith, and Van Bezooyen (1998) reviews some other arguments
supporting lifecycle switching of portfolios for retirement plan participants. One
important reason is the possibility of younger investors being more inclined to
invest in stocks if this asset class has low correlation to the value of their future
labour income (residual human capital). The preference for stocks, however,
would decline with age as the overall proportion of human wealth to total wealth
declines. Second, since it is difficult or impossible to use retirement account
balances for consumption prior to retirement, the participants may place
significant discounts on the value of assets in pension accounts and therefore,
may select high-risk investment strategies. This effect would be more
pronounced the farther they are away from retirement and decline as they
approach it. Finally, there is the concept of people becoming more risk averse
when they are nearing retirement because they get used to certain level of
consumption and are unwilling to adjust that level downwards.20 Samuelson
(1989) finds merit in the argument that if investors care about accumulating a
target wealth outcome to ensure subsistence in old age, there would be a
tendency to switch from equities to fixed income assets before retirement.
However, according to optimal consumption and investment rules derived by
Dybvig (1995) under the extreme condition of intolerance for any decline in
standard of living, the equity allocation should be increased when the market
returns increase and vice versa. As a strategy, this is quite the opposite of what
is suggested by the proponents of mean reversion in equity markets and
therefore it does not sit comfortably with the time diversification rationale for
adopting lifecycle strategies.
20 In economics literature, this is known as habit formation in consumption.
45
Whilst all lifecycle funds start with high initial concentration in stocks and
gradually move towards bonds and cash, this practice does not enjoy universal
approval from all theorists. Many authors, who make assumptions about the
correlation of stock returns with labour income different from Viceira (2001),
actually find that younger investors should invest less in stocks and increase the
allocation as they age. Benzoni, Collin-Dufresne, and Goldstein (2004) argue
that if one considers the correlation between stock returns and labour income
through time, younger investors should be well advised not only to invest less in
stocks but to actually short the stock market. Lynch and Tan (2004) argue that
young people should hold a lower proportion of stocks than older people, given
that when stock returns are low (as in periods of recession), there is also lower
mean income growth and higher volatility.
Lifecycle investment strategies offered by retirement plans constitute a critical
component of this thesis. The above review of the literature suggests that design
of lifecycle strategies is a complex and contentious affair. It is evident that such
strategies differ considerably from one another not only in their initial and final
allocation but also in terms of key switching characteristics like the timing,
mode, and direction of the switch. Also, deterministic switching according to
some pre-set rule may not be optimal considering the dynamic nature of
portfolio risk and returns. We examine these issues in chapter 6 and 7. However,
our investigation chooses to focus only on financial assets in the retirement plan
and ignore any possible impact that human capital may have on asset allocation
decisions of participants in investing their plan contributions.
2.5 Optimal Asset Allocation Strategy for DC plans
In nominating a default among available investment choices, a prudent approach
for DC plan providers is to examine the risk-return trade-off for individual
46
strategies. The strategy with the optimal risk-return combination can then be
selected as the default option. While some researchers have attempted to
optimise risk and return through theoretical approaches by applying dynamic
programming techniques, most research on asset allocation strategies in the
literature for DC plans have been based on this empirical approach of evaluating
currently used strategies and some of the alternatives. This doctoral dissertation
also adopts the empirical route to explore the research problems.
Research investigating the optimality of strategic asset allocation strategies for
DC plans is mostly very recent. Among these works, Butler and Domian (1991)
simulate outcomes for strategies that invested in stocks, bonds, and lifecycle
accounts and derive probability distributions for terminal wealth. Their results
suggest that common stocks are the best vehicle for long-term retirement
savings. The lifecycle portfolio in their study outperforms a portfolio comprising
of 100% stocks in only about 8 percent of cases. Ho, Milevsky, and Robinson
(1994) also emphasize the importance of stocks, arguing that investments with
high return-risk trade-off may be necessary to minimize the chances of outliving
one’s assets after retirement.
Very few studies on DC plans examine the entire distribution of terminal wealth.
Kim and Wong (1997) employ simulation and stochastic dominance tests to
evaluate merits of different allocation strategies using US asset return data since
1926. Their results indicate that the optimal allocation strategy should generally
be one heavily tilted towards equities till the individual is close to retirement. In
fact, under more restrictive assumptions of second order stochastic dominance,
they find a 100% equity strategy dominant over all other strategies for horizons
of 25 years or longer. However, they do not find any benefit for retirement
investors in adding international stocks to their portfolio.
47
Asset allocation strategies following the lifecycle principle of investing may
differ in terms of switching rules. Hickman, Hunter, Byrd, Beck, and Terpening
(2001) conduct a simulation study of two lifecycle switching rules: (i) Malkiel’s
(1996) rule, and (ii) the “100-minus age” rule, and also compare the results with
a strategy that invests 100% in the Standard & Poors’ (S&P) 500 index fund.21
Using a 30-year holding period, the two lifecycle approaches yield very similar
outcomes and produce median wealth at retirement that is almost half of that
associated with the index fund. Only in about 15 percent of the simulations the
life-cycle approaches are able to outperform the S&P 500, which suggests that
occasionally the switch to bonds and money market securities at later ages may
prove to be a correct strategy. However, the authors question whether this small
benefit of protection against such relatively rare adverse outcomes warrant
accepting large reduction in expected terminal wealth.
Among other research scrutinising lifecycle strategies, Booth and Yakoubov
(2000) investigate both accumulated amount at retirement and annuity value for
DC plan participants for five different lifecycle strategies. Using both empirical
data and stochastic modelling, they find no evidence to support the superiority
of lifecycle strategies that advocate gradually moving from predominantly
equity based portfolio to investments like bonds and cash as the investor
approaches retirement. Although their finding suggests that automatic switching
to less volatile assets before retirement may not be appropriate for DC plan
participants, the authors are not able to draw a strong conclusion that continuing
with the equity based strategy is necessarily better. They recommend the
member participant maintain a well diversified strategy until retirement.
A handful of scholarly work so far has examined the impact of asset allocation
on the potential of confronting extremely adverse outcomes at retirement.
Ludvik (1994) finds that if predictability of ‘floor’ level (only 5% of outcomes
21 Malkiel’s switching rule is explained in 2.4.
48
are below this level) matter most to the DC investor, 100% bonds or 100% cash
strategies produce superior outcomes to 100% equity or a lifecycle switching
strategy. However, the floor level of the 100% equity strategy is higher than
those for 100% bonds or 100% cash strategies. The lifecycle strategy, according
to his results, has improved ‘floor’ level relative to 100% bonds and 100% cash
strategies and reduced volatility of the floor level relative to 100% equity
strategy. Blake, Cairns, and Dowd (2001) evaluate a range of static and dynamic
asset allocation strategies for DC plans by estimating the value at risk (VaR)
measure for target pension outcomes.22 They find that the VaR estimates are
extremely sensitive to their choice of asset allocation strategy. Their results
indicate that a static diversified asset allocation strategy with high equity content
delivers superior results to dynamic strategies including the lifecycle approach
over a long horizon (40 years in their study).23 Also, conservative bond-based
asset allocation strategies require much higher contributions to match the
outcomes of equity-based strategies.
Hibbert and Mowbray (2002) investigate various asset allocation strategies
including various forms of lifecycle strategies using a stochastic model. Like
most other studies, their results show that 100% equity strategy generates the
highest expected retirement income although the range of potential outcomes is
very wide. Lifecycle strategies are useful in reducing the dispersion of outcomes
in their study but they do so at the cost of lowering the expected value. Vigna
and Haberman (2002), among others, uses dynamic programming techniques to
determine an optimal investment strategy for DC plan participants. They find
that the conventional lifecycle strategy is optimal for a risk-averse investor
while for a risk-neutral investor the optimal allocation is 100% equities without
any switch. However, the different downside risk measures used in their study 22 VaR, a measure of tail risk, is discussed in the next section. 23 This strategy resembled the average allocation of UK pension funds in 1998 with 5% in treasury bills, 51% in UK equities, 20% in international equities, 15% in UK bonds, 4% in international bonds, and 5% in UK property.
49
give conflicting indications about optimality of the various strategies considered
in their study.
Using actual lifetime earnings data for a large sample of households to model
plan contributions and combining these with simulated patterns of asset returns,
Poterba, Roth, Venti, and Wise (2006) examine the distribution of retirement
wealth for DC plan participants to evaluate lifecycle strategies vis-à-vis age-
invariant strategies that hold the fraction of portfolio allocated to each asset class
constant. Their analysis shows that the distribution of retirement wealth for
lifecycle strategies is similar to age-invariant strategies which hold equal
proportion of stocks as the average stock holding in the lifecycle strategies.
They also find that expected utility associated with these strategies and their
relative rankings is very sensitive to the expected equity premium, the plan
participant’s risk aversion and the presence of wealth outside the DC plan.
In contrast to the above studies which discuss theoretical allocation strategies
and their impact on retirement outcomes, Blake et al. (2004) focuses directly on
asset allocation structures of default funds actually offered in pension schemes.
According to their findings, an allocation strategy with high fixed income
content, which is conventionally regarded as a low risk-low return approach,
produces worse VaR outcomes for pension ratios at 5% level than some other
strategies with higher allocation to equities. This shows that conservative
strategies may not be synonymous with ‘low risk’ strategies for retirement
investors with long horizons as returns from these may fail to keep pace with
that of equities as well as long term wage growth of the individual. Their results
indicate that lifecycle strategies are effective in reducing risk but at the cost of
reducing the terminal wealth outcome of the retiree. Also, they find very little
benefit in holding long gilts over cash in the final year before retirement.
50
Shiller (2005a) observes that lifecycle funds currently offered in the U.S. market
are not exactly the same. This shows that considerable difference in opinion
exists about the optimality of their asset allocation structure to investors with
similar horizon. For example, as of September 30, 2004, the Vanguard Target
Retirement 2045 fund (aimed at investors in their twenties who are expecting to
retire around 2045), allocates 89% to stocks (domestic and international), and
the remaining 11% to fixed income securities. This, according to their
prospectus, would gradually change to a target allocation of approximately 30%
in stocks, 65% in fixed income, and 5% in cash at the time of retirement (target
date). About 5 years after the target date, the allocation would resemble that of
Vanguard Target Retirement Income Fund (aimed at current retirees) which
allocates 20% to stocks, 50% to bonds, 5% to money market instruments, and
25% to inflation-protected securities. In contrast, T. Rowe Price Retirement
2045 Fund currently invests 93.5% in stocks and 6.5% in bonds. This allocation
gradually changes to approximately 50% stocks, 40% bonds, and 10% short
term investments at the point of retirement. The proportion of stocks would
continue to decline gradually for another 30 years after target date when it
would reach 20% and would remain fixed at that level.
An important issue that has been drawing attention from researchers recently is
the switching criteria for lifecycle strategies. As discussed above, most lifecycle
strategies currently in practice adopt a deterministic switching policy where shift
of allocations from equities to bonds and cash is done gradually following a
preset rule. Ludvik (1994) argues for a ‘self-modifying’ strategy that increases
allocation to safer assets when the accumulated fund is ahead of some specified
‘target’. Arts and Vigna (2003) proposes a dynamic switching criterion from
equities to bonds which takes into consideration actual realisations of returns on
assets (equities and bonds). The switching from equities to bonds occurs earlier
if returns from equities in the initial part of the accumulation phase are high and
vice versa. Among theoretical models for switching in lifecycle strategies,
51
Cairns, Blake, and Dowd (2006) use the stochastic properties of the asset class
returns and member’s salary progression to derive optimal solutions while Vigna
and Haberman (2002) include risk aversion and time to retirement as key
switching parameters.
Arts and Vigna (2003) also develop an alternative to the conventional lifecycle
investment strategy which gradually switches the DC account accumulations
from equities to bonds. In their model, the individual initially invests
contributions to equities for a certain time. Thereafter, further (new)
contributions are allocated to bonds while the previous accumulation in the
account is allowed to remain invested in equities until retirement when it is
converted into bonds. They compare their new switch strategy with conventional
lifecycle strategy and find that while the mean for the latter is higher it also has
higher probability of falling below the target outcome.
It is evident from the above studies that there is no consensus on the optimal
asset allocation for DC plan investors although there seems to be some
agreement about the superiority of portfolios with high allocation to stocks over
bonds and cash, which is a result of the return differential between these asset
classes. Also, lifecycle strategies do not find the same amount of support from
academic researchers as they do from investment practitioners. Although most
of the research cited above considers conventional lifecycle strategies where
investors switch investments from stocks to bonds and cash as they approach
retirement, some academics allude to other possibilities. Shiller (2005b) argues
that since young people have relatively less income than older workers, a
lifecycle portfolio would be prone to investing less money in stocks. Similarly,
at middle and old ages when their earnings tend to peak, lifecycle strategies
would actually move investments out of stocks to assets which are less risky and
generate lower returns. In that case the lifecycle investment approach would
actually undermine the investment objective of maximizing retirement wealth
52
and DC plan participants would do better by following a strategy that does just
the opposite– invest funds in bonds and cash during early years when their
earnings (and therefore, contributions) are low and to stocks in the middle and
late years when their earnings are high. However, this type of investment
strategy has not been developed and empirically tested so far. The third and
fourth essays in this dissertation examine some of these unorthodox asset
allocation approaches discussed in this section to maximize the welfare of the
DC plan participant.
2.6 Strategic Asset Allocation: Role of Equity Premium
The role of equity premium is central to our research in evaluating alternative
approaches to asset allocation.24 This is because the investment outcomes of any
strategy which invests in equities would undoubtedly be very sensitive to the
equity premium used by the researcher. The estimation about the exact long-run
equity premium is often a determinant of the weighting assigned to equities
(relative to other asset classes) in the portfolio of the DC plan participant.
According to Utkus (2005), one of the investment principles that are part of
most participant education programs in United States is an expectation that
positive equity risk premium would continue in the future. This, he points out,
can influence the plan sponsors’ choice of default options. Historical evidence
supports the existence of a positive equity risk premium, more so, over long
holding periods. Investment horizons of DC plan participants can be considered
as long, since these are typically well in excess of thirty years. This should call
for an allocation policy which is tilted towards stocks. There is also an implicit
24 The concept of equity risk premium i.e. excess returns of common stocks over fixed income and cash investments is well documented and debated in finance literature.
53
assumption that the expected equity risk premium is an adequate compensation
for the volatility of stock returns.
Mehra and Prescott (1985) study asset returns in US market for the 1889-1978
period and find that investment in stocks, on average, generated 6.2 % additional
return over investment in short-term government debt. According to them, such
a high premium, even when one considers the higher risk associated with stocks,
is puzzling. Siegel (1992) analyses returns for a longer period (1802-1990) and
finds that equity premium is actually not as large when one considers this
extended time span. He observes that real returns on bonds have been
particularly lower in the middle part of the twentieth century resulting in higher
equity premiums. But bond returns during the 1980-1990 period, the last ten
years of his study, bounced back to their highest levels for more than a century,
Siegel cautions that it is likely that the premium associated with holding equity
is likely to decline in future although he agrees that equities may still prove to be
the best route to long term wealth accumulation.
Dimson et al. (2002) study returns of different asset classes in USA over 25, 50,
75 and 100 year sub-periods during the last century. Their results indicate that
although real return on equities has increased continuously during the twentieth
century, so has real returns for bonds and bills. The gap between real returns on
equities and bonds has actually decreased for the 25 year sub-period compared
to 50 year sub-period to 2001. In fact, over the ten years until the end of 1990,
US bonds generated an annualized return of 13.7% to outperform equities which
returned 12.6% annually during the same period.
While the US investors enjoyed large positive equity premium (geometric risk
premium of 5.8% relative to bills and 5% relative to bonds) over the last
century, one needs to consider whether the experience has been similar in other
important markets outside US before drawing any definitive conclusion. Jorion
54
and Goetzmann’s (1999) report returns for 39 financial markets for the 1921-
1996 period and find real return for US equities to be the highest. They argue
that the high premium obtained for US is likely to be the exception rather than
the rule. However, not all commentators agree with their view. Dimson et al.
(2002) document the returns from equities, bonds and bills across 16 countries
during twentieth century. They find that while the equity risk premium relative
to bills differs across countries, the 101 year averages fall within a narrow range.
The average equity risk premium relative to bills for the world index is 4.9%,
which is 0.9% below the same premium for US. The equity premium relative to
bills for Australia is 7.1% which exceeds that for US (5.8%) and UK (4.8%).
The equity premium relative to bonds for most countries, expectedly, is lower
than that relative to bills. The world average of 4.6% is 0.4% lower than that of
US. Once again, the premium for Australia (6.3%) exceeds both US (5%) and
UK (4.4%).
While the equities had a good run in recent history, bond investors had a very
rough time for most of the time. Davis (1995) points out that not only bonds in
most countries offered a much lower return, but returns were also marked with
high degree of volatility. He finds that during the period 1967-1990 mean real
return for bonds has been negative for many countries including US (-0.5%),
UK (-0.5%), Sweden (-0.9%), and Australia (-2.7%). The corresponding
standard deviation of returns for these four countries has been 14.3%, 13%,
8.5%, and 14.7% respectively. Remarkably, for USA, the standard deviation of
real returns for bonds almost matched that for equities (14.4%) during this
period.
Given the existence of an equity premium for most of the last century and very
little probability of it turning negative when one considers a longer holding
period (Siegel, 2003), some commentators feel that retirement plan participants
should invest nearly all of their contributions in equities, especially when they
55
are young and therefore, have a long investment horizon25. Using US market
data for the 1926-1997 period, Hickman et al. (2001) examine relative
performance of bills, bonds, and stocks by employing sampling with
replacement and estimating period-by-period return differentials. They conclude
that for investors with holding periods of 20 years or more, investing in any
asset class other than equity results in substantially less expected terminal
wealth, while imparting little risk reduction benefits in compensation.
By examining the case of college and university endowment funds that
traditionally hold a 60:40 mix of stocks and bonds, Thaler and Williamson
(1994) demonstrates that an allocation of 100% of their assets to equities with
some tactical adjustments is likely to provide superior results most of the time.
Although individual retirement accounts under defined contribution pension
plans do not have a quasi-infinite investment horizon as enjoyed by university
endowment funds, a holding period of 30-40 years, as is the case for most
employees may be considered sufficiently long to warrant more aggressive
allocation than currently chosen by most plan sponsors for their default
investment options. An examination of the international evidence presented by
Dimson et al. (2002) seems to validate this point. The real returns for equities
for every 30-year and 40-year period starting at 1900 and observed at 10 year
intervals thereafter till 2000 has always been positive for most countries
including US, UK, and Australia. The equity premium has also been positive for
all the corresponding periods. However, the same cannot be said about the real
returns for bond and bills since both of these asset classes generated negative
returns for some of the observed 30-year and 40-year holding periods during the
last century. For example, real returns for Australian bonds were negative for 3
out of 8 observed 30-year periods (1940-1969, 1950-1979, and 1960-1989) and
2 out of 7 observed 40-year periods (1940-1979 and 1950-1989). Bills in
Australia fared even worse with 3 out of 8 observed 30-year periods (1930-
25 The theoretical basis for this argument is discussed later in this chapter.
56
1959, 1940-1969, and 1950-1979) and 4 out of 7 observed 40-year periods
(1920-59, 1930-69, 1940-1979 and 1950-1989) yielding negative real returns
and 1 observed 40-year period (1910-1949) yielding zero real return to the
investors.
2.7 Measures of Risk
An analysis of the arguments used in the previous sections reveal that differing
perceptions and definitions of risk used by the opposing camps lie at the heart of
the debates related to the superiority of equities for long term investors and time
diversification. In investment management, risk plays a central role along with
expected return in analysis the desirability of different outcomes. According to
Ludvik (1994), the perception of risk and its measurement is critical to the
choice of an investment strategy. Since this research seeks to evaluate the risk-
return trade-off of alternative asset allocation strategies, it would be appropriate
to review some of the important risk measures which can be employed by our
study.
The Oxford Dictionary describes risk as ‘hazard, chance of bad consequences,
loss etc’. Traditionally, the standard deviation (or its square, the variance) has
been the most widely used measure of risk in finance. In his seminal work,
Markowitz (1952) adopted the use of standard deviation to measure portfolio
risk and it has been used as a general measure of risk by finance researchers ever
since. Variance is given by
∑=
−=k
r
rk 1
22 )(1 µσ (19)
where � is the mean return, r is the return for a particular period and k is the
number of periods. This is used under the assumption that higher the variance
(or standard deviation), higher is the risk. If return distributions are normally
57
distributed or the investors have quadratic utility functions, variance or standard
deviation is a suitable measure of asset or portfolio risk (Oberuc, 2004).
By its very definition, standard deviation captures the dispersion on both sides
of the mean and therefore serves as a good statistical measure of variability. In
case of investment returns, it measures the volatility of returns over a given
period of time. But according to many academics and practitioners, volatility or
uncertainty is not necessarily risk because most people think about risk as the
possibility of unpleasant outcome (Balzer, 1994; Dowd, 2002). Their criticism
of standard deviation is principally based on the fact that it treats upside and
downside deviations equally. Therefore, if standard deviation (or variance) is
used as a risk measure, above-average performance (causing upside deviations)
are penalised as much as below-average performance (causing downside
deviations). Most investors may find this counterintuitive to their perception of
risk since they are likely to be more concerned about the below-average
performance of their investment. Among other shortcomings of standard
deviation as a measure of investment risk is that it leads to misleading
propositions when return distributions are not normal (Balzer, 1994, 2005).
It has long been recognized that investors view risk as the possibility of not
being able to meet their investment objectives i.e. chance of failing to meet their
target outcome.26 In such case, risk is only influenced by the returns below the
target and therefore, below-target losses are weighed more heavily by investors
than gains. This view of ‘downside’ risk has been noted by many researchers in
finance, economics, and psychology.27 Roy’s (1952) concept that an investor
may prefer the safety of principal first when facing uncertainty first drew the
26 For institutional investors, this may mean the risk of underperforming a particular benchmark index like ASX All Ordinaries and for pension plan participants it can be the risk of underperforming the rate of inflation. 27 For a comprehensive review of early literature, see Libby and Fishburn (1979).
58
attention of academic community towards downside risk measures. Markowitz
(1959) recognized the importance of minimizing downside risk in a portfolio
selection context if (i) returns are not normally distributed (as assumed in mean-
variance framework) or (ii) only downside risk or safety first is relevant to an
investor. He suggested using a semivariance computed from mean return
(below-mean semi-variance) in the first case and a semi-variance computed
from a target return (below-target semivariance).28 The theoretical superiority of
semi-variance over variance as measure of risk has later been demonstrated by
several researchers (Quirk & Saposnik, 1962; Ang & Chua, 1979). Mao (1970)
also argues strongly that investors are only interested in downside risk and
therefore semivariance is the relevant measure of risk.
Research on downside risk measures received boost from the development of
the lower partial moment (LPM) risk measure by Bawa (1975) and Fishburn
(1977). This risk measure could accommodate different forms of known Von
Neumann-Morgenstern utility functions unlike variance or semi-variance where
investor’s utility function always needs to be quadratic. The LPM can represent
different attitudes of human beings towards risk like risk averse, risk seeking,
and risk neutral. In other words, with LPM there is no limitation on the value of
the risk aversion coefficient used in investment analysis. If λ denotes the risk
tolerance of the investor, then lower partial moment is given by:
λ
λ ∑=
−=K
TTRtMax
KtLPM
1
)](,0[1
),( (20)
where k is the number of periods, t is the target return, TR is the actual return
during the time period T, and Max is the maximization function that selects the
larger between the numbers 0 and )( TRt − . The term λ , which is known as the
degree of lower partial moment (LPM), differentiates LPM from variance or
28 Although different terminologies exist for different semivariance measures like relative semivariance and downside deviation, we would use below-mean and below-target semivariance as these describe the measures more accurately (Nawrocki, 1999).
59
semivariance (and their square root counterparts) because in case of former it
can theoretically assume any value (even fractions) whereas in case of the latter
it is restricted to a single value i.e. 2.
For λ = 0, LPM gives the probability of shortfall i.e. how often the return can
fall below the target although it does not consider how severe the shortfall is
likely to be. If λ = 1, LPM weighs shortfalls (target return less below target
returns) with linear weighting. This is also defined as expected shortfall. For λ
= 2, as explained above, LPM is same as below-target semi-variance. Bawa
(1975) shows that LPM is mathematically related to stochastic dominance when
risk tolerance (λ ) is 0, 1 or 2. For example, for λ = 0, LPM is equivalent to
first order stochastic dominance and therefore investors with common von
Neumann-Morgenstern utility can use LPM (0) to evaluate the return
distribution of investment portfolios. The choice of appropriate shortfall
measure may be guided by the investor’s degree of risk aversion (Bawa, 1978;
Harlow and Rao, 1989) with risk averse investors choosing LPM with λ > 0.
One of the psychological concepts which is increasingly used in economic
analysis is loss aversion. Kahneman and Tversky (1979) first proposed this in
the framework of prospect theory and later also defined for choice under
uncertainty by Tversky and Kahneman (1991). An important aspect of loss
aversion is the fact that it can resolve several paradoxes in traditional choice
theory as well as the criticism of expected utility put forward by Rabin (2000)
and Rabin and Thaler (2001) who showed that reasonable degrees of risk
aversion for small and moderate stakes imply unreasonable high degrees of risk
aversion for large stakes. If DC plan participants are believed to be loss averse
towards the value of their retirement assets, which can be considered as a ‘large
stake’, the plan sponsors may decide to select asset allocation strategies that
have more chance of avoiding the most disastrous outcomes. In other words, DC
60
plans would select strategies that lower the estimates of tail risk of the
probability distribution of retirement wealth as their default investment option.
A popular measure of tail risk increasingly used by academics and practitioners
is value at risk (VaR). Pioneered by JP Morgan, it was originally used as a
single aggregate measure of risks across different trading positions of an
institution which gave the management an estimate of maximum likely loss for
the next trading day (Dowd, 2005).
In a portfolio context, if p represents the probability of worst percentage of
outcomes the investor is concerned about, α is the confidence level and p is set
such that α−= 1p , and if qpis the p-quantile of a portfolio’s prospective
profit/loss over some holding period, then the portfolio VaR at that confidence
level is given by
VaR = -qp (21)
In other words, VaR is represented by the negative of the qpquantile of the
profit/loss distribution. The parameter α indicates the likelihood that the
investor would not get an outcome worse than VaR. The VaR, therefore, is
critically dependent on the choice of confidence level (α ) as well as the length
of the holding period (Dowd, 2005).
The concept of VaR is simple and straightforward and easy to understand.
Losses greater than VaR are suffered only in extreme circumstances the
probability of occurrence of which can be specified by the user. Therefore, VaR
for time period T is given by TR such that Probability (TR <VaR) = α , where
α is set by the investor according to his or her degree of risk aversion. The
higher the degree of risk aversion, higher is the value of α and vice versa. In
case of distributions that are not normal or lognormal, where standard deviation
61
is not a good indicator for volatility especially downside risk, VaR can be
effectively used because one can empirically determine at what point in the data
set probability ( TR <VaR) equals α (Messina, 2005).
VaR, as a risk measure, is not without distinctive shortcomings. Although it
specifies the amount at risk at a particular probability level, it gives the users no
idea about the amount at risk at higher or lower levels of probability (Balzer,
1994). The failure of VaR to consider magnitude of losses greater than itself can
lead to serious underestimation of risk. Dowd (2005) points out that investors
may be exposed to extremely unfavourable outcomes if they use VaR as the
only measure of risk since they may accept any investment that increases
expected return regardless of the possible loss provided that such loss is only
insufficiently probable. A more serious drawback of VaR is that it is not
subadditive29 and therefore cannot fulfil a necessary axiom of being qualified as
a coherent risk measure (Acerbi, 2004).
While VaR has its use as a quantile measure, expected shortfall (ES) or expected
tail loss (ETL) is often forwarded as a better candidate for risk measurement
since it overcomes the limitation of VaR in satisfying the axioms of coherency.
Dowd (2005) defines it as the probability weighted average of tail losses. This
can be formally represented by
∫−=
1
1
1
αα α
dpqETL p (22)
Therefore, ETL is actually the average of the worst 100(1- )α % of the
outcomes. Risk-return decision rules based on ETL are valid under more
general conditions and consistent with expected utility maximisation where risks
29 The theory of coherent risk measures proposed by Artzner et al. (1997, 1999) postulates that the axioms of coherency includes the property of subadditivity, which means that aggregating risks does not increase overall risk. This is consistent with investment theory that diversification leads to reduction of risk when assets are not perfectly correlated. If assets are perfectly correlated, diversification would leave level of risk unchanged.
62
are rankable by second-order stochastic dominance, whereas decision rules
based on VaR are valid under more stringent conditions and only consistent with
expected utility maximization if risks are rankable by first order stochastic
dominance (Yoshiba & Yamai, 2002). Apart from being theoretically superior as
a risk measure, expected shortfall also offers an important practical advantage
over VaR because it tells the user about the potential exposure to losses for
outcomes that are worse than VaR (Dowd, 2005). However, Yoshiba and Yamai
(2002) show that expected shortfall fails to take into account extreme loss events
and may lead to incorrect selection for investments not ranked by second-order
stochastic dominance. They find the second lower partial moment to be more
effective in such cases.
2.8 Measures of Investment Performance
Measuring investment outcomes is critical to the current research since this
would form the basis of evaluating different asset allocation strategies. There are
two general approaches that have been most used by researchers to evaluate the
attractiveness of investment return distributions. The first approach is to select a
preference function and use its expected value as decision criterion. The
classical route to model preferences in finance theory is by means of a utility
function, the shape of which represents the risk attitude of the individual. The
modern portfolio theory developed by Markowitz (1952) uses expected return of
individual assets and their variance-covariance to derive an efficient frontier
such that every portfolio lying on it maximised the expected return for a given
variance of the portfolio. Selecting a portfolio from those lying on the efficient
frontier is a risk-return trade-off problem for the investor which according to
Markowitz is accomplished by maximising his or her quadratic utility function
of the following form:
63
2)( kwwwU −= (23)
where w is the wealth level and 0>k
Hicks (1962) and Arrow (1971) has pointed out this implies increasing absolute
risk aversion (IARA). But this contradicts with research evidence that indicates
decreasing absolute risk aversion (DARA) is more consistent with observed
human behaviour (Pratt, 1964; Arrow, 1971). In such a scenario, mean-variance
paradigm can only be valid if returns are normally distributed (Cass & Stiglitz,
1970). But this assumption is not acceptable to most analysts and practitioners
(Michaud, 1998).
Behavioural research in recent times also point out that preferences of
individuals cannot be characterised by one global degree of risk aversion.
Kahneman and Tversky (1979) show that an individual may demonstrate
different degrees of risk aversion at different future wealth levels relative to
current wealth. According to them, for values of future wealth below current
wealth, the investors would be risk-seeking in their behaviour while for values
above current wealth, they are likely to show risk aversion.
Because of the lack of specificity in investors’ utility functions (e.g. Rubinstein,
1973) and complexity involved in dealing with them, there have been attempts
to depart from the utility based framework and use more objective criteria to
rank portfolios. This has given birth to risk-adjusted performance measures
which combine a return and a risk measure into a composite measure to rank
investment alternatives. Unlike preference functions, they do not involve any
explicit modelling of the investors’ risk attitudes. These measures are generally
devised by dividing the return measure by the risk measure or by subtracting the
latter from the former (Platinga & De Groot, 2005).
64
Traditionally, both academics and practitioners in investment management have
favoured use of reward-to-risk ratios as measures of portfolio performance. The
best example of this is the Sharpe (1966) measure, popularly known as the
Sharpe Ratio (SR). This is given by
pfp RRSR σ/)( −= (24)
where pR is the return on the portfolio, fR is the riskless rate of return, and
pσ is the standard deviation of the portfolio.
A similar reward to risk ratio has also been given by Treynor (1965) which is
exactly the same as Sharpe Ratio except that it employs beta, a measure of
systematic risk of the portfolio, instead of standard deviation in its denominator.
This is represented mathematically as
pfp RRTreynor β/)( −= (25)
In addition to the Sharpe and Treynor measures, a number of other performance
measures have been developed from the modern portfolio theory and the capital
asset pricing model (CAPM). Most of these measures employ a benchmark
portfolio to calculate the performance outcome. Most well known of this
measures is given by Jensen (1968) which is based on CAPM and evaluates the
performance of the portfolio relative to that of the market index.
However, not all performance measures strictly work within the risk-return
framework of Portfolio theory. As discussed in 2.7, researchers have
increasingly questioned the concept of risk given by mean-variance paradigm of
Markowitz. Roy (1952) proposes an alternative known as safety first principle.
According to this an investor is concerned about limiting the risk of
unfavourable outcomes and therefore, specifies a minimum acceptable rate of
return30. According to Roy, the investor would prefer the investment which has
lowest probability of producing return below such specified floor rate. This
30 Roy refers to this as ‘disaster level’
65
leads to the formulation of an alternative reward to variability ratio (also known
as safety first ratio) mathematically represented by
Roy’s Reward-to-variability Ratio = ptp RR σ/)( − (26)
where tR is the minimum acceptable return (MAR) to the investor. The investor
would choose the investment which maximizes the safety first ratio which is
equivalent to minimizing the probability of returns below the minimum
acceptable level. A closer look at the safety first criterion would reveal that it is
very similar to the previously discussed reward-risk ratios. For example, if the
minimum acceptable return (tR ) for the investor is equal to the riskless rate of
return ( fR ), the safety first ratio becomes identical to the Sharpe ratio. In fact, it
has been mathematically proven that the portfolio that maximizes Roy’s safety
first criterion must lie along the efficient frontier in the mean-variance space
(Elton and Gruber, 1995).
Since the above performance measure depends on the assumption of normal
distribution of returns, researchers have questioned their validity. Klemkosky
(1973), and Ang and Chua (1979) demonstrate that these measures can lead to
incorrect rankings of performance and suggest the reward-to-semivariance
(R/SV) ratio as an alternative. While the numerator in this ratio represents the
excess return above target i.e. ( tp RR − ), the semivariance used in the
denominator is usually the ‘below target semivariance’.
The concept of downside deviation has been used to suggest several risk-
adjusted performance measures, especially in practitioner literature. The most
well-known among these is the Sortino ratio introduced by Sortino and Price
(1994). This is given by
δtp RR
Sortino−
= (27)
66
where δ denotes downside deviation. Thus, the Sortino ratio constructs a risk-
adjusted performance measure by replacing the standard deviation with the
downside risk measure and therefore, is equivalent to the Sharpe ratio but in a
mean-downside deviation space. Due to this formulation, it does not penalise
performance for volatility above the target rate of return for the investor unlike
the Sharpe ratio.
Recent research in behavioural finance suggests that, contrary to the
prescriptions of the portfolio theory, individuals may not be seeking the highest
return for a given level of risk. Statman and Shefrin (1998) claim that investors
seek upside potential with downside protection. According to the normative
utility function of Fishburn (1977), individuals are risk averse below a minimum
acceptable rate of return and risk neutral above it. Sortino, Van der Meer, and
Platinga (1999) propose a performance statistic that accommodates the above
suggestions. They do so by suggesting that the return should be replaced with
the upside potential of an investment relative to MAR. This is known as the
upside potential ratio (UPR) and measures upside potential relative to the
downside variance. Mathematically,
( )
( )2
1
2
−
−=
∑
∑
∞−
∞
t
t
R
tp
Rtp
RR
RR
UPR (28)
The numerator of the UPR is the probability weighted summation of returns
above the minimum acceptable rate and therefore represents the upside
potential. The denominator is same as the downside risk calculated by Sortino
and Van der Meer (1991).
Nawrocki (1999) is critical of the popular performance measures based on
downside risk because they do not include the different levels of the investor’s
67
risk aversion. For example the UPR only uses the square root of the below target
semivariance (when risk tolerance parameter a=2) and therefore, ignores other
levels of risk aversion that are available to the users of lower partial moment.
This problem may be overcome by employing more general reward-to-LPM
ratio and setting the value of n to match the degree of risk aversion of the
investor.
In evaluation of investment alternatives, whether based on maximization of
expected utility or risk-adjusted performance, it is generally assumed that the
investor is only exposed to the ‘risk’ which is inherent in the returns and
therefore can successfully trade this off against expected rewards. However,
Ellsberg (1961) among others, argues that the investors may not have all of the
information required to form such expectations because of uncertainty about the
future state of the world. In this situation of ambiguity, investors may
demonstrate loss aversion (as discussed in 2.7) where they want to make sure
that they would be able to provide for themselves if the future conditions fall
short of their expectations. Savage (1951) discusses the minmax principle and
suggests an alternative- the minmax-regret principle.31 Among recent work,
Shirland and Gatti (2005) propose a ‘maxi-min’ and ‘mini-max’ framework for
portfolio choice. The former selects the alternative which maximises the worst n
percentile of outcomes, where n is set by the investors according to their risk
tolerance level. Alternatively, the ‘mini-max’ rule chooses the strategy which
minimizes regret.32 Quantile risk measures like VaR, which ensures that the
investor’s wealth does not fall below a certain specified level qpwith a
probability level of at least α (as shown in 2.7 ) can be used in this kind of
framework to rank alternative asset allocation strategies.
31 Minmax is a well accepted technique in the statistical decision making literature (see e.g. Wald, 1950). 32 The authors measure this as difference between the pay-off from maxi-min strategy and the highest pay-off that would prevail in some better state of the world.
68
3. Methodology and Data
3.1 Model Description
We follow the steps outlined in Dowd (2005) in applying the simulation
methodology to the retirement wealth problem. The first of these involves
designing a model to generate retirement wealth outcomes which accommodates
the stochastic variable(s) of interest and other variables embedded in DC plans.
It is important to bear in mind that this model for generating retirement wealth
outcomes is distinct from the asset return generating model described in 3.2.
3.1.1 General Structure
We develop a DC plan accumulation model which uses stochastic simulation to
determine the expected distribution of retirement wealth outcome for the
accumulation phase, which is measured in terms of the ratio of the terminal
wealth at the point of retirement to the final salary of the plan participant.
The terminal value of DC plan portfolio is given by
∏∑−
+=
−
=++−=
1
1
1
0
)1()1()1(R
tuut
R
ttt rrSpkW (29)
where W = value of plan assets accumulated at the point of retirement
k = plan contribution rate
=tp probability of unemployment in year t
=tS annual salary in year t
=tr rate of investment return earned in year t
=R number of years in the plan before retirement
69
To estimate W, we need to model the (i) contribution cash flows and (ii)
investment returns for each period. The contribution cash flows primarily
depend on two variables: annual salary and contribution rate. The annual salary
for any year depends on starting salary, salary growth rate, and the number of
years elapsed since commencing employment. This is given by
10 )1( −+= t
t gSS (30)
where =0S starting salary of the plan participant
=g annual salary growth rate
To model the contribution cash flows, we have also included probability of
unemployment as a variable in our model, because the flow of plan
contributions is likely to be affected by the employment state.
Investment returns are dependent on returns on individual asset classes (included
in the portfolio) and the weights assigned to them. The latter is determined by
the asset allocation strategy of the plan. Mathematically,
∑= titit rwr ,, (31)
where =tiw , weight assigned to the thi asset in year t
=tir , return on the thi asset in year t
While asset allocation strategy is our primary variable of interest, we need to
assign values to other variables in the DC plan accumulation model for
modelling retirement wealth outcomes. Assumptions of DC plan researchers on
simulation model parameters have ranged from illustrative and arbitrary
suppositions (Johnston et al. 2001) to hypothetical estimates based on modelling
with historical data (Blake et al. 2001). For our baseline case, we assign values
that can be considered as reasonable in the current economic context. Although
there is some degree of arbitrariness involved in the process, this is not likely to
70
influence our investigation of the research issue focus on the outcomes of
alternative asset allocation strategies while holding other factors constant.
3.1.2 Control Variables
The model includes three control variables that are set either by the plan
provider or the plan participant.
a) Asset Allocation Strategy ( )iw :
This is the key variable of interest in the model which decides the weights of
different asset classes in the portfolio. For examining our first research question,
we consider actual fixed weight asset allocation strategies used by Australian
superannuation funds in chapter 4. These allocations would be maintained by
annual rebalancing. In chapter 6, we would examine lifecycle and contrarian
asset allocation strategies. In addition to conventional lifecycle strategies,
chapter 7 considers a dynamic asset allocation whereiw would be modified
according to past portfolio performance.
b) Employment Life (R):
The starting age is the age when the employee commences employment and
therefore, becomes a member of the DC plan. In our baseline case, the DC plan
participant joins the plan at the age of 25 years.33 The retirement age is the age
when the contribution to the DC plan ceases. For our baseline case, this is set at
65 years, the current age for Australian males to be eligible for Age Pension.
The employment life (25-65 years) for our baseline case is consistent with
standard assumptions in DC plan literature (e.g. Blake et al., 2001; Dowd, 2005) 33 Although many job starters in Australia belong to the 15-24 years age group, a bulk of such employment is part-time or casual and labour force participation rate is lower compared to those aged 25 years and above. However, the participant rate is also low for 55 years and above category (Australian Bureau of Statistics Year Book Australia, 2006).
71
c) Contribution Rate (k)
For our baseline case, the contribution rate is assumed to be fixed at 9% of the
member’s annual salary, which under Superannuation Guarantee legislation, is
the mandatory minimum rate for employer contributions on behalf of
employees. A more general analysis could consider the possibility of including
voluntary contributions from members as well as future changes in mandatory
contribution rate. For the sake of simplicity, we assume that contributions are
made annually at the end of the year.
3.1.3 Other Variables
a) Asset Class Returns (tir , ):
For chapters 4 and 5, annual real returns for Australian asset classes such as
equities, bonds, and bills are employed. Real returns from US equities and bonds
are used to proxy those from international stocks and bonds respectively. For
chapters 6 and 7, we use nominal returns on US stocks, bonds, and bills. Details
of the dataset are reported in 3.4.1.
b) Earnings ( 0S , g):
Except in chapter 5, where we confront the gender inequity problem in
retirement savings, the earning estimates used in this research are hypothetical.
However this is certainly not going to have any bearing on the results of our
analysis as we hold the estimate constant for all competing allocation strategies
discussed within a chapter. In chapter 4, we assume that the starting annual
salary for the employee to be $25,000. The annual salary is assumed to grow at a
constant real rate of 2%, which closely follows Australia’s growth in real GDP
per person of 2.6% between 1994 and 2004 (Australian Bureau of Statistics
72
[ABS], 2005). In chapter 5, we use actual salary estimates for male and female
Australian workers from ABS. Chapters 6 and 7 use an arbitrary starting salary
estimate of $25,000 and a constant nominal growth rate of 4% for hypothetical
employees enrolled in DC plans in USA.
c) Probability of Unemployment (tp ):
For our simulation experiments in chapters 4 and 5, unemployment is modelled
as a binary variable (1 if employed, 0 if unemployed). The probability of
unemployment during any period of the baseline employee’s working life is
assumed to be constant at 5%. This is equal to the unemployment rate among
Australian workers with post-school qualifications (Kryger, 1999; Richardson,
2006). However we ignore this variable in modelling wealth outcomes in
chapters 6 and 7 since it is not relevant to the concerned research problems.
3.2 Asset Class Return Generating Process
To generate simulated returns for our trials, we employ both Monte Carlo and
bootstrap resampling methods in this thesis. The latter is our preferred return
generating process, the reasons for which are explained later in this section.
However they have two important similarities. First, in our research, both the
processes are modelled under the assumption that asset class return during any
period is serially uncorrelated to its own past returns. In other words, we assume
asset class returns are randomly distributed over time. Second, both methods use
the past returns data of different asset class returns to generate future return
scenarios. The appropriateness of our assumptions and return generation
approach is briefly discussed below.
73
Our assumption that asset class returns follow random walk has its roots in the
well accepted notion of efficiency of financial markets as shown by Samuelson
(1965) and Fama (1965, 1970).34 According to Samuelson, in an information-
efficient market, price changes cannot be predicted if they fully incorporate
information and expectations of all market participants. Fama encapsulated this
idea of efficient markets succinctly- prices fully reflect all available
information.35 Though subsequent empirical research has presented conflicting
evidence on this issue, the random walk still remains arguably the dominant
paradigm for researchers in this field.
Several studies like Goetzmann (1990) and Kim, Nelson, and Startz (1988) have
modelled serial independence of monthly and annual stock returns and have
rejected the notion of mean reversion of long term stock returns in favour of the
more parsimonious random walk model. Poterba and Summers (1988), who find
evidence that financial markets may be subject to time-varying expected returns,
admit that the lack of enough independent observations makes it difficult to
draw convincing conclusions about predictability of returns for low frequency
data. Most empirical studies which have found evidence against the random
walk (for example, Lo and Mackinlay, 1988) have used high frequency data like
daily and weekly returns. Since all the studies included in this dissertation use
annual returns from different asset categories, this is obviously not a major
concern in our case. Also, in recent times, many researchers (for example, Ang
and Bekaert, 2005; Campbell and Yogo, 2006) have shown that predictability in
returns is mainly a short horizon phenomenon and not a long horizon
34 An early version of the random walk hypothesis was proposed in 1900 by French mathematician Louis Bachelier in his doctoral thesis Théorie de la Spéculation. Bachelier’s pioneering work on behaviour of security prices is widely acknowledged by Samuelson and others (Bernstein, 1992) 35 The notion of efficient market hypothesis, however, is distinct from random walk hypothesis. As LeRoy (1973) and many others have shown, random walk is neither a necessary nor a sufficient condition for rationally determined security prices.
74
phenomenon.36 Therefore, the issue may not be of significant importance for
strategic asset allocation decisions of long horizon investors in our research.
3.2.1 Monte Carlo Simulation
This first essay (chapter 4) in this dissertation employs Monte Carlo simulation
(MCS) methodology to evaluate alternative asset allocation strategies by
estimating the DC plan outcomes. MCS was first introduced by Metropolis and
Ulam (1949) and, since then, have been used in several different fields like
physics, biology, and engineering to solve complex problems. This method has
been employed by finance researchers since late 1970s to price derivatives (e.g.
Boyle, 1977) and more recently to estimate VaRs and other financial risk
measures (e.g. Picoult, 1998). It has also been favoured by academics and
actuaries in evaluating risk of both DC and DB type pension plans (Blake et al.,
2001, 2005; Scott, 2002; Johnston, Forbes & Hatem, 2005). The MCS method is
appropriate for this research because it can handle complex and
multidimensional problems like those encountered in investigating DC plans,
where the retirement outcome is dependent on more than one risk variable. It
can address problems related to factors like path dependency, non-linearity, and
optionality, which most analytical approaches have difficulty in dealing with.
MCS is a general method of modelling stochastic processes by simulating them
using random numbers drawn from probability distributions that are assumed to
describe accurately the uncertain elements of the processes being modelled.
Unlike historical simulation, which does not assume any theoretical distribution,
36 Campbell (2003) reports long horizon predictability for UK, France, and Germany. But Ang and Baekart (2005) points out that this conclusion is critically dependent on their use of Newey-West (1987) standard errors and disappears when Hodrick (1992) standard errors, more appropriate for small samples as argued by the authors, are employed. Using other error correction methods like Richardson and Smith (1991) also supports their conclusions.
75
MCS estimates statistical parameters (like standard deviation and correlation)
from historical data series and then expose these to random changes to simulate
future outcomes. In its common form, the one which would be used in this
research, MCS assumes that returns from different asset classes are normally
distributed and their correlations are stable over time.37
The general idea for Monte Carlo studies as described in Kennedy (2003) is to
(i) model the data generating process, (ii) generate several sets of artificial data,
(iii) employ the data and estimator to create several estimates, and (iv) use these
estimates to gauge the sampling distribution properties of the estimator. We
briefly describe these stages below in relation to our study.
The key objective of this study is to draw comparisons between retirement
wealth outcomes of alternative asset allocation strategies. In doing so, perhaps
the most critical step is to develop a model which generates returns for different
asset classes over multiple periods. In Monte Carlo methods, a sample size of N
is considered to fix the parameters at certain values and then draw repeated
samples from the distribution of the error term. Since we follow standard Monte
Carlo simulation assuming that asset returns are drawn from a multivariate
normal distribution, the implication is that mean and standard deviation of asset
returns are time invariant and the returns are independent over the time horizon.
At each stage of the simulation horizon, the random shocks generated by the
multivariate normal model are adjusted so as to follow the average cross-
sectional correlation observed in the historical data. The correlation-based
dependence structure for Monte Carlo analysis is derived through either
Cholesky decomposition or principal component analysis (Picoult, 1998). The
former method is used in this research. If ijlL =1 is the lower-triangular
37 Incorporating complex features like fat tails, skewness, and dynamic correlations is desirable for accurate estimates of outcomes. But since in this research, we are primarily concerned with evaluating outcomes of alternative strategies to comment on their relative appeal, the basic Monte Carlo method is expected to adequately serve the purpose.
76
Cholesky decomposition of the correlation matrix ,C iµ be mean return on the
asset ,i and iσ be the standard deviation of return on asset ,i then for a
portfolio of n assets, the multivariate normal Monte Carlo model dictates that
∑=
=n
jjiji lZ
1
ξ (32)
where ξ denotes an independent standard normal random variable
(i.i.d. ))1,0(N≈ and where iZ represents a correlated standard normal variable
for asset i . The simulated return on asset i is then obtained as
iiii Zr σµ += (33)
Having selected the model, we estimate the parameters of asset classes – mean,
standard deviations, correlations – on the basis of historical return data, which is
described in 3.3.1. With the model of the data generating process already built in
MATLAB, we can generate several sets of artificial data sets for asset class
returns using random numbers. The MATLAB function MVNRND (MU,
SIGMA) returns an n-by-d matrix R of random vectors chosen from the
multivariate normal distribution with mean vector MU and covariance matrix
SIGMA. MU is an n-by-d matrix, and MVNRND generates each row of R
using the corresponding row of MU. SIGMA is d-by-d symmetric positive
semi-definite matrix, or a d-by-d-by-n array. These simulated return paths are
then combined with individual asset class weightings to obtain simulated
portfolio returns under each asset allocation strategy under investigation for
every period of the investment horizon.
The above portfolio returns are applied to contribution flows for the
corresponding periods to derive hypothetical retirement wealth outcomes
according to the simulation model for retirement wealth described in 3.1.1. The
simulation trials are then repeated many times to be reasonably confident that
the simulated distribution would be sufficiently close to the actual distribution.
77
The Monte Carlo simulation method as described above is not free from
shortcomings. The major concern for the researcher is that it requires strict
assumptions about the probability distribution of asset class returns. Although
we generate returns for the asset classes under the standard assumption that they
follow a multivariate normal distribution, the presence of skewness and fat tail
to some degree in data for different sample periods cannot be ruled out.38
Second, the simulation method assumes that the asset class returns are
independently distributed over time i.e. there is no correlation of returns of any
asset class with its own past returns. This disregards the possibility of any return
persistence or mean reversion in asset class returns. Finally, the assumption that
cross-asset correlation is constant over time may be inaccurate and simplistic if,
for instance, the equity risk premium is believed to be time-varying.
3.2.2 Bootstrap Resampling
The Monte Carlo method relies on strong assumptions about the distribution of
returns. In any Monte Carlo study errors must be drawn from a known
distribution. For instance, we assume asset class return distributions over long
horizons are multivariate normal. However, imposing such explicit distributional
assumptions on the return generating process is open to question and may at
times pose a serious threat to the acceptance of the results of such exercise by
the research community. This is a major drawback of the traditional Monte
Carlo method. Therefore, to adjust for this problem, we resort to an alternative
non-parametric method of return generation namely bootstrap resampling which
does not require the researcher to make such an onerous assumption.
38 However, this is more of a problem with high frequency data (for example, daily or weekly returns). In general, research suggests that monthly returns are well described by normal distributions (for example, Hagerman (1978))
78
The basic idea of resampling is to pick repeated samples at random from a
hypothetical population of interest. Very often this is based on the data sample
in hand. Since authentic data on past returns goes back to little more than the last
hundred years, it can be considered as a sample of the whole unknown
population. Hence we have to take several samples out of this sample as a way
of understanding the consequences of sampling variability for making inferences
about the unknown population based on our dataset, which itself is a sample of
the whole population. This, in essence, is resampling.
There are several methods of drawing random samples from a given sample of
data. Two well-known methods are the jackknife introduced by Quenouille
(1956) and the bootstrap introduced by Efron (1979). In both these methods, the
given data sample is reused many times to generate further samples. The
jackknife method, which deletes a number of datapoints at each cycle of
computation, is not commonly used in econometrics (Maddala, 2002). The
bootstrap method, which is frequently used in this research to generate asset
class returns, is briefly described below.
The bootstrap procedure is a popular econometric technique generally employed
to estimate sampling distributions by using only the original data and so “pulls
itself by its own bootstrap” (Kennedy, 2003). The asset class return data in our
sample are randomly drawn, with replacement, every period to create new return
samples over the investment horizon. If ( ),....., 21 irrr be the given sample and we
draw a sample of size n (= number of periods) with replacement, then
),......,( 21 nj RRRB = represents a bootstrap sample if each iR is randomly
selected from ( ),....., 21 irrr . The process is repeated for mj ,......2,1= where m is
the number of simulation trials.
79
It is no trivial matter that we choose to resample with replacement. It has to be
borne in mind that the actual population of interest is much bigger than our
sample of data ( ),....., 21 irrr . For example, in our dataset, i = 105 whereas the
sample size usually used in our simulation experiments is given by n = 40 (often
the length of investment horizon of the retirement plan participant) which means
there are only 2 complete non-overlapping samples in the dataset. In order to
make the dataset appear larger than it is, we need to draw repeated samples of
size n = 40 from the dataset with replacement. This allows for creation of
virtually unlimited number of samples to enable inferences to be drawn about
the unknown parameter of interest. To conduct bootstrap resampling with
replacement, we employ a MATLAB program called resamp developed by
Kaplan (1999). When applied to a data in the form of a matrix p x q, resamp (n,
data) randomly draws row by row n times i.e. n number of vectors (if the chosen
sample size is n). In other words, the random sampling process continues until
the number of drawn observations corresponds to the length of the investment
horizon. For M number of trials, the resampling process is repeated M times.
Since the given data can be rearranged in numerous different combinations,
bootstrapping can generate a dramatically larger number of future scenarios
compared to historical simulations which sample data sequentially. Since we
allow for resampling with replacement, the possibility of observing a wider
range of scenarios is also considerably larger which is informative in assessment
of extreme downside risk. Like the Monte Carlo method, the bootstrap
resampling destroys any serial correlation that may exist in the return data for
individual asset classes.39 This does not allow the researcher to capture any
positive (persistence) or negative (mean reversion) serial correlation in asset
39 Resampling can also be conducted using a ‘moving block bootstrap’ method introduced by Carlstein (1986) and Künsch (1989) which aim to capture any time dependence structure in the dataset as well as preserve cross-sectional correlation within the block, the length of which has to be specified by the researcher. However, as discussed earlier, we assume that asset class returns are serially uncorrelated and therefore, refrain from employing such approach in generating future returns from historical data.
80
class returns. However, the row-by-row resampling permits preservation of the
cross-asset correlation.
For the first study in this dissertation, we use both MCS and bootstrap
resampling separately to simulate asset class returns which are then used to
estimate potential wealth outcomes. Since the results after many trials are found
to be extremely close in the two cases, we use the latter method only in the
subsequent chapters (5, 6, and 7). Our preference for the bootstrap resampling
method is obviously influenced by its relative advantage (over MCS) in not
requiring the researcher to make any kind of assumption about the distribution
of future asset class returns.
3.3 Data
To evaluate the retirement wealth outcomes of different asset allocation
strategies using the simulation model discussed in 3.1.1, it has to be provided
with two key inputs. These are return data and the respective weight of each
asset class. Historical data for asset class returns would be used to generate
simulated investment return for each asset class for every period of the
investment horizon. The weights of the individual asset classes, which depend
on the allocation strategy, would be multiplied by their respective simulated
returns and then added up to generate the portfolio return for every period.
3.3.1 Asset Class Returns
As many authors have indicated, the issue of strategic asset allocation for long
horizon investors like DC plan participants should be based on historical
81
observations of asset class returns over decades rather than short periods.40 This
is essential to neutralise the undue influence that recent investment performance
(of these asset classes) may have on long-term risk assessment and asset
allocation decisions. Ceteris paribus, a longer period of data has a higher chance
of capturing the wide-ranging effects of favourable and unfavourable events of
history on returns of individual asset classes.
The source of the asset class return for this research program is the dataset of
global returns compiled by Dimson et al. (2002) and commercially available
through Ibbotson Associates, Chicago. An updated version of this dataset which
provides global returns from 1900 to 2004 has been used in this dissertation.
This is the only authentic dataset available for long term nominal and real
returns from bills, bonds, and equities in 16 countries including Australia. It is
unique in the sense that it covers a period of more than 100 years starting from
1900. Apart from returns on Australian asset classes, the returns for US
equities, bonds, and bills used in this thesis are also sourced from this dataset.
All returns are annual and include reinvested income and capital gains. Return
data is available in the domestic currency (Australian dollars for Australian asset
classes) as well as in US dollars. For chapters 4 and 5, returns in Australian
Dollars are used while for chapters 6 and 7, we use return data measured in US
Dollars.
The above dataset has used equity return data compiled by Officer which is
described in Ball, Brown, Finn, and Officer (1989). Officer uses a variety of
indexes in his work including Lamberton’s (1958) classic study to calculate
Australian equity return data for the early period. This is linked for the period
over 1958-74 to an accumulation index of fifty shares from the Australian
Graduate School of Management (AGSM) and for 1975-1979 to the AGSM
40 Short term return data, however, is useful if the focus is on short term volatility (Dimson et al. 2002)
82
value-weighted accumulation index. The Australia All-Ordinaries index is used
thereafter.
For bonds, the returns are based on the yields on New South Wales government
securities for 1900-1914, Commonwealth Government Securities of at least five
years maturity for 1915-1949, and ten-year Commonwealth Government Bonds
during 1950-1986. From 1987, JP Morgan Australian Government Bond Index
has been used to compute returns.
The dataset uses a 3-month time deposit rate to calculate cash returns for 1900-
1928. Then onwards, the Treasury bill rate has been used. Inflation rate has been
based on the GDP deflator (1900-01), retail price index (1902-48), and
consumer price index (1949 onwards). The switch from Australian pounds to
Australian dollars in 1966 has also been taken into account while computing
returns.
For computing the returns for US stocks, the dataset uses the Wilson-Jones
index data for the period 1900-25. For 1926-1961, the returns are obtained using
the University of Chicago’s Center for Research in Security Prices (CRSP)
capitalisation-weighted index of all stocks listed in New York Stock Exchange
(NYSE). For 1962-70, the dataset uses the CRSP capitalisation-weighted index
of NYSE and Amex stocks. The Wiltshire 5000 index is employed from 1971
onward.41 All the indices include reinvested dividends.
To compute returns from US bonds, the dataset uses 4 percent government
bonds for 1900-18 period. Returns for 1919-25 are based on Federal Reserve
ten-to-fifteen year bond index. Thereafter, the Ibbotson Associates’ long bond
index is used to calculate bond returns.
41 By end of 2000, this index included over 7000 stocks listed in NYSE, Amex, Nasdaq, and other exchanges.
83
The US bill returns are based on commercial bills during 1900-18. From 1919
onward, the return series is based on US treasury bills.
3.3.2Asset Allocation of Default Strategies
For our analysis in chapter 4, we examine several asset allocation strategies that
are actually used as default choices by superannuation funds in Australia. We
select funds that have been highly rated for their performance by SuperRatings,
an independent research organisation which rates Australian superannuation
funds annually. Details of the data used in this research are provided in 4.3.
3.3.3 Earnings Data
The earnings data for Australian male and female workers by age categories
used in chapter 5 are sourced from Australian Bureau of Statistics (ABS) 2001
Census of Population and Housing. Details of the dataset are available in 5.3.1.
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4. Evaluation of Fixed Weight Strategies as Default Options
4.1 Introduction
4.1.1 Background
In most developed countries policymakers are encouraging funded private
retirement plans (generally sponsored by employers or other private providers)
known as defined contribution (DC) plans, where employee participants build
up retirement savings through mandatory or voluntary contributions in their
individual retirement accounts. Retirement benefits of participants in these
plans are entirely dependent on the accumulation of plan contributions and
investment returns earned on those assets. A growing trend in DC plans is to
give the individual participants more control over investment of their plan
assets. For instance, DC plan participants are expected to select an investment
option from a menu of investment choices provided by the plan sponsor. This
investment decision is critical because it determines future investment returns on
their plan assets, and therefore, influences the wealth accumulated in the
retirement account at the end of the participant’s working life.
A substantial body of recent research demonstrates that although members of
retirement plans have the option to exercise choice, most accept the default
arrangements offered by their plans. The work of Choi et al. (2003) finds that
American employees tend to accept default arrangements in their plans for
critical features like contribution rate and investment choice. In their study, up
to 80 % of assets in different plans are invested in the default fund. In a recent
study conducted by Beshears et al. (2006), around 9 out of 10 existing
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employees who were subject to automatic enrolment in the company retirement
plan were found to have some of their assets invested in default fund, with
around two-thirds having all their assets in the default fund.
The apparent reluctance of the plan participants to exercise active investment
choice is corroborated by international evidence. According to consulting firm
Hewitt Bacon and Woodrow, around 80 % of group personal pension scheme
members in UK accept the default option provided by their plans (Bridgeland,
2002). Similarly, Cronqvist and Thaler (2004) find that since 2003 only 10% of
the new participants in Swedish retirement plans actually made any choice. In
Australia, about two-thirds of all retirement plan assets are invested in default
investment options (APRA, 2005). It seems that for a large majority of DC plan
participants worldwide, the investment of plan contributions are dictated by the
default arrangement of their respective plans.
Given that most plan participants tend to accept default investment options in
their plans, perhaps it is more important, from a practical standpoint, to question
whether these default investment options are appropriately designed to meet the
retirement goals of the participants. This issue has received little research
interest, which is surprising because financial well being for a majority of plan
participants after retirement is directly linked to the performance of the default
options. Moreover, international evidence like Blake, Byrne, Cairns, and Dowd
(2006) indicates that there is serious lack of agreement on this subject which is
reflected in the wide disparity in benchmark asset allocation of default funds
chosen by different plan providers.
The question of appropriateness of the default options is no less pertinent for
countries where these are less heterogeneous in terms of strategic asset
allocation. For instance, Utkus (2004) points out that majority of the plans in
the United States choose a money market or stable value fund as default
86
investment option although such arrangements are inconsistent with two of the
‘prudent investor’ principles on asset allocation underlying most participant
education programs: first, the existence of positive equity risk premium; and,
second, the change in the investor’s risk-taking capacity with age.42
4.1.2 Research Description
In this chapter, we examine the appropriateness of various asset allocation
strategies adopted by DC plans in Australia as default options. The importance
of asset allocation in influencing investment performance has been well
demonstrated by many researchers (Brinson et al., 1986; Blake et al., 1999).
Therefore, one would expect that the asset allocation strategies of default
options are decided with utmost care - not only because a majority of
participants passively accept the default options offered by their plans - but also
considering that there is evidence (Beshears et al., 2006) to suggest that many
individuals perceive the default choice as recommendation or endorsement of a
particular course of action by the provider.
To investigate the issue of appropriateness of asset allocation strategies used as
default investment vehicles, we find Australian DC plans provide an interesting
avenue for research for three reasons. First, Australia has a well established
private retirement system with nine out of ten employees currently members of
DC plans (APRA, 2005). Since 1992, the Australian Government has made it
compulsory for all employers to make contributions to these plans (known as
‘superannuation funds’) on behalf of their employees (members) at a minimum
42 Utkus (2004) also observes that extant legal provisions permit investments that result in short-term losses to pursue long term gains and do not require the trustees to invest in ‘safe’ assets.
87
specified rate (currently nine % of wage and salary).43 Contribution rates
remaining equal, the differences in the accumulated value of the plan assets for a
vast majority of the members with similar earnings profile is largely reliant on
the investment returns generated by the default investment strategy, which in
turn is heavily influenced by its benchmark asset allocation.
Second, members in Australian superannuation funds directly confront the
classical portfolio choice problem as they are expected to choose an asset
allocation strategy (or a combination of strategies) from a menu of pre-selected
asset allocation strategies provided by the plan providers to invest plan
contributions. This is different from say 401 (k) plans in USA where
participants are offered a choice of mutual funds rather than actual asset classes.
The default investment choice of every Australian superannuation fund clearly
specifies the target allocation among available asset classes; there is no scope for
the researcher to make any conjecture about the precise classification of mutual
funds and commit any error in the process.
Finally, to examine the issue of effectiveness of any strategic asset allocation
policy in the context of wealth accumulation in DC plans, we need to consider
its optimality from the perspective of an investor with long horizon, typically
equalling the participant's employment life. Many plans like 401 (k) may allow
distribution of account balances for participants who change jobs as well as
include loan features against account balances, the investment horizon relevant
to many participants may actually be much shorter. Superannuation funds in
Australia, on the other hand, are prohibited from permitting withdrawal of
superannuation assets by members before they reach the preservation age
(currently 60 years for those born after June 1964).44 These funds also do not
offer any loan feature to members against balance in their individual
43 Many employees are employed under awards that require them to contribute an additional three % of wage to superannuation. 44 Restricted withdrawals are permitted in some extreme circumstances.
88
superannuation accounts. Therefore, the asset allocation structure of the default
options offered by Australian pension funds can be expected to be designed
from a truly long term perspective and less concerned with the impact of short
term volatility in returns on the participant's account balance.
Past research on DC plan investment choices have mostly examined
hypothetical asset allocation strategies. In contrast, our study considers asset
allocation strategies which are actually used by plan providers as default
investment choices. We use more than a hundred years of data for real returns
on different asset classes to simulate the retirement wealth outcomes for a
typical participant whose plan contributions are invested following the default
asset allocation strategies of the top rated superannuation funds in Australia.
For the benefit of analysis, we also simulate wealth outcomes under two
hypothetical allocation strategies: (i) 100% stocks; and, (ii) default option
average (DOA) strategy. The outcomes are then compared to assess their
relative appeal to be nominated as default investment option in DC plans. To
capture the possibility that past returns on any asset class may not represent the
complete range of its expected future returns, we use both parametric and non-
parametric methods in this study to generate simulated returns for the asset
classes.
Poterba et al. (2006) attempt to rank wealth outcomes associated with different
asset allocation strategies for 401(k) plans by using a utility function of
retirement wealth. However, we use risk-adjusted performance measures in lieu
of a utility-based framework to avoid making specific assumptions about the
form of the utility function of DC plan participants. Also, in contrast to most
other studies, we consider downside risk (the risk of the participants falling short
of reaching their target wealth accumulation at retirement) as an important
criterion in selecting an appropriate default strategy for DC plans.
89
To evaluate alternative allocation rules in terms of their ability to meet the
wealth accumulation objective of the plan participants, we employ lower partial
moments as robust measures of downside risk and performance measures which
are adjusted for downside risk. This study also considers the possibility that the
risk of extreme events can influence the plan providers’ choice of default
strategy. We compare these risk estimates under each asset allocation strategy
to rank them in terms of their ability to reduce the potential and severity of the
most adverse outcomes. We also measure variability of outcomes for every
strategy under consideration and compare these estimates as this can form the
basis for selection of default in case plans aim to reduce the disparity in wealth
outcomes between different employee cohorts.
4.1.3 Summary of Findings
Our study reports several key findings. First, asset allocation strategies with
higher allocation to stocks can be expected to result in higher wealth outcomes
for participants. At the same time, the range of wealth outcomes generated by
such strategies can also be expected to be wider. Second, the downside risk of
falling short of the participant’s target wealth outcome is reduced with increased
allocation to stocks in terms of probability as well as magnitude of shortfall.
This holds for participants with different levels of risk tolerance. Our results
also indicate that on most occasions a strategy which invests entirely in stocks
offers highest upside potential and lowest downside risk in relation to retirement
wealth accumulated by participants. Third, contrary to popular belief, we find
that the potential and severity of the most extreme outcomes for DC plan
participants do not seem to increase much with increasing allocation to stocks.
In fact, there is little evidence that the extreme downside or tail-related risks of
DC plan outcomes are sensitive to the choice of asset allocation strategies.
Fourth, the lifecycle strategies which are currently used as defaults by a few
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Australian plans seem to impart little or no protection to participants from
downside risk. On the other hand, these strategies are found to considerably
erode the value of expected retirement wealth the participants can potentially
accumulate by keeping the initial asset allocation unchanged till retirement.
Therefore, like Booth and Yakoubov (2000), we find little basis for plans
switching assets as participants approach retirement.45
Our findings, although based on simulated wealth outcomes using historical
return data for Australian asset classes, may have important implications for
default investment options for retirement plans in other industrialised nations.
This is because the returns on various asset classes in many of these markets
have displayed broadly similar trend over the last century (Dimson et al., 2002).
4.2 Metrics for Evaluating Retirement Wealth Outcomes
To evaluate asset allocation strategies and assess their appropriateness as default
investment options in DC plans, we need to make plausible assumptions about
the rationale that may guide the selection of a specific asset allocation strategy
as a default option from many competing candidates. The basic motivation
behind instituting retirement savings plans is to generate adequate income for
the participating employees after retirement. In that case, performance of DC
plans should be measured in terms of their ability to generate sufficient
retirement income (Baker et al., 2005). Therefore, it is assumed that the
principal investment objective of such plans is to maximize the terminal value of
plan assets at the point of retirement since that would directly determine the
amount of annuity the retiring employees are able to purchase for sustenance
45 We desist from drawing any general conclusion on lifecycle strategies since we have very few funds in our sample using such strategies and the mode of switching is also different from that of typical lifecycle funds in other countries.
91
during post-retirement life. Past studies have mainly considered the absolute
value of the participant’s accumulated assets at retirement. However, we
employ a ratio which compares the terminal wealth of the participant’s
retirement account to their terminal income because it is very likely that the
participant’s post-retirement income expectations are closely linked to their
immediate income before retirement.46 We call this measure the ‘retirement
wealth ratio’ (RWR). To evaluate asset allocation strategies on the basis of
terminal wealth outcomes we consider the mean, the median, and the quartiles of
the RWR distribution.
Higher estimates of different measures of RWR outcomes do not automatically
qualify a particular strategy to be selected as default option. The trustees also
need to consider the risk associated with investment of plan assets since
participants would want a better exploitation of trade-off between risk and
reward. In finance, the optimal trade-off between reward and risk is generally
determined through Markowitz’s (1952) mean-variance analysis. Yet it can be
shown that in the presence of time-varying investment opportunities, predictable
variation in expected equity risk premium, or mean reversion in stock returns,
risk can be viewed differently by long-term investors than short-term investors
(Campbell and Viciera, 2002). They also point out that mean-variance model
also do not allow for periodic rebalancing of portfolio which is essential for
long-term investors to maintain their strategic asset allocation. Finally, the use
of variance as a measure of risk is questionable especially for long-term
investors like DC plan participants. McEnally (1985) shows that the appropriate
measure for investment risk is the variability of the terminal wealth outcomes
that arise by holding an asset for the intended investment horizon and not the
variability of periodic returns of the asset around its average return. This study
46 This is supported by Booth and Yakoubov (2000), who employ a similar benchmark, that is, the value of accumulated fund at retirement in terms of employee’s salary. In addition, this study uses a broader range of metrics in evaluating the risk-reward characteristics of the outcomes.
92
uses measures of terminal wealth to compute risk (and reward) associated with
different asset allocation strategies. However, we consider shortfall below target
outcome instead of variability of terminal wealth outcomes as measure of risk.
As previously discussed, we assume that the ultimate goal of the DC plan
participants is to attain a specific amount of wealth in DC plan accounts in terms
of their terminal income, which we call the target retirement wealth
ratio )( TRWR . Under this assumption, the investment risk most relevant to
participants is that of failure of their chosen asset allocation strategy to
generate TRWR . This type of ‘downside risk’ is not new to economics or
finance literature. Roy (1952) developed the target rate of return approach in a
portfolio selection context where the investor is concerned about minimizing the
probability of falling below the disaster level or minimum acceptable rate of
return. Mao (1970) presents evidence to show that decision makers conceive
risk as the possibility of outcomes below target. Olsen (1997) also finds that
two of the most important attributes of perceived investment risk are potential
for below target returns and potential for large loss. We capture these two risk
attributes by employing downside risk and tail-related risk metrics respectively.
In this essay, we employ the LPM (Bawa, 1975; Fishburn, 1977) to measure
downside risk of different asset allocation strategies. The relative advantages of
using LPM as a measure of risk have already been enumerated in 2.7. In the
retirement portfolio context, if λ denotes the risk tolerance of the plan
participant, then lower partial moment of retirement wealth outcomes is given
by
λ
λ ∑=
−=n
ttT RWRRWRMax
nLPM
1
)](,0[1
(34)
where TRWR is the target outcome, tRWRis the outcome for the t-th
observation, n is the number of observed RWR outcomes, and Max is the
93
maximization function that selects the larger between the numbers 0
and )( tT RWRRWR − . The termλ , which is known as the degree of lower partial
moment (LPM) can theoretically assume any value depending on the risk
aversion of the participant.
We compute the lower partial moments for wealth outcomes under different
asset allocation strategies for participants with λ = 0, 1, and 2. For λ = 0,
0LPM gives the probability of shortfall, that is, how often the actual RWR can
fall below the target. If λ = 1, 1LPM weighs shortfalls ( TRWR less ‘below
TRWR ’ outcomes in the context of our problem) with linear weighting.47 This
provides an estimate of how severe the shortfall can be. Forλ = 2, 2LPM gives
the below-target semi-variance.
We also use Sortino and UPR as performance measures which are adjusted for
downside risk in evaluating alternative asset allocation strategies. These have
already been discussed in 2.8. In the context of our problem, the Sortino Ratio is
given by
Sortino 2
1
2 ][LPM
RWRRWR TM −= (35)
where MRWR denotes the mean RWR. The denominator in (2) denotes the
downside deviation of wealth outcomes.
The UPR, which measures the upside potential relative to the downside risk, can
be denoted in the context of our problem as
( )
[ ] 21
2LPM
RWRRWR
UPR TRWRT∑
∞
−= (36)
Next, we consider the risk of extremely adverse wealth outcomes for plan 47 This is also referred by some as the expected shortfall.
94
participants. If DC plan participants are believed to be loss averse towards the
value of their retirement assets, which can be considered as a ‘large stake’ as
discussed in Rabin and Thaler (2001), the plan sponsors may decide to select
asset allocation strategies that have more chance of avoiding the most disastrous
outcomes. In other words, DC plans would select strategies that lower the
estimates of tail risk of the probability distribution of retirement wealth as their
default investment option.
To evaluate the extreme retirement wealth outcomes of alternative asset
allocation strategies, we use two common measures of estimating tail risk -
value at risk (VaR) and expected tail loss (ETL). The use of VaR in risk
management is widespread (Jorion, 2000). In the context of our problem,
if p represents the probability of worst percentage of RWR outcomes that the
participants are concerned about,α is the confidence level and p is set such that
α−= 1p , and if pRWR represents the p-quantile of the RWR distribution, then
from equation (21) VaR at that confidence level is given by
pRWRVaR= (37)
An outcome worse than VaR can occur only in extreme circumstances, the
probability of which can be specified by the user by specifyingα , which
indicates the likelihood that the investor would not get an outcome worse than
VaR. The higher the degree of risk aversion, higher is the value of α and vice
versa.
As VaR at a given probability gives us no idea about the amount at risk at higher
or lower levels of probability (Balzer, 1994) and suffers from lack of sub-
additive feature (Artzner, Delbaen, Eber, and Heath, 1999), we also employ
expected tail loss (ETL), which is often proposed as a better candidate as a
coherent measure of risk (Yoshiba and Yamai, 2002; Dowd, 2005). ETL gives
the probability weighted average of estimates that fall below VaR. In our case,
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if iRWR is the i th outcome and i is the probability of the i th outcome, then
iRWRETLi
i .1
1
0∑
=−=
α
α α (38)
Therefore, in the context of wealth accumulation of participants, ETL is actually
the average of the worst 100(1- α ) % of the RWR outcomes.
Finally, employee participants belonging to the same plan and following an
identical investment strategy but retiring a few years apart can face widely
different wealth outcomes (Burtless, 2003). Plan providers may feel that it is
important to minimize the disparity in real retirement wealth among different
employee cohorts whose investments are governed by the same default
strategy.48 In that case, they would be prompted to select such an asset
allocation strategy as default which results in least variation in real retirement
wealth outcomes between different employee cohorts, in other words, the real
retirement wealth outcomes under different investment return scenarios fall
within a narrow range. Our simulations produce a range of possible RWR
outcomes for every strategy. The terminal wealth outcome in every case is
dependent on the simulated path for asset class returns. Which of these return
paths would actually govern the investments of participants following a specific
strategy would entirely depend on the future state of the world. The future
return path, however, would be identical for participants belonging to the same
cohort while it is likely to be different for participants belonging to different
cohorts.49 Therefore participants from different cohorts may have different
terminal wealth outcomes even when their investments are directed by identical
default option.
48 Cross-cohort differences in retirement preparedness as a result of variation in wealth accumulated through retirement plans may also not be desirable from a policy perspective. 49 It is easy to see that parts of the return paths experienced by different cohorts would be overlapping for the cohorts who share overlapping employment periods.
96
To compare the variability of retirement wealth outcomes under different asset
allocation strategies, we use two common measures of dispersion. First, we
estimate coefficient of variation (CV) for simulated retirement wealth outcomes
under every strategy which is the standard deviation of RWR outcomes divided
by the mean RWR. To supplement this metric, we also estimate the inter-
quartile range ratio (IQRR) which is obtained by dividing the difference
between the 75th percentile RWR and the 25th percentile RWR by the median
RWR for each strategy under consideration.
4.3 Methodology
To analyse the wealth outcomes generated by different asset allocation
strategies, we use the DC plan accumulation model described in 3.1 which uses
stochastic simulation of asset class returns to determine the expected distribution
of wealth outcome at retirement. As discussed in previous section, the wealth
outcome is measured as retirement wealth ratio (RWR).
We base our analysis on simulated wealth outcomes for an employee who joins
the plan at the age of 25 years and retires at the age of 65 years. The starting
salary of the employee is assumed to be 25,000 Australian Dollars and the
growth in real wages to be 2% per year, which closely follows growth rate of
Australia's real GDP per capita of 2.6% per annum from 1994 through 2004
(Australian Bureau of Statistics, 2005). The contribution rate is fixed at 9%
which is the legislated minimum prescribed by the Australian government. No
contribution is made during periods of unemployment, the probability of which
is assumed to be 5%. This is equal to the unemployment rate among Australian
workers with post-school qualifications (Kryger, 1999; Richardson, 2006). For
the sake of simplicity, we assume that the contributions are credited annually to
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the accumulation fund at the end of every year (in practice, the Australian
Government has recently legislated that contributions needs to be made, at a
minimum, on a quarterly basis). The portfolios are also rebalanced at the end of
each year to maintain the target asset allocation. We assume that plan
contributions and investment returns are not subject to any tax. We also ignore
any transaction cost that may be incurred in managing the investment of the plan
assets.
For generating asset class returns, we initially employ Monte Carlo simulation
which estimates statistical parameters from historical data series under a
theoretical distribution and then exposes these to random changes in simulating
future outcomes. Following standard Monte Carlo simulation methodology, we
assume that asset class returns are drawn from a multivariate normal
distribution. This implies that mean and standard deviation of asset class returns
are time invariant and the returns are independent over the time horizon. At
each stage of the simulation horizon, the random shocks generated by the
multivariate normal model are adjusted so as to follow the average cross-
sectional correlation observed in the historical data. The Monte Carlo method
employed in this study is discussed further in 3.2.1.
Since Monte Carlo simulation imposes explicit distributional assumptions in
generating asset class returns, we run a parallel test for generating wealth
outcomes using non-parametric bootstrapping which draws asset class returns
from the empirical return distribution. Here the historical return data series for
the asset classes is randomly resampled with replacement to generate portfolio
returns for every period of the 40 year investment horizon of the DC plan
participant. In other words, each bootstrap sample is a random sample of asset
class returns for a particular period drawn with replacement from historical
observations over several periods. Thus we retain the cross-correlation between
the asset class returns as given by the historical data while assuming that asset
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class return series is independently distributed over time. More details about the
resampling method employed in this study are provided in 3.2.2.
4.4 Data
To investigate the issue of strategic asset allocation for long horizon investors
like DC plan participants, it is essential that we generate simulated returns based
on historical observations of asset class returns over several decades. This is
done to minimize the undue influence that recent investment performance (of
these asset classes) may have on long-term risk assessment and asset allocation
decisions. Moreover, it is often argued that a longer period of data has greater
chance of capturing wide-ranging effects of favourable and unfavourable events
of history on returns of individual asset classes. Since participants are likely to
be concerned with the effect of inflation on the value of their retirement wealth,
we need to use real investment returns to simulate terminal wealth outcomes for
different asset allocation strategies. This study uses an updated version of the
dataset of returns on stocks, bonds, and bills originally compiled by Dimson et
al. (2002) and commercially available through Ibbotson Associates for 16
countries including Australia for a period of 105 years spanning from 1900 to
2004. All returns are annual real returns and include reinvested income and
capital gains.
For the full 105 year period from 1900 to 2004, the mean annual real return for
Australian stocks has been 9.09% while the same for Australian bonds and bills
has been 2.27% and 0.72% respectively. When we consider only data after the
Second World War, from 1947 through 2004, the mean annual real returns for
the three asset classes were smaller, recorded at 8.05%, 1.08%, and 0.62% for
stocks, bonds, and bills respectively. However, real returns for all three classes
seem to have been significantly higher in recent times. During the most recent
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30 year period in our dataset, 1975 through to 2004, mean annual real returns for
stocks, bonds, and bills have been 10.93%, 4.97%, and 3.20% respectively.
Going by the higher mean real returns produced by stocks, one would also
expect much higher standard deviation for stocks in comparison to that for
bonds and bills. This has certainly been the case with the standard deviation of
annual real returns on stocks, bonds, and bills being 17.74%, 13.36%, and
5.51% from 1900 through 2004. The corresponding estimates for post war
period (1947-2004) were 21.06%, 11.47%, and 5.09% while those most recent
30-year period (1975-2004) were 20.54%, 11.13%, and 3.76%.
Since DC plan participants have long investment horizons, typically between 30
and 40 years, asset class returns for long holding periods would be of more
interest in examining their case. From asset class return data between 1900
through 2004, we find that the real returns from bonds have been negative for 29
of the 76 observed 30 year holding periods and 20 out of 66 observed 40-year
holding periods. Bills recorded further underperformance with 32 of the 76
observed 30-year holding periods and 20 of the 66 observed 40-year holding
periods yielding negative real returns for the investors. In contrast, the real
returns from Australian stocks for every 30-year and 40-year holding period
between 1900 and 2004 were positive. The real equity premium over bond and
bills has also been positive for each of these holding periods.
We also use data on default investment strategy for major Australian
superannuation funds. In Australia, it is a regulatory requirement for trustees to
identify a default strategy where investment choice is offered to standard
employer-sponsored members. Most superannuation funds offer a balanced
diversified investment strategy to their member participants as the default
investment choice. The guidelines for trustees provided by the regulatory
authority emphasises the benefits of diversification as, according to them, it
would ‘result in a lower overall level of risk to achieve desired return’ (APRA,
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1999). At the end of June 2004, the majority of default strategy assets of
superannuation funds were held in stocks: 33% in Australian stocks and 21% in
international stocks. A further 15% was invested in Australian fixed interest,
6% in international fixed interest, 7% in cash, 6% in property, and 12% in other
assets (APRA, 2005).
In 2005-06, SuperRatings, an independent research house, conducted a
comprehensive analysis of 120 superannuation funds including major industry,
corporate, and public sector funds as well as commercial master trusts, most of
which hold more than $500 million of assets.50 Together, the funds cover in
excess of $300 billion of retirement savings on behalf of nearly 10 million
member accounts. The funds are rated on the basis of their performance by
aggregating several factors including investment methodology, returns, fees,
administration and governance/risk framework. A total of seventeen of these
funds (representing the top 15% of their universe) received the highest or
‘platinum’ rating. We limit our study to these ‘platinum’ rated funds since most
of these funds can be expected to have default investment strategies that are
relatively well designed compared to those of funds with lower ratings. The
asset allocation data for individual default investment strategies is collected
from the product disclosure statements available in the respective websites of
these funds as at March 2006.
In our study, only 3 of the 17 default investment options change their allocation
with the age of the participant. But unlike typical ‘target retirement funds’ in
the US and elsewhere where the benchmark asset allocation is changed
continuously and gradually to achieve a more conservative asset allocation as
the members grow older and approach retirement, the change in asset allocation
here is done instantaneously when the members reach specified age threshold(s).
50 More details of the survey and rankings are available on SuperRating’s website, www.superratings.com.au
101
For each of these three default options, we examine two different allocation
rules: one assuming that their initial asset allocation remains unchanged till the
retirement of the participant (which is equivalent to a fixed weight strategy) and
another following the exact switch in allocations given by the actual default
option i.e. lifecycle strategy. This enables us to directly compare the results and
determine whether this type of lifecycle strategies can be expected to produce
superior outcomes for the participants, particularly in terms of reducing risk. In
addition, we examine two hypothetical strategies: (i) default option average
(DOA) strategy whose allocation is the same as the average allocation of default
options for all Australian superannuation funds as of June 2004; and, (ii) 100%
stocks strategy.
Initially we conduct our analysis under the assumption that the DC plan assets
are invested in Australian stocks, bonds, and bills. Allocations of the default
options to international stocks and international bonds are, therefore, included in
domestic stocks and bonds respectively. We, later, repeat the simulations by
including international stocks and international bonds as separate asset classes
but do not present the results in Appendix 4C since these lead to very similar
conclusions.51 Although ‘property’ is an important asset class for investment by
these funds, we do not include it as a separate asset class in our analysis because
of the paucity of reliable long-term return data. Similarly ‘alternative
investments’ which mainly comprise investments in infrastructure, hedge funds,
and commodities, cannot be included because of the lack of specific information
on their composition and therefore of any reliable index to measure returns.
While examining investment strategies of Australian superannuation funds, we
handle their allocation component to ‘properties’ and ‘alternative investments’
in a manner similar to that of other well-known studies like Brinson et al., 51 This may be due to the reason that we use US stocks and US bonds, which are highly correlated with their Australian counterparts, as proxies for international stocks and international bonds.
102
(1986) and Arshanapalli, Coggin, and Nelson (2001), where the percentage
allotted to ‘others’ is divided between equities, bonds and bills on a pro-rata
basis. However, we choose to direct the allocations against ‘property’ and
‘alternative investments’ only to equities and bonds (and not bills) on a pro-rata
basis, because we believe that the risk-return profile of these asset classes is far
removed from that of bills (cash). The asset allocation data for every strategy
included in our analysis are provided in Table 4.1.
Out of the seventeen ‘platinum’ rated funds used in our analysis, eight funds
have their default option’s initial allocation to stocks ranging between 60% and
70% which typically represents a balanced diversified fund. The DOA strategy
also has an asset allocation profile similar to these strategies. Of the remaining
funds, four funds have their default strategy’s initial allocation to stocks between
70% and 80% while the default strategies of other five funds are highly
aggressive with more than 80% of assets invested to stocks. Only three of the
default strategies (#18, #19, and #20) change their initial asset allocation with
the age of the member. To examine the efficacy of these lifecycle strategies, we
devise three corresponding fixed weight strategies (#6, #7, and #16) by
assuming that their initial asset allocations remain constant throughout the
investment horizon. Therefore, we have seventeen fixed weight strategies
(fourteen actual and three devised), three lifecycle strategies, and two
hypothetical strategies, that is, twenty-two strategies in total available for our
analysis.
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Table 4.1: Asset Allocation of Default Investment Options The following table reports the asset allocation structure of default investment options of seventeen superannuation funds in Australia which received ‘platinum rating from SuperRatings Australia in 2005-2006. For three of these funds that have age-based lifecycle strategy as default option, we treat their initial asset allocation as a separate strategy in addition to the original lifecycle strategy. We also include a default option average asset allocation strategy as given by APRA. Allocation to international stocks and bonds are included in stocks and bonds respectively. Allocation to alternative asset classes is proportionately split between stocks and bonds.
Stocks (%) Bonds (%) Cash (%) FIXED WEIGHT STRATEGIES
A. Conservative (Stocks w < 70% stocks) 66 29 5 1. UniSuper Balanced 64 36 0 2. Equipsuper Balanced Growth 65 30 5 3. HOSTPlus Balanced 66 32 2 4. Sunsuper Balanced 66 32 2 5. REST Core 66 24 10 6. Telstra Balanced* 67 33 0 7. First State Super Diversified# 68 17 15 8. CARE Super Balanced 69 26 5
B. Moderate Agg. (Stocks 70% ≥ w < 80%) 76 22 2
9. Westcheme Trustee's Selection 73 27 0
10. Vision Balanced Growth 74 23 3 11. HESTA Core Pool 77 21 2 12. NGS Diversified 79 18 3 C. High Aggressive (Stocks w ≥ 70%) 85 13 2 13. ARF Balanced 80 18 2
14. STA Balanced 83 15 2
15. Cbus Super 83 14 3 16. Health Long Term Growth^ 88 12 0 17. MTAA 93 4 3
L IFECYCLE STRATEGIES
18. Telstra: Under 60 years (Balanced) 67 33 0 60 years and above (Conservative) 32 48 20 19. First State Super: Up to 56 years (Diversified) 68 17 15 Above 56 years (Balanced) 47 28 25 20. Health: Less than 50 years (Long Term Grow.) 88 12 0 50 to 60 years (Medium Term Growth) 64 36 0 Above 60 years (Balanced) 41 59 0
HYPOTHETICAL STRATEGIES 21. Default Option Average 67 26 7 22. 100% Stock 100 0 0
* Initial allocation of lifecycle strategy #18; # Initial allocation of lifecycle strategy #19; ^ Initial allocation of lifecycle strategy #20
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4.4 Results and Discussion
Based on the wealth accumulation model described in 3.1, we simulate RWR
outcome for all the twenty-two asset allocation strategies. We conduct two
separate sets of simulation experiments using the Monte Carlo and bootstrap
resampling methods for return generation respectively. For both sets of
experiments, we conduct 5,000 iterations for every asset allocation strategy
under consideration to generate 5,000 different investment return paths over 40-
year periods. These simulated returns are applied every year on corresponding
cash flows in the participant’s account to produce a range of 5,000 RWR
outcomes under every strategy at the end of the 40-year horizon. Each set of
experiments is initially conducted based on historical asset class returns for the
entire period of available data, 1900 through 2004. However, it is quite possible
that structural changes in the domestic and the international economy may
render data from the very distant past, especially before the Second World War,
less relevant in projecting future asset class returns. Therefore, we repeat the
simulations using two more recent datasets: one for the entire post-war period
(1947-2004) and another for the most recent 30 year period (1975-2004). Since
the estimates obtained by the Monte Carlo and the bootstrap resampling
experiments are very similar, we report only the results of the former in Tables
4.2, 4.3, and 4.4.52
We set the wealth accumulation target TRWR for the plan participant at 8.0 i.e.
800% of salary at retirement. Booth and Yakoubov (2000) uses a target wealth
of 500% of salary at retirement which translates into a TRWR of 5.0. Although
there is no consensus on what can be considered as an adequate wealth to
income ratio for Australian retirees, we choose to set TRWR at a higher level for
52 Summary results of trials using the bootstrap resampling method to generate asset class returns are provided in Appendix 4B.
105
two reasons. First, several commentators consider the current wealth to income
levels as grossly inadequate in view of increasing life expectancy and growing
health care costs. Second, since our study ignores the taxes on retirement
savings and investment returns as well as transaction costs while modelling
terminal wealth outcomes, we feel the need to compensate it by setting the target
wealth outcome on the higher side. However, setting TRWR at a different value
is not expected to alter the relative ranking of asset allocation strategies as long
as we hold it constant for all the simulations.
4.4.1 RWR Distribution
The distribution of RWR for each asset allocation strategy provides us with the
range of wealth outcomes the participant may expect to confront at the point of
retirement. In addition to mean and median RWR, we estimate the first and
third quartile estimates of the distribution for every allocation strategy to assess
their relative appeal. For any of these parameters, a higher value would
generally make a strategy more attractive. Table 4.2 provides the distribution
parameters of RWR for each of the asset allocation strategies. The results
indicate that RWR varies significantly across asset allocation strategies. The
mean and the median RWR seem to increase for strategies with higher allocation
to stocks and are highest for the strategy which invests entirely in stocks. The
median RWR for the 100% stocks strategy is over 50% higher than that of DOA
strategy, which only has two-thirds of assets invested in stocks. Although in a
few cases, the mean and median RWR are not higher for the strategy with higher
proportion of stocks, we find that the allocations to stocks in these cases are very
close, and the difference in outcome seems to be more influenced by the
difference in their allocation splits between bonds and cash.
Table 4.2: Distribution Parameters of Retirement Wealth Ratio (RWR)
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Table 4.2 reports the distribution of RWR from the Monte Carlo simulation (multivariate normal). A total of 5,000 iterations for every asset allocation strategy under consideration to generate different investment return paths over 40-year periods. Max., Min., Q1, and Q3 denote maximum, minimum, first quartile, and third quartile RWR outcomes respectively. CV and IQRR measure the dispersion of RWR outcomes and stands for coefficient of variation and interquartile range ratio for the distribution of RWR outcomes respectively.
PANEL A: SIMULATION RESULTS BASED ON 1900-2004 DATA Mean Median Max. Min. Q1 Q3 CV IQRR FIXED WEIGHT STRATEGIES
A. Conservative (Avg.) 9.87 8.34 81.11 1.38 5.80 12.17 0.62 0.76 1. UniSuper Balanced 9.73 8.21 75.73 1.19 5.70 12.05 0.62 0.77 2. Equipsuper Bal.
Growth 9.61 8.16 82.63 1.46 5.69 11.90 0.60 0.76
3. HOSTPlus Balanced 9.85 8.24 73.28 1.44 5.72 12.10 0.64 0.77 4. Sunsuper Balanced 9.98 8.33 99.95 1.50 5.84 12.34 0.63 0.78 5. REST Core 9.56 8.17 74.64 1.56 5.70 11.70 0.60 0.73 6. Telstra Balanced 10.06 8.54 82.95 1.44 5.83 12.36 0.65 0.76 7. First State Super Div. 9.70 8.33 66.52 1.17 5.82 12.05 0.59 0.75 8. CARE Super Balanced 10.43 8.77 93.14 1.25 6.06 12.84 0.64 0.77
B. Moderate Agg. (Avg.) 11.63 9.49 92.89 1.26 6.34 14.51 0.69 0.86 9. Westscheme Trustee's
Sel. 11.32 9.19 98.41 1.27 6.18 14.15 0.69 0.87
10. Vision Balanced Growth
11.12 9.14 67.29 1.33 6.20 14.02 0.65 0.86
11. HESTA Core Pool 11.83 9.61 89.89 1.26 6.38 14.72 0.69 0.87 12. NGS Diversified 12.24 10.03 115.97 1.19 6.58 15.13 0.72 0.85 C. High Aggressive (Avg.) 13.71 10.91 129.16 1.38 6.98 16.98 0.75 0.92 13. ARF Balanced 12.54 10.17 153.85 1.32 6.55 15.58 0.72 0.89
14. STA Balanced 13.24 10.50 133.49 1.31 6.76 16.22 0.77 0.90 15. Cbus Super 13.16 10.57 114.17 1.47 7.00 16.37 0.73 0.89 16. Health Long Term
Growth 14.31 11.24 136.11 1.28 7.12 17.71 0.74 0.94
17. MTAA 15.28 12.07 108.19 1.50 7.49 19.03 0.78 0.96 L IFECYCLE STRATEGIES
18. Telstra 9.02 7.78 49.18 1.56 5.46 11.12 0.58 0.73 19. First State Super 8.64 7.56 47.90 1.31 5.40 10.66 0.54 0.70 20. Health 9.47 8.12 65.26 1.49 5.66 11.54 0.61 0.72
HYPOTHETICAL STRATEGIES 21. Default Option
Average 9.90 8.37 72.27 1.69 5.84 12.34 0.62 0.78
22. 100% Stock 17.37 12.88 194.55 1.13 7.78 21.48 0.90 1.06
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Table 4.2 (cont’d): Distribution Parameters of Retirement Wealth Ratio (RWR)
PANEL B: SIMULATION RESULTS BASED ON 1947-2004 DATA
Mean Median Max. Min. Q1 Q3 CV IQRR FIXED WEIGHT STRATEGIES
A. Conservative (Avg.) 7.76 6.32 77.41 0.93 4.22 9.53 0.71 0.84 1. UniSuper Balanced 7.53 6.11 122.60 1.14 4.13 9.19 0.74 0.83 2. Equipsuper Bal.
Growth 7.53 6.14 56.56 0.77 4.17 9.30 0.68 0.84
3. HOSTPlus Balanced 7.75 6.32 70.14 0.90 4.14 9.52 0.71 0.85 4. Sunsuper Balanced 7.73 6.28 114.36 0.90 4.17 9.55 0.73 0.86 5. REST Core 7.80 6.45 47.83 1.02 4.30 9.66 0.67 0.83 6. Telstra Balanced 7.83 6.33 73.43 0.97 4.20 9.59 0.73 0.85 7. First State Super Div. 7.88 6.45 67.46 0.88 4.34 9.67 0.69 0.82 8. CARE Super Balanced 8.01 6.45 66.90 0.88 4.30 9.77 0.72 0.85
B. Moderate Agg. (Avg.) 9.09 6.98 101.60 0.90 4.51 11.31 0.81 0.98 9. Westscheme Trustee's
Sel. 8.90 6.90 77.26 0.97 4.53 11.05 0.79 0.95
10. Vision Balanced Growth
8.86 6.86 159.40 0.98 4.52 10.94 0.83 0.94
11. HESTA Core Pool 9.15 7.11 87.00 0.75 4.45 11.45 0.81 0.98 12. NGS Diversified 9.43 7.06 82.73 0.90 4.53 11.81 0.82 1.03 C. High Aggressive (Avg.) 10.76 7.81 179.96 0.74 4.75 13.07 0.96 1.06 13. ARF Balanced 9.47 7.25 87.65 0.94 4.58 11.50 0.84 0.95 14. STA Balanced 10.58 7.57 269.15 0.87 4.76 12.69 1.08 1.05 15. Cbus Super 10.49 7.71 210.27 0.76 4.69 12.78 0.93 1.05 16. Health Long Term
Growth 11.26 8.14 167.64 0.58 4.83 13.72 0.96 1.09
17. MTAA 12.01 8.38 165.10 0.57 4.90 14.64 0.99 1.16
L IFECYCLE STRATEGIES 18. Telstra 6.92 5.78 60.38 0.79 4.01 8.53 0.63 0.78 19. First State Super 7.03 5.87 59.13 1.15 4.07 8.53 0.65 0.76 20. Health 7.44 6.07 47.68 0.88 4.13 9.15 0.68 0.83
HYPOTHETICAL STRATEGIES 21. Default Option
Average 7.77 6.31 87.21 0.99 4.29 9.49 0.71 0.82
22. 100% Stock 13.63 8.92 228.03 0.76 5.11 16.54 1.14 1.28
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Table 4.2 (cont’d): Distribution Parameters of Retirement Wealth Ratio (RWR)
PANEL C: SIMULATION RESULTS BASED ON 1975-2004 DATA
Mean Median Max. Min. Q1 Q3 CV IQRR FIXED WEIGHT STRATEGIES
A. Conservative (Avg.) 16.42 13.50 146.22 1.81 9.04 20.44 0.69 0.84 1. UniSuper Balanced 15.99 13.29 115.88 1.41 8.88 19.85 0.68 0.83 2. Equipsuper Bal.
Growth 16.21 13.36 135.89 1.82 9.05 19.80 0.68 0.80
3. HOSTPlus Balanced 16.82 13.64 131.48 1.90 9.24 20.75 0.69 0.84 4. Sunsuper Balanced 16.88 13.90 154.42 1.90 9.26 21.21 0.69 0.86 5. REST Core 15.81 13.15 149.30 2.25 8.91 19.76 0.66 0.82 6. Telstra Balanced 16.57 13.69 173.81 1.87 9.08 20.54 0.69 0.84 7. First State Super Div. 15.92 13.24 161.27 1.61 8.87 19.88 0.66 0.83 8. CARE Super Balanced 17.18 13.75 147.68 1.69 9.04 21.70 0.73 0.92 B. Moderate Agg. (Avg.) 19.29 15.09 249.66 1.48 9.60 23.84 0.81 0.94 9. Westscheme Trustee's
Sel. 18.52 14.55 148.00 1.74 9.52 22.77 0.76 0.91
10. Vision Balanced Growth
18.81 14.96 197.04 1.44 9.51 23.22 0.77 0.92
11. HESTA Core Pool 19.49 15.05 223.53 1.31 9.61 23.93 0.84 0.95 12. NGS Diversified 20.33 15.79 430.06 1.42 9.76 25.42 0.85 0.99 C. High Aggressive (Avg.) 22.45 16.42 346.70 1.31 9.90 27.76 0.92 1.08 13. ARF Balanced 20.47 15.64 331.79 1.39 9.73 25.57 0.86 1.01 14. STA Balanced 21.31 15.96 278.44 1.70 9.94 26.65 0.85 1.05 15. Cbus Super 21.91 16.03 276.49 1.47 9.89 26.91 0.90 1.06 16. Health Long Term
Growth 23.67 17.11 375.28 1.01 9.97 29.19 0.95 1.12
17. MTAA 24.88 17.34 471.52 0.98 9.95 30.50 1.04 1.18
L IFECYCLE STRATEGIES
18. Telstra 15.16 12.67 107.95 1.75 8.70 18.76 0.63 0.79
19. First State Super 14.64 12.45 146.95 2.27 8.71 17.83 0.63 0.73
20. Health 16.01 13.29 136.60 2.07 8.99 19.67 0.91 0.80
HYPOTHETICAL STRATEGIES 21. Default Option
Average 16.32 13.42 130.57 1.71 8.97 20.40 0.68 0.85
22. 100% Stock 28.15 18.17 460.72 1.34 9.78 33.45 1.19 1.30
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The first and third quartile outcomes also tend to increase as we move from
strategies with lower proportion of stocks to those with higher proportion of
stocks. The difference between first quartile outcomes of different strategies are
relatively smaller compared to the spread between the third quartile outcomes.
For example, the first quartile outcomes for the strategy with the lowest and
highest allocation to stocks are 5.70 and 7.48 respectively. The corresponding
estimates for their third quartile outcomes are 12.04 and 19.02. Again, the
100% stocks strategy results in the best first and third quartile RWR outcomes.
The increasing trend in RWR outcomes with aggressiveness of the asset
allocation strategy is graphically demonstrated in Figure 4.1. Generally, more
aggressive is the strategy, higher (lower) is the maximum (minimum) RWR
outcome. Also, the minimum outcomes for different strategies lie within a
narrow range (0.57 to 1.13) which shows that there is not much to choose
between the strategies on the basis of their worst outcomes.
Figure 4.1 RWR distribution parameters of Asset Allocation Strategies
The plot uses results of simulation using full period (1900-2004) data. IQRR denotes the interquartile range ratio which is used as a measure of dispersion of RWR outcomes. RWR distribution parameters for lifecycle strategies are not included since these have changing allocation to stocks over time.
110
The results of Monte Carlo simulations using returns data for 1947-2004 and
1975-2004 give similar indications about the effect of asset allocation strategies
on terminal wealth outcomes. While the RWR estimates for various strategies
vary when we use data for different periods, strategies with higher allocations to
stocks consistently dominate those with lower allocation to stocks in terms of
mean, median, first quartile, and third quartile outcomes. As before, the 100%
stocks strategy result in the best outcomes for all these parameters except the
first quartile outcome for the simulations using 1975-2004 data. The best result,
in this case, is produced by a strategy which invests 88% of assets in stocks and
remaining in bonds.
Our simulations produce a range of possible RWR outcomes for every strategy.
It is important to measure the dispersion of RWR outcomes for each strategy in
order to form a view on possible future retirement wealth disparity among
different cohorts following that strategy. The estimates for both CV and IQRR
indicate that the dispersion of RWR outcomes tends to increase with increase in
allocation to stocks although the rate of increase seems to be very small. For
instance, the IQRR for the strategy with lowest stock allocation (64%) is 0.7725
while that for the strategy with highest allocation to stocks (93%) is 0.9559. The
hypothetical 100% stocks strategy produces an IQRR of 1.0631. These
estimates indicate that the disparity in wealth outcomes between the cohorts who
meet very positive investment return scenarios and those who confront relatively
unfavourable investment returns during their employment life while being
enrolled in the same default option may be dependent on the allocation policy of
the plan. Nevertheless, the difference in disparity across cohorts for strategies
with different proportions of stocks may not be very large. This is well
demonstrated by the flatness of the IQRR curve when plotted against strategies
with changing allocation to stocks. The simulation results using data for recent
periods also support these findings.
111
By comparing the RWR distribution parameters of each of the lifecycle
strategies (#18, #19, and #20) with those of the corresponding strategy that
maintains its initial asset class weighting (#6, #7, and #16 respectively), we find
that former produces lower mean, median, first quartile, and third quartile
outcomes in every case. Yet the minimum outcome in almost all cases is
slightly higher for the lifecycle strategies.53 Since the CV and IQRR are also
always lower for lifecycle strategies, it seems that switching to a conservative
allocation as the employee approaches retirement may actually reduce the
dispersion in RWR outcomes. In other words, if these strategies do not switch
their asset allocation with the members approaching retirement, the range of
expected wealth outcomes gets wider.
4.4.2 Downside Risk and Risk-Adjusted Performance Estimates
We use lower partial moments with risk aversion parameters 0, 1, and 2 so that
the investors with different levels of risk tolerance can use these estimates to
evaluate alternative asset allocation strategies. Table 4.3 reports the downside
risk estimates for RWR under different asset allocation strategies.
Estimates for all the LPM measures steadily increase with decrease in allocation
to stocks indicating a clear inverse relationship. For instance, the 0LPM for the
strategy with 64% allocation to stocks is 0.4826 which indicates that there is a
48.26% probability that the RWR would fall below TRWR (close to the toss of a
fair coin). In comparison, the probability of shortfall for the strategy with 77%
stocks is 38.58% and for the strategy with 93% stocks is 28.06%. Interestingly,
the 100 % stocks strategy has only 26.22%, or around one-in-four, probability of
53 However, the minimum outcome may not serve as a useful evaluation criterion because there is only a 1 in 5,000 chance of getting that outcome.
112
falling below TRWR , which is the lowest of all strategies, while DOA strategy
has almost 47 % chance of underperforming that target.
Similar trends are also observed for measures of magnitude of shortfall
)( 1LPM and below target semivariance )( 2LPM indicating that the downside
risk is reduced by increasing allocation to stocks in the portfolio. Figure 4.2
graphically depicts this trend. The slopes of LPM curves reveal that the rate of
decline of downside risk gets higher with increasing risk aversion, that is, more
averse the participants are to the downside risk of failing to meet their wealth
accumulation objective, more appealing would the aggressive strategies relative
to balanced or conservative strategies.
Figure 4.2 Downside risk estimates of Asset Allocation Strategies Lower partial moments for RWR outcomes have been computed for simulation using full period
(1900-2004) data using three different degrees of risk aversion: 0, 1, and 2. TRWR is set at 8.0. Lifecycle strategies are not included since these have changing allocation to stocks over time.
113
Table 4.3: Estimates for Downside Risk and Performance Measures
Table 4.3 reports estimates for downside risk and performance measures from the Monte Carlo simulation.
OLPM , 1LPM , and 2LPM measure downside risk and represent lower partial moment with
degree )(λ 0, 1, and 2 respectively. The downside risk adjusted performance measures SR and UPR
denote Sortino ratio and upside potential ratio respectively. A target retirement wealth ratio ( TRWR ) of
8.0 has been used in the simulations to estimate these measures.
PANEL A: SIMULATION RESULTS BASED ON 1900-2004 DATA
0LPM 1LPM 2LPM SR UPR
FIXED WEIGHT STRATEGIES A. Conservative (Avg.) 0.4719 1.1608 3.9099 0.9465 1.5335
1. UniSuper Balanced 0.4826 1.2058 4.1128 0.8544 1.4490 2. Equipsuper Balanced Growth 0.4864 1.1960 4.0210 0.8014 1.3978 3. HOSTPlus Balanced 0.4812 1.1992 4.0933 0.9149 1.5076 4. Sunsuper Balanced 0.4708 1.1609 3.9432 0.9979 1.5825 5. REST Core 0.4858 1.1813 3.9251 0.7862 1.3825 6. Telstra Balanced (Under 60) 0.4580 1.1329 3.8144 1.0571 1.6371 7. First State Super Div. (Up to 56) 0.4722 1.1514 3.8447 0.8673 1.4544 8. CARE Super Balanced 0.4384 1.0589 3.5243 1.2927 1.8567
B. Moderate Aggressive (Avg.) 0.3920 0.9510 3.2046 2.0339 2.5650
9. Westscheme Trustee's Selection 0.4094 0.9874 3.2778 1.8359 2.3812
10. Vision Balanced Growth 0.4108 1.0025 3.4088 1.6925 2.2355 11. HESTA Core Pool 0.3858 0.9287 3.1060 2.1707 2.6977 12. NGS Diversified 0.3620 0.8855 3.0256 2.4365 2.9456
C. High Aggressive (Avg.) 0.3240 0.7813 2.6410 3.5427 4.0229 13. ARF Balanced 0.3554 0.8721 2.9170 2.6610 3.1716
14. STA Balanced 0.3408 0.8280 2.8008 3.1317 3.6264
15. Cbus Super 0.3302 0.7711 2.6087 3.1931 3.6705 16. Health LT Growth (Less than
50) 0.3132 0.7531 2.5702 3.9329 4.4027
17. MTAA 0.2806 0.6820 2.3084 4.7946 5.2435 L IFECYCLE STRATEGIES
18. Telstra 0.5194 1.3100 4.4336 0.4855 1.1076
19. First State Super 0.5438 1.3565 4.5678 0.3001 0.9348
20. Health 0.4868 1.2202 4.196 0.7189 1.3146
HYPOTHETICAL STRATEGIES
21. Default Option Average 0.4696 1.1455 3.8546 0.9681 1.5516 22. 100% Stock 0.2622 0.6415 2.2062 6.3074 6.7393
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Table 4.3 (cont’d): Estimates for Downside Risk and
Performance Measures
PANEL B: SIMULATION RESULTS BASED ON 1947-2004 DATA
0LPM 1LPM 2LPM SR UPR
FIXED WEIGHT STRATEGIES A. Conservative (Avg.) 0.6520 2.0445 8.2208 -0.0840 0.6290
1. UniSuper Balanced 0.6758 2.1418 8.6593 -0.1588 0.5690 2. Equipsuper Balanced Growth 0.6708 2.1008 8.3474 -0.1627 0.5644 3. HOSTPlus Balanced 0.6500 2.0645 8.4223 -0.0869 0.6244 4. Sunsuper Balanced 0.6520 2.0616 8.3608 -0.0927 0.6203 5. REST Core 0.6422 1.9866 7.9223 -0.0719 0.6339 6. Telstra Balanced (Under 60) 0.6508 2.0519 8.2799 -0.0606 0.6525 7. First State Super Div. (Up to 56) 0.6404 1.9645 7.8222 -0.0420 0.6604 8. CARE Super Balanced 0.6342 1.9842 7.9524 0.0034 0.7070
B. Moderate Aggressive (Avg.) 0.5773 1.8048 7.2803 0.4019 1.0708
9. Westscheme Trustee's Selection 0.5854 1.8215 7.3011 0.3321 1.0062
10. Vision Balanced Growth 0.5904 1.8280 7.3254 0.3192 0.9946 11. HESTA Core Pool 0.5688 1.7991 7.3513 0.4231 1.0867 12. NGS Diversified 0.5644 1.7707 7.1433 0.5332 1.1957
C. High Aggressive (Avg.) 0.5179 1.6236 6.6785 1.0751 1.7032 13. ARF Balanced 0.5610 1.7444 7.1135 0.5523 1.2063
14. STA Balanced 0.5328 1.6290 6.5471 1.0092 1.6458 15. Cbus Super 0.5236 1.6430 6.7266 0.9618 1.5953 16. Health LT Growth (Less than
50) 0.4936 1.5611 6.4333 1.2868 1.9023
17. MTAA 0.4786 1.5407 6.5718 1.5652 2.1662 L IFECYCLE STRATEGIES
18. Telstra 0.7112 2.2890 9.2494 -0.3543 0.3983
19. First State Super 0.7160 2.2379 8.8958 -0.3265 0.4239
20. Health 0.6768 2.1413 8.6017 -0.1900 0.5401
HYPOTHETICAL STRATEGIES 21. Default Option Average 0.6512 2.0240 8.0674 -0.0794 0.6333 22. 100% Stock 0.4494 1.4613 6.2095 2.2612 2.8477
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Table 4.3 (cont’d): Estimates for Downside Risk and
Performance Measures
PANEL C: SIMULATION RESULTS BASED ON 1975-2004 DATA
0LPM 1LPM 2LPM SR UPR
FIXED WEIGHT STRATEGIES A. Conservative (Avg.) 0.1892 0.3738 1.0884 8.0830 8.4413 1. UniSuper Balanced 0.1976 0.4018 1.1840 7.3444 7.7136 2. Equipsuper Balanced Growth 0.1846 0.3588 1.0403 8.0477 8.3995 3. HOSTPlus Balanced 0.1838 0.3705 1.0869 8.4585 8.8138 4. Sunsuper Balanced 0.1788 0.3502 1.0037 8.8621 9.2116 5. REST Core 0.1948 0.3725 1.0416 7.6533 8.0183 6. Telstra Balanced (Under 60) 0.1890 0.3810 1.1402 8.0291 8.3859 7. First State Super Div. (Up to 56) 0.1982 0.3824 1.1074 7.523 7.8864 8. CARE Super Balanced 0.1868 0.373 1.1027 8.7461 9.1013
B. Moderate Aggressive (Avg.) 0.1756 0.3726 1.1485 10.5329 10.8807
9. Westscheme Trustee's Selection 0.1782 0.3543 1.0350 10.3392 10.6874
10. Vision Balanced Growth 0.1738 0.3691 1.1365 10.1426 10.4888 11. HESTA Core Pool 0.1768 0.3871 1.2170 10.419 10.7699 12. NGS Diversified 0.1734 0.3799 1.2054 11.2307 11.5767 C. High Aggressive (Avg.) 0.1688 0.3856 1.2764 12.7748 13.116 13. ARF Balanced 0.1694 0.3691 1.1599 11.5822 11.9249
14. STA Balanced 0.1626 0.3547 1.1071 12.6542 12.9913 15. Cbus Super 0.1700 0.3774 1.2588 12.3981 12.7345 16. Health LT Growth (Less than
50) 0.1680 0.3949 1.3534 13.4668 13.8062
17. MTAA 0.1742 0.4319 1.5029 13.7728 14.1251 L IFECYCLE STRATEGIES
18. Telstra 0.2038 0.3566 0.9211 7.4590 7.8306
19. First State Super 0.2014 0.3639 0.9836 6.6922 7.0592
20. Health 0.1876 0.3591 1.0184 7.9387 8.2945
HYPOTHETICAL STRATEGIES 21. Default Option Average 0.1868 0.3744 1.1073 7.9102 8.2659 22. 100% Stock 0.1812 0.4641 1.6793 15.551 15.9092
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Simulation results using post-war data also suggest that LPM estimates are
generally smaller for strategies with higher allocation to stocks. However, the
results are not as conclusive when we use recent 30-year returns data as
simulation input. While the 0LPM estimates are still lower for more aggressive
strategies, albeit by a much smaller margin, this is not true for 1LPM and
2LPM . The estimates for 1LPM do not exhibit any clear trend with similar
estimates observed for strategies with significantly different proportion of
stocks. For 2LPM , the estimates are generally lower for strategies holding a
lower proportion of stocks. The evidence for lifecycle strategies also follows
the same pattern. The simulation results using full period and post-war period
data shows that the downside risk actually increases by making lifecycle
switching whereas results with the recent 30-year returns data indicates mixed
trends - 0LPM estimates are higher (higher downside risk) while 1LPM and
2LPM estimates are lower (suggesting lower downside risk) for lifecycle
strategies compared to corresponding strategies where the initial asset
weightings remain unchanged.
While the terminal wealth outcomes and associated risks involved with each
allocation strategy under consideration can be assessed from the parameters of
the simulated RWR distribution and various measures of LPM, composite
performance measures are essential to rank the strategies based on overall risk-
reward profile. We compute estimates for Sortino and UPR, performance
measures that are adjusted for downside risk and also produce these results in
Table 4.3. For simulations using full period data, Sortino and UPR are generally
found to increase with rising proportion of stocks in the strategy. This is almost
always the case with strategies with more than 70% allocation to stocks. The
100% stock strategy results in the highest Sortino and UPR.
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The above results come as no surprise since we earlier found strategies with
higher stock allocation to be superior in terms of terminal wealth outcomes as
well as downside risk based on our simulation with the full period data. Of
more interest is the performance estimates for simulations using data for the
other two sub-periods because downside risk estimates in these cases lead to
conclusions that were different from those of simulation with the full period
data, particularly for 1LPM and 2LPM . However, we find that the risk-adjusted
performance estimates for the sub-periods are supportive of the rankings
indicated by the full-period simulation. Estimates for both Sortino and UPR in
these cases indicate that an allocation rule dominated by stocks results in better
risk adjusted performance and therefore, are consistent with the findings based
on simulation using full period data. Also, lifecycle strategies produce inferior
risk-adjusted performance estimates in all cases compared to their fixed weight
counterparts.
4.4.3 Tail-Related Risk Estimates
As discussed in 4.2, it is plausible that plan participants may care more about the
most adverse outcomes that can occur for a given strategy which makes it
important to analyse the risk of these extreme events. Plan providers in that case
are likely to use ‘maxi-min’ rule to select a strategy which maximizes the worst
‘n’ percentile of outcomes. In this study, we estimate VaR and ETL at 95%
confidence level, which means we assume that the participants are concerned
about the worst 5 % of RWR outcomes. While it is theoretically possible that
some participants may demonstrate an even greater degree of risk aversion, that
is, they may only consider RWR outcomes that are below an even lower
threshold (say 1%), we believe that in reality the 5th percentile outcome would
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serve as an adequate indicator of extreme risk for majority of participants.
Moreover, for participants who are concerned about outcomes falling below 5th
percentile, the ETL measure provides the expected value of such an outcome.
The results for VaR and ETL estimates are produced in Table 4.4. The results
for simulations using full period data indicate that the VaR estimates, in general,
tend to increase with aggressiveness of the asset allocation strategy although
strategies with a higher proportion of stocks do not always result in better
outcomes than a strategy with a slightly lower proportion of stocks. More
importantly, it is observed that the difference between the VaR estimates of
different asset allocation strategies is very small.
The lowest observed VaR estimate is 3.3936 given by the strategy with lowest
allocation to stocks. This means that by employing this strategy there is a 5% (or
one-in-twenty) chance of the RWR falling below that level. The highest VaR
estimate (4.0033) is produced by the 100% stock strategy, which goes against
the conventional logic that stocks, being most volatile among the asset classes,
can potentially result in the most adverse outcomes. The results for ETL also
support these conclusions.
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Table 4. 4: Tail Risk Estimates for RWR Distribution Table 4.4 reports tail risk estimates for the RWR Distribution from the Monte Carlo simulation. Value at Risk (VaR) and Expected Tail Loss (ETL) for RWR outcomes are estimated at 95% confidence level. Therefore, there is a 5% probability of the RWR falling below the VaR estimate. Conditional to the RWR falling below VaR i.e. for the worst 5% of RWR outcomes, the expected value is given by ETL.
PANEL A: SIMULATION RESULTS BASED ON 1900-2004 DATA VaR ETL FIXED WEIGHT STRATEGIES
A. Conservative (Avg.) 3.4926 2.8843 1. UniSuper Balanced 3.3936 2.8416 2. Equipsuper Balanced Growth 3.4528 2.8546 3. HOSTPlus Balanced 3.3961 2.7940 4. Sunsuper Balanced 3.4546 2.8623 5. REST Core 3.5509 2.9596 6. Telstra Balanced (Under 60) 3.5407 2.8946 7. First State Super Diversified (Up to 56) 3.5439 2.9209 8. CARE Super Balanced 3.6079 2.9467 B. Moderate Aggressive (Avg.) 3.6832 2.9878 9. Westscheme Trustee's Selection 3.6781 3.0074 10. Vision Balanced Growth 3.6085 2.9194 11. HESTA Core Pool 3.7601 3.0432 12. NGS Diversified 3.6860 2.9813 C. High Aggressive (Avg.) 3.8715 3.0732 13. ARF Balanced 3.8085 3.0626 14. STA Balanced 3.8493 3.0136 15. Cbus Super 3.8785 3.0489 16. Health Long Term Growth (Less than
50) 3.8527 3.0394
17. MTAA 3.9685 3.2016
L IFECYCLE STRATEGIES
18. Telstra 3.3876 2.8527
19. First State Super 3.3596 2.8547
20. Health 3.4053 2.7809
HYPOTHETICAL STRATEGIES 21. Default Option Average 3.4616 2.8893 22. 100% Stock 4.0033 3.2043
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Table 4.4 (cont’d): Tail Risk Estimates for RWR Distribution
PANEL B: SIMULATION RESULTS BASED ON 1947-2004 DATA
VaR ETL FIXED WEIGHT STRATEGIES
A. Conservative (Avg.) 2.4815 2.0249 1. UniSuper Balanced 2.4104 1.9786 2. Equipsuper Balanced Growth 2.5638 2.0846 3. HOSTPlus Balanced 2.4318 1.9809 4. Sunsuper Balanced 2.4679 2.0144 5. REST Core 2.5063 2.0462 6. Telstra Balanced (Under 60) 2.4900 2.0005 7. First State Super Diversified (Up to 56) 2.5059 2.0445 8. CARE Super Balanced 2.4761 2.0495 B. Moderate Aggressive (Avg.) 2.5007 2.0231 9. Westscheme Trustee's Selection 2.5348 2.0462 10. Vision Balanced Growth 2.4820 2.022 11. HESTA Core Pool 2.4687 1.9800 12. NGS Diversified 2.5171 2.0443 C. High Aggressive (Avg.) 2.4912 1.9582 13. ARF Balanced 2.4241 1.9788 14. STA Balanced 2.6014 2.0458 15. Cbus Super 2.5400 1.9845 16. Health Long Term Growth (Less than
50) 2.5301 1.9845
17. MTAA 2.3603 1.7973
L IFECYCLE STRATEGIES
18. Telstra 2.4083 2.0388
19. First State Super 2.4798 2.1051
20. Health 2.4494 1.973
HYPOTHETICAL STRATEGIES 21. Default Option Average 2.5196 2.028 22. 100% Stock 2.4100 1.8323
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Table 4.4 (cont’d): Tail Risk Estimates for RWR Distribution
PANEL C: SIMULATION RESULTS BASED ON 1975-2004 DATA
FIXED WEIGHT STRATEGIES VaR ETL
A. Conservative (Avg.) 5.1661 4.1850 1. UniSuper Balanced 5.0125 4.1038 2. Equipsuper Balanced Growth 5.2719 4.2175 3. HOSTPlus Balanced 5.1698 4.1914 4. Sunsuper Balanced 5.2555 4.2777 5. REST Core 5.2100 4.3105 6. Telstra Balanced (Under 60) 5.0357 4.0709 7. First State Super Diversified (Up to 56) 5.1787 4.1742 8. CARE Super Balanced 5.1950 4.1339 B. Moderate Aggressive (Avg.) 5.0663 4.0294 9. Westscheme Trustee's Selection 5.1885 4.2363 10. Vision Balanced Growth 5.1203 4.0174 11. HESTA Core Pool 4.9902 3.9311 12. NGS Diversified 4.9661 3.9327 C. High Aggressive (Avg.) 4.8861 3.7811 13. ARF Balanced 5.1072 3.9737 14. STA Balanced 5.0853 4.0408 15. Cbus Super 4.8199 3.7760 16. Health Long Term Growth (Less than
50) 4.8043 3.6031
17. MTAA 4.6138 3.512
L IFECYCLE STRATEGIES
18. Telstra 5.4205 4.5456
19. First State Super 5.2575 4.3972
20. Health 5.2157 4.3255
HYPOTHETICAL STRATEGIES
21. Default Option Average 5.1974 4.1088 22. 100% Stock 4.3970 3.2636
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The simulation results based on data for other periods present a slightly different
picture but do not alter the fundamental conclusion of the previous simulation.
Using data for 1947-2004 period, the VaR estimates of individual strategies are
found to lie within a very close range (2.3603-2.6014) and do not seem to follow
any clear pattern. The 100% stock strategy produces a VaR estimate of 2.41
which is almost the same as that of the strategy with the lowest stock allocation
(64%) but slightly lower than that of DOA strategy which has 67% allocation to
stocks and produces a VaR estimate of 2.5196. Similarly, the ETL estimates are
generally higher for the balanced strategies but only marginally, as with VaR
estimates.
Figure 4.3 Tail Risk Estimates of Asset Allocation Strategies VaR and ETL estimated at 95 % confidence level for simulations using asset class returns data for full period (1900-2004), post-war period (1947-2004), and most recent 30-year period (1975-2004). Lifecycle strategies are not included since these have changing allocation to stocks over time.
Simulation with data for 1975-2004 period results in higher VaR and ETL
estimates for balanced strategies compared to the more aggressive strategies.
Generally, VaR and ETL estimates seem to gradually deteriorate with increasing
123
stock allocation. This is quite the opposite of our results using 1900-2004 data
but the range of VaR estimates is still very narrow. The lowest estimate of
4.3970 is given by the 100% stocks strategy, which means that the participants
who invest in this strategy have a 5% chance of accumulating wealth that is less
than 4.39 times their final annual salary. The highest estimate of 5.4205 is
produced by lifecycle strategy #18 which invests two-thirds in stocks for
participants below 60 years and one-third thereafter. By adopting this strategy,
participants would have a 5% chance of having their plan account balance at
retirement less than 5.42 times their final annual salary. It is easy to see that the
gap between these two situations can hardly be considered as the difference
between a ruinous and a non-ruinous outcome. This is confirmed by the ETL
estimates which range from 3.2636 to 4.5456 indicating even the below 5%
outcomes are not very different between different allocation strategies. Thus our
evidence clearly implies that the risk of confronting extremely poor retirement
wealth outcomes may not be very sensitive to the choice of asset allocation
strategy.
The evidence on the most adverse outcomes for lifecycle strategies and their
corresponding fixed weight strategies is mixed. While simulations using data
for the full period and the post-war period result in lower VaR estimates for
lifecycle strategies compared to corresponding fixed weight strategies, the
results are quite the opposite for simulations based on the most recent 30 year
period (1975-2004) when all three lifecycle strategies are found to slightly
improve the VaR estimates. The ETL estimates also follow the same pattern
except for simulations with post war data where two of the three lifecycle
strategies produce higher estimates than their corresponding fixed weight
strategies. Based on this evidence, the claim of lifecycle strategies reducing the
risk of most unfavourable outcomes does not appear to be strong. Even in cases
where they reduce the severity of the extreme outcomes, the benefits appear to
be marginal.
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4.5 Conclusion
Given the fact that Australian stocks have significantly outperformed fixed
income securities over long horizons in the past, it is no surprise that differences
between default investment options with respect to their exposure to stocks
result in large differences in simulated terminal wealth outcomes for DC plan
participants. More revealing is our finding that very high allocations to stocks
may actually prove to be less risky on most occasions if risk is viewed in the
context of falling short of the participant’s wealth accumulation target, in terms
of both probability and magnitude of shortfall.
At present, regulators in most countries, including Australia, do not prescribe
any asset allocation structure for default investment options. But very often they
emphasise the importance of diversification in coping with risk by optimizing its
trade-off with returns. Our results, however, raise serious questions about the
benefits of diversification for very long term investors like DC plan participants,
who seem to have higher likelihood of being better off by concentrating their
investments in stocks alone. We have demonstrated that the strategies that are
heavily tilted towards stocks not only reduce the chance of failure in meeting the
participants’ wealth accumulation target but also seem to diminish the extent of
shortfall in case the participants fail to achieve such objective. At the same
time, they seem to offer strong upside potential of generating terminal wealth
outcomes that outperform the participant's accumulation target at retirement.
Past research in this area like Booth and Yakoubov (2000) and Blake et al.
(2001) argue that a diversified portfolio with high equity content would yield
best results for the retirement plan investors. While our results are supportive of
their findings to the extent of their recommending a tilt towards equities in the
investors’ portfolios, we do not see much benefit arising from diversification.
The most powerful evidence against selecting balanced diversified strategies or
125
even moderately aggressive strategies as default options is provided by our
results for tail-related risk. As stock returns are essentially considered to be
more volatile than other asset class returns, one would have normally expected
their presence in the portfolio to cause more extreme outcomes. However, our
results indicate that the extreme wealth outcomes occur mostly at the upper tail
of the wealth distribution, which is actually favourable to the plan participant.
The measures for the extreme outcomes at the lower tail of retirement wealth
distribution suggest that higher allocation to stocks do not necessarily increase
the risk of confronting these adverse outcomes and in some cases, may even
reduce their severity. In our study, the risk of extremely adverse outcomes does
not seem to vary considerably with change of asset allocation which implies that
extreme loss aversion should have minimal role to play in the asset allocation
decision for default investment options.
Turning specifically to the issue of investment horizon, Thaler and Williamson
(1994) demonstrate that, for college and university endowment funds, who
traditionally hold a 60:40 mix of stocks and bonds, an allocation entirely to
stocks is likely to provide superior results most of the time. Although individual
retirement accounts under DC plans do not have a quasi-infinite investment
horizon as enjoyed by university endowment funds, it appears that the typical
DC plan participant’s holding period of 30 to 40 years may be considered
sufficiently long to warrant more aggressive allocation than what is currently
chosen by most plan sponsors for their default investment options. Like Poterba
et al. (2006) we find that 100% allocation of stocks is optimal for DC retirement
investors but we do not find this optimal allocation rule to change with the
degree of risk aversion of the plan participant, especially when we consider
performance adjusted for downside risk. Even when the participants demonstrate
an unreasonably high degree of risk aversion like when they care only about the
worst 5% outcomes, the case for plan providers nominating a conservative or
balanced strategy as default option does not appear to be strong.
126
Trustees using conservative or balanced diversified strategies as defaults may
argue that these strategies tend to reduce the variability of outcomes and
therefore can potentially minimize the problems associated with disparity in
wealth accumulated by different employee cohorts. But selection of defaults
primarily on this criterion can be deemed as flawed given that the trade-off
involves much lower accumulation of retirement wealth and therefore, defeats
the very purpose of instituting these plans. By nominating such ‘safe’ strategies
as defaults, plan providers may actually be instrumental in creating future
generations of retirees who are ‘more equal’ but ‘poorer’ instead of retiree
cohorts who are ‘less equal’ but nevertheless ‘wealthier’. This is also the case
with the lifecycle strategies considered in our study which reduce the variability
of wealth outcomes but at the cost of producing much lower retirement wealth
on average than what the participants could potentially achieve by not switching
to a relatively conservative allocation rule as they near retirement.
Shiller (2003) opines that merely defining and implementing the default option
correctly for individual accounts within social security can prove to be the most
effective tool for intervention. It appears that the same also applies to individual
accounts in DC plans. This study strongly suggests the possibility of widely
different wealth outcomes confronting many DC plan participants simply as a
result of the existing disparity in asset allocation structure between their plans'
default investment options. It demonstrates that the balanced diversified
strategies nominated by many plan providers in Australia as default investment
options may not be well suited to optimise the retirement benefits of the
participants. The problem may be even more serious for countries like the US,
where DC plans typically adopt an even more conservative approach towards
asset allocation.
127
Annexure 4A
Figure 4A.1: Simulated RWR Distribution
PANEL A: SIMULATION RESULTS BASED ON 1900-2004 DATA
PANEL B: SIMULATION RESULTS BASED ON 1947-2004 DATA
128
PANEL C: SIMULATION RESULTS BASED ON 1975-2004 DATA
129
Annexure 4B: Bootstrap Simulation Results
Table 4B.1 Distribution Parameters for RWR We run a parallel test for generating wealth outcomes using non-parametric bootstrapping which draws asset class returns from the empirical return distribution. Here the historical return data series for the asset classes is randomly re-sampled with replacement to generate portfolio returns for every period of the 40 year investment horizon of the DC plan participant. A total of 5,000 iterations for every asset allocation strategy under consideration to generate different investment return paths over 40-year periods. We report the results from the various fixed weight strategies: conservative average, moderate average, and high aggressive average, the default option average and the 100 % stock options.
SIMULATION RESULTS BASED ON 1900-2004 DATA
Mean Median Max. Min. Q1 Q3 CV IQRR A. Conservative (Avg.) 9.87 8.36 71.50 1.24 5.79 12.18 0.61 0.76
B. Moderate Agg. (Avg.) 11.59 9.48 101.57 1.28 6.30 14.39 0.70 0.85
C. High Aggressive (Avg.) 13.67 10.87 137.58 1.33 6.96 17.05 0.76 0.93 Default Option Average 10.02 8.42 88.29 1.47 5.91 12.20 0.64 0.75 100% Stock 17.44 13.26 138.81 1.38 7.92 22.19 0.84 1.08
SIMULATION RESULTS BASED ON 1947-2004 DATA A. Conservative (Avg.) 7.79 6.35 80.92 0.92 4.22 9.65 0.70 0.85
B. Moderate Agg. (Avg.) 9.08 7.09 83.30 0.78 4.54 11.26 0.78 0.95
C. High Aggressive (Avg.) 10.67 7.79 150.19 0.89 4.75 13.05 0.93 1.06 Default Option Average 7.78 6.40 54.48 0.90 4.26 9.62 0.69 0.84 100% Stock 13.46 8.98 313.09 0.51 5.07 16.21 1.12 1.24
SIMULATION RESULTS BASED ON 1975-2004 DATA A. Conservative (Avg.) 16.57 13.69 128.54 2.11 9.25 20.54 0.67 0.82 B. Moderate Agg. (Avg.) 19.18 15.22 244.04 1.95 9.77 23.82 0.77 0.92 C. High Aggressive (Avg.) 22.14 16.46 297.49 1.70 10.04 27.50 0.89 1.06 Default Option Average 16.73 13.89 116.11 2.05 9.24 20.75 0.67 0.83 100% Stock 28.31 18.78 577.66 1.32 10.65 34.82 1.13 1.29
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Table 4B.2 Estimates for Downside Risk & Performance Measures
SIMULATION RESULTS BASED ON 1900-2004 DATA
0LPM 1LPM 2LPM SR UPR
A. Conservative (Avg.) 0.47 1.16 3.96 0.94 1.52
B. Moderate Agg. (Avg.) 0.39 0.98 3.34 1.97 2.50 C. High Aggressive (Avg.) 0.33 0.81 2.82 3.42 3.90 21. Default Option Average 0.46 1.11 3.71 1.05 1.63 22. 100% Stock 0.25 0.63 2.26 6.27 6.70
SIMULATION RESULTS BASED ON 1947-2004 DATA A. Conservative (Avg.) 0.65 2.04 8.25 -0.07 0.64
B. Moderate Agg. (Avg.) 0.57 1.79 7.28 0.40 1.06
C. High Aggressive (Avg.) 0.52 1.64 6.75 1.03 1.66 Default Option Average 0.65 2.01 8.07 -0.08 0.63 100% Stock 0.44 1.46 6.22 2.19 2.77
SIMULATION RESULTS BASED ON 1975-2004 DATA
0LPM 1LPM 2LPM SR UPR
A. Conservative (Avg.) 0.18 0.33 0.91 8.99 9.33
B. Moderate Agg. (Avg.) 0.16 0.33 0.97 11.34 11.68
C. High Aggressive (Avg.) 0.16 0.33 1.02 13.98 14.31 Default Option Average 0.18 0.33 0.91 9.16 9.50 100% Stock 0.15 0.36 1.19 18.66 18.99
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Table 4B.3 Tail Risk Estimates
PANEL A: SIMULATION RESULTS BASED ON 1900-2004 DATA
VaR ETL A. Conservative (Avg.) 3.47 2.87 B. Moderate Agg. (Avg.) 3.57 2.89 C. High Aggressive (Avg.) 3.72 2.97 Default Option Average 3.56 2.96 100% Stock 3.89 3.05
PANEL B: SIMULATION RESULTS BASED ON 1947-2004 DATA A. Conservative (Avg.) 2.44 1.99 B. Moderate Agg. (Avg.) 2.44 1.95 C. High Aggressive (Avg.) 2.44 1.95 Default Option Average 2.52 2.07 100% Stock 2.39 1.85
PANEL C: SIMULATION RESULTS BASED ON 1975-2004 DATA A. Conservative (Avg.) 5.41 4.45 B. Moderate Agg. (Avg.) 5.31 4.28 C. High Aggressive (Avg.) 5.21 4.16 Default Option Average 5.45 4.42 100% Stock 5.01 3.88
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Annexure 4C: Monte Carlo Simulation Results with 5 Asset Classes
Table 4C.1 Asset Allocation for Default Investment Options
Stocks (%) Int’l
Stocks Bonds (%) Int’l
Bonds Cash (%) A. Conservative (Stocks w < 70% stocks) 43 23 17 12 5
UniSuper Balanced 39 25 21 15 0 Equipsuper Balanced Growth 45 20 17 13 5 HOSTPlus Balanced 43 23 19 13 2 Sunsuper Balanced 43 23 19 13 2 REST Core 46 20 15 9 10 Telstra Balanced* 44 23 23 10 0 First State Super Diversified# 38 29 5 12 16 CARE Super Balanced 49 20 16 10 5
B. Moderate Agg. (Stocks 70% ≥ w < 80%) 51 25 14 8 2 Westcheme Trustee's Selection 55 18 18 9 0 Vision Balanced Growth 46 28 14 9 3 HESTA Core Pool 52 25 14 7 2 NGS Diversified 49 30 11 8 2
C. High Aggressive (Stocks w ≥ 80%) 60 26 8 4 2 ARF Balanced 57 23 11 7 2 STA Balanced 58 25 10 5 2 Cbus Super 58 25 9 5 3 Health Long Term Growth^ 53 35 7 5 0 MTAA 72 21 3 1 3
Default Option Average 46 21 20 6 7 100% Stock 100 0 0 0 0
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Table 4C.2 Distribution Parameters of Retirement Wealth Ratio (RWR)
PANEL A: SIMULATION RESULTS BASED ON 1900-2004 DATA Mean Median Max. Min. Q1 Q3 CV IQRR A. Conservative (Avg.) 10.40 8.36 112.30 1.18 5.52 12.82 7.56 0.87
UniSuper Balanced 10.22 8.35 95.48 1.32 5.49 12.66 7.18 0.86 Equipsuper Bal. Growth 10.24 8.20 107.17 1.17 5.50 12.44 7.56 0.85 HOSTPlus Balanced 10.51 8.30 218.11 1.38 5.56 13.01 7.98 0.90 Sunsuper Balanced 10.52 8.52 106.61 1.01 5.51 13.13 7.48 0.89 REST Core 10.42 8.27 97.39 1.15 5.41 12.98 7.73 0.92 Telstra Balanced 10.70 8.44 115.72 1.13 5.56 13.04 8.29 0.89 First State Super Div. 9.88 8.27 68.18 1.08 5.55 12.24 6.40 0.81 CARE Super Balanced 10.71 8.55 89.77 1.22 5.61 13.07 7.83 0.87
B. Moderate Agg. (Avg.) 12.35 9.59 146.57 1.04 6.04 15.32 9.86 0.97 Westscheme Trustee's Sel. 12.13 9.35 170.50 1.25 5.86 14.83 10.10 0.96 Vision Balanced Growth 11.70 9.29 103.28 1.01 5.95 14.51 8.72 0.92 HESTA Core Pool 12.67 9.70 157.90 0.92 6.07 15.82 10.34 1.00 NGS Diversified 12.90 10.01 154.62 0.97 6.27 16.13 10.30 0.98
C. High Aggressive (Avg.) 14.41 10.65 204.57 1.01 6.52 17.79 13.05 1.06 ARF Balanced 12.96 9.87 145.79 1.29 6.22 16.01 10.88 0.99 STA Balanced 13.85 10.26 206.34 0.90 6.39 17.09 12.53 1.04 Cbus Super 14.05 10.68 168.29 0.82 6.38 17.56 11.87 1.05 Health Long Term Growth 14.43 10.92 196.98 1.22 6.78 17.74 12.46 1.00 MTAA 16.73 11.49 305.47 0.84 6.83 20.55 17.53 1.19
Default Option Average 10.49 8.35 132.04 0.85 5.43 12.75 8.03 0.88 100% Stock 18.59 12.99 229.71 0.56 7.54 22.97 18.78 1.19
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Table 4C.2 (cont’d): Distribution Parameters of Retirement Wealth Ratio (RWR)
PANEL B: SIMULATION RESULTS BASED ON 1947-2004 DATA Mean Median Max. Min. Q1 Q3 CV IQRR
A. Conservative (Avg.) 10.49 8.91 78.41 1.50 6.16 12.97 6.52 0.76
UniSuper Balanced 10.05 8.69 72.75 1.64 6.14 12.44 5.78 0.72 Equipsuper Bal. Growth 10.36 8.75 77.97 1.38 6.03 12.77 6.57 0.77 HOSTPlus Balanced 10.45 8.82 74.52 1.56 6.11 12.96 6.60 0.78 Sunsuper Balanced 10.36 8.90 67.39 1.53 6.18 12.71 6.23 0.73 REST Core 10.42 8.82 79.32 1.47 6.09 12.90 6.45 0.77 Telstra Balanced 10.68 8.93 87.29 1.35 6.11 13.20 7.00 0.79 First State Super Div. 10.52 9.13 60.82 1.63 6.39 13.03 5.96 0.73 CARE Super Balanced 11.08 9.22 107.24 1.45 6.22 13.72 7.59 0.81
B. Moderate Agg. (Avg.) 12.42 10.06 105.76 1.37 6.64 15.49 8.77 0.88 Westscheme Trustee's Sel. 11.89 9.66 88.46 1.11 6.37 14.97 8.19 0.89 Vision Balanced Growth 11.96 9.94 81.03 1.67 6.61 15.04 7.86 0.85 HESTA Core Pool 12.73 10.12 131.15 1.27 6.65 15.76 9.49 0.90 NGS Diversified 13.10 10.53 122.41 1.43 6.94 16.17 9.55 0.88
C. High Aggressive (Avg.) 14.73 11.24 213.93 1.22 7.00 18.20 12.57 1.00 ARF Balanced 13.54 10.70 252.02 1.09 6.80 16.74 10.64 0.93 STA Balanced 13.96 10.65 153.83 1.51 6.71 17.31 11.77 1.00 Cbus Super 13.89 11.05 142.33 1.19 6.95 17.16 10.82 0.92 Health Long Term Growth 15.39 12.05 270.20 1.11 7.61 19.15 12.34 0.96 MTAA 16.85 11.75 251.27 1.19 6.91 20.66 17.27 1.17
Default Option Average 10.87 8.90 89.70 1.38 6.09 13.32 7.36 0.81 100% Stock 19.19 13.28 218.12 0.81 7.78 23.55 18.83 1.19
135
Table 4C.2 (cont’d): Distribution Parameters of Retirement Wealth Ratio (RWR)
PANEL C: SIMULATION RESULTS BASED ON 1975-2004 DATA Mean Median Max. Min. Q1 Q3 CV IQRR A. Conservative (Avg.) 16.74 14.03 148.72 2.08 9.58 20.78 10.76 0.80
UniSuper Balanced 16.25 13.88 143.41 2.29 9.72 20.16 9.76 0.75 Equipsuper Bal. Growth 16.65 13.76 155.59 2.63 9.47 20.70 10.74 0.82 HOSTPlus Balanced 16.83 14.33 124.84 1.89 9.79 20.79 10.54 0.77 Sunsuper Balanced 17.09 14.28 158.16 1.51 9.75 21.23 11.20 0.80 REST Core 16.22 13.43 187.78 1.76 9.17 20.09 10.85 0.81 Telstra Balanced 17.25 14.17 168.14 2.62 9.66 21.50 11.38 0.84 First State Super Div. 16.13 13.70 108.84 2.36 9.54 20.20 9.55 0.78 CARE Super Balanced 17.51 14.66 142.99 1.60 9.56 21.55 12.02 0.82
B. Moderate Agg. (Avg.) 19.21 15.48 185.67 1.65 10.09 23.96 13.93 0.90 Westscheme Trustee's Sel. 18.98 15.25 201.13 1.53 9.71 23.43 14.56 0.90 Vision Balanced Growth 18.82 15.34 146.00 2.12 10.19 23.67 12.82 0.88 HESTA Core Pool 19.31 15.42 201.42 1.42 10.05 24.10 14.19 0.91 NGS Diversified 19.74 15.91 194.13 1.52 10.41 24.64 14.15 0.89
C. High Aggressive (Avg.) 22.64 17.09 358.39 1.60 10.56 28.13 19.84 1.03 ARF Balanced 20.85 16.19 171.54 2.03 10.40 25.77 16.31 0.95 STA Balanced 21.72 16.71 418.69 1.71 10.30 27.31 18.53 1.02 Cbus Super 22.05 16.89 320.29 1.02 10.50 27.20 19.10 0.99 Health Long Term Growth 23.05 17.92 193.13 2.04 11.42 28.62 18.20 0.96 MTAA 25.52 17.73 688.30 1.19 10.15 31.77 27.08 1.22
Default Option Average 16.77 14.02 123.32 2.26 9.46 20.92 11.16 0.82 100% Stock 28.45 19.89 506.25 1.10 11.55 33.82 29.04 1.12
136
Table 4C.3 Estimates for Downside Risk and Performance Measures
PANEL A: SIMULATION RESULTS BASED ON 1900-2004 DATA
0LPM 1LPM 2LPM SR UPR
A. Conservative (Avg.) 0.4712 1.2699 4.5960 1.1200 1.7124
UniSuper Balanced 0.4698 1.2793 4.6107 1.036 1.6318 Equipsuper Balanced Growth 0.4846 1.2929 4.6551 1.0395 1.6388 HOSTPlus Balanced 0.4732 1.2399 4.3872 1.1986 1.7906 Sunsuper Balanced 0.4632 1.2599 4.6015 1.1733 1.7607 REST Core 0.4788 1.3261 4.9029 1.0919 1.6908 Telstra Balanced (Under 60) 0.4646 1.2598 4.5816 1.2625 1.8511 First State Super Div. (Up to 56) 0.477 1.2654 4.53 0.8827 1.4772 CARE Super Balanced 0.4584 1.2358 4.4993 1.2753 1.8579
B. Moderate Agg. (Avg.) 0.3948 1.0633 3.8659 2.2210 2.7616 Westscheme Trustee's Selection 0.4142 1.1255 4.106 2.0385 2.5939 Vision Balanced Growth 0.4044 1.091 3.984 1.8556 2.4022 HESTA Core Pool 0.387 1.052 3.8452 2.3818 2.9182 NGS Diversified 0.3734 0.9846 3.5284 2.608 3.1322
C. High Aggressive (Avg.) 0.3497 0.9377 3.4481 3.4684 3.9732 ARF Balanced 0.3778 1.0121 3.7071 2.5778 3.1035 STA Balanced 0.368 0.9698 3.531 3.1148 3.6309 Cbus Super 0.3542 0.9764 3.617 3.1834 3.6968 Health LT Growth (Less than 50) 0.3244 0.8528 3.077 3.6651 4.1513 MTAA 0.3242 0.8776 3.3086 4.8011 5.2836
Default Option Average 0.4752 1.3274 4.9693 1.1173 1.7128 100% Stock 0.2744 0.7414 2.7468 6.3868 6.8341
137
Table 4C.3 (cont’d): Estimates for Downside Risk and Performance Measures
PANEL B: SIMULATION RESULTS BASED ON 1947-2004 DATA
0LPM 1LPM 2LPM SR UPR
A. Conservative (Avg.) 0.4246 1.0078 3.3082 1.3720 1.9262
UniSuper Balanced 0.437 1.0136 3.2637 1.1328 1.6939 Equipsuper Balanced Growth 0.4392 1.06 3.514 1.26 1.8255 HOSTPlus Balanced 0.4336 1.0235 3.3123 1.3486 1.911 Sunsuper Balanced 0.4194 0.9973 3.2863 1.3044 1.8545 REST Core 0.4304 1.0326 3.4396 1.3073 1.8641 Telstra Balanced (Under 60) 0.428 1.0362 3.4615 1.4411 1.9981 First State Super Div. (Up to 56) 0.4042 0.9025 2.8201 1.5026 2.04 CARE Super Balanced 0.4048 0.9967 3.3681 1.6794 2.2224
B. Moderate Agg. (Avg.) 0.3527 0.8596 2.8929 2.6191 3.1243 Westscheme Trustee's Selection 0.3732 0.9543 3.3268 2.1347 2.6579 Vision Balanced Growth 0.3608 0.8512 2.7955 2.3657 2.8747 HESTA Core Pool 0.3484 0.8574 2.8966 2.7816 3.2853 NGS Diversified 0.3284 0.7753 2.5527 3.1942 3.6794
C. High Aggressive (Avg.) 0.3154 0.7941 2.7714 4.061 4.538 ARF Balanced 0.3326 0.8269 2.8515 3.2836 3.7733 STA Balanced 0.3384 0.8475 2.9138 3.4938 3.9903 Cbus Super 0.3184 0.7946 2.7748 3.5344 4.0114 Health LT Growth (Less than 50) 0.2748 0.6592 2.2239 4.958 5.4001 MTAA 0.313 0.8425 3.0932 5.0347 5.5137
Default Option Average 0.427 1.0274 3.4383 1.5502 2.1042 100% Stock 0.263 0.6693 2.4065 7.2162 7.6477
138
Table 4C.3 (cont’d): Estimates for Downside Risk and Performance Measures
PANEL C: SIMULATION RESULTS BASED ON 1975-2004 DATA
0LPM 1LPM 2LPM SR UPR
A. Conservative (Avg.) 0.1585 0.2875 0.7799 9.9700 10.2956
UniSuper Balanced 0.1484 0.2565 0.6576 10.1736 10.4899 Equipsuper Balanced Growth 0.1622 0.2926 0.7972 9.6894 10.0171 HOSTPlus Balanced 0.149 0.2665 0.7117 10.4717 10.7877 Sunsuper Balanced 0.154 0.2641 0.6946 10.9114 11.2283 REST Core 0.179 0.3498 0.992 8.2529 8.6041 Telstra Balanced (Under 60) 0.1532 0.2813 0.7701 10.542 10.8625 First State Super Div. (Up to 56) 0.1548 0.2637 0.6671 9.9522 10.2751 CARE Super Balanced 0.1674 0.3253 0.9486 9.7664 10.1004
B. Moderate Agg. (Avg.) 0.1463 0.2784 0.7847 12.7386 13.0527 Westscheme Trustee's Selection 0.161 0.3196 0.9283 11.3906 11.7223 Vision Balanced Growth 0.1376 0.2506 0.6745 13.1702 13.4753 HESTA Core Pool 0.1504 0.2906 0.8321 12.3992 12.7178 NGS Diversified 0.136 0.2528 0.7037 13.9942 14.2955
C. High Aggressive (Avg.) 0.1420 0.2979 0.9241 15.356 15.665 ARF Balanced 0.1426 0.2939 0.8925 13.599 13.91 STA Balanced 0.1468 0.2976 0.9047 14.4207 14.7337 Cbus Super 0.141 0.2889 0.8754 15.0165 15.3253 Health LT Growth (Less than 50) 0.1182 0.2346 0.6891 18.1242 18.4068 MTAA 0.1614 0.3745 1.259 15.6175 15.9512
Default Option Average 0.1742 0.3453 1.0013 8.7601 9.1051 100% Stock 0.1272 0.281 0.902 21.5333 21.8292
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Table 4C.4 Tail Risk Estimates for RWR Distribution
PANEL A: SIMULATION RESULTS BASED ON 1900-2004 DATA
VaR ETL A. Conservative (Avg.) 3.1612 2.5772
UniSuper Balanced 3.1546 2.5424 Equipsuper Balanced Growth 3.2471 2.6534 HOSTPlus Balanced 3.1508 2.5849 Sunsuper Balanced 3.0615 2.5037 REST Core 3.1525 2.5135 Telstra Balanced (Under 60) 3.2125 2.6559 First State Super Diversified (Up to 56) 3.1294 2.5206 CARE Super Balanced 3.1809 2.6428
B. Moderate Agg. (Avg.) 3.3492 2.6766 Westscheme Trustee's Selection 3.3103 2.6026 Vision Balanced Growth 3.2708 2.6484 HESTA Core Pool 3.3348 2.6747 NGS Diversified 3.4809 2.7806
C. High Aggressive (Avg.) 3.3961 2.6699 ARF Balanced 3.3741 2.6405 STA Balanced 3.3645 2.6669 Cbus Super 3.3218 2.6495 Health Long Term Growth (Less than 50) 3.5917 2.7977 MTAA 3.3286 2.595
Default Option Average 2.9724 2.366 100% Stock 3.6058 2.827
140
Table 4C.4 (cont’d): Tail Risk Estimates for RWR Distribution
PANEL B: SIMULATION RESULTS BASED ON 1947-2004 DATA
VaR ETL A. Conservative (Avg.) 3.6947 3.0637
UniSuper Balanced 3.7454 3.1211 Equipsuper Balanced Growth 3.6021 3.0031 HOSTPlus Balanced 3.7125 3.1368 Sunsuper Balanced 3.7266 3.0414 REST Core 3.6102 2.9767 Telstra Balanced (Under 60) 3.5936 2.9844 First State Super Diversified (Up to 56) 3.9517 3.3055 CARE Super Balanced 3.6155 2.9408
B. Moderate Agg. (Avg.) 3.7699 3.0903 Westscheme Trustee's Selection 3.5452 2.9051 Vision Balanced Growth 3.8586 3.1539 HESTA Core Pool 3.7359 3.0703 NGS Diversified 3.9398 3.2317
C. High Aggressive (Avg.) 3.7586 2.9520 ARF Balanced 3.7785 2.9617 STA Balanced 3.6993 2.9599 Cbus Super 3.7011 2.9172 Health Long Term Growth (Less than 50) 4.1472 3.2108 MTAA 3.4667 2.7102
Default Option Average 3.6438 2.9046 100% Stock 3.7767 2.9469
141
Table 4C.4 (cont’d): Tail Risk Estimates for RWR Distribution
PANEL C: SIMULATION RESULTS BASED ON 1975-2004 DATA
VaR ETL A. Conservative (Avg.) 5.6572 4.6345
UniSuper Balanced 5.8948 4.8666 Equipsuper Balanced Growth 5.6456 4.5802 HOSTPlus Balanced 5.8153 4.7477 Sunsuper Balanced 5.7712 4.7728 REST Core 5.2649 4.328 Telstra Balanced (Under 60) 5.6887 4.6105 First State Super Diversified (Up to 56) 5.8637 4.872 CARE Super Balanced 5.3135 4.2981
B. Moderate Agg. (Avg.) 5.7315 4.5944 Westscheme Trustee's Selection 5.4226 4.3513 Vision Balanced Growth 5.8704 4.7959 HESTA Core Pool 5.7027 4.5109 NGS Diversified 5.9302 4.7194
C. High Aggressive (Avg.) 5.4623 4.2830 ARF Balanced 5.4622 4.3268 STA Balanced 5.5865 4.3028 Cbus Super 5.4657 4.3592 Health Long Term Growth (Less than 50) 5.8868 4.664 MTAA 4.9103 3.762
Default Option Average 5.2839 4.2621 100% Stock 5.5097 4.2337
142
5. Gender-sensitive Contribution and Asset Allocation Strategies in Superannuation Plans
5.1 Introduction
5.1.1 Background
A common concern expressed in pension literature is that the retirement system in
most developed countries is biased against women. With the concept of welfare state
in many of these countries taking a backseat in the last few decades, as evidenced by
policies aimed at retrenchment of public pension coupled with growing emphasis on
private savings for retirement, the problem of gender inequity in pensions is bound
to erupt like never before.54 Private retirement systems are designed to reward long
and continuous periods of employment and penalize breaks. While this benefits the
typical male worker with uninterrupted working life, the retirement provisions of the
female workforce, whose participation in the labour market is often constrained by
their child bearing and family care responsibilities, is adversely affected. Career
profiles of most working women in Australia are characterised by a broken
employment pattern in early and middle years. Even where women work full-time,
their earnings are significantly lower compared to men. The result is a significantly
lower level of superannuation for women at retirement. How the relative
disadvantage in labour market would result in inferior retirement wealth outcomes
for women is well documented by several authors (see Rosenman & Winocur, 1994;
Sharp, 1995 among others).
The body of work looking into the problem confronting Australian women in
retirement is vast.55 Several authors focus specifically on the issue of gender
54 The dependence of female Australian workers on age pension in the face of lower superannuation outcomes has been demonstrated in earlier papers like Preston and Austen (2001). 55 Jefferson (2005) reviews this literature.
143
inequity in accumulation outcomes at retirement (Brown, 1994; Donath, 1998;
Preston & Austen, 2001). But much of this work stops at pointing out the
inadequacies of the current private superannuation plans in ensuring sufficient
accumulation for female workers in their accounts to maintain their lifestyle after
retirement. Some authors suggest changes to the existing arrangements but the
proposals put forward are often too subjective and imprecise to bring about any
significant change to the accumulation level of female workers within the current
superannuation framework. For example, Olsberg (2004) argues for greater equity
for women in workforce, more education on superannuation and investments, and
increasing female representation in governance of superannuation funds. One cannot
discount the impact of some of these proposals in addressing the problem of low
retirement income for Australian women. But the precise manner in which they
would impact retirement savings (and to what extent) is not clear.
5.1.2 Research Description
This essay aims to demonstrate the impact of gender sensitive savings and asset
allocation policies in alleviating differences between superannuation wealth
accumulation outcomes for male and female workers of Australia. While one would
expect higher contribution rates for female workers would result in minimizing the
gender-based inequality in superannuation outcomes, the role of asset allocation in
addressing the inequality problem is not obvious. The importance of asset allocation
as a key determinant of long term investment performance has been universally
acknowledged since the publication of the seminal work by Brinson, Hood, and
Beebower (1986). In a study conducted among pension funds in UK, it was found
that more than 99% of the total return generated could be explained by the long-run
asset allocation specified by the plan sponsors (Blake, Lehmann, and Timmerman,
1998). Surprisingly, the possibility of using asset allocation to reduce the gender gap
144
in retirement wealth has not yet been considered by academic researchers or
policymakers in any country. We address this issue in this study.
5.1.3 Summary of Findings
We show that the current policy of having gender-neutral savings and investment
options for the workforce is almost always bound to result in lower superannuation
for the average female worker compared to her male counterpart. Specifically, the
distribution of superannuation assets for the average male member exhibits first
degree stochastic dominance over that for the average female member. However, we
find that establishing a different default arrangement (by superannuation funds) for
female workers may significantly alter this situation.56 This can be achieved through
either changing the mandatory contribution rate or changing the default asset
allocation strategy of the plans (or a combination of both) for the female member.
5.2 Methodology
This study uses stochastic simulation methods to compare the expected distributions
of superannuation accumulation outcomes of an average female plan member to that
of her male counterpart under several alternative savings and investment strategies.
We assume that the average male and female member joins the superannuation plan
at the age of 20 years and stays in the plan till their retirement at the age of 65 years.
56 We focus on default savings and investment arrangements since a vast body of contemporary scholarly work (for example, Choi et al., 2004; Cronqvist & Thaler, 2004) indicates that majority of employees passively accept the default contribution rates and investment strategies chosen by the trustees of their respective funds. In the Australian superannuation context, the importance of default choices is highlighted in Gallery, Gallery, and Brown (2004). As per the estimate of Australian Prudential Regulatory Authority, nearly two-third of all superannuation assets are invested in default investment options of various plans (APRA, 2005).
145
Our baseline case represents an average male worker with no voluntary break from
employment whose superannuation contribution is 9% of earnings which is equal to
the mandatory contribution rate for all Australian workers. The contributions of this
hypothetical male worker is assumed to be invested in a balanced fund holding 60%
of the assets in shares, 30% in bonds and the remaining 10% in cash. The asset
allocation structure of this classic balanced fund is akin to that of the average default
investment option offered by superannuation funds in Australia.57 The accumulation
outcome of the baseline male is then compared with those of an average female
worker under three alternative assumptions: (i) no voluntary break from
employment, (ii) a voluntary break of 5 years duration between the age of 26 and 30
and (iii) a voluntary break of 5 years between the age of 31 and 35. Under each of
these alternative scenarios, we use different contribution and asset allocation rules
for modeling the wealth outcomes at retirement. The details of these are discussed in
the section 5.4.
To estimate the terminal wealth outcomes for different contribution rates and asset
allocation strategies, we use a simple accumulation model which uses stochastic
simulation of asset class returns to determine the expected distribution of wealth
outcome at retirement. This has already been described in 3.1.1. In this chapter, we
assume uninterrupted contributions are made into the superannuation accounts the
male and female worker as long as they are not unemployed or not having voluntary
breaks from employment. For the sake of simplicity, we assume that the
contributions are credited annually to the accumulation fund at the end of every
year.58 The portfolios are also rebalanced at the end of each year to maintain the
target asset allocation. We also assume that plan contributions and investment
57 At the end of June 2004, the average default investment option had 33 % of assets held as Australian shares and 21 % in international shares. A further 15 % was invested in Australian fixed interest, 6 % in international fixed interest, 7 % in cash, 6 % in property, and 12 % in other assets (APRA, 2005). 58 In practice, the Australian Government has recently legislated that contributions need to be made, at a minimum, on a quarterly basis.
146
returns are not subject to any tax. Any transaction cost that may be incurred in
managing the investment of the plan assets is not considered.
For generating asset class returns, this study employs non-parametric bootstrapping
which draws asset class returns from the empirical return distribution.59 Here the
historical return data series for the asset classes is randomly resampled with
replacement to generate portfolio returns for every period of the 45 year investment
horizon of the male or female employee. In other words, each bootstrap sample is a
random sample of asset class returns for a particular period drawn with replacement
from historical observations over several periods. Thus we retain the cross-
correlation between the asset class returns as given by the historical data while
assuming that asset class return series is independently distributed over time. More
details about the resampling method employed in this study are provided in 3.2.2.
The asset class return vectors are then combined with the weights accorded to the
asset classes in the portfolio (which is governed by the asset allocation strategy) to
generate portfolio returns for each year in the 45 year horizon. The simulated
investment returns are applied to the retirement account balance at the end of every
year to arrive at the terminal wealth in the account. Each set of simulation
experiment is iterated 5,000 times for both the male and the female worker under
different employment scenarios resulting in a range of wealth outcomes confronting
the employee at the point of retirement.
To compare the distribution of terminal superannuation wealth outcomes of the
women under different assumptions about employment breaks, contribution rates,
and asset allocation strategies with that of the baseline male worker, we compute the
mean, median, and the quartiles of the distribution in every case. Comparing these
parameter estimates would give us some idea about the relative standing of different
59 We feel that this approach is superior to alternative parametric methods as the latter make strong assumptions about the empirical distribution of asset class returns. For example, Blake et al. (2001) assume annual asset returns are generated following multivariate normal stochastic process.
147
savings and asset allocation rules in improving superannuation outcomes for women.
However we are more interested in finding out how effective these strategies are in
offsetting the gender inequality in superannuation. To be effective any strategy
should be able to reduce the chance of the female worker underperforming the
baseline male worker. Also, as long as a strategy does not diminish that chance of
underperformance to zero, we need to estimate the magnitude of such
underperformance.
We compute a statistic called the probability of shortfall which represents the chance
of a female worker ending with less accumulated wealth than the baseline male
worker. This probability of shortfall is given by
0
1
)](,0[1∑
=−=
n
tfms WWMax
nP (39)
where mW and fW represents the terminal superannuation wealth for the male and
female worker respectively, and n the number of trials. While SP estimates the odds
of the hypothetical woman worker doing worse than the baseline male worker in
different situations, it does not describe the how large the shortfall in wealth
outcome for the former would be compared to that of the latter. To estimate the
magnitude of underperformance of the woman worker, we measure the expected
shortfall which is given by
∑=
−=n
tfms WWMax
nE
1
)](,0[1
(40)
SP and SE are equivalent to LPM of degree 0 and 1 respectively discussed in 2.7
and equations (39) and (40) are derived by modifying equation (20) in the context of
this problem.
To compare the most adverse outcomes for various strategies, we compute the VaR
estimates at 95% confidence level for the baseline male worker who uses a relatively
conservative allocation strategy with those generated by the more aggressive
148
strategies used by the hypothetical female worker. Further, we also compare ETL at
95% level of confidence for different allocation strategies which is the probability
weighted average of all outcomes which are below 5th percentile of the wealth
distribution.60 This statistic, in other words, considers all outcomes that are below
the 5th percentile outcome and provides the average of such conditional outcomes.
Details on VaR and ETL as measures of tail risk have already been discussed in 2.7.
5.3 Data
5.3.1 Earnings Data
For modeling wage and contributions, we employ weekly income data for
individuals from Australian Bureau of Statistics (ABS) 2001 Census of Population
and Housing. The dataset reports weekly individual incomes of Australian males and
females over 15 years in the following age ranges: 15-19 years, 20-24 years, 25-34
years, 35-44 years, 45-54 years, 55-64 years, 65-74 years, and above 75 years. In
this study, we base our analysis on simulated wealth outcomes for a male and a
female employee who joins the plan at the age of 20 years and retires at the age of
65 years. In other words, we ignore the ‘15-19 years’, ‘65-74 years’, and ‘above 75
years’ categories in building the wage profile of a typical male and a typical female
employee. This is done because a vast majority of the population in the ‘15-19
years’ range is reported to have either little (below $80 a week) or no income while
those above 65 years possibly derive most of their income from outside the labour
market. Table 5.1 provides the truncated income data used in this chapter.
60 Expected tail loss is an important risk measure used in actuarial science (see Dowd, 2005) and satisfy the criteria of coherent risk measures proposed by Artzner et al (1997, 1999)
149
Table 5.1: Weekly Individual Income of Australian Men and Women by Age
Income Category
20-24 years
25-34 years
35-44 years
45-54 years
55-64 years
MEN
Negative/Nil income
36,821 34,224 30,192 32,397 28,416
$1-$39 4,909 3,153 3,763 4,320 4,314 $40-$79 10,083 4,087 4,602 5,759 6,415 $80-$119 24,508 10,355 9,658 11,110 12,785 $120-$159 37,662 40,180 35,754 35,659 49,087 $160-$199 46,783 63,915 62,539 66,639 101,199 $200-$299 58,687 68,197 74,341 77,068 92,803 $300-$399 65,853 69,107 69,638 65,950 68,532 $400-$499 85,475 116,578 104,420 94,418 74,028 $500-$599 75,387 154,635 135,571 119,605 80,621 $600-$699 50,153 135,630 120,395 99,925 59,914 $700-$799 35,185 125,427 115,388 94,215 50,237 $800-$999 30,418 174,725 178,586 147,618 66,713 $1,000-$1,499 15,919 169,907 228,868 204,720 77,062 $1,500 or more 4,349 81,317 150,719 142,083 58,447
WOMEN
Negative/Nil income
35,351 77,744 85,450 100,419 67,002
$1-$39 5,817 19,376 26,253 18,673 12,696 $40-$79 14,258 44,375 45,163 23,418 16,078 $80-$119 28,565 53,367 51,468 29,647 24,552 $120-$159 38,865 60,141 63,989 58,617 70,625 $160-$199 45,537 70,180 82,906 97,987 150,701 $200-$299 77,057 135,167 166,293 142,454 149,838 $300-$399 82,885 150,200 175,262 130,954 83,128 $400-$499 79,570 137,611 160,047 132,643 62,363 $500-$599 69,610 129,242 128,658 117,193 48,556 $600-$699 45,414 106,851 93,661 85,681 32,422 $700-$799 27,891 90,659 73,497 66,452 24,187 $800-$999 16,504 114,820 94,653 89,650 29,458 $1,000-$1,499 5,667 80,605 87,967 88,792 27,156 $1,500 or more 1,399 28,580 36,612 29,726 11,622
Source: Australian Bureau of statistics 2001 Census of Population and Housing
150
However, one has to exercise caution about several limitations of modelling the
career wage profile of individuals using the above ABS dataset. First, to accurately
model career wage profiles the researcher would need a longitudinal dataset which
tracks earnings of individuals through their working lives - from commencement of
employment to retirement. But the ABS data gives the average weekly earnings for
individuals in different age ranges at a particular point in time (2001 in this case)
and therefore does not show the actual career wage experience of a particular
generational cohort throughout their working life. Second, between the
commencement of employment and retirement of our typical male and female
employee in this chapter (20 and 64 years respectively), the ABS data provides
income data for only 5 age ranges (20-24 years, 25-34 years, 35-44 years, 45-54
years, and 55-64 years). This leaves us with only 5 data-points or observations to
construct their career wage profiles. Also, we ignore any growth in real wages due to
economy wide productivity gains that individuals may experience over the next 45
years.
Another shortcoming of the dataset is that it provides number of individuals of
different age categories whose weekly incomes are within ranges which, in some
cases, can be as large as $500 (i.e. $1,000 to $1,499). This does not allow for correct
estimation of the average earning of individuals in a particular range because one
has no idea how evenly the actual individual earnings are spread within such income
range. For the purpose of simplicity, we take the midpoint of each income range as
the average income of the individuals in that range. Finally for all age groups, the
dataset aggregates all individuals earning more than $1,500 into a single income
category. In our modeling, we use $1,500 as the average income for individuals in
this range. Although this is bound to result in underestimating the average income
for individuals belonging to the highest income range in this dataset, the
consequences may not be very severe on our modeling of career wage profile given
151
that the size of this group is relatively small in most cases compared to those of the
lower income categories.
Figure 5.1: Income Distribution of Australian Population
Income Distribution of Australian Pouplation Betwee n 20 and 64 years
0100,000200,000300,000400,000500,000600,000700,000800,000
Negativ
e/Nil i
ncome
$1-$3
9
$40-$
79
$80-$
119
$120
-$15
9
$160
-$19
9
$200
-$29
9
$300
-$39
9
$400
-$49
9
$500
-$59
9
$600
-$69
9
$700
-$79
9
$800
-$99
9
$1,00
0-$1,499
$1,50
0 or m
ore
Number of Men
Number of Women
Several interesting observations can be made from the income data for individuals.
The income distribution of the male and female population between the age of 20
and 64 years are shown in Figure 5.1. For income categories below $500 per week,
women on aggregate outnumber men. This is also true when we compare the
genders across different age categories. However, as we move towards higher
income categories, number of women steadily declines relative to men. For the
highest income category in our dataset i.e. above $1,500, women are outnumbered
by men by a ratio greater than 4:1. The highest number of women workers fall
within the income category of $200-$299 per week closely followed by number of
women with weekly earnings in the $300-$399 and $400-$499 categories
respectively. Together these three categories account for almost one-third of all
women income earners. In contrast, the highest number of male income earners fall
within income category of $1000-$1499 followed by the income categories of $800-
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$999 and $500-$599. Also noteworthy is the fact that the number of women with nil
or negative income is more than double the corresponding number of men.
Figure 5.2: Earnings Profile of Australian Population by Age
Earnings Profile of Average Male and Female Between 20 and 64 Years
0
5000
10000
15000
20000
25000
30000
35000
40000
45000
20-24 years 25-34 years 35-44 years 45-54 years 55-64 years
Age
Inco
me
($)
Male
Female
Figure 5.2 plots the earnings profile of the average male and female worker between
the age of 20 and 64 years. Both demonstrate a hump-shaped pattern with earnings
growing in the initial years, reaching a plateau in the middle years and then
declining in later years although the hump is more pronounced in the case of the
average male worker. Earnings for the typical Australian female worker grow at a
relatively slower pace in the initial years. They also appear to peak much sooner
(between 25 to 34 years) compared to that of the male counterpart and then drop
slightly only to recover between 45 and 54 years. Thereafter the rate of decline is
similar to that of a male worker. Apparently the data not only lends support to the
existence of a substantial gender wage gap in Australia across all categories but also
reveals the differences between the lifetime earnings profiles of men and women.
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5.3.2 Asset Class Returns
To resample asset class returns, this study uses an updated version of the dataset of
real returns for Australian stocks, bonds, and bills reported by Dimson, Marsh, and
Staunton (2002) and commercially available through Ibbotson Associates. This
annual return data series covers a period of 105 years between 1900 and 2004. Since
the dataset spans over several decades, it captures wide-ranging effects of favourable
and unfavourable events of history on returns of individual asset classes within our
test. The returns include reinvested income and capital gains. The descriptive
statistics for this data is provided in Appendix A. During this 105 year period, the
mean annual real return for Australian stocks has been 9.09% while the same for
Australian bonds and bills has been 2.27% and 0.72% respectively. The standard
deviation for stocks has also been higher at 17.74% compared to that for bonds
(13.36%) and bills (5.51%).
5.4 Results and Discussion
5.4.1 Contribution Rate
Initially, we focus on the impact of changing the superannuation contribution rate in
addressing the gender inequity in accumulation outcomes. Therefore, we need to
hold the asset allocation strategy constant for the male and female worker. We
assume that all superannuation contributions are invested in the balanced fund
described in 5.2. For the hypothetical male worker, which represents our baseline
case, the contribution rate is 9%. For the hypothetical female worker, we examine
the impact of a continuous career as well as that of a voluntary career break of 5
years. In our simulation model, we assume that this break occurs either at the age of
25 years or at 30 years although we acknowledge that these breaks can happen at
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different ages for different woman. Also, our assumption of a continuous break for 5
years may not be representative of many women who may experience more than one
career break at different stages of their career. The contribution rates for the female
workers range from 9% to 16%. For every trial for the hypothetical female worker
under alternative assumptions about employment breaks, a parallel trial is conducted
for the baseline male worker. The results are given in Table 5.2.
For the female worker with no career break (Panel A), the results indicate the stark
differences between the accumulation outcomes of Australian men and women. In
case the contribution rate is same for both the genders, the projected outcomes for
the male dominate those of the females for all 5000 simulation trials i.e. there is
stochastic dominance of the first order. The mean and median accumulation of the
male worker exceeds that of his female counterpart by more than $186,000 and
$156,000 respectively. This result is significant as it gives an idea about the quantum
of shortfall in accumulation that would be experienced by an average woman worker
under the current regime of gender-blind superannuation plans even if she does not
take any voluntary break during her career.
The gap in accumulation between the genders grows even further if the hypothetical
woman worker has a voluntary career break, a distinct possibility confronted by
most Australian women. Every outcome for female worker under this condition is
dominated by the corresponding outcome of the male worker. A 5-year break from
employment at the age of 25 (Panel B) results in a mean accumulation for the
average female worker that is almost $300,000 less compared to that of the average
male worker. The median account balance for the former is also less than that of the
latter by a staggering amount of more than $ 237,000. The average wealth
differential between the male and the female worker also increases to $288,485. If
the female worker defers this career break till she is 30 (Panel C), the probability of
underperforming the baseline outcome still remains at 100%. However, the average
shortfall in this case declines slightly to $263,981.
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Table 5.2 Accumulation Outcomes for Different Female contribution Rates
Table 5.2 reports the superannuation accumulation results of simulation trials for a hypothetical male and female worker in Australia who join the workforce at the age 20 and retire at the age of 64 for different contribution rates of the latter. The accumulation outcomes of the male worker are compared to those for a female with no voluntary break in employment (Panel A), with a voluntary break in employment between 25 and 30 years (Panel B) and with a voluntary break in employment between 30 and 35 years (Panel C).
SP represents the probability of the accumulation of the female worker falling below that of the male worker.
SE is the expected shortfall of the female accumulation outcome i.e. the probability weighted average of the amount by which the accumulation for the female worker falls short of that of the male worker. Contribution Rate Mean Median
25th Percentile
75th Percentile SP
SE
PANEL A
Male: 9% 660,322 551,392 373,595 820,129 Female: 9% 476,274 395,222 265,286 591,562 100% 184,047 Male: 9% 656,535 552,043 378,813 820,179 Female: 12% 622,897 520,463 354,068 781,262 100% 33,638 Male: 9% 656,127 554,317 371,646 814,304 Female: 12.5% 647,603 544,548 362,465 806,628 86% 9,974 Male: 9% 659,953 546,966 367,199 831,464 Female: 12.75% 663,940 547,558 364,778 837,870 49% 2,850
PANEL B Male: 9% 654,039 544,186 361,446 822,651 Female: 9% 365,554 306,831 205,162 459,603 100% 288,485
Male: 9% 662,048 559,897 370,630 822,965 Female: 12% 492,761 420,946 282,163 610,859 100% 169,287 Male: 9% 660,129 554,277 368,665 825,380 Female: 15% 614,193 520,776 349,338 762,904 92% 46,630 Male: 9% 669,069 561,338 373,178 835,128 Female: 16% 663,421 564,586 378,691 828,662 47% 15,993
PANEL C
Male: 9% 660,051 555,442 369,869 820,576 Female: 9% 396,069 331,281 222,340 492,675 100% 263,981 Male: 9% 666,186 555535 368005 838751 Female: 12% 533,711 442640 294861 664923 100% 132,475
Male: 9% 655,380 545769 362952 821870 Female: 15% 655,179 542623 363448 816312 49% 12,000
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The above results spring no surprise given the existence of the gender wage gap in
the Australian labour market. Lower earnings for women over the lifecycle are
bound to result in lower superannuation contributions which in turn produce less
terminal wealth at retirement relative to male workers in the same cohort as both the
sexes experience the same investment return path. The likelihood of longer absence
from paid work for women further widens the mismatch. One way of reducing the
imbalance in wealth outcomes would be to increase the superannuation contribution
rate for women. But the key question is to what extent it needs to be increased. Our
simulation results throw light on this issue. For the woman worker with no voluntary
break from employment, increasing the contribution rate to 12% reduces the average
size of the terminal wealth shortfall to $33,638 (compared to $184087 in case of 9%
contribution). But still every accumulation outcome falls short of the corresponding
outcome for the baseline male worker. However, if the contribution rate for the
female worker goes up further to 12.5%, the probability of underperforming male
accumulation outcomes at retirement comes down to 86% and the size of
underperformance dramatically decreases to below $10,000. A further increase of
female contribution rate to 12.75% actually turns the odds slightly in favour of the
female workers. The probability of underperforming the male baseline is now only
49% i.e. there is now a 51% chance of the female worker retiring with a higher
superannuation balance. The corresponding average shortfall is now below $3000.
At a contribution rate of 13%, the female accumulation outcomes dominate
corresponding male projected outcomes in 86% of cases.
While a contribution rate of 12.5% would give the woman worker with continuous
employment almost an even chance of doing as well as men in superannuation, this
is not a realistic scenario for most Australian women who spend less time in paid
work than typical men. To assess the amount of contribution for women with broken
employment record required to match the outcome of the baseline male worker, we
look at the results presented in panels B and C of Table 5.2. As expected an increase
in female contribution rate to 12% does not lead to a dramatic reduction in the size
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of average shortfall. A break for 5 years at the age of 25 would lead to an expected
shortfall of $169,287 relative to the male worker with no break in employment. If
the break is experienced at the age of 30, the expected shortfall would be still very
large at $132,475. A contribution rate of 16% (if break occurs at 25) or 15% (if
break occurs at 30) would be necessary for the female worker to bring down the
probability of shortfall relative to the baseline male worker below 50%. But the
average size of shortfall at $15993 and $12000 respectively in these cases are still
higher than that of the woman with no career break and contribution rate of 12.75%.
5.4.2 Asset Allocation
While the above results underlines the significance of higher contributions for
Australian women workers to reduce the gender disparity in retirement wealth
outcomes, a novel alternative approach to tackling this issue may lie in the
investment strategy chosen by the worker participants. Since the only investment
decision made by superannuation fund members in Australia is asset allocation i.e.
how to divide the contributions in their account among various asset classes, we
examine the impact of changing the asset allocation strategy on terminal wealth at
retirement.61 Empirical evidence for most developed nations overwhelmingly
suggests that the probability of growth assets like stocks underperforming less
volatile assets like bonds over longer holding periods is extremely low.62 However,
the average default investment strategy for superannuation funds in Australia
allocates only about 54% of their assets to shares (APRA, 2005). If one includes
investments in asset categories like property, the total allocation to growth assets for
the average default fund increases to 60%. Given the long investment horizon of 61 American workers, in contrast, have the option to choose between an array of funds offered by different fund managers in investing their plan contributions. 62 The literature on this subject is vast. Siegel (1994) provides a good account in the US market while Jorion and Goetzmann’s (1999) studies this phenomenon in international markets.
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superannuation members and the large equity premium prevalent in Australian and
major international markets over last several decades, this asset allocation strategy
may be regarded as unduly conservative.63 Therefore, it as an attractive option for
the researcher to investigate whether resorting to a more aggressive investment
strategy can actually help Australian women to overcome the gender inequity in
retirement wealth outcomes.
For all simulation trials conducted in this part of our investigation, we hold the
contribution rate for both the male and female worker constant at the current
mandatory rate of 9%. For the sake of simplicity, we assume investments are made
only in Australian shares, bonds, and bills.64 The asset allocation strategy adopted by
the baseline male worker always resembles a balanced fund holding 60% of its
assets in shares, 30% in bonds and the remaining 10% in cash. For the woman
worker, in addition to the classic balanced fund described above, we explore wealth
outcomes under alternative strategies with increasing allocation to growth assets i.e.
shares. This is compensated by an equal reduction in the proportion of assets
invested in bonds and cash. However, to meet liquidity requirements of the fund, the
allocation to cash is assumed to never go below 5% (apart from the extreme case
where allocation to share is 100%). For example, a 10% increase in allocation to
shares from 60 to 70% is matched by a 5% decline in allocation to bonds (from 30 to
25%) and 5% decline in allocation to cash (from 10% to 5%). But a further increase
of share investments to 80% leads to a 10% decline in allocation to bonds (from
25% to 15%) while the allocation to cash remains unchanged at 5%.
63 This is also supported by our findings in chapter 4. 64 Most Australian superannuation funds, obviously, would invest in international shares and bonds. But this is not expected to alter our results significantly since a majority of these assets are held in US and UK markets, the returns of which are highly correlated with those in Australian domestic market. We also ignore properties and alternative assets in our analysis because of the paucity of reliable long run data on their returns.
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Table 5.3: Accumulation Outcomes for Different Female Asset Allocation Strategies
Table 5.3 reports the superannuation accumulation results of simulation trials for a hypothetical male and female worker in Australia who join the workforce at the age 20 and retire at the age of 64 for different asset allocation strategies employed by the latter. The accumulation outcomes of the male worker are compared to those for a female with no voluntary break in employment (Panel A), with a voluntary break in employment between 25 and 30 years (Panel B) and with a voluntary break in employment between 30 and 35 years (Panel C). The allocation of the male worker to shares is constant at 60 % while allocation to shares for the female worker is changed for each set of simulation experiment consisting of 5000 trials.
SP represents the probability of the accumulation of
the female worker falling below that of the male worker. SE is the expected shortfall of the female
accumulation outcome i.e. the probability weighted average of the amount by which the accumulation for the female falls short of that of the male worker.
Allocation to Shares Mean Median
25th Percentile
75th Percentile
SP SE
PANEL A
Male: 60% 664,015 561,477 372,063 830,892 Female: 70% 597,295 480,357 301,116 746,496 94% 71,427 Male: 60% 668,332 559,850 372,673 832,108 Female: 75% 669,681 518,907 323,422 840,281 69% 38,036
Male: 60% 659,571 553,586 368,400 823,700 Female: 80% 726,348 559,311 343,222 909,111 49% 24,081
PANEL B
Male: 60% 662,048 559,897 370,630 822,965 Female: 70% 455,140 372,421 239,193 571,582 100% 206,908
Male: 60% 660,129 554,277 368,665 825,380 Female: 80% 550,210 432,049 272,157 687,667 93% 117,130 Male: 60% 669,069 561,338 373,178 835,128 Female: 90% 686,090 508,750 303,123 856,292 66% 61,792 Male: 60% 650,186 540,071 359,247 814,638 Female: 95% 729,388 521,922 306,261 905,812 56% 50,834
Male: 60% 653,648 540,748 376,424 804,847 Female: 100% 824,474 577,415 335,566 999,982 43% 35,733
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Table 5.3 (Cont’d): Accumulation Outcomes for Different Female Asset Allocation Strategies
Allocation to Shares Mean Median
25th Percentile
75th Percentile
SP SE
PANEL C
Male: 60% 659,571 553,586 368,400 823,700 Female: 70% 493,391 397,345 255,693 613,685 100% 166,280 Male: 60% 668,332 559,850 372,673 832,108 Female: 80% 617,311 469,332 288,962 770,442 82% 79,834
Male: 60% 651,560 541,275 360,441 817,378 Female: 90% 734,711 526,463 311,239 905,739 55% 44,318 Male: 60% 652,260 539,453 375,357 804,919 Female: 95% 814,457 574,486 338,685 992,775 43% 33,870
The results under different asset allocation rules adopted by the female worker vis-à-
vis the baseline male worker is presented in Table 5.3. For the woman who does not
go through any voluntary break in employment, an increase in allocation to shares to
70% slightly reduces the chance of underperforming the male outcome to 94%
(compared to 100% in case both the genders follow the same balanced allocation
strategy). But it leads to a remarkable decline in the average size of the
underperformance. The average size of shortfall relative to the accumulation
outcome for the baseline male worker is now $71,427 which is less than 40% of
what it would be ($184,087) had the female worker invested in the same balanced
strategy chosen for the male worker. If the allocation to shares is increased by
another 5% to 75%, the impact is a dramatic drop in the probability of shortfall to
69%. In other words, there is almost a 1 in 3 chance now that the female worker
would outperform the baseline male worker. A further increase in allocation to
shares to 80% for the former gives her more than an even (1 in 2) chance of ending
with a higher superannuation account balance in retirement than the latter.
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For the alternative scenario of the woman worker experiencing 5-year breaks from
employment, the impact of pursuing more aggressive investment strategies is far less
spectacular in terms of reducing the chance of underperforming the baseline male
worker. If the break happens at the age of 25, even an investment strategy with 80%
allocation to stocks would result in a modest improvement in shortfall probability to
93%. The results indicate that unless the entire superannuation contribution is
invested in a portfolio with almost 100% allocation to shares, this female worker has
less than an even chance to match the accumulation of the baseline male worker. If
the break happens later in her career at the age of 30, a similar result is achieved
with an allocation of 95% to shares, which is still very high. The aggressive asset
allocation strategies, however, prove effective in trimming down the magnitude of
underperformance relative to the baseline male case. For example, by employing an
allocation rule which invests 90% of assets in shares, the female worker with 5 year
employment break at the age of 25, reduces the expected shortfall to $61,792 which
is less than a quarter of the expected shortfall she would be exposed to if she invests
using the same allocation rule as the baseline male.
However employing highly aggressive asset allocation strategies to improve
terminal wealth outcomes for female workers (or reducing the expected shortfall)
may have pitfalls. The higher volatility of returns from share market is the key
concern here. While mean reversion is a well demonstrated feature of past history of
stock market returns (Poterba and Summers, 1988; Fama and French, 1988),
theoretically, the chance of many consecutive years of low or negative returns from
investments in shares in future cannot be ruled out. In the case of such an
occurrence, the wealth outcome for a highly aggressive strategy can be extremely
adverse. A large number of simulation trials (5000 in this study) which resample
past returns, positive and negative, with replacement can potentially capture these
extremely adverse outcomes at the lower end of the wealth distribution for each
investment strategy. The results for these extremely adverse outcomes are presented
in Table 5.4.
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Table 5.4: Extreme Adverse Outcomes for Different Female Asset Allocation Strategies
Table 5.4 reports estimates of the most adverse outcomes for different asset allocation strategies employed by a hypothetical female worker in Australia who join the workforce at the age 20 and retire at the age of 64. The Value-at-Risk (VaR) estimate is computed at 95% level of confidence. The Expected Tail Loss is a conditional measure given by the probability weighted average of all accumulation outcomes that are below VaR. Panels A, B, and C represents the accumulation outcomes for a female with no voluntary break in employment with a voluntary break in employment between 25 and 30 years and with a voluntary break in employment between 30 and 35 years respectively.
Allocation to Shares VaR ETL
PANEL A
60% 150,557 121,550 70% 160,141 130,509 75% 170,147 133,984 80% 169,519 131,978
PANEL B
60% 122,870 100,646 70% 131,662 107,764 80% 137,945 109,093 90% 150,471 116,962
PANEL C
60% 129,018 104,652 70% 136,643 109,155 80% 150,902 117,670 90% 152,912 117,752
Contrary to expectations, they show that the risk of encountering extremely adverse
outcomes by pursuing a more aggressive strategy is not significantly different from
following a less aggressive one. For the female employee with continuous
employment record, the VaR estimates are actually better for strategies with higher
allocation to shares. For example, allocating 70% to shares results in a VaR estimate
of $160,141 whereas increasing the allocation of shares to 75% produces a
corresponding estimate ($170,147) which is higher by more than $10,000.
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Increasing the allocation to shares further to 80%, however, results in a slightly
lower VaR estimate at $169,519. The ETL estimates are also extremely close for
different asset allocation strategies. When we look at the woman worker with
breaks, the results indicate that more aggressive strategies generally produce better
outcomes at the lower tail of the wealth distribution. This is clear from the
increasing trends in both the VaR and the ETL estimate with an increase in
allocation to stocks. This is apparently confounding due to their inconsistency with
the conventional notion of risk and return going hand in hand. Yet our results are
well supported by the empirical evidence showing that the risk of investing in shares
over less volatile assets like bond and cash decrease over longer holding periods.
This is demonstrated to be true both under assumptions that future returns are
random drawings from distribution of past returns (Butler and Domian (1991)) and
mean reversion of returns in the long run (Thaler and Williamson (1994)).
5.4.3 Combination
So far we have demonstrated the effectiveness of increasing contribution rates and
adopting aggressive asset allocation approaches in mitigating the gender inequality
in superannuation outcomes. Yet one cannot discount the fact that prescriptive
changes of this scale are difficult to implement in practice. To give the female
worker, who has a very high chance of experiencing a career break for childbearing
and caring requirements, an even chance of accumulating as much in superannuation
as the baseline male worker, her contributions have to be raised to 15% or 16% from
the current 9% level. To fill this gap is no easy task for the policymakers as it is
bound to meet with strong opposition from employers or the employees depending
on who is made to pay for this increase in contributions. If the mandatory employer
contribution rates are increased significantly for female workers, it may give rise to
discrimination against employing women by many employers. On the other hand, if
the female workers themselves are subjected to a compulsory or voluntary
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contribution regime to fill this gap, it is unlikely to find much favour as it involves
substantial trade-off with their current consumption needs.
The alternative solution of setting aggressive portfolio strategies for female workers
may be even more controversial although this does not require any extra
contributions from the employer or the employees. International research evidence
finds women to be more risk averse than men and this is reflected in their preference
for relatively conservative investment strategies (see e.g. Bajtelsmit, Bernasek, &
Jianakoplos, 1999; Bernasek & Shwiff, 2001).65 Therefore, any default arrangement
that allocates more than 90% of female superannuation assets to the share market (as
our results suggest) in order to match male retirement outcomes could be viewed as
reckless by current standards.
A third approach to address the problem would be to use a combination of higher
contributions and aggressive asset allocation for the woman employee. We put this
to the test by conducting simulations that set female contribution at a slightly higher
level of 12% and then adjust the asset allocation to match the superannuation
outcomes of the baseline male worker. The results are reported in Table 5.5. For the
woman with no voluntary break in employment, the consequence is astounding.
With a modest increase in contribution rate (to 12%) and exposure to shares (to
70%), the accumulation outcomes for the woman now dominates those of her male
counterpart most of the time. The probability of the female doing worse than a male
is reduced to a meagre 9% with an expected shortfall of only $800. The median
outcome for the female worker outperforms that of the baseline male by nearly
$80,000.
65 In Australia, Gerrans and Clark-Murphy (2004) finds support for this assertion. Some researchers, however, find that with equal access to financial knowledge and information, there is little difference between the investment behaviour of men and women (see for instance Dwyer, Gilkeson & List, 2002). .
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Table 5.5: Accumulation Outcomes for Different Female Contribution Rates and Asset Allocation Strategies
Table 5.5 reports the superannuation accumulation results of simulation trials for a hypothetical male and female worker in Australia who join the workforce at the age 20 and retire at the age of 64. The contribution rate and asset allocation for male worker is constant while the female worker has a constant but higher contribution rate and employs a range of different asset allocation strategies. The accumulation outcomes of the male worker are compared to those for a female with no voluntary break in employment (Panel A), with a voluntary break in employment between 25 and 30 years (Panel B) and with a voluntary break in employment between 30 and 35 years (Panel C). The contribution rate of the male worker remains constant at 9 % and allocation to shares is also constant at 60 %.
SP represents the probability of the accumulation of the female worker falling below that of the male worker. SE is the expected shortfall of the female accumulation outcome.
Contribution Rate
Allocation to Shares Mean Median
25th Percentile
75th Percentile SP
SE
PANEL A
Male 9% 60% 661,619 558,777 371,128 819,093 Female 12% 70% 794,187 637,462 401,755 988,134 0.09 800
PANEL B
Male 9% 60% 660,322 551,392 373,595 820,129 Female 12% 70% 605,406 491,184 323,197 757,062 0.92 59,461 Male 9% 60% 656,535 552,043 378,813 820,179 Female 12% 80% 725,501 576,141 360,670 910,521 0.43 18,927
PANEL C Male 9% 60% 662,048 559,897 370,630 822,965 Female 12% 70% 648,023 524,302 333,364 809,337 0.75 33,693 Male 9% 60% 669,069 561,338 373,178 835,128 Female 12% 75% 730,192 570,722 360,411 916,911 0.44 15,581
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The above results for the female worker using a combination of ‘higher contribution
rate’ and ‘aggressive asset allocation’ are far superior to those obtained previously
when we employed these strategies individually (Tables A and B respectively). For
instance, with a contribution rate of 12% alone, the female with no voluntary break
in employment was always certain to accumulate less than the baseline male i.e.
probability of shortfall was 100%. The average size of the shortfall was also much
larger (more than $33,000). If on the other hand the female worker contributed the
same 9% as the baseline male worker but invested in a more aggressive portfolio of
70% of assets in shares, she would still be underperforming the male worker in 94%
of cases with an even larger expected shortfall exceeding $71,000.
The combination approach also seems to work well for the hypothetical woman with
voluntary breaks in employment although the break in contributions needs to be
compensated by holding a more aggressive portfolio if her contribution rate remains
unchanged at 12%. To give the woman worker a more than even chance to
outperform the baseline male accumulation at retirement (i.e. SP < 0.5), our results
indicate that her portfolio exposure to shares has to be between 75% and 80%
depending on the timing of the break. Again, had the female worker relied on an
increased contribution rate of 12% alone, she had little chance of matching the
accumulation of the baseline male. The expected shortfall, for the woman with
career breaks at the age of 25 and 30 years would be $169,287 and $132,475
respectively which is considerably higher compared to $18,927 and $15,581, the
value of expected shortfalls in case the same woman employed the combination
approach. Similarly by holding a portfolio with 80% of assets invested in shares
(without altering the contribution rate), she would have struggled to match the male
accumulation outcomes in most cases (93% and 82% respectively for breaks at the
age of 25 and 30) and confronting a higher expected shortfall ($117,130 and $79,834
respectively for breaks at the age of 25 and 30).
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5.5 Conclusion
Hill and Tigges (1995) like many other authors point out that pension systems were
historically developed ‘by men with men in mind’. The Australian superannuation
system, which is assuming a prominent place in the retirement income landscape of
the workforce, is no exception. Inequality in labour market performance is bound to
put Australian women at a serious disadvantage in retirement compared to men.
Many studies in the past have highlighted the problem of gender inequity in
retirement. But there has been little research done on examining the solutions to the
problem especially in terms of quantifying their precise impact on differences in
superannuation account balances of male and female workers. Among those like
Preston and Austen (2001) that have put forward proposals like increases in
contribution rates or removal of exemptions for employer contributions tax have not
explained how these measures would neutralise the relative disadvantage of women
to men in retirement plan accumulation.
In this chapter, we have examined the effectiveness of two alternative strategies –
higher contribution rates and aggressive asset allocation for female workers– in
addressing the inherent, albeit inadvertent, discrimination in the current
superannuation arrangement. Whilst our results suggest that both these approaches
are individually useful in mitigating the gender inequality in wealth outcomes at
retirement, we find that their effectiveness grows manifold when used in tandem. A
combined approach is also appealing from policymaker’s perspective since it
demands relatively modest changes to current mandatory contribution rates and
default asset allocation of the average superannuation fund.
As Thomson (1999) points out an equal treatment of the genders by the
superannuation system would result in unequal outcomes in presence of women’s
enduring disadvantage in the labour market. The evidence presented in this chapter
supports this contention and suggests that there is a compelling case for instituting
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gender specific contribution and investment strategies in superannuation plans. It
may be argued, perhaps not entirely without merit, that such a policy would actually
hope to nullify women’s inferior performance in one market (labour) partly by
increasing their exposure to the performance risk in another market (investment).
But while women’s relative disadvantage in the former market is almost certain to
continue for many years in future, our past experience on long term performance of
the latter provides strong ground for optimism.
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6. Portfolio Size Effect and Lifecycle Asset Allocation
6.1 Introduction
6.1.1 Background
Lifecycle funds have gained great popularity in recent years. Sponsors of defined
contribution (DC) plans offer more and more of these funds as investment options to
their participants. In many cases, these funds serve as default investment vehicles for
plan participants who do not make any choice about investment of their plan
contributions. The findings of the Mercer 2000 survey of DC plans in UK (as cited
in Blake, 2006) show that these funds were the most common default options
covering 55% of funds. As reported by Vanguard (2006), one of the largest pension
plan managers in USA, two thirds of their plans offered lifecycle options in 2005, up
from one-third in 2000. Assets under lifecycle funds amounted to $160 billion in
2005 compared to below $10 billion in 1996 (Gordon & Stockton, 2006).66 The
rapid growth in lifecycle investment programs in DC plans is often attributed to the
fact that they simplify asset allocation choice for millions of ordinary investors who
supposedly lack the knowledge or inclination to adjust their portfolios over time. For
them, the lifecycle fund offers an automatic one-step solution by modifying the asset
allocation of retirement investments periodically in tune with the investors’
changing capacity to bear risk.
66 Not all lifecycle funds change their asset allocation over time. Static allocation funds offered by various providers which have the same exposure to various asset classes throughout the investment horizon are also sometimes categorised as lifecycle or lifestyle funds. In contrast, the lifecycle funds we discuss in this and the next chapter change their allocation over time and therefore are often referred to as age-based or target retirement funds. It is this type of age-based lifecycle funds that has witnessed the highest growth in the last few years (Mottola and Utkus, 2005).
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The central theme of the lifecycle model of investing is that one’s portfolio should
become increasingly conservative with age (See, for example, Malkiel, 1996) In
retirement plans, this is done by switching investments from more volatile assets
(like stocks) to less volatile assets (fixed interest securities like bonds and cash) as
the participant approaches retirement. For example, the Vanguard Target Retirement
Funds prospectus states that ‘It is also important to realize that the asset allocation
strategy you use today may not be appropriate as you move closer to retirement. The
Target Retirement Funds are designed to provide you with a single Fund whose
asset allocation changes over time as your investment horizon changes. Each
Fund’s asset allocation becomes more conservative as you approach retirement.’
While lifecycle funds offered by different providers differ from one another with
respect to how and when they switch assets, there is total unanimity about the
overall direction of the switch – from stocks to bonds and cash.
The practitioners’ belief that one’s exposure to risky assets should decrease with age
(and consequent shortening of investment horizon) has been theoretically refuted by
Samuelson (1963) and more recently by Bodie (1995) among others. Their argument
holds under a ‘random walk’ model of stock returns, an assumption that is open to
question. On the other hand, there is no dearth of theoretical work that lends support
to the concept of horizon based investing (for example, Merrill and Thorley, 1996;
Levy and Cohen, 1998). The riskiness of stocks over longer horizons seem to reduce
much faster than what is predicted by the random walk model, a phenomenon which
can be attributed to mean-reverting behaviour of stock returns observed in empirical
data. In contrast, returns on fixed income securities like bonds and bills are found to
be mean-averting in many cases (Siegel, 2003).67
67 If asset returns follow a random walk, the annualized standard deviation over a holding period of n
years is given by nσ where σ is the standard deviation over one year. The fact that the shrinkage of standard deviation for stock returns over long horizon is higher than this prediction of random walk model is often cited as an evidence of mean reversion. For fixed income assets, the empirical evidence is quite the opposite i.e. the shrinkage is lower than the prediction of the model.
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More recently, Campbell and Viceira (1999, 2002) have studied this question under
the assumption of time-varying expected stock returns. They find it optimal for long
horizon investors to have a strategic tilt in their portfolio towards equities.68
However the idea of age-based investing focused on mean-reversion is a
controversial area in finance with ongoing debate about the robustness of the
statistical evidence on stock return predictability. Some research disputes this
evidence (Goyal & Welch, 2007), while others find it acceptable (Lewellen, 2004;
Campbell & Thomson, 2007).69
The relationship between horizons and investment risk has also been examined by
empirical researchers with different conclusions.70 Much of the empirical work,
however, considers the case of a multi-period investor who invests in a portfolio of
assets at the beginning of the first period and reinvests the original sum and the
accumulated returns over several periods in the investment horizon.71 The situation
of retirement plan participants, however, is more complex because they make fresh
additional investments in every period till retirement in the form of plan
contributions. As a result, the retirement plan participant’s terminal wealth is not
only determined by the strategic asset allocation governing investment returns but
also by the contribution amounts that go into the retirement account every period
since these alter the size of the portfolio at different points on the horizon.
68 However they argue against a buy and hold strategy in view of the mean reverting behaviour of stock prices. They recommend a periodic revision in allocation in response to change in market conditions. 69 A completely different justification for age-based lifecycle investing is provided by considerations about human capital (Bodie, Merton, and Samuelson, 1992). An excellent review of the literature on optimal asset allocation under different assumptions about riskiness of human capital is provided by Viceira (2007) 70 For example, McEnally (1985) and Butler and Domian (1991) examine the effect although they reach different conclusions. This is, however, a result of different measures of risk employed by the researchers. While the former views variability of terminal wealth as risk, the latter uses probability of stocks underperforming bonds and T-bills over long horizons as the risk measure. 71 An exception to this is Hickman et al. (2001) who model the terminal value of a retirement investor’s portfolio where contributions are made every month. However, they assume that contributions remain equal throughout the horizon.
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6.1.2 Research Description
A recent observation by Robert Shiller (2005b) harps on this issue and questions the
intuitive foundation of conventional lifecycle switching for retirement investors.
Shiller argues that “a lifecycle plan that makes the percent allocated to stocks
something akin to the privately- offered lifecycle plans may do much worse than a
100% stocks portfolio since young people have relatively little income when
compared to older workers…... The lifecycle portfolio would be heavily in the stock
market (in the early years) only for a relatively small amount of money, and would
pull most of the portfolio out of the stock market in the very years when earnings are
highest.” The statement is remarkable in asserting that the portfolio size of plan
participants at different points of time is significant from the asset allocation
perspective. If the above is true, then lifecycle funds may be missing a trick by
ignoring the growing size of the participant’s portfolio over time while switching
assets.
The size of the participant’s retirement portfolio is likely to grow over time, not only
because of possible growth in earnings and size of contributions as Shiller indicates,
but also due to regular accumulation of plan contributions and investment returns. In
such case, it would make little sense for the investor to follow the prescriptions of
conventional lifecycle asset allocation. By moving away from stocks to low return
asset classes as the size of their funds grow larger, the investor in effect would be
foregoing the opportunity to earn higher returns on a larger sum of money invested.
But there is another side to this story. Advocates of lifecycle strategies point out that
a severe downturn in the stock market at later stages of working life can have
dangerous consequences for the financial health of a participant holding a stock-
heavy retirement portfolio, not only because it can significantly erode the value of
the nest egg but also because it leaves the participant with very little time to recover
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from the bad investment results. Lifecycle funds, on the other hand, are specifically
designed to preserve the nest egg of the investor nearing retirement. By gradually
switching investments from stocks to less volatile assets over time, they aim to
lessen the chance of confronting very adverse investment outcome during that
period.
In this chapter, we examine whether by reducing the allocation to stocks as the
participants approach retirement, the lifecycle investment strategy benefits or works
against the retirement plan participant’s wealth accumulation goal. We are
particularly interested to test whether growing size of the accumulation portfolio in
later years indeed calls for a higher allocation to stocks to produce better outcomes
despite the looming danger of facing sharp decline in stock prices close to
retirement. Since an important objective of lifecycle strategy is to avoid the most
disastrous outcomes at retirement, we examine various possible scenarios,
particularly the most adverse ones, to assess their efficacy as the investment vehicle
of choice for DC plan participants.
6.1.3 Summary of Findings
Using stochastic simulation, we report that the existence of a portfolio size effect in
retirement plan investments causes the terminal wealth to be more sensitive to the
asset allocation strategy employed closer to retirement than that followed in the
early years after joining the plan. Since lifecycle strategies systematically switch
investments away from growth assets during the years leading to retirement, they
seem to dampen the growth potential of the retirement investor’s portfolio. The
sooner the lifecycle strategy starts switching from stocks to bonds and cash, more
pronounced is the dampening effect. On the other hand, by switching to less volatile
assets lifecycle strategies appear to reduce the severity of disastrous wealth
outcomes in a few cases caused by stock market downturns within a few years prior
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to retirement. But, as we argue in this essay, the switching seems to be justified only
when the portfolio value matches or exceeds the participant’s target accumulation.
We further discuss the case against deterministic lifecycle switching in chapter 7.
6.2 Methodology
We examine the case of a hypothetical retirement plan participant with starting
salary of $25,000 and contribution rate of 9%. The growth in salary is taken as 4%
per year. The participant’s employment life is assumed to be 41 years during which
regular contributions are made into the retirement plan account. For the sake of
simplicity, we assume that the contributions are credited annually to the
accumulation fund at the end of every year and the portfolio is also rebalanced at the
same time to maintain the target asset allocation. Therefore, the first investment is
made at the end of the first year of employment followed by 39 more annual
contributions to the account.
A number of studies in recent years including Hickman et al. (2001) and Shiller
(2005a) compare terminal wealth outcomes of 100% stocks portfolios with those of
lifecycle portfolios and find little reason for investors to choose lifecycle strategies
for investing retirement plan contributions. But these studies are not specifically
designed to test whether the allocation towards stocks should be favoured during the
later stages of the investment horizon because of the growth in size of one’s
portfolio. This is because the competing strategies invest in different asset classes
for different lengths of time and therefore they are bound to result in different
outcomes simply because of the return differentials between the asset classes. For
example, one may argue that a 100% stocks portfolio may dominate a lifecycle
portfolio purely because the former holds stocks for longer duration. The role played
by the growing size of the portfolio over time and its interplay with the asset
allocation in influencing the final wealth outcome is not very clear from this result.
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6.2.1 Lifecycle and Contrarian Strategy Pairs
To find out whether the growth in size of contributions and overall portfolio with the
investor’s age renders the conventional lifecycle asset allocation model counter-
productive, as Shiller conjectures, we formulate a novel test. We consider
hypothetical strategies which invest in less volatile assets like bonds and cash when
the participants are younger and switch to stocks as they get older i.e. strategies that
reverse the direction of asset switching of conventional lifecycle models. These
strategies, which we call contrarian strategies in the remainder of this chapter, are
well placed to exploit the high returns offered by the stock market as the participants
accumulation fund grow larger during the later part of their career. Moreover, we
design these strategies in such a manner that they hold different asset classes for
identical lengths of time as corresponding lifecycle strategies. This is necessary to
ensure that we are not comparing apples to oranges which would be the case if we
compare the outcomes of any lifecycle strategy with a fixed weight strategy like one
holding 100% stocks throughout the horizon or even with another lifecycle strategy
which holds stocks (and other asset classes) for an unequal length of time.72
Initially we construct four stylised lifecycle strategies, all of which initially invest in
a 100% stocks portfolio but start switching assets from stocks to less volatile assets
(bonds and cash) at different points of time - after 20, 25, 30, and 35 years of
commencement of investment respectively.73 We make a simplified assumption that
the switching of assets takes place annually in a linear fashion in such a manner that
in the final year before retirement all four lifecycle strategies are invested in bonds
and cash only. The proportion of assets switched from stocks every year is equally
72 An exception would be the case where the average allocation of the lifecycle strategy to any asset class over the investment horizon exactly matches that of the fixed weight strategy it is compared with. 73 Blake (2006) observes that the most common switchover period among lifecycle funds offered in UK is 5 years prior to retirement followed by 10 years prior to retirement.
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allocated between bonds and cash.74 Next we pair each lifecycle strategy with a
contrarian strategy that is actually its mirror image in terms of asset allocation. In
other words, they replicate the asset allocation of lifecycle portfolios in the reverse
order. All four contrarian strategies invest in a portfolio comprising only bonds and
cash in the beginning and then switch to stocks linearly every year in proportions
which mirror the asset switching for corresponding lifecycle strategies. The four
pairs of lifecycle and contrarian strategies are described below.
Figure 6.1: Asset Allocation over Investment Horizon (Pair A)
74 Information about precise asset allocation of existing lifecycle funds at every point on the horizon is rarely made available in the providers’ prospectus. Our formulation follows the general direction of the switch and does not try to consciously replicate the allocation of any of the existing funds.
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Pair A. The lifecycle strategy (20, 20) invests only in stocks for the first 20 years
and then linearly switches assets towards bonds and cash over the remaining period.
At the end of the 40 years, all assets are held in bonds and cash. The corresponding
contrarian strategy (20, 20) invests only in bonds and cash in the initial year of
investment. It linearly switches assets towards stocks over the first 20 years at the
end of which the resultant portfolio comprises only of stocks. This allocation
remains unchanged for the next 20 years. Figure 6.1 graphically demonstrates this
allocation rule.
Figure 6.2: Asset Allocation over Investment Horizon (Pair B)
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Pair B. The lifecycle strategy (25, 15) invests only in stocks for the first 25 years
and then linearly switches assets towards bonds and cash over the remaining period.
At the end of the 40 years, all assets are held in bonds and cash. The corresponding
contrarian strategy (15, 25) invests only in bonds and cash in the initial year of
investment. It then linearly switches assets towards stocks over the first 15 years at
the end of which the resultant portfolio comprises only of stocks. This allocation
remains unchanged for the remaining 25 years. Figure 6.2 graphically demonstrates
this allocation rule.
Figure 6.3: Asset Allocation over Investment Horizon (Pair C)
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Pair C. The lifecycle strategy (30, 10) invests only in stocks for the first 30 years
and then linearly switches assets towards bonds and cash over the remaining period.
At the end of the 40 years, all assets are held in bonds and cash. The corresponding
contrarian strategy (10, 30) invests only in bonds and cash in the initial year of
investment. It linearly switches assets towards stocks over the first 10 years at the
end of which the resultant portfolio comprises only of stocks. This allocation
remains unchanged for the remaining 30 years. Figure 6.3 graphically demonstrates
this allocation rule.
Figure 6.4: Asset Allocation over Investment Horizon (Pair D)
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Pair D. The lifecycle strategy (35, 5) invests only in stocks for the first 35 years and
then linearly switches assets towards bonds and cash over the remaining period. At
the end of the 40 years, all assets are held in bonds and cash. The corresponding
contrarian strategy (5, 35) is initially invested 100% in bonds and cash. It linearly
switches assets towards stocks over the first 5 years at the end of which the resultant
portfolio comprises only of stocks. This allocation remains unchanged for the
remaining 35 years. Figure 6.4 graphically demonstrates this allocation rule.
The above test formulation allows us to directly compare wealth outcomes for a
lifecycle strategy to those of a contrarian strategy that invest in stocks (and
conservative assets) for the same duration but at different points on the investment
horizon. The allocation of any lifecycle strategy is identical to that of the paired
contrarian strategy in terms of length of time they invest in stocks (and conservative
assets). They only differ in terms of when they invest in stocks (and conservative
assets) - early or late in the investment horizon. For example, in case of pair A, both
lifecycle (20, 20) strategy and contrarian (20, 20) strategy invests in a 100% stocks
portfolio for 20 years and allocate assets between stocks, bonds, and cash for the
remaining 20 years in identical proportions. However, the former holds a 100%
stocks portfolio during the first 20 years of the horizon in contrast to the latter which
holds a 100% stocks portfolio during the last 20 years of the horizon. The same is
graphically demonstrated in Figures 6.1.
6.2.2 Bootstrap Resampling
To generate investment returns under every strategy, we randomly draw with
replacement from the empirical distribution of asset class returns. The historical
annual return data for the asset classes over several years is randomly resampled
with replacement to generate asset class return vectors for each year of the 40 year
investment horizon of the DC plan participant. Thus we retain the cross-correlation
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between the asset class returns as given by the historical data series while assuming
that returns for individual asset classes are independently distributed over time. The
asset class return vectors are then combined with the weights accorded to the asset
classes in the portfolio (which is governed by the asset allocation strategy) to
generate portfolio returns for each year in the 40 year horizon. The simulated
investment returns are applied to the retirement account balance at the end of every
year to arrive at the terminal wealth in the account. For each lifecycle and contrarian
strategy the simulation is iterated 10,000 times. Thus, for each of the eight strategies,
we have 10,000 investment return paths that result in 10,000 wealth outcomes at the
end of the 40-year horizon. More details about the resampling method employed in
this study are provided in 3.2.2.
6.2.3 Data
To resample returns, this study uses an updated version of the dataset of nominal
returns for US stocks, bonds, and bills originally compiled by Dimson, Marsh, and
Staunton (2002) and commercially available through Ibbotson Associates. This
annual return data series covers a period of 105 years between 1900 and 2004. Since
the dataset spans several decades, we are able to capture the wide-ranging effects of
favourable and unfavourable events of history on returns of individual asset classes
within our test. The returns include reinvested income and capital gains. More
details about the data have been discussed in 3.3. The descriptive statistics for the
dataset is provided in Appendix C.
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6.3 Results and Discussion
6.3.1 Terminal Wealth Estimates
Comparing various parameters of the terminal wealth distribution for the lifecycle
strategies and their contrarian counterparts provide us with a fair view of their
relative appeal to the retirement investor. In particular, we look at the mean, the
median, and the quartiles of the terminal wealth distribution under the different asset
allocation strategies. These are reported in Table 6.1. Even a cursory glance reveals
that there are significant differences between these estimates under the lifecycle and
contrarian strategy in every pair.
For each of the four pairs, we observe that the contrarian strategies result in much
higher expected value (mean) than the lifecycle strategies. The difference is most
striking for pair A and pair B as the mean wealth at retirement for the contrarian
strategies exceed those for the corresponding lifecycle strategies by more than half a
million dollars. While the differences between expected values for the other two
lifecycle and contrarian pairs (C and D) are less spectacular, they are still very large.
However, it is important to note that the mean is not the most likely outcome or even
average likely outcome for any of the strategies. This is apparent from the skewness
of the terminal wealth distributions. The means of the distributions are much higher
than the medians indicating the probability of achieving the mean outcome is much
less than 50%. In other words, the participants should have ‘better than average’
luck to come up with the mean outcome at retirement. The average outcome in this
case is, therefore, much more accurately represented by the median of all outcomes.
But even when one looks at the median estimates, the story does not change at all.
For all pairs, the contrarian portfolios easily beat the lifecycle portfolios. For
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example, the contrarian (20, 20) strategy in pair A results in a median final wealth of
$1,425,387. The corresponding lifecycle (20, 20) strategy manages only $1,160,225
thus falling short by a whooping $265,162. The same margins for pair B, C, and D,
are $270,763, $176,531, and $121,584 respectively.
Table 6.1: Terminal Value of Retirement Portfolio in Nominal Dollars
Strategy
Mean
Median
25th
Percentile 75th
Percentile Pair A Lifecycle (20,20) 1,420,332 1,160,225 793,371 1,724,852 Contrarian (20,20) 1,959,490 1,425,387 838,796 2,435,856 CONT - LCYL (%) 38.0 22.9 5.7 41.2 Pair B Lifecycle (25,15) 1,645,154 1,275,577 825,149 2,004,439 Contrarian (15,25) 2,173,389 1,546,339 889,496 2,702,427 CONT - LCYL (%) 32.1 21.2 7.8 34.8 Pair C Lifecycle (30,10) 1,909,918 1,411,168 876,711 2,355,363 Contrarian (10, 30) 2,335,373 1,587,699 909,020 2,864,003 CONT - LCYL (%) 22.3 12.5 3.7 21.6 Pair D Lifecycle (35,5) 2,253,731 1,578,405 918,483 2,764,413 Contrarian (5,35) 2,491,247 1,699,990 964,222 3,032,984 CONT - LCYL (%) 10.5 7.7 5.0 9.7 CONT – LYCL = Contrarian Strategy Terminal Value – Lifecycle Strategy Terminal Value (Expressed as percentage of the lifecycle strategy terminal value)
We also compare the 75th percentile and 25th estimates which represent the mid-
point of the above average and the below average outcomes respectively. For the
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75th percentile estimates, which are practically the medians of the ‘above median’
outcomes, the differences between the lifecycle and the corresponding contrarian
portfolios grow even wider than those for median estimates. For pair A, the 75th
percentile outcome for the contrarian portfolio is about 41% larger than the lifecycle
portfolio which translates a wealth difference of more than $700,000 i.e. Even for
pair D, where the results for the two strategies are the closest, the contrarian
portfolio is still better off by more than a quarter million dollars.
For 25th percentile estimates, which represents the medians of the ‘below median’
outcomes, one would normally expect the lifecycle strategies to perform better given
they are specifically designed to protect the retirement portfolio against the adverse
market movements in the final years. Well, they certainly do better in terms of
closing the gap with but are still not able to outperform contrarian strategies for any
of the pairs. Even for pair C, where the two estimates are the closest, the result for
the contrarian (10, 30) strategy is almost 4% ($32,000) higher than that for the
corresponding lifecycle (30, 10) strategy.
Although the dominance of contrarian strategies over their lifecycle counterparts is
clearly visible for all pairs, the difference between the outcomes of the two strategies
gets monotonically smaller as we move from pair A to pair D. This is expected as
each subsequent pair of strategies has greater overlap in terms of holding the same
asset class at the same point on the horizon (i.e. identical allocation) than the
previous pair. For example, at no point of time do the lifecycle (20, 20) strategy and
the contrarian (20, 20) strategy in pair A have identical allocation to the asset
classes. In stark contrast, the lifecycle (35, 5) and the contrarian (5, 30) strategies in
pair D have identical allocation for 30 years (between 6th and 36th year), during
which both are invested in 100% stocks portfolio, thus resulting in final wealth
outcomes that are closer to one another than those produced by other pairs where the
lifecycle and contrarian strategies have shorter overlapping periods of identical
allocation.
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6.3.2 Accumulation Paths over Horizon
The above results indicate that if the plan participant’s objective is to maximise
wealth at the end of horizon, lifecycle strategies vastly underperform relative to the
contrarian strategies. Shiller’s emphasis on exposing the portfolio in later years to
higher returns offered by stock market seems to be a possible candidate in
explaining the superior 40-year performance of the contrarian strategies. But to have
proper understanding of the interaction between portfolio size and asset allocation, it
is necessary to track the accumulation paths of the lifecycle and corresponding
contrarian strategies in the early, middle, and final years. In other words, to obtain
more compelling evidence of the portfolio size effect, we need to plot the simulated
portfolios over the entire 40 year period. Figures 6.5 to 6.8 depict the accumulation
paths over 40 years for each pair of lifecycle and contrarian strategies.
It is evident from the figures that for every lifecycle and contrarian strategy, the
slopes of the accumulation curves generally steepen as they move along the horizon
which seems to indicate that the potential for rapid growth in retirement nest egg
comes only in the later years. What is most striking in this respect is that every
lifecycle strategy and its paired contrarian strategy display very similar
accumulation outcomes in the initial years despite the difference in their asset
allocation structures. In fact, till half way through the 40-year horizon, there is very
little to choose between the accumulation patterns of the lifecycle strategy and those
of the contrarian strategy. It is only when the accumulation plots move well beyond
the half-way mark they start looking markedly different.75 This seems to suggest
that, in the initial years, accumulation in the retirement account may not be very
sensitive to the asset allocation strategy chosen by the participant.
75 Two dimensional accumulation plots provided in the annexure to this chapter also make this very clear.
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Figure 6.5: Simulated Accumulation Paths over Investment Horizon (Pair A)
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Figure 6.6: Simulated Accumulation Paths over Investment Horizon
(Pair B)
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Figure 6.7: Simulated Accumulation Paths over Investment Horizon
(Pair C)
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Figure 6.8: Simulated Accumulation Paths over Investment Horizon
(Pair D)
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The slopes of the accumulation curves under lifecycle strategies and those of the
corresponding contrarian strategies become conspicuously different during the later
years. The lifecycle portfolios generally enjoy a smooth climb as they move along
the horizon while the contrarian portfolios have far steeper ascent. This clearly
demonstrates the effect of portfolio size on the terminal wealth outcome. By
allowing exposure of large portfolios to stock market in later years, the contrarian
strategies produce spectacular growth opportunities. A closer examination of the
plots would reveal that in many cases the contrarian portfolios leapfrog over the
lifecycle portfolios only at very late stages in the investment horizon but still
manage to result in huge differences in terminal balance. For example, accumulation
balances for the contrarian (20, 20) strategy in pair A lags behind those of the
lifecycle (20, 20) strategy for the best part of 40 years. However not only do they
manage to catch up the lifecycle portfolios in the final years before retirement but
actually leave them way behind by the time the investors reach the finishing line.
It does not escape our attention that the accumulation profiles for the contrarian
strategies get much rougher towards the end of the horizon. This is certainly
indicative of higher variability of outcomes. But does this indicate higher risk?
Looking at the skewness of the terminal wealth distributions under contrarian
strategies, it is clear that the higher variability is mainly the result of some extremely
large accumulation outcomes. If the plan participant’s goal is to avoid the possibility
of disastrous outcomes, this kind of variability would be of little relevance in
gauging actual risk.
6.3.3 Adverse Outcomes and Tail Risk
Looking at the lower tail of the distribution which comprises of the adverse wealth
outcomes however, would be more sensible to compare the riskiness of the
competing strategies. It is quite possible that higher volatility of returns for
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contrarian strategies in the later years can result in large losses and very poor
terminal accumulations at least in some cases. In other words, lifecycle strategies
may actually generate better outcomes at the lower tail of the terminal wealth
distribution compared to contrarian strategies. From results reported in Table 6.1, we
have already observed that the first quartile outcomes of contrarian strategies
dominate those for lifecycle strategies in every case. Now we compare various
percentiles of distribution within the first quartile range which may be considered as
the zone of most adverse outcomes for the plan participant. Table 6.2 tabulates the
VaR estimates at 99%, 95%, 90%, 85%, and 80% levels of confidence under
different lifecycle and contrarian strategies.
Table 6.2: VaR Estimates for Lifecycle & Contrarian Strategies
Asset Allocation Strategy VaR estimates at Differen t Confidence Levels ($) 99% 95% 90% 85% 80% Pair A Lifecycle (20,20) 370,049 483,800 577,066 654,132 728,573 Contrarian (20,20) 258,637 407,053 532,291 639,031 738,534 LCYL – CONT (%) 43.08 18.85 8.41 2.36 -1.35 Pair B Lifecycle (25,15) 343,326 466,203 571,193 662,194 744,045 Contrarian (15,25) 259,630 424,103 557,240 673,115 778,744 LCYL – CONT (%) 32.24 9.93 2.50 -1.62 -4.46 Pair C Lifecycle (30,10) 318,211 470,271 585,107 685,409 781,134 Contrarian (10, 30) 249,829 434,660 567,613 682,174 803,828 LCYL – CONT (%) 27.37 8.19 3.08 0.47 -2.82 Pair D Lifecycle (35,5) 301,184 455,267 589,409 700,323 817,011 Contrarian (5,35) 264,326 446,592 600,863 719,279 843,420 LCYL – CONT (%) 13.94 1.94 -1.91 -2.64 -3.13 LYCL - CONT = Lifecycle Strategy Terminal Value - Contrarian Strategy Terminal Value ((Expressed as percentage of the contrarian strategy terminal value)
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It is evident from comparing the VaR estimates that lifecycle strategies do produce
better outcomes than their contrarian counterparts when we consider only the
outcomes in the lowest decile (10th percentile or below) of the distribution. However
this is not without exception as we observe that the VaR estimate for the lifecycle
(35, 5) strategy in pair D at 90% confidence level is lower than that of the
corresponding contrarian strategy. The difference between the VaR estimates for
every pair is highest at 99% confidence level and reduces gradually as we decrease
the level of confidence. But what is remarkable is that the final wealth under the
contrarian strategies in the worst case scenarios falls short of the corresponding
lifecycle strategies by a margin which is far less significant relative to the size of the
overall accumulation. For the VaR estimates at confidence level of 99% (and 95%),
this ranges from a little more than $100,000 (and $75,000) for pair A to about
$37,000 (and $8,000) for pair D. The difference between the estimates seems to
become less significant around the 85% confidence level with the contrarian
strategies resulting in slightly higher estimates for pairs B and D. For estimates at
80% confidence level, the dominance of the contrarian strategies is clearly visible
for all the four pairs.
The above results show that lifecycle strategies do not always fare better than the
contrarian strategies even in terms of reducing the risk of adverse outcomes. Only
when we compare the VaR estimates at confidence level of 90% and above,
lifecycle strategies fare slightly better. A chance of encountering poorer outcomes is
less than 1 in 10. However, it is very unlikely that investors in reality would select a
lifecycle asset allocation model with the sole objective of minimizing the severity of
these extremely adverse outcomes, should they occur, because the cost of such
action is substantial in terms of foregone wealth. For example, if the 10th percentile
outcome (which is equivalent to the 90% VaR estimate) is confronted at retirement,
one could be better off only by about 8% by following the lifecycle (20, 20) strategy
rather than the contrarian (20, 20) strategy. But for the 90th percentile outcome,
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which is equally likely to happen, one would be 55% better off by following the
contrarian (20, 20) strategy instead of the lifecycle (20, 20) strategy.76 Choosing one
strategy over the other in this case can result in considerable difference in lifestyle
after retirement.
The opportunity for risk reduction varies considerably between various lifecycle
strategies. These are more visible for lifecycle strategies that start changing their
asset allocation relatively earlier in the investment horizon than those that do so
later. For example, the 95% VaR estimate for lifecycle (20, 20) strategy is almost
19% higher than the contrarian (20, 20) strategy. The same estimate for lifecycle
(25, 15), (30, 10), and (35, 5) strategies, which switch to conservative assets
relatively later, vis-à-vis corresponding contrarian strategies 10%, 8%, and 2%
respectively indicating declining risk reduction advantage for lifecycle strategies that
delay switching to conservative assets. Ironically, reducing the risk of extreme
outcomes by switching early to conservative assets involves a very heavy penalty in
terms of foregone accumulation of wealth. This becomes apparent from the variation
in terminal wealth outcomes for the four lifecycle strategies in question.
6.4 Conclusion
The apparently naïve contrarian strategies which, defying conventional wisdom,
switch to risky stocks from conservative assets produce far superior wealth outcomes
relative to conventional lifecycle strategies in all but the most extreme cases. This
demonstrates that the size of the portfolio at different stages of the lifecycle exerts
substantial influence on the investment outcomes and therefore should be carefully
considered while making asset allocation decisions. The evidence presented in this
chapter lends support to Shiller’s view that the growing size of the participants’
76 The 90th percentile terminal wealth estimates, although not provided in this chapter, are available from the author on request.
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contributions in the later years calls for aggressive asset allocation which is quite the
opposite of what is currently done by lifecycle asset allocation funds.
It is important to emphasize here that we are clearly not suggesting that one should
follow any of the contrarian asset allocation strategies to allocate retirement plan
assets. We have formulated and used them in this study only to conduct a fair test of
the hypothesis that by investing conservatively in middle and later years lifecycle
funds work against the participant’s investment objectives. Our results show that, in
most cases, the growth in portfolio size experienced in the later years of employment
seems to justify holding a portfolio which is at least as aggressive as that held in the
early years. For some participants, this may well mean holding 100% stocks
throughout the horizon.
By their own admission, financial advisors recommending lifecycle strategies focus
on two objectives: maximizing growth in the initial years of investing and reducing
volatility of returns in the later years. Our findings suggest that the bulk of the
growth in value of accumulated wealth actually takes place in the later years. The
first objective, therefore, has little relevance to the overarching investment goal of
augmenting the terminal value of plan assets. We do find some support for pursuing
the second objective of reducing volatility in later years to lessen the impact of
severe market downturns but this comes at a high cost of giving up significant
upside potential. In other words, the effect of portfolio size on wealth outcomes over
long horizons is so large that it outweighs the volatility reduction benefit of lifecycle
strategies in most cases. Therefore, switching to less volatile assets a few years
before retirement can only be rationalized if the employee participants have already
accumulated wealth which equals or exceeds their target accumulation at retirement.
Several studies in the past like Ludvik (1994), Booth and Yakoubov (2000), Blake et
al. (2001) have found lifecycle asset allocation strategies to be sub-optimal for
pension plan participants. The results of this chapter, therefore, are in agreement
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with these findings. However, unlike past studies, we have taken a step further to
reveal the specific reason why age based (but performance blind) lifecycle switching
causes inferior outcomes for the retirement plan investor. The portfolio size effect,
as has been demonstrated in this chapter, plays a major role behind the poor
performance of conventional lifecycle strategies.
If lifecycle strategies aim to preserve accumulated wealth, then it seems one has to
first ensure sufficient accumulation in the retirement investor’s account before
recommending switch towards conservative investments. Unfortunately, this is not
the case with lifecycle funds currently used in DC plans, where the asset switching is
done following a pre-determined mechanistic allocation rule and without giving any
cognizance to the actual accumulation in the account. It seems that retirement
investors would be better off by refraining from blindly adopting these age-based
investment strategies that are keen on preservation even when there is not much to
preserve.
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ANNEXURE 6A: Two Dimensional Accumulation Plots
Figure 6A.1: Two-Dimensional View of Accumulation Paths over Horizon (Pair A)
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Figure 6A.2: Two-Dimensional View of Accumulation Paths over Horizon (Pair B)
198
Figure 6A.3: Two-Dimensional View of Accumulation Paths over Horizon (Pair C)
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Figure 6A.4 Two-Dimensional View of Accumulation Paths over Horizon (Pair D)
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7. A Dynamic Asset Allocation Framework for Lifecycle Investing in Retirement Plans
7.1 Introduction
7.1.1 Background
Lifecycle or target retirement funds have gained favour with retirement plan
investors in recent years. As a rule of thumb, these funds have high initial
concentration in stocks but gradually move towards less volatile assets like bonds
and cash. Thus, it is often argued, they offer the best of both worlds – robust
portfolio growth in the early years of employment and preservation of the
accumulated wealth as the investors approach retirement. Also, once enrolled there
is no need for the investors to keep constant vigil over their investment strategy. The
switching of assets (from stocks to fixed income) over the years happens
automatically following a preset glide path laid down by the plan provider.
But does the predisposition of lifecycle funds to systematically switch out of equities
benefit the investors of target retirement funds? Empirical research in the past has
generally found that a switch to low-risk assets prior to retirement can reduce the
risk of confronting the most extreme negative outcomes. Lifecycle strategies are also
said to reduce the volatility of wealth outcomes making them desirable to investors
who seek a reliable estimate of final pension a few years before retirement.77 On the
other hand, there is near unanimity among most researchers that these benefits come
at a substantial cost to the investor - giving up significant upside potential of wealth
accumulation offered by more aggressive strategies. Authors like Siegel (1992) and
77 For example, see Ludvik (1994) or Blake et al. (2001).
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Kim and Wong (1997) find that holding a portfolio heavily tilted towards stocks is
the optimal investment strategy for long horizon investors like retirement plan
participants.
7.1.2 Research Description
This study questions the rationale of the deterministic nature of switching from
stocks to fixed income assets as is the prevalent practice among most lifecycle
funds. The most common argument cited by the proponents of the lifecycle strategy
in retirement plans is apparently straightforward – the probability that returns from
stocks would outperform (underperform) those from bonds and cash increases
(decreases) with the length of the investment horizon. If this is true, then long
horizon investors may prefer to have a higher allocation to stocks in their portfolio
compared to investors with shorter investment horizons.78 It is also argued that
younger investors in retirement plans should heavily invest in stocks not only
because of the prospect of higher returns but also for the reason that investors have
enough time to recover from stock market downturn(s) should that happen. On the
other hand, for older investors with a few years to retire, holding such an aggressive
portfolio can spell disaster. A major slump in the stock market just before retirement
can potentially wipe away years of investment gains with little time to salvage the
situation. But would this imply that investors should automatically reduce the
proportion of stocks in their retirement portfolio as years go by? The following
example would explain why the answer may not be always in the affirmative.
78 This is sometimes referred to as ‘time diversification’. Samuelson (1989, 1994) shows that if returns are independently and identically distributed such long horizon effect cannot exist. While Samuelson’s argument is mathematically sound, mean reversion in stock returns is a well documented empirical phenomenon. For example, Poterba and Summers (1988), provides evidence from the US market.
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Suppose an investor has a horizon of 40 years. Following popular lifecycle
strategies, she decides to invest her money in stocks for the initial 20 years and then
gradually switch to bonds and cash over the last 20 years. Once this allocation
decision is made, she puts it on an autopilot (like most lifecycle funds) for the next
40 years. However, the stock market returns following the investment decision do
not augur well for the investor. Due to a prolonged bear market there are several
years of negative returns eroding the value of her portfolio. After 20 years, the
balance in her account is next to nothing and this gets gradually switched to bonds
and cash. Subsequent returns in the account are stable but low. In this case, after 40
years the investor would find herself in a financial situation quite different from
what was anticipated while setting the investment strategy.79
Undoubtedly the above example is an extreme one and describes only one of the
several possibilities that an investor can expect to encounter over a long horizon. Yet
it reveals the Achilles’ heel of the lifecycle funds currently in market. These funds
follow a pre-determined performance-blind asset allocation strategy where not only
the switching of assets is always unidirectional – from stocks to fixed income –and it
is done in proportions that are pre-specified at the inception of the fund. In our
example, had the stock market offered very high returns during the last 20 years, the
investor would stand to gain very little because her investments were automatically
switched from stocks to bonds and cash during that period following the allocation
strategy she had set on autopilot. The pre-programmed lifecycle strategy was blind
to the fact that she had accumulated too little wealth in the initial years to necessitate
switching to conservative assets. The asset switching in that case virtually ensures
that she misses the only realistic chance she had to reverse her bad fortune.
The problem for the retirement plan members enrolled in lifecycle funds is more
complex than the hapless investor of our example. Typically the plan members make
79 It is not inconceivable that she even finds herself poorer in real terms than what she was 40 years ago.
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regular contributions to the retirement account as opposed to a single investment
made at the beginning of the 40 year period in our example. As contributions are
normally a fixed percentage of the members’ salaries, they are expected to grow
larger over time with growth in earnings. Therefore, as Shiller (2005b) points out,
the lifecycle strategy invests heavily in the stock market in the early years when the
contribution size is relatively small and switches out of it when earnings and
contributions grow larger in later years. This can be counterproductive as by moving
away from stocks to low return assets just when the size of their contributions (and
accumulation fund) are growing larger, the investor may be foregoing the
opportunity to earn higher returns on a larger sum of money invested. We have
already demonstrated this in chapter 6 of this thesis.
One cannot help question the fact that why lifecycle funds need to have their
benchmark asset allocation over the entire horizon cast in stone. A possible
alternative would be to switch to conservative assets a few years before retirement
when a plan member feels that the wealth in the retirement account adequately meets
his or her accumulation objective and therefore needs to be preserved. By the same
token, the plan member may be unwilling to switch to less volatile but low return
assets in case the past performance of the portfolio has been unsatisfactory, leaving
him or her with inadequate wealth relative to the accumulation target. Thus, the
decision to switch or not to switch and even how much to switch at any stage in this
case largely depends upon the cumulative performance of the retirement portfolio in
the preceding years.
In this chapter, we extend the abovementioned alternative approach by proposing a
dynamic lifecycle strategy which is flexible in adjusting its allocation between
growth and conservative assets while approaching retirement depending on the
extent that the plan member’s wealth accumulation objective has been achieved at
that time. In other words, this strategy is responsive to past performance of the
portfolio relative to the investor’s target return in determining the right mix of assets
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in future periods. While initially it invests heavily in equities just as any other
lifecycle strategy, the switching criterion is different in the sense that switch to fixed
income is not automatic. It only takes place if the investor has accumulated wealth in
excess of the target accumulation at the point of switch. Also, after switching to
conservative assets, if the accumulation falls below the target in any period, the
direction of switch is reversed by moving away from fixed income and towards
stocks. But does this strategy result in improved outcomes for the retirement plan
member? To find out we compare and contrast the outcomes of such a dynamic
strategy with those achieved by following a regular lifecycle strategy.
Blake et al. (2001) test a similar lifecycle strategy with performance feedback
although their benchmark is set in terms of a replacement ratio i.e. ratio of pension
to final salary. The similarity between their threshold strategy and the dynamic
lifecycle strategy proposed in this chapter is that both resort to an aggressive asset
allocation strategy if the portfolio underperforms the set benchmark (or lower
threshold in their case) and vice versa. However, their strategy switches assets
based on performance feedback right after the member joins the retirement plan
while in our case the asset switching starts a few years before retirement which is
more akin to the conventional lifecycle model.
Arts and Vigna (2003) also suggest an asset allocation model with a switch criterion
based on performance feedback. Switching from equities to bonds takes place only if
the cumulative returns on equities have been high prior to the switch and vice versa.
However, in their model the switching is irreversible i.e. once assets are switched to
bonds, they cannot be reallocated to equities. Moreover, the switching from stocks to
bonds is not gradual but total at the point of switch.80 Unlike their paper, the
switching criterion in our proposed allocation strategy is dynamically applied over
the horizon.
80 This is an extreme case and not encountered ordinarily among lifecycle funds in practice.
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7.1.3 Summary of Findings
In Chapter 6 we demonstrated that naive age-based lifecycle switching results in loss
of significant upside potential while the trade-off in terms of avoiding most adverse
outcomes at retirement appeared inadequate. In light of our findings in that study,
we conjectured that a better strategy might be one that periodically incorporates the
information on past portfolio performance on asset switching mechanisms. In this
chapter, we put this dynamic strategy to test. Our results clearly suggest that a
deterministic asset switching rule, following conventional lifecycle strategies
produce inferior wealth outcomes for the investor compared to strategies that
dynamically alter allocation between growth and conservative asset classes at
different stages based on cumulative portfolio performance relative to a set target.
The dynamic lifecycle strategies exhibit clear second-degree stochastic dominance
over conventional lifecycle strategies which switch assets unidirectionally without
cognizance to the portfolio performance.
7.2 Methodology
7.2.1 Conventional Versus Dynamic Lifecycle Strategy
In comparing conventional lifecycle and dynamic lifecycle strategies, we consider
the case of a hypothetical individual who joins the plan with starting salary of
$25,000. The earnings grow linearly at the rate of 4% per annum over the next 41
years, which is the duration of the individual’s employment life. Throughout this
period, the member makes regular annual contributions amounting to 4% of earnings
in the retirement plan account. We assume that the contributions are credited
annually to the member’s accounts at the end of every year. This means that the first
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contribution by the member is made at the end of first year followed by 39 more
contributions in as many years. No contribution is made in the final year of
employment.
Our hypothetical plan member can choose between a conventional lifecycle strategy
and a dynamic strategy to invest the contributions. We consider two variations of the
conventional lifecycle strategy, namely 20,20LC and 10,30LC , which invest in a 100%
stocks portfolio for 20 years and 30 years respectively following the first
contribution. Thereafter both of them linearly switch from stocks to bonds and cash
over the remaining 20 (and 10) years in such a manner that at the point of retirement
all assets are held in bonds and cash. This type of allocation is akin to that of a
typical lifecycle or target retirement funds which invest heavily in equities in the
initial years and gradually switch to fixed income instruments as they approach
maturity. Similarly the dynamic strategy has two variations, namely 20,20DLC and
10,30DLC , corresponding to the above lifecycle strategies. They invest in the same
100% stocks portfolio as the two lifecycle strategies during the first 20 (and 30)
years. Thereafter every year the strategies review how the portfolio has performed
relative to the investor’s accumulation objective. If the value of the portfolio at any
point is found to equal or exceed the investor’s target, the portfolio partially
switches to conservative assets. Otherwise, it remains invested 100% in stocks.
From our formulation of the strategies, it is clear that while 20,20DLC and 10,30DLC
uses performance feedback control in switching assets, 20,20LC and 10,30LC do not.
Although people may have different accumulation objectives on retirement, we need
to make a plausible assumption about the accumulation target set by the hypothetical
individual employing the dynamic allocation strategies in this study. Dimson,
Marsh, and Staunton (2002) have compiled returns for US stocks, bonds, and bills
from 1900. We use an updated version of their dataset and find the geometric mean
return offered by US stocks between 1900 and 2004 is 9.69%. We assume that the
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second individual sets a target of achieving a return close to this rate, say 9%, on the
retirement plan investments. In other words, the retirement portfolio under the
dynamic strategy aims to closely match the compounded accumulation of a fund
where contributions are annually reinvested at a 9% nominal rate of return.
For 20,20DLC which invests in 100% stocks portfolio for 20 years, we assume that
the individual sets a target of 9% compounded annually on investments for the initial
20 year period. At the end of 20 years, if the actual accumulation in the retirement
account exceeds the accumulation target, the assets are switched to a relatively
conservative portfolio comprising of 80% stocks and 20% fixed income (equally
split between bonds and cash). However, if the actual accumulation in the account is
found to fall below the target, the portfolio remains invested in 100% stocks. This
performance review process is carried out annually for the next 10 years and asset
allocation is adjusted depending on whether the holding period return outperforms or
underperforms the target. In the final 10 years the same allocation principle is
applied with only one difference. If the value of the portfolio in any year during this
period matches or exceeds the investor’s target accumulation at that point, 60% of
assets are invested in equities and 40% in fixed income (equally split between bonds
and cash). Failing to achieve the target return for the holding period, results in all
assets being invested in a 100% stocks portfolio.
For 10,30DLC , which invests in 100% stocks for the 30 years after making the first
contribution, the investor has the same target return of 9% compounded annually.
After 31 years, if the portfolio value in any year matches or exceeds the target
accumulation, 20% assets are switched to fixed income (equally split between bonds
and cash). A failure to achieve the target performance results in the portfolio being
invested in 100% equities. The performance of the portfolio relative to the target is
monitored annually and the asset allocation is adjusted accordingly. In the final 5
years before retirement, if the portfolio performance at any point matches or exceeds
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the target accumulation at that point, 40% of assets are switched to fixed income
(equally split between bonds and cash).
7.2.2 Bootstrap Resampling
To generate simulated investment returns under the two conventional lifecycle
strategies (say 20,20LC and 10,30LC ) and their corresponding dynamic lifecycle
strategies ( 20,20DLC and 10,30DLC ) we use the same updated version of the dataset
of annual nominal returns for US stocks, bonds, and bills originally compiled by
Dimson et al. (2002) used in the previous chapters. The dataset spans a long period
of 105 years between 1900 and 2004 and thus capture both favourable and
unfavourable returns on the individual asset classes over the entire twentieth century
within our simulation trials. However, to examine holding period returns for assets
over horizons as long as 40 years, 105 years worth of returns data may not be
sufficient. There are only two independent, non-overlapping 40-year holding period
observations within our dataset. Any conclusion based on a sample of two
observations cannot be deemed reliable.
To get around the problem of insufficient data, we use bootstrap resampling. The
empirical annual return vectors for the three asset classes in the dataset is randomly
resampled with replacement to generate asset class return vectors for each year of
the 40 year investment horizon confronting the two hypothetical retirement plan
investors. Since we randomly draw rows (representing years) from the matrix of
asset class returns, we are able to retain the cross-correlation between the asset class
returns as given by the historical data series while assuming that returns for
individual asset classes are independently distributed over time. More details about
the resampling method employed in this study are provided in 3.2.2.
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As the resampling is done with replacement, a particular data point from the original
data set could appear multiple times in a given bootstrap sample. This is particularly
important while examining probability distribution of future outcomes. For example,
1931 is the worst year for stock market in our 105 year long dataset. In that year
return from stocks was -44% while bonds and bills offered returns of 1% and -5%
respectively. Although this is only one observation in the century long data, a
bootstrap sample of 40 annual returns can include this return observation for 1931
many times in any sequence. Similarly, return observations for other years, good or
bad, can also be repeated a number of times within a bootstrap sample. Since this
method allows for inclusion of such extreme possibilities (like a -44% return
occurring a number of times in a particular 40-year long return path), by obtaining a
large number of bootstrap samples from the observed historical data, one can capture
a much wider range of future possibilities.
The asset class return vectors obtained by bootstrap resampling are combined with
their respective weightings under each asset allocation strategy to generate portfolio
returns for each year in the 40 year horizon. The simulation trial is iterated 10,000
times for lifecycle strategy 20,20LC and its corresponding dynamic strategy 20,20DLC
thereby generating 10,000 independent 40 year return paths that would govern the
possible wealth outcomes for the individuals following them. A separate set of
experiment (comprising of another 10,000 trials) is conducted for the other pair of
lifecycle and dynamic strategies, 10,30LC and 10,30DLC . For the purpose of doing a
comparative analysis, we include two other allocation strategies – (i) a 100% stocks
strategy and (ii) a balanced strategy which allocates in the ratio of 60:30:10 between
stocks, bonds, and cash in both sets of experiments and provide the results in 7.3.
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7.2.3 Stochastic Dominance
While we compare the terminal wealth distribution parameters like the mean,
median, and the lower and upper quartile outcomes of the dynamic strategies
( 20,20DLC and 10,30DLC ) with their conventional lifecycle counterparts ( 20,20LC and
10,30LC ), the superiority of one over the other cannot be established with certainty
without comparing the entire range of outcomes under the two approaches.
Stochastic dominance is a well known criterion used in this type of situation to rank
investment alternatives because it relies on the entire distribution of outcomes.81 It
also places minimal restrictions on the investors’ utility functions and makes no
assumption (like normality) about the return distributions.82 We use this approach
here to find out whether investors would prefer terminal wealth distribution under
one asset allocation strategy over that of the other.
Bawa (1975) provides the necessary and sufficient conditions for various degrees of
stochastic dominance in the context of ranking portfolios. Formally, given utility of
wealth is a non-decreasing function i.e. 0)( ≥′ WU , if F and G represents
respectively the cumulative distributions of terminal wealth outcomes under the
dynamic lifecycle strategy and the conventional lifecycle strategy, the former
dominates the latter under the first degree stochastic dominance (FSD) rule if and
only if:
)()( WGWF ≤ W∀ (41)
This means that the dynamic lifecycle strategy would dominate the corresponding
conventional lifecycle strategy by the FSD criterion if the cumulative distribution of
terminal wealth outcomes under it always remains below the cumulative wealth
distribution of the conventional lifecycle strategy.
81 Since the distribution of wealth outcomes get increasingly asymmetric over long horizons, the mean-variance framework is not useful in this situation. We also refrain from making any strong assumption on the utility function (like quadratic) of the retirement plan members. 82 See Elton and Gruber (1995) for a thorough discussion on this subject.
211
Due to the strong conditionality it imposes regarding the cumulative distributions
not intersecting each other even once, FSD cannot be applied in ordering
distributions in many cases. The second degree stochastic dominance criterion
(SSD) which is a weaker condition than FSD can be useful in these situations. SSD
can be applied to a large class of problems because it works within the framework of
risk aversion, an assumption widely used in finance literature (Hadar and Russell,
1969). Formally, given 0)( ≥′ WU and 0)( ≤′′ WU , the dynamic lifecycle strategy
dominates the conventional lifecycle strategy under the SSD criterion if and only if:
∫ ∫∞ ∞
≤0 0
)()( dWWGdWWF (42)
This implies that the area under F has to be equal or less than the area under G for
the dynamic strategy to dominate the conventional strategy by the SSD rule. Unlike
FSD, SSD allows for F and G to cross each other as long as the above condition is
met.
7.2.4 Shortfall Measures for Dynamic Strategy
We compute a statistic called the probability of shortfall which represents the chance
of the dynamic lifecycle strategy ending with less accumulated wealth than the other
strategies in our simulation trials. Using equation (20) in context of this problem,
this probability of shortfall is given by
0
1,0 )](,0[
1∑
=−=
n
tDLCXDLC WWMax
nLPM (43)
where n denotes the number of trials, XW represents the terminal wealth under any
strategy and DLCW represents the terminal wealth under the dynamic strategy. While
DLCLPM ,0 estimates the odds of the dynamic strategy doing worse (or better) than
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the other strategies in different future states of the world, it does not describe how
large the shortfall in wealth outcome for the former would be compared to that of the
latter. To estimate the magnitude of underperformance of the dynamic strategy
relative to other strategies, we measure the expected shortfall given by equation (20)
in the context of this problem as
∑=
−=n
tDLCXDLC WWMax
nLPM
1,1 )](,0[
1 (44)
The use of LPM family of downside risk measures has already been discussed in
2.7.
7.3 Results and Discussion
7.3.1 Terminal Wealth Estimates
The resampling method described above generates a range of terminal wealth
outcomes under the conventional lifecycle strategies and their corresponding
dynamic strategies. The parameter estimates for the wealth distribution under the
different strategies are reported in Table 7.1. From panel A, which provides the
results for the conventional lifecycle and dynamic lifecycle strategies which always
remain invested in 100% stocks for the first 20 years, the difference is stark. The
mean and the median outcome for the dynamic lifecycle strategy 20,20DLC exceeds
those for the conventional lifecycle strategy 20,20LC by more than half a million
dollars. The first quartile and the third quartile estimate for the former are also
greater than the latter by $245,033 and $704,324 respectively. For the lifecycle
strategies which always invest in the 100% stock portfolio for the first 30 years, the
results appear in Panel B. As in panel A, we find that the dynamic lifecycle strategy
10,30DLC produces much higher mean, median, first and third quartile outcomes than
the conventional lifecycle strategy 10,30LC . The gap between the outcomes in this
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case, however, is lower than what it was between 20,20DLC and 20,20LC . This is
expected as 10,30DLC and 10,30LC strategies invest in the same portfolio (100%
stocks) for ten more years.
Table 7.1: Terminal Value of Retirement Portfolio in Nominal Dollars
Table 7.1 reports the simulation estimates for terminal wealth under different asset allocation strategies. Panel A provides the results for the set of 10,000 trials where both the lifecycle and the dynamic strategy invest in a 100% stocks portfolio for the first 20 years and then commence switching. Panel B provides the results for the set of 10,000 trials where both the lifecycle and the dynamic strategy invest in a 100% stocks portfolio for the first 30 years and then switch assets.
Strategy Mean Median
25th
Percentile 75th
Percentile Panel A Dynamic( 20,20DLC ) 1,978,387 1,733,256 1,037,838 2,432,030 Lifecycle( 20,20LC ) 1,426,510 1,163,836 792,805 1,727,706 100% Stocks 2,523,681 1,715,014 981,005 3,040,650 Balanced 1,273,744 1,117,258 804,466 1,562,407
Panel B Dynamic( 10,30DLC ) 2,243,825 1,762,712 988,573 2,695,902 Lifecycle( 10,30LC ) 1,919,124 1,408,545 876,404 2,340,550 100% Stocks 2,547,867 1,716,608 965,411 3,102,896 Balanced 1,276,875 1,118,547 799,502 1,573,030
In addition to the conventional and the dynamic lifecycle strategies, which are of
primary interest to this study, we also simulate wealth outcomes for the 100% stock
and the balanced strategy. The mean outcomes for the 100% stock strategy are
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higher than both the conventional and dynamic strategy pairs. Given the existence of
large positive equity premium in our data, this result is unsurprising. While the
median and the first quartile outcomes for the 100% stocks strategy is higher than
those of 20,20LC and 10,30LC they fall short of both 20,20DLC and 10,30DLC . This
suggests that dynamic strategies are superior in protecting the investors from the risk
of adverse wealth outcomes than both the aggressive 100% stocks strategy and the
conventional lifecycle strategy which adopts a pre-determined conservative
allocation principle in later years.
The ineffectiveness of lifecycle switching in protecting investors from the risk of
confronting adverse wealth outcomes on retirement is clear when we look at the
balanced fund simulation results. The balanced fund, whose mean and median
outcomes are inferior to all the other three strategies, outperforms 20,20LC in terms
of the first quartile estimate. This apparently puts a question mark on the efficacy of
the conventional lifecycle strategies in improving the floor level of outcomes.
Dynamic lifecycle strategies, again, seem to produce better results in this respect.
But we take up this issue later in this chapter.
7.3.2 CDF and Stochastic Dominance Test
Figure 7.2 demonstrates the cumulative distributions of terminal wealth achieved
under 20,20LC and 20,20DLC strategies. Again for the purpose of comparison, we also
show cumulative wealth distributions for the 100% stocks and the balanced
strategies. The horizontal axis of the graph represents the nominal dollar value of
the portfolio at the point of retirement. As explained above, if the CDF for one
strategy lies under (or to the right of) other CDFs, it is likely to result in a superior
outcome relative to other strategies. Also, if CDF for a strategy is generally steeper
than the others, the strategy can be considered to result in less variable outcomes.
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Figure 7.1: Cumulative Distribution Plots for First Pair of Lifecycle and Dynamic Strategies ( 20,20LC and )20,20DLC
It is clear that except for a very small part on the left of the point X, the cumulative
distribution plot of 20,20DLC remains much under that of 20,20LC . Therefore,
although the dynamic lifecycle strategy does not dominate the conventional lifecycle
strategy by the strict FSD criterion, it does dominate under SSD because the area
under cumulative distribution F of the dynamic strategy is clearly far less than that
under cumulative distribution G of the conventional lifecycle strategy. Except for a
very small section on the left of point X representing wealth outcomes of about
$500,000 or less after 41 years, we can infer from the cumulative distributions that
the investor employing 20,20DLC has higher chance of achieving any particular
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accumulation outcome than the investor employing 20,20LC . For example, the former
has about 75% probability of accumulating more than one million dollars at
retirement whereas the later has got only a 60% chance of crossing that milestone. If
investors set a target of achieving a compounded return of 9% minimum on their
investments, which amounts to an accumulated wealth of at least $1.69 million at
retirement, our results indicate that the 20,20DLC strategy would achieve this goal
with almost 50% certainty. With 20,20LC strategy, this probability drops to only
25%. The gap between the cumulative distribution functions for the two strategies
widens as we move up further towards higher accumulation figures although after a
point (approximately around 2 million dollars) it starts to diminish gradually.
A comparison of the cumulative distributions of the lifecycle strategies 20,20LC and
20,20DLC with that of the 100% stock strategy reveals two important results. First,
we find that the distribution of conventional lifecycle strategy 20,20LC always
remains above that of 100% stock strategy except for the small section on the left of
point X (representing only about the worst 5% of outcomes). This undermines the
effectiveness of conventional lifecycle strategies in protecting the wealth of
investors from the vagaries of stock market downturns. Had it been the case, we
would have found X much to the right of its current location i.e. 20,20LC would have
dominated the 100% stock strategy for a much larger percentage of outcomes in the
lower end of the distribution. In contrast, we find the cumulative distribution of
20,20DLC remains below that of the 100% stock strategy for a much longer section
(the left side of Y). This clearly suggests its effectiveness in reducing the risk of
investor’s wealth breaching any floor level of wealth to the left of Y. Although it
does not dominate the 100% stocks strategy under the SSD criterion, it does much
better in terms of producing superior outcomes in the below median range, which is
likely to be viewed as the zone of risk for most investors. Remarkably it is obvious
from the diagram that our hypothetical investor has a slightly higher chance of
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achieving the target wealth outcome of $1.69 million by employing the 20,20DLC
instead of the 100% stocks strategy.
Now we turn our attention to the cumulative wealth distribution functions for the
other lifecycle and dynamic strategy pair - 10,30LC and 10,30DLC . This is presented in
Figure 7.2. As before, we also show cumulative wealth distributions for the 100%
stocks and the balanced strategies.
Figure 7.2: Cumulative Distribution Plots for Second Pair of Lifecycle and Dynamic Strategies ( 10,30LC and )10,30DLC
Apart from a small part in the extreme lower tail of the distributions representing
terminal wealth outcomes below $500,000, the cumulative wealth distribution
function of 10,30DLC (F) always remains below that of 10,30LC (G). Thus, there is
clear second degree stochastic dominance of 10,30DLC over 10,30LC indicating that
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any risk averse investor would find the former more appealing to the latter. As is the
case with 20,20LC and 20,20DLC pair, the distance between the CDF plots is larger in
the middle than in the extremes. In other words, the dynamic strategy dominates the
conventional strategy over for a vast range of outcomes by a staggering margin.
In relation to the target accumulation outcome of $1.69 million at retirement, Figure
7.2 indicates that the 10,30LC strategy would achieve this goal with about 40%
certainty. Although this is significant improvement compared to the performance
of 20,20LC , it still falls short of the corresponding dynamic strategy, 10,30DLC , which
surpasses the target on more than 50% of occasions. The reason behind 10,30LC
putting up a superior performance relative to 20,20LC strategy in attaining the target
may be attributed mainly to the fact that the former invests in a 100% stocks
portfolio for a longer duration (30 years) compared to that of the latter (20 years).
However to apply the same argument to explain the dominance of dynamic
strategies over corresponding lifecycle strategies appears too simplistic. Had this
been the only reason, 100% stocks strategy would have outperformed other
strategies in terms exceeding the target accumulation. But it is evident from Figure
7.2, the probability of achieving the target wealth outcome with 10,30DLC strategy is
clearly higher than that with 100% stocks strategy. Also, the median outcome for
10,30DLC strategy is larger than that of 100% stocks strategy.
7.3.3 Shortfall Estimates for Dynamic Strategy
But what is the success (or failure) rate of the dynamic strategy over other strategies
in different possible future states of the world? This knowledge is important to the
investor yet comparing cumulative probability distributions of terminal wealth under
different competing strategies would not provide a clear answer. This is because in
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doing so we are comparing the n-th percentile outcome of one strategy with the n-th
percentile outcome of the other. In plain words, the good scenarios under one
strategy are compared to the good scenarios under another and likewise the bad
outcomes are pitted against the bad outcomes. But for any particular future state of
the world (with a particular asset return path over the investment horizon), this
comparison may not be very useful. For example, if stock returns turn out to be very
poor compared to other assets in a particular state of the world, the 100% stocks
strategy would produce inferior outcome relative to a balanced strategy no matter
how attractive or dominating the wealth distribution of the former appears compared
to the latter.
Table 7.2: Shortfall Measures of Dynamic Strategies Relative to Other Asset Allocation Strategies
Asset Allocation Strategy
Shortfall Probability )( ,0 DLCLPM
Average Shortfall ($) )( ,1 DLCLPM
20,20DLC
Lifecycle ( 20,20LC ) 0.19 34,462 100% Stocks 0.51 582,815 Balanced 0.1 6,110
10,30DLC
Lifecycle ( 10,30LC ) 0.26 50,273 100% Stocks 0.43 343,890 Balanced 0.11 6,907
Recall that the asset class return path over the 41 year horizon is unique for each
trial in our simulation experiment. Each of those 10,000 trials represents a different
220
possible future state of the world.83 Therefore, for each trial, we compare the wealth
outcomes under all four strategies, the main point of interest being how the dynamic
strategy performs vis-à-vis other strategies. To be specific, we compute the shortfall
probability (given by DLCLPM ,0 ) of 20,20DLC and 10,30DLC as well as their average
size of shortfall (given by DLCLPM ,1 ) compared to the other three strategies. These
shortfall measures are likely to constitute an important part of what the investors
view as downside risk of adopting the dynamic allocation strategy. The results
provided in Table 7.2 show that the dynamic strategy has small chance of
underperforming the conventional lifecycle strategy. For only 19% of trials the
wealth outcome of the dynamic strategy 20,20DLC falls short of that of the
corresponding lifecycle strategy 20,20LC . For 10,30DLC , the chance of it
underperforming the corresponding lifecycle strategy 10,30LC however increases to
26%, i.e. about one in four. However, the average size of the shortfall in both cases
is quite miniscule ($34462 and $50273) compared to the average size of terminal
wealth outcomes for both the strategies.
Further comparing individual trial outcomes, we find that the 20,20DLC strategy and
the 100% stocks strategy run close to each other in terms of dominance. The chance
of doing better with either strategy in different future states of the world is almost
even with the 100% stocks strategy emerging the winner in 51% of the trials. But
when compared with 10,30DLC , the 100% stocks strategy fares better only in 43% of
trials i.e. the dynamic strategy emerges the winner in a majority of cases. The
average size of the shortfall for the dynamic strategy in both cases, however, is quite
high at $582,815 and $343,890 respectively. This is not unexpected with the 100%
stocks strategy producing spectacularly large wealth outcomes in the above median
and particularly in the upper quartile range. Relative to the balanced strategy, the
chance of underperformance of the dynamic strategy is minimal. 20,20DLC and
83 The actual number of possibilities is obviously infinite.
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10,30DLC strategy underperforms the balanced strategy only in 10% and 11% of the
trials respectively. The average size of shortfall in both cases is extremely small at
$6,110 and $6,907 respectively.
7.3.4 Extreme Adverse Outcomes
While our evidence so far overwhelmingly suggests superiority of dynamic
strategies over conventional lifecycle strategies, the saving grace for the latter may
lie in the zone of most adverse outcomes. This is represented by the left portion of X
in the CDF plots in Exhibits 2 and 3 where the lifecycle strategies actually dominate
corresponding dynamic strategies. It is also apparent from the diagrams that this
zone is constituted by outcomes that are below the 10th percentile mark for every
strategy. To have some idea about how large the differences actually are between the
adverse outcomes under different strategies, we report the VaR estimates at
confidence levels of 99%, 95%, and 90% and ETL estimates at 95% confidence
level for both sets of simulation trials in Table 7.3.
As is evident in the CDF plots, both the lifecycle strategies 20,20LC and 10,30LC
produce higher 95% and 99% VaR estimates compared to their dynamic
counterparts (and 100% stocks strategy). The differences between the 95% VaR
estimates are less than $25,000. But when one compares the 99% VaR estimates, the
differences between the lifecycle and dynamic strategy grow considerably larger.
The 99% VaR estimate for 20,20LC strategy is almost $100,000 more than that of the
corresponding dynamic strategy 20,20DLC . Between 10,30LC and 10,30DLC , the
difference, however, is smaller than $50,000. The results are similar for ETL
estimates with the lifecycle strategy faring slightly better than the dynamic strategy
for both sets of trials. It is also to be noted that the dynamic strategy outperforms the
100% stocks strategy in terms of VaR and ETL estimates for both sets of trials.
222
Table 7.3: VaR Estimates for Different Asset Allocation Strategies
Asset Allocation Strategy
VaR at Different Confidence Levels ETL at 95% Confidence Level
99% 95% 90%
Panel A Dynamic ( 20,20DLC ) 275,914 461,640 607,872 344,437 Lifecycle ( 20,20LC ) 375,810 486,156 578,814 417,804 100% Stocks 271,458 447,330 592,348 337,980 Balanced 361,326 505,209 597,506 422,350
Panel B Dynamic ( 10,30DLC ) 274,968 444,468 599,673 340,901 Lifecycle ( 10,30LC ) 321,875 468,598 581,526 377,114 100% Stocks 274,657 443,251 595,398 339,980 Balanced 369,362 501,541 599,863 423,124
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Yet one would be reluctant to declare lifecycle funds to be the preferred investment
strategy even under the unreasonable assumption that investors care only about the
zone of extremely adverse wealth outcomes (below 90% VaR in this case). This is
because the balanced fund produces better 95% VaR estimates than both 20,20LC and
10,30LC . In terms of 99% VaR estimate, the balanced fund outperforms 10,30LC but
underperforms 20,20LC . When we consider 95% ETL, the balanced fund produces
estimates that are higher than both 20,20LC and 10,30LC . These results suggest that if
the retirement plan investors are concerned about improving the floor level of
possible wealth outcomes or protection from extreme downside risk, they are more
likely to be better off by investing in a static balanced fund rather than a
conventional lifecycle fund.
7.4 Conclusion
The evidence presented in this chapter exposes the inherent weakness of traditional
lifecycle investing for members of retirement plans. While pulling out of volatile
assets like stocks while the plan member nears retirement is generally accepted as
sensible investment advice, traditional lifecycle funds appear to implement this
strategy in a dogmatic manner that completely disregards the investors’ wealth
accumulation objectives. As we have demonstrated in this study, the mechanistic
switching strategy from growth to conservative assets following any age based rule
of thumb is clearly sub-optimal to a dynamic strategy that considers the actual
accumulation in the retirement account before switching assets. We propose a
specific dynamic asset allocation strategy where the switching of assets at any stage
is based on cumulative investment performance of the portfolio relative to the
224
investors’ set expectations at that stage. Unlike conventional lifecycle asset
allocation rules where the switching of assets is preordained to be unidirectional, this
dynamic strategy can switch assets in both directions: from aggressive to
conservative and vice versa. Using simple rules of stochastic dominance, we show
that such a dynamic lifecycle strategy vastly outperforms a conventional lifecycle
strategy in terms of accumulation outcomes over long horizon.
On comparing adverse outcomes in our trials, we find lifecycle strategies to do
better than the dynamic strategies only for ‘below 95%’ VaR outcomes. However,
the differences do not appear to be large enough to negate the appeal of dynamic
strategies to the average investor in view of their overall dominance over lifecycle
strategies. Even for these extremely adverse wealth outcomes in our trials, we find
that the static balanced asset allocation strategy generally does better than lifecycle
strategy. Therefore an investor whose sole concern is improving the floor level of
the extremely adverse wealth outcomes is likely to prefer investing in a balanced
fund rather than a lifecycle fund.
We have conducted a large number of trials in this study to capture different
possibilities about future asset class returns over the investment horizon of the
retirement plan investor. According to our results, the chance of the dynamic
strategy underperforming the lifecycle strategy at the end of such long horizon is
small (although not insignificant). Not only does the dynamic strategy produce
superior terminal wealth outcomes compared to the lifecycle strategy in a vast
majority (about 75% to 80%) of cases, it appears to have a fair chance of
outperforming an all equity strategy. In fact, the dynamic lifecycle strategy 10,30DLC
in this study which invests in an all equity portfolio for the first 30 years and then
adjusts asset allocation on an annual basis, seems to have more than even chance of
beating the strategy which invests in an all equity portfolio for the entire horizon.
225
The only authoritative past study to have considered a dynamic allocation rule with
performance feedback for DC plan investments is Blake et al. (2001). Unlike this
research, their results for the UK market indicate that the dynamic strategy (called
‘threshold strategy’ by the authors) underperforms the conventional lifecycle
strategy. This, we suspect, is caused by the relatively conservative upper and lower
thresholds they originally set in their study to prompt switching of assets. When the
sensitivity of the dynamic strategy to changes in thresholds (equivalent to ‘target’ in
this chapter) is tested by those authors, they observe that setting aggressive
thresholds clearly leads to superior performance. By using annualised holding period
return offered by the US stocks over last century as the performance target, which
can be considered as very aggressive, we find that the dynamic lifecycle strategy
dominates the conventional lifecycle strategy for vast majority of outcomes.
Therefore our results are not in disagreement with the results of Blake et al. (2001)
Apart from its relative superiority over other allocation strategies from a risk-return
perspective, the dynamic strategy proposed in this chapter has another distinct
appeal for the retirement plan investors from the behavioural angle. Since the
allocation is responsive to performance feedback, it may provide them some sense of
control over their investment decision on a continual basis. Without giving up the
basic tenet of lifecycle investing - seeking reduced volatility in the value of the
accumulation fund as one gets closer to retirement – the dynamic strategy
overcomes its limitations to a large extent.
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8. Conclusion
8.1 Scholarly Contributions
This dissertation makes several important contributions to the field of pension fund
investments specifically to the area of strategic asset allocation for individual plan
participants in DC plans. Asset allocation choices offered in DC plans is a relatively
new area of research interest but has been drawing significant attention from
academics in the last few years. In sharp contrast to the existing body of work, we
have investigated various asset allocation strategies using estimates of upside
potential and downside risk, both of which rely on a target based approach to
investing to assess return and risk. The essays, therefore, in addition to uncovering
new evidence and providing new insight into specific asset allocation issues within
DC plans, put forward an alternative framework for researchers to assess investment
outcomes for long horizon investors. The following key findings that emerge from
this thesis would be informative to the existing literature.
The thesis presents strong evidence in support of holding stocks by retirement plan
participants. While few other studies in the past have indicated the superiority of
equity over other assets in the long term with respect to the probability of
underperforming the latter, the risk of extremely adverse outcomes for different
asset allocation strategies has remained a territory largely unexplored. This study,
for the first time to the best of our knowledge, has demonstrated that the extremely
adverse outcomes for retirement plan investors have very little sensitivity to their
asset allocation choices. This is a significant finding which contradicts the
commonly held notion among academics and practitioners that the risk of disastrous
outcomes is significantly higher for more aggressive strategies. Moreover, by using
the LPM family of risk measures, we have shown that the preference for aggressive
strategies remains unchanged for investors with different degrees of risk aversion.
227
The existing literature on asset allocation in DC plans has mostly used data from the
USA or UK market in drawing conclusions. Using long run data for Australian asset
classes, we have shown that the default investment options for most of the highly
ranked funds may suffer from sub-optimal asset allocation choice for their members.
This can result in insufficient wealth outcomes for the vast majority of potential
retirees. The problem of inadequacy of retirement wealth, as many scholars have
pointed out in the past, is aggravated for female workers due to their relative
disadvantage in the labour market. This thesis has investigated the potential of a
gender sensitive asset allocation policy in reducing the gender gap in retirement
wealth accumulation. The results suggest that aggressive asset allocation strategies,
in addition to modest changes in default contribution rates, can have dramatic impact
on the wealth outcomes for female workers.
A major contribution of this dissertation emerges from its investigation of the role of
lifecycle funds in retirement plans. The current state of scholarship in this area is not
well developed with research studies mainly considering the relative standing of
lifecycle strategies vis-à-vis constant weight allocation strategies. One of the
important research questions we have explored in this thesis - the implication of
growing portfolio size over the horizon for portfolio choice decisions – provides
insight that is more fundamental to the understanding of lifecycle funds in the
context of retirement plans. In chapter 6 of this thesis, we have demonstrated that the
existence of portfolio size effect results in greater sensitivity of wealth outcomes to
asset allocation strategy adopted by the investors when they are nearer to retirement
than when they are farther from it. Thus lifecycle strategies may prove
counterproductive to the participant’s wealth accumulation objective since they
systematically switch away from stocks as the portfolio size becomes larger. This
explains findings of past research that lifecycle strategies tend to underperform fixed
weight strategies tilted towards equities. The sacrifice of portfolio growth
opportunity in the later part of the horizon by lifecycle strategies does not seem to be
228
compensated adequately in terms of reducing the risk of potentially adverse
outcomes at retirement.
Further to presenting new evidence to support past studies that find the lifecycle
asset allocation model inferior to many other static allocation models, our research
takes a major leap to address the shortcomings of conventional age-based lifecycle
investing in retirement plans. We propose a dynamic lifecycle model which
systematically incorporates past performance feedback in the asset allocation
decision. While dynamic strategies have been proposed and tested in the literature,
albeit sparingly, in chapter 7 of this thesis we have formally established the
stochastic dominance of the dynamic lifecycle strategy over deterministic lifecycle
strategies currently used by most retirement plans in terms of wealth accumulated at
the point of retirement. Moreover, the dynamic strategy is found to produce better
results compared to other strategies in achieving the target outcome of matching
historical returns offered by the stock market.
The current opinion of researchers on the subject of asset allocation over long
horizons is deeply divided. To support the long term case for holding more equity,
the proponents have mostly relied on the existence of mean reversion of returns, a
phenomenon which itself has been open to challenge. Without having to assume any
form of autocorrelation in historical returns on different asset categories, we are still
able to obtain results that broadly favour equity dominated allocation strategies for
individual participants. This, we believe, is mainly due to our use of target based
metrics that captures the DC plan participant’s perception of risk more effectively
than the measures of volatility often used by academics.
The evidence from different chapters, when synthesized, does not offer unqualified
support to the recommendation of holding an all equities portfolio by the DC plan
participant till retirement. Nor do we find any justification for deterministic lifecycle
switching of assets (from stocks to fixed income) for participants approaching
229
retirement. The results suggest that a dynamic lifecycle strategy that initially invests
heavily in equities but later uses performance feedback in switching assets would be
able to produce superior wealth outcomes to those of conventional lifecycle
strategies while reducing the risk of extremely adverse outcomes compared to an all
equity strategy. In other words, by not giving away too much of the upside the
dynamic lifecycle strategy provides downside risk protection at a lower cost to the
investor.
8.2 Relevance
The findings of this thesis have important implications for retirement plan sponsors,
investors, and policymakers. Since there is overwhelming global evidence that a vast
majority of plan participants are enrolled in the default investment options of their
respective plans, it is vital that the plan sponsors prudently design the default option
to meet the participant’s investment objective. The essays in this dissertation provide
useful insights in evaluating the appropriateness of different asset allocation
strategies as default options in defined contribution plans. The same applies for
investors who make active asset allocation choices within their plans. Without being
prescriptive, the research findings suggest that aggressive asset allocation strategies
are more likely to bear fruitful investment outcomes for the retirement plan
participants.
Despite their intuitive appeal conventional lifecycle asset allocation strategies do not
appear to yield any significant advantage according to our results. In relation to the
most adverse outcomes, the risk reduction benefit offered by a lifecycle fund is at
least matched if not bettered by a static diversified balanced fund. However, the
dynamic strategy proposed in this dissertation addresses the shortcomings of the
conventional lifecycle strategy and appears to result in superior wealth outcomes.
The dynamic strategy adopts a significantly different approach from asset allocation
230
strategies currently offered within pension plans as it considers past performance
(relative to a preset accumulation target) as an important input in asset allocation
decision. These findings have an important bearing on portfolio choice decisions not
only for retirement plan participants but for all long horizon investors. Our evidence
indicates that practitioners need to consider a target based approach to design
lifecycle funds.
The issue of adequacy of retirement wealth is of overwhelming concern to
policymakers all over the globe. Any study that aims to throw light in this area
would potentially draw their interest. Although the topic of retirement income
adequacy is beyond the scope of our dissertation, it is informative to public policy in
at least two ways. First, the study highlights the importance of default options
offered by retirement plan providers in ensuring the economic well being of future
generation of retirees. In light of our evidence, policymakers may consider
instituting optimal default investment option for new participants in retirement
plans. At the very least, guidelines on default asset allocation could be included for
trustees of these plans to help them in discharging their fiduciary responsibilities.
Second, the current system in most countries has resulted in the gender gap in
retirement wealth accumulation. Following the suggestion of this thesis, gender-
sensitive defaults could be considered in addressing this long-standing problem.
8.3 Limitations & Avenues for Future Research
Five issues related to our study deserve further attention. First, our results,
undoubtedly, have been influenced by the large premium that stocks have enjoyed
historically over bonds and bills in the Australian and the US market. By using long
run data for these asset classes over a hundred years, we have attempted to ensure
that our results are not biased by returns for any asset class in a particularly
favourable (or unfavourable) period. Yet, as many commentators have observed,
231
even a century of data may be inadequate to predict the entire scope of future
possibilities. Analysing the impact of potential fall in the real equity premium on the
appropriateness of default investment choice in DC plans can be an area which
future research would do well to investigate.
Second, the simulation experiments in this dissertation do not consider the
possibility of autocorrelation in future returns for different asset classes. As
discussed elsewhere in this thesis, some researchers have observed negative
autocorrelation in stock returns and positive autocorrelation in returns for fixed
income securities. For example, if mean reversion in stock returns is correct, then
the all equity portfolio, however tempting it may appear over long horizons, may not
be the optimal portfolio to hold for the retirement plan investor. In this case,
sufficiently high returns in the past would drive down expected future returns from
the stock market and the investors may actually reduce their allocation to equities. It
would be a fruitful exercise to investigate how these variations in asset class returns,
claimed to be predictable by some scholars, alters the level of appropriateness of
various asset allocation strategies in DC plans.
Third, we have not considered wealth outside retirement plan in this thesis. This may
be an important factor in portfolio choice decision for individuals particularly at
higher levels of income distribution who have substantial level of savings outside
retirement accounts. For them, tax efficiency of the investments may be important
consideration. Differential tax treatment of income derived from stocks and fixed
income assets held outside the plan would influence allocating funds between these
asset classes within the plan. Other factors like home ownership and social security
benefits also deserve attention as this may exert significant influence on investment
policy pursued by investors in relation to their retirement plan contributions.
Fourth, the role of human capital in allocation of retirement plan assets holds
considerable appeal for future investigation. If indeed, for most members in the
232
retirement plans, human capital is perceived to be of low risk and earnings are
uncorrelated to the stock market, a propensity towards holding more stocks when
young than when old could be justified. However, true riskiness of human capital as
well as correlation of labour market earnings with returns from financial asset
categories are topics of ongoing debate among economists. Therefore, the sensitivity
of optimal asset allocation rules under different sets of assumptions about human
capital needs to be examined.
Finally, while we have assumed annual rebalancing of portfolios, the impact of
associated transaction costs has been ignored in our analysis. To the extent these
transaction costs differ between different asset allocation strategies, the results of
this study can be affected. For example, an all equity strategy with no rebalancing
cost would be at a relative advantage vis-à-vis other fixed weight strategies, lifecycle
strategies, or even the dynamic strategies discussed in this thesis, all of which
involve substantial transaction cost on account of rebalancing.
233
References
Acerbi, Carlo, 2004, Coherent representations of subjective risk aversion, in G. Szego, ed.: Risk Measures for the 21st Century (John Willey & Sons, Chichester).
Agnew, Julie, Pierluigi Balduzzi, and Annika Sunden, 2003, Portfolio choice and
trading in a large 401(k) Plan., American Economic Review 93, 193-215. Ameriks, John, and Stephen P. Zeldes, 2001, How do household portfolio shares
vary with age? Columbia University Unpublished Paper. Ang, James S., and Jess H. Chua, 1979, Composite measures for the evaluation of
investment performance, Journal of Financial and Quantitative Analysis 14, 361-384.
ARF Super Fund, 2006, Member Investment Choice Guide, (ARF Super). Available
at http://www.arf.com.au/files/1/PDS_MIC.pdf (Accessed on 01.03.2006) Arnott, Robert D., and Robert M. Lovell, 1993, Rebalancing: Why? When? How
often? Journal of Investing 2, 5-10. Arrow, Kenneth J., 1971. Essays in the Theory of Risk-Bearing. (Markham,
Chicago). Arshanapalli, Bala, T., Daniel Coggin, and William Nelson, 2001, Is fixed-weight
asset allocation really better? Journal of Portfolio Management 27, 27- 38. Arts, Bas, and Elena Vigna, 2003, A switch criterion for defined contribution
pension schemes, in Proceedings of the 13th International AFIR Colloquium (Maastricht).
Artzner, Philippe, Freddy Delbaen, Jean-Marc Eber, and David Heath, 1997,
Thinking coherently, Risk 10, 68-71. Artzner, Philippe, Freddy Delbaen, Jean-Marc Eber, and David Heath, 1999,
Coherent measures of risk, Mathematical Finance 9, 203-228. Australian Bureau of Statistics, 2004, Australian Social Trends, 2004, ABS,
Canberra. Australian Bureau of Statistics, 2005. Year Book Australia, 2005, ABS, Canberra.
234
Australian Bureau of Statistics, 2006. Year Book Australia, 2006, ABS, Canberra. Australian Prudential Regulation Authority, 1999, Superannuation Circular No.
II.D.1: Managing investments and investment choice, APRA, Canberra. Australian Prudential Regulation Authority, 2005, Annual Superannuation Bulletin,
APRA, Sydney. Baker, August J., Dennis E. Logue, and Jack S. Rader, 2005. Managing Pension
And Retirement Plans: A Guide for Employers, Administrators, and Other Fiduciaries (Oxford University Press, New York).
Bajtelsmit, Vickie L., Alexanadra Bernasek, and Nancy A. Jianakoplos, 1999,
Gender differences in defined contribution pension decisions, Financial Services Review 8, 1-10.
Balzer, Leslie A., 1994, Measuring investment risk: A review, Journal of Investing
3, 47-58. Balzer, Leslie A., 2005, Investment risk: A unified approach to upside and downside
returns, in Frank A. Sortino, and Stephen E. Satchell, eds.: Managing Downside Risk in Financial Markets (Elsevier Butterworth-Heinemann, Oxford).
Bateman, Hazel, 2003, Regulation of Australian Superannuation, Australian
Economic Review 36, 118-127. Bawa, Vijay S., 1975, Optimal rules for ordering uncertain prospects, Journal of
Financial Economics 2, 95-121. Bawa, Vijay S., 1978, Safety first, stochastic dominance, and optimal portfolio
choice, Journal of Financial and Quantitative Analysis 13, 255-271. Benari, Yoav, 1988, An asset allocation paradigm, Journal of Portfolio Management
14, 47-51. Benartzi, Shlomo, and Richard H Thaler, 2002, How much is investor autonomy
worth? Journal of Finance 57, 1593-1616. Benartzi, Shlomo, and Richard H. Thaler, 2001, Naive diversification strategies in
defined contribution saving plans, American Economic Review 91, 79-98. Benzoni, Luca, Pierre collin-Dufresne, and Robert S. Goldstein, 2004, Portfolio
choice over the life-cycle in the presence of trickle-down labour income,
235
Working Paper No. 11247, National Bureau of Economic Research, Cambridge, MA.
Bernasek, Alexandra, and Stephanie Shwiff, 2001, Gender, risk, and retirement,
Journal of Economic Issues 35, 345-356 Bernstein, Peter L., 1992, Capital Ideas: The Improbable Origins of Modern Wall
Street (The Free Press: New York) Beshears, John, James J. Choi, David Laibson, and Brigitte C. Madrian, 2006, The
Importance of default options for retirement savings outcomes: Evidence from the United States, Working Paper No. 12009, National Bureau of Economic Research, Cambridge, MA.
Blake, David, 2006, Pension Finance (John Wiley & Sons, Chichester). Blake, David, Alistair Byrne, Andrew Cairns, and Kevin Dowd, 2006, Default funds
in UK defined-contribution plans, Financial Analysts Journal 63, 42-51 Blake, David, Andrew J. G. Cairns, and Kevin Dowd, 2001, Pensionmetrics:
Stochastic pension plan design and value-at-risk during the accumulation phase, Insurance: Mathematics and Economics 29, 187-215.
Blake, David, Bruce N. Lehmann, and Allan Timmermann, 1999, Asset allocation
dynamics and pension fund performance, Journal of Business 72, 429-461. Bodie, Zvi, 1995, On the risk of stocks in the long run, Financial Analysts Journal
51, 18-22. Bodie, Zvi, and Dwight B Crane, 1997, Personal investing: Advice, theory, and
evidence, Financial Analysts Journal 53, 13-23. Bodie, Zvi, Robert C. Merton, and William F. Samuelson, 1992, Labor supply
flexibility and portfolio choice in a life cycle model, Journal of Economic Dynamics and Control 16, 427-449.
Bodie, Zvi, and William Samuelson, 1989, Labour supply flexibility and portfolio
choice, NBER Working Paper Series, 3043. Booth, Philip, and Yakoub Yakoubov, 2000, Investment policy for defined-
contribution pension scheme members close to retirement: An analysis of the “lifestyle” concept, North American Actuarial Journal 4, 1-19.
Bowman, Lisa, 2003, A matter of choice, www.MoneyManagement.com.au.
236
Boyle, Phelim P., 1977, Options: A Monte Carlo approach, Journal of Financial
Economics 4, 323-338. Brennan, Michael J., Eduardo S. Schwartz, and Ronald Lagnado, 1997, Strategic
asset allocation, Journal of Economic Dynamics and Control 21, 1377-1403. Bridgeland, Sally, 2002, Choices, choices, Pension Management Institute Trustee
Group News 3-5 Brinson, Gary P., Randolph Hood, and Gilbert L. Beebower, 1986, Determinants of
portfolio performance, Financial Analysts Journal 42, 39-44. Brown, C., 1994, The distribution of private sector superannuation by gender, age
and salary of members, Retirement Income Modelling Task Force Conference Paper 94/2, Retirement Income Modelling Task Force, Canberra.
Buetow, Gerald W Jr., Ronald Sellers, Donald Trotter, Elaine Hunt, and Willie A
Whipple Jr., 2002, The benefits of rebalancing, Journal of Portfolio Management 28, 23-32.
Burtless, Gary, 2003, What do we know about the risk of individual account
pensions? Evidence from industrial countries, American Economic Review 93, 354-359.
Butler, Kirt C., and Dale L. Domian, 1991, Risk, diversification, and the investment
horizon, Journal of Portfolio Management 17, 41-48. Byrne, Alistair, 2004, Employee saving and investment decisions in defined
contribution pension plans: Survey evidence from the UK, Pensions Institute Discussion Paper, London.
Cairns, Andrew J.G., David Blake, and Kevin Dowd, 2006, Stochastic lifestyling:
Optimal dynamic asset allocation for defined contribution pension plans, Journal of Economic Dynamics and Control 30, 843-877.
Campbell, John Y., 2003, Consumption-based asset pricing, in G. Constantinides,
M. Harris, and R. Stulz eds.: Handbook of the Economics of Finance, (North-Holland, Amsterdam)
Campbell, John Y., and Luis M. Viceira, 1999, Consumptions and portfolio
decisions when expected returns are time varying, Quarterly Journal of Economics 114, 433-495.
237
Campbell, John Y., and Luis M. Viceira, 2002. Strategic Asset Allocation: Portfolio Choice for Long-term Investors (Oxford University Press, New York).
Campbell, John Y., and Samuel B. Thomson, 2007, Predicting stock returns out of
sample: Can anything beat the historical average? in forthcoming Review of Financial Studies.
Canner, Niko, N. Gregory Mankiw, and David N Weil, 1997, An asset allocation
puzzle, The American Economic Review 87, 181-191. CARESuper, 2005, Super Member Guide, (CARE). Available at
http://www.caresuper.com.au/ (Accessed on 01.03.2006) Carlstein, Edward, 1986, The use of sub series values for estimating the variance of
a general statistic from a stationary sequence, Annals of Statistics 14, 1171-1195.
Cass, David, and Joseph Stiglitz, 1970, The structure of investor preferences and
asset returns, and separability in portfolio allocation: A contribution to the pure theory of mutual funds, Journal of Economic Theory 2, 122-160.
Chen, Andrew, and William Reichenstein, 1992, Taxes and pension fund asset
allocation, Journal of Portfolio Management 18, 24-27. Choi, James J., David Laibson, Brigitte C. Madrian, and Andrew Metrick, 2002.
Defined contribution pensions: Plan rules, participant decisions, and the path of least resistance, in James Poterba, ed.: Tax Policy and the Economy (MIT Press, Cambridge MA).
Choi, James J., David Laibson, Brigitte C. Madrian, and Andrew Metrick, 2003, For
better or for worse: Default effects and 401 (k) savings behavior, in David Wise, ed.: Perspectives in the Economics of Aging (University of Chicago Press, Chicago).
Cocco, Joao F., Francisco J. Gomes, and Pascal J. Maenhout, 2005, Consumption
and portfolio choice over the life cycle, Review of Financial Studies 18, 491-533.
Congressional Budget Office, 2004, The retirement prospects of the baby boomers,
Economic and Budget Issue Brief , Washington D.C. Construction and Building Industry Super, 2005, Investment Choice, (Cbus).
238
Cronqvist, Henrik, and Richard H. Thaler, 2004, Design choices in privatized social-security systems: Learning from the Swedish experience, American Economic Review 94, 424-428.
Davis, E. Philip, 1995. Pension Funds: Retirement-income Security, and Capital
Markets: An International Perspective (Oxford University Press, New York). Delorme, Luke, Alicia H. Munnell, and Anthony Webb, 2006, Empirical irregularity
suggests retirement risks, An Issue in Brief, Centre for Retirement Research at Boston College.
Dimson, Elroy, Paul Marsh, and Mike Staunton, 2002, Triumph of the Optimists:
101 Years of Global Investment Returns (Princeton University Press, Princeton).
Donath, Susan, 1998, The continuing problem of women’s retirement income, 7th
Australian Women’s Studies Association Conference (University of South Australia, Adelaide).
Dowd, Kevin, 2002. An Introduction to Market Risk Measurement (John Wiley &
Sons, Chichester). Dowd, Kevin, 2005. Measuring Market Risk (John Wiley & Sons, Chichester). Drew, Michael E., and Jon D. Stanford, Principal and agent problems in
superannuation funds, Australian Economic Review 36, 98-107. Drury, Barbara, 2005, Set and forget, Sydney Morning Herald, Online Edition,
October 18. Duffield, Jeremy, and Pat Burke, 2003, Lessons in member investment choice, 11th
Annual Colloquium of Superannuation Researchers (University of New South Wales, Sydney).
Dwyer, Peggy D., James H. Gilkeson, and John A. List, 2002, Gender differences in
revealed risk taking: Evidence from mutual fund investors. Economics Letters 76, 151-158.
Dybvig, Philip H., 1995, Duesenberry's ratcheting of consumption: Optimal dynamic consumption and investment given intolerance for any decline in standard of living, Review of Economic Studies 62, 287-313.
239
Effron, Brad, 1979, Bootstrap methods: Another look at the jackknife, Annals of Statistics 7, 1-26
Ellsberg, Daniel, 1961, Risk, ambiguity, and the Savage axioms, Quarterly Journal
of Economics 75, 643–669. Elton, Edwin. J., and Martin J. Gruber, 1974, The multi-Period consumption
investment problem and single period analysis, Oxford Economic Papers New Series 26, 289-301.
Elton, Edwin. J., and Martin J. Gruber, 1995. Modern Portfolio Theory and
Investment Analysis (John Wiley & Sons, New York). Elton, Edwin. J., and Martin J. Gruber, 2000, The rationality of asset allocation
recommendations, Journal of Financial and Quantitative Analysis 35, 27-42. Equipsuper, 2004, Personal Superannuation, (Equipsuper). Available at
http://www.equipsuper.com.au/downloads/pdf/PDS/EquipPersPDS_PlusSupp_1105.pdf (Accessed on 01.03.2006)
Exley, Jon, Shyam Mehta, Andrew Smith, and Jeroen van Bezooyen, 1997, Life
style strategies for Defined Contribution Pension Schemes, Group for Economic and Market Value Based Strategies (GEMS), Available: www.gemstudy.com (Accessed on October 17, 2005).
Fama, Eugene F., 1965, Random walks in stock market prices, Financial Analysts
Journal 21, 55-59. Fama, Eugene F., 1970, Efficient capital markets: A review of theory and empirical
work, Journal of Finance 25, 383- 417. Fama, Eugene F., and Kenneth R. French, 1988, Dividend yields and expected stock
returns, Journal of Financial Economics 22, 3-25. Feinberg, Phyllis, 2004, Lifestyle strategy grows as DC default option, Pensions &
Investments 32, 3. First State Super, 2004, First State Super Member Guide, (First State
Super).Available at http://www.firststatesuper.nsw.gov.au/pdf2/Publication_YourMemberGuide_0904.pdf (Accessed on 01.03.2006)
Fishburn, Peter, 1977, Mean-risk analysis with risk associated with below-target
returns, American Economic Review 67, 116-126.
240
Fry, Tim, Richard Heaney, and Warren Mckewon, 2007, Will investors change their
superannuation fund given the choice? Accounting and Finance 47, 267-283. Gallery, Gerry, Natalie Gallery, and Kerry Brown, 2004, Superannuation Choice:
The pivotal role of the default. option, Journal of Australian Political Economy 53, 44-66.
Gatti, James, and Larry Shirland, 2005, Max-min decision rule, long-run portfolio
allocation, and implications for time diversification, Working paper, University of Vermont.
Gerrans, Paul, and M.Clark-Murphy, 2004, Gender differences in retirement savings
decisions. Journal of Pension Economics & Finance 3, 145-164. Gibson, Roger C., 2000. Asset allocation: Balancing Financial Risk (McGraw Hill,
New York) Goetzmann, William N., 1990, Bootstrapping and simulation tests of long-term
stock market efficiency, PhD dissertation, Yale University. Gordon, Catherine D. and Kimberley A. Stockton, 2006, Funds for retirement: The
'life-cycle' approach, Research Report, Vanguard Investment Counselling & Research.
Goyal, Amit, and Ivo Welch, 2006, A comprehensive look at the empirical
performance of equity premium prediction, forthcoming in Review of Financial Studies
Graduate Careers Australia, 2005, Graduate starting salaries 'strong and stable',
GCA, Parkville. Greer, Boyce, 2004, The case for age-based lifecycle investing, Viewpoint
Investment Concepts White Paper, Fidelity Investments. Guo, Binbin and Max Darnell, 2005, Time diversification and long term asset
allocation, Journal of Wealth management 8, 65-76. Haberman, Steven, and Elena Vigna, 2002, Optimal investment strategies and risk
measures in defined contribution pension schemes, Insurance: Mathematics and Economics 31, 35-69.
Hagerman, Robert L., 1978, More evidence on the distribution of security returns,
Journal of Finance 33, 1213-1221.
241
Harlow, W.V., and Ramesh K. S. Rao, 1989, Asset pricing in a generalized mean-
lower partial moment framework: Theory and evidence, Journal of Financial and Quantitative Analysis 24, 285-312.
Haugen, Robert A., 2001, Modern Investment Theory (Prentice Hall, Upper Saddle
River). Health Super Fund, 2005, Product Disclosure Statement, (Health Super) Available at
http://www.healthsuper.com.au/pdfs/PDS_Final260805.pdf (Accessed on 01.03.2006)
Heath, Chip, and Amos Tversky, 1991, Preference and belief: Ambiguity and
competence in choice under uncertainty, Journal of Risk and Uncertainty 4, 5-28.
Hensel, Chris R., and D. Don Ezra, 1991, The importance of the asset allocation
decision, Financial Analysts Journal 47, 65–72. Hesta Super Fund, 2005, Product Disclosure Statement, (Hesta Super). Available at
http://www.hesta.com.au/files/documents/mem_book_app.pdf (Accessed on 01.03.2006)
Hibbert, John, and Philip Mowbray, 2002, Understanding investment policy choices
for individual pension plans, Pensions & Investments 8, 41-62. Hickman, Kent, Hugh Hunter, John Byrd, John Beck, and Will Terpening, 2001,
Life cycle investing, holding periods, and risk, Journal of Portfolio Management 27, 101-111.
Hicks, John R., 1962, Liquidity, Economic Journal 72, 787-802. Hill, Dana C.D., and Leann M. Tigges, 1995, Gendering welfare state theory: a cross
national study of women’s public pension quality, Gender and Society 9, 99-119
Ho, Kwok, Moshe Arye Milevsky, and Chris Robinson, 1994. Asset allocation, life
expectancy and shortfall, Financial Services Review 3, 109–126. Hodrick, Robert J., 1992, Dividend yields and expected stock returns: Alternative
procedures for inference and measurement, Review of Financial Studies 5, 357–386.
242
HostPlus Super, 2005, Member Guide, (HostPlus Super). Available at http://www.hostplus.com.au/pdfs/hostplus/MGuide.pdf (Accessed on 01.03.2006)
Iyengar, Sheena S., and Mark R. Lepper, 2000, When choice is demotivating: Can
one desire too much of a good thing? Journal of Personality and Social Psychology 79, 995-1006.
Jahnke, William, 1997, The asst allocation hoax, Journal of Financial Planning 10,
109-113. Jagannathan, Ravi, and Narayan R. Kocherlakota, 1996, Why should older people
invest less in stocks than younger people? Federal Reserve Bank of Minneapolis Quarterly Review Summer, 11-23.
Jefferson, Therese, 2005, Women and retirement incomes in Australia: A review,
Economic Record, 81, 273-291. Jensen, Michael C., 1968, The performance of mutual funds in the period 1945-
1964, Journal of Finance 23, 389-416. Johnston, Ken, Shawn Forbes, and John Hatem, 2001, A comparison of state
university defined benefit and defined contribution pension plans: A Monte Carlo simulation, Financial Services Review 10, 37-44.
Jorion, Philippe, 2000, Value at risk: The new benchmark for managing financial
risk (McGraw Hill, New York). Jorion, Philippe, and William N. Goetzmann, 1999, Global stock markets in the
twentieth Century, Journal of Finance 54, 953-980. Kahneman, Daniel, and Amos Tversky, 1979, Prospect theory: An analysis of
decision under risk, Econometrica 47, 263-291. Kaplan Daniel T., 1999, Resampling Stats in MATLAB, (Resampling Stats:
Arlington) Kennedy, Peter, 2003, A Guide to Econometrics (MIT Press, Cambridge, MA) Keynes, John M., 1936. The General Theory of Unemployment, Interest, and Money
(Macmillan, London).
243
Kim, Myung J., Charles R. Nelson, and Richard Startz, 1991, Mean reversion in stock prices? A reappraisal of the empirical evidence, Review of Economic Studies 58, 515-528.
Kim, Chang-Soo, and K. Matthew Wong, 1997, Asset allocation strategies for
personal pension contributions, Financial Practice and Education 7, 35-46. Künsch, Hans R., 1989, The jacknife and the bootstrap for general stationary
observations, Annals of Statistics 17, 1217-1241. Klemkosky, Robert C., 1973, The bias in composite performance measures, Journal
of Financial and Quantitative Analysis 8, 505-514. Kritzman, Mark P., 2000. Puzzles of Finance: Six Practical Problems and Their
Remarkable Solutions (John Wiley, New York). Kroll, Yoram, Haim Levy, and Harry Markowitz, 1984, Mean-variance versus direct
utility maximization, Journal of Finance 39, 47-61. Kryger, Tony, 1999, The risk of unemployment, Parliament of Australia Research
Note 16 (1998-99). Lamberton, D. McL., 1958. Share Price Indices in Australia (Law book Company,
Sydney). Laughhunn, Dan J., John W. Payne, and Roy Crum, 1980, Managerial risk
preferences for below-target returns, Management Science 26, 1238-1249. Leroy, Stephen F., 1973, Risk aversion and the Martingale property of stock prices,
International Economic Review 14, 436-446. Levy, Haim, 1994, Absolute and relative risk aversion: An experimental study,
Journal of Risk and Uncertainty 8, 289-307. Levy, Haim, and Harry M. Markowitz, 1979, Approximating expected utility by a
function of Mean and Variance, Journal of Finance 69, 308-317. Levy, Haim, and Allon Cohen, 1998, On the risk of stocks in the long run:
Revisited, Journal of Portfolio Management 24, 60-69 Lewellen, Jonathan, 2004, Predicting returns with financial ratios, Journal of
Financial Economics 74, 209-235
244
Libby, Robert, and Peter Fishburn, 1977, Behavioral models of risk taking in business decision: A survey and evaluation, Journal of Accounting Research 15, 272-292.
Lo, Andrew and A. Craig Mackinlay, 1988, Stock market prices do not follow
random walks: Evidence from a simple specification test, Review of Financial Studies 1, 41-66.
Loewenstein, George, 2000, Emotions in economic theory and economic behavior,
American Economic Review 90, 426-432. Ludvik, Peter, 1994, Investment strategy for defined contribution plans, in the 4th
AFIR International Colloquium (Orlando). Lynch, Anthony, and Sinan Tan, 2004, Labor income dynamics at business-cycle
frequencies, Working Paper No. 11010, National Bureau of Economic Research, Cambridge, MA.
Maddala, G.S., 2002, Introduction to Econometrics (John Wiley & Sons,
Chichester). Madrian, Brigitte C., and Dennis F. Shea, 2001, The power of suggestion: Inertia in
401(k) participation and savings behavior, Quarterly Journal of Economics 116, 1149-1187.
Malkiel, Burton G., 1996. A Random Walk Down Wall Street: The Time Tested
Strategy for Successful Investing (W.W.Norton, New York). Mao, James C.T., 1970, Models of capital budgeting, E-V vs. E-S, Journal of
Financial and Quantitative Analysis 5, 657-676. Markowitz, Harry, 1952, Portfolio Selection, Journal of Finance 7, 77-91. Markowitz, Harry, 1959. Portfolio Selection: Efficient Diversification of Investment
(John Wiley & Sons, New York). McEnally, Richard W., 1985, Time Diversification: Surest Route to Lower Risk?
Journal of Portfolio Management 11, 24-26. Mehra, Rajnish, and Edward C. Prescott, 1985, The equity premium: A puzzle,
Journal of Monetary Economics 15, 145-61. Merrill, Craig, and Steven Thorley, 1996, Time diversification: Perspectives from
option pricing theory, Financial Analysts Journal 53, 13-19.
245
Merton, Robert C., 1992, Lifetime portfolio selection under uncertainty: The
continuous-time case, Review of Economics and Statistics 51, 247-257. Merton, Robert C., 1971, Optimal consumption and portfolio rules in a continuous-
time model, Journal of Economic Theory 3, 373-413. Merton, Robert C., 1992, Continuous-Time Finance (Blackwell, Malden). Messina, Joseph, 2005, An evaluation of value at risk and the information ratio (for
investors concerned with downside risk), in Frank A. Sortino, and Stephen E. Satchell, eds.: Managing Downside Risk in Financial Markets: Theory, Practice and Implementation (Elsevier Butterworth-Heinemann, Oxford).
Metropolis, Nicholas, and Stanislaw Ulam, 1949, The Monte Carlo method, Journal
of the American Statistical Association. 44, 335-341. Michaelides, Alexander G., and Francisco Gomes, 2005, Optimal life-cycle asset
allocation: Understanding the empirical evidence, Journal of Finance 60, 869-904.
Michaud, Richard, 1998. Efficient Asset Management: A Practical Guide to Stock
Portfolio Optimization and Asset Allocation (Harvard Business School Press, Boston).
Mitchell, Olivia S., and Stephen P. Utkus, 2004, Lessons from behavioral finance, in
Olivia S. Mitchell, and Stephen P. Utkus, eds.: Pension Design and Structure (Oxford University Press, New York).
Mottola, Gary R, and Stephen P Utkus, 2005, Life-cycle funds mature: Plan sponsor
and participant adoption, Vanguard Centre for Retirement Research 20, 1-14.
MTAA Superannuation Fund, 2006, Member Investment Choice Handbook,
(MTAA). Available at http://www.mtaasuper.com.au/docs/MICHandbook.pdf (Accessed on 01.03.2006)
Nawrocki, David N, 1999, A brief history of downside risk measures, Journal of
Investing 8, 9-25. Newey, Whitney K., and Kenneth D. West, 1987, A simple, positive semi-definite,
heteroskedasticity and autocorrelation consistent covariance matrix, Econometrica 55, 703–708.
246
Non-Government Schools Superannuation Fund, 2005, Product Disclosure
Statement, (NGS Super). Available at http://www.ngssuper.com.au/html/acrobat/pdf/ProductDisclosureStatementforParticipatingEmployersandMembers.pdf (Accessed on 01.03.2006)
Oberuc, Richard E., 2004, Dynamic Portfolio Theory and Management: Using
Active Asset Allocation to Improve Profits and Reduce Risk (McGraw-Hill, New York).
Officer, Robert. R., 1989, Rates of return to shares, bond yields and inflation rates:
A historical perspective, in Ray Ball, Philip Brown, Frank J. Finn, and Robert R. Officer, eds.: Share Markets and Portfolio Theory (University of Queensland Press, St. Lucia).
Olsberg, Diana, 2004, Women and superannuation: Still Ms…ing out, Journal of
Australian Political Economy 53, 161-177. Olsen, Robert A., 1997, Investment risk: The experts' perspective, Financial
Analysts Journal 53, 62-66. Palme, Martin, Annika Sunden, and Paul Soderlind, 2005, Investment Choice in the
Swedish Premium Pension Plan, Working Paper, Centre for Retirement Research at Boston College.
Pensions Regulator, The, 2005, Guidance from the Pension Regulator, Brighton,
UK. Perold, Andre F., and William F. Sharpe, 1988, Dynamic strategies for asset
allocation, Financial Analysts Journal 44, 16-27. Picoult, Evan, 1998, Calculating value-at-risk with Monte Carlo simulation, in
Bruno Dupire, ed.: Monte Carlo: Methodologies and Applications for Pricing and Risk Management (Risk, London).
Platinga, Auke, and Sebastian de Groot, 2005, Preference functions and risk-
adjusted performance measures, in Frank Sortino, and Stephen E. Satchell, eds.: Managing Downside Risk in Financial Markets (Elsevier Butterworth-Heinemann, Oxford).
Plaxco, Lisa M., and Robert D. Arnott, 2002, Rebalancing a global policy
benchmark, Journal of Portfolio Management 28, 9-22.
247
Poterba, James M., and Lawrence H. Summers, 1988, Mean reversion in stock prices: Evidence and implications, Journal of Financial Economics 22, 27-59.
Poterba, James M., and David Wise, 1996, Individual financial decisions in
retirement saving plans and the provision of resources for retirement, Working Paper No. 5762, National Bureau of Economic Research, Cambridge, MA.
Poterba, James M., Joshua Roth, Steven Venti, and David Wise, 2006, Lifecycle
asset allocation strategies and the distribution of 401 (k) retirement wealth, Working Paper No. 11974, National Bureau of Economic Research, Cambridge, MA..
Poterba, James M., and Andrew Samwick, 2001, Household portfolio allocations
over the lifecycle, in S. Ogura, T. Tachibanaki, and D. Wise, eds.: Aging Issues in U.S. and Japan (University of Chicago Press, Chicago).
Preston, Alison, and Siobhan Austen, 2001, Women, superannuation, and the SGC,
Australian Bulletin of Labour 27, 272-95. Pratt, John W., 1964, Risk aversion in the small and in the large, Econometrica 32,
122-136. Quenouille, M.H., 1956, Notes on bias in estimation, Biometrika 43, 353-360. Quirk, James P., and Rubin Saposnik, 1962, Admissability and measurable utility
functions, Review of Economic Studies 29, 140-146. Rabin, Matthew, 2000, Risk aversion and expected-utility theory: A calibration
theorem, Econometrica 68, 1281-1292. Rabin, Matthew, and Richard H. Thaler, 2001, Anomalies: Risk aversion, Journal of
Economic Perspectives 15, 219-232. Radcliffe, Robert C., 1997, Investment: Concepts, Analysis, Strategy (Addison-
Wesley, Reading). Read, Daniel, and George Lowenstein, 1995, Diversification bias: Explaining the
discrepancy in variety seeking between combined and separated choices, Journal of Experimental Psychology: Applied 1, 34-49.
Retail Employees Superannuation Trust, 2005, Personal Superannuation Member
Guide, (REST).
248
Richardson, Matthew and Tom Smith, 1991, Tests of financial models in the
presence of overlapping observations, Review of Financial Studies 4, 227–254.
Richardson, Sue, 2006, Unemployment in Australia, National Institute of Labour
Studies Discussion Paper. Roy, Andrew D., 1952, Safety first and the holding of assets, Econometrica 20, 431-
449. Rosenman, Linda, and Sharon Winocur, 1994, Women’s work patterns and the
impact upon provisions for retirement, in Economic Planning and Advisory Council (EPAC) & Office for the Status of Women (OSW), eds.: Women and Superannuation: EPAC Background Paper no 41, Commonwealth of Australia, Canberra, 95-104.
Rubinstein, Mark E., 1973, A comparative statics analysis of risk premiums, The
Journal of Business 46, 605. Samuelson, Paul A., 1963, Risk and uncertainty: A fallacy of large numbers,
Scientia 98, 108-113. Samuelson, Paul A., 1965, Proof that properly anticipated prices fluctuate randomly,
Industrial Management Review 6, 41-49. Samuelson, Paul A., 1969, Lifetime portfolio selection by dynamic programming,
Review of Economics and Statistics 51, 239-246. Samuelson, Paul A., 1989, The judgment of economic science on rational portfolio
management: Timing and long-horizon effects, Journal of Portfolio Management 16, 4-12.
Samuelson, Paul A., 1994, The long-term case for equities, Journal of Portfolio
Management, 21, 15-24. Savage, Leonard J., 1951, The theory of statistical decision, Journal of the American
Statistical Association 46, 55–67. Scott, Jason, 2002, Outcomes-based investing with efficient Monte Carlo
simulation, in Olivia S. Mitchell, Zvi Bodie, P. Brett Hammond, and Stephen Zeldes., eds.: Innovations in Retirement Financing (University of Pennsylvania Press, Philadelphia).
249
Sharp, Rhonda, 1995, Women and superannuation: Super bargain or raw deal, in Anne Edwards and Susan Magarey eds.: Women in a Restructuring Australia: Work and Welfare (Allen & Unwin, Crows Nest)
Sharpe, William F., 1966, Mutual Fund Performance, The Journal of Business 39,
119-138. Shiller, Robert, 2003, Social security and individual accounts as elements of overall
risk-sharing, American Economic Review 93, 343-347. Shiller, Robert, 2005a, The life-cycle personal accounts proposal for social security:
An evaluation, National Bureau of Economic Research Working Paper No. 11300.
Shiller, Robert, 2005b, Life-Cycle portfolios as government policy, The Economists'
Voice 2, Article 14. Siegel, Frederick W., and Jr. James P. Hoban, 1982, Relative Risk Aversion
Revisited, Review of Economics and Statistics 64, 481-487. Siegel, Jeremy J., 1992, The equity premium: Stock and bond returns since 1802,
Financial Analysts Journal 48, 28-38. Siegel, Jeremy J., 2003, Stocks for the Long Run, The Definitive Guide to Financial
Market Returns and Long-term Investment Strategies (McGraw Hill, New York).
Simon, Herbert A., 1955, A behavioral model of rational choice, Quarterly Journal
of Economics 69, 99-118. Simonson, Itamar, 1990, The effect of purchase quantity and timing on variety-
seeking behavior, Journal of Marketing Research 27, 150-162. Sortino, Frank, Robert van der Meer, and Auke Platinga, 1999, The Dutch triangle,
Journal of Portfolio Management 26, 50-58. Sortino, Frank, and Lee N. Price, 1994, Performance measurement in a downside
risk framework, Journal of Investing 3, 59-64. Sortino, Frank, and Robert Van der Meer, 1991, Downside risk, Journal of Portfolio
Management 17, 27-32.
250
STA Super, 2005, Investment Choice Booklet, (Superannuation Trust of Australia). Available at http://www.stasuper.com.au/SiteDocuments/doc41226.pdf (Accessed on 01.03.2006)
Statman, Meir, and Hersh Shefrin, 2000, Behavioral portfolio theory, Journal of
Financial and Quantitative Analysis 35, 127-151. Sugden, Roger, 1985, Regret, recrimination and rationality, Theory and Decision 19,
77-99. Sunden, Annika, 2004, How do individual accounts work in the Swedish Pension
System? Issue in Brief 22, Centre for Retirement Research, Boston College. SunSuper, 2006, Investment Guide, (SunSuper). Available at
http://www.sunsuper.com.au/SiteDocuments/doc41226.pdf (Accessed on 01.03.2006)
SuperRatings, 2006, Fund ratings 2005/06, (SuperRatings). Szpiro, George G., 1986, Measuring risk aversion: An alternative approach, Review
of Economics and Statistics 68, 156-159. T.RowePrice,2006, T. Rowe Price Retirement Funds. Available at
http://www.troweprice.com/common/index3/0,3011,lnp%253D10106%2526cg%253D920%2526pgid%253D7592,00.html (Accessed on 06.01.2006)
Taylor, Richard, and Donald J. Brown, 1996, On the risk of stocks in the long run: A
note, Financial Analysts Journal 52, 69-71. TelstraSuper, 2005, Member Investment Choice, (Telstra Super). Available at
http://www.telstrasuper.com.au/pdf/mic_booklet.pdf (Accessed on 01.03.2006)
Thaler, Richard H. and J. Peter Williamson, 1994, College and university
endownment funds: Why not 100% equities? Journal of Portfolio Management 21, 27-37.
Thompson, Merrin, 1999, Women and retirement incomes in Australia: Social
rights, industrial rights and property rights, Social Policy Research Centre Discussion Paper No. 98.
Thorley, Steven R, 1995, The time-diversification controversy, Financial Analysts
Journal 51, 68-76.
251
Tobin, James, 1958, Liquidity preference as behavior towards risk, Review of
Economic Studies 25, 65-86. Treynor, Jack L., 1965, How to rate management of investment funds, Harvard
Business Review 43, 63-75. Tversky, Amos, and Daniel Kahneman, 1991, Loss aversion in riskless choice: A
reference dependent model, Quarterly Journal of Economics 106, 1039-61. UniSuper, 2005, Product Disclosure Statement, (UniSuper). Available at
http://www.unisuper.com.au/booklets/unis000008.pdf (Accessed on 01.03.2006)
Utkus, Stephen P., 2005, Selecting a default fund for defined contribution plan,
Vanguard Centre for Retirement Research 14, 1-19. Vanguard Center for Retirement Research, 2006, How America saves 2006: A report
on Vanguard 2005 defined contribution plan data, The Vanguard Group. Vanguard, 2006, Target Retirement Funds Prospectus, (Vanguard). Available:
http://flagship4.vanguard.com/VGApp/hnw/FundsProspectusReports?FundId=0306&FundIntExt=INT (Accessed on 07.01.2006)
Viceira, Luis M., 2001, Optimal portfolio choice for long-horizon investors with
nontradable labor income, Journal of Finance 56, 433-470. Viceira, Luis M., 2007, Life-cycle funds, manuscript, Harvard University. VisionSuper, 2005, Product Disclosure Statement, (Vision Super). Available at
http://www.visionsuper.com.au/Documents/Superplans.pdf (Accessed on 01.03.2006)
Vittas, Dimitri, 1992, The simple(r) algebra of pensions, mimeo, World Bank,
Washington DC. Wald, Abraham, 1950, Statistical Decision Functions (John Wiley & Sons, New
York). Weaver, R. Kent, 2004, Design and implementation issues in Swedish individual
pension accounts, Social Security Bulletin 65, 38-56. Weller, Christian E., 2002, Retirement out of reach, Economic Policy Institute
Briefing Paper 129, Washington D.C.
252
Westscheme, 2005, Member Handbook, (Westscheme). Available at
http://www.westscheme.com.au/general/pubs/publications/WESTSCHEMEPDS130206.pdf (Accessed on 01.03.2006)
Yoshiba, Toshinao, and Yasuhiro Yamai, 2002, Comparative analyses of expected
shortfall and VaR(2): Expected utility maximisation and tail risk, Monetary and Economic Studies 20, 95-116..
253
APPENDIX A: Real Return Data for Australian and US Asset classes
1900-2004 Data
I. Descriptive Statistics
Australian
Stocks US Stocks Australian
Bonds US
Bonds Bills Mean 0.090952 0.084571 0.022667 0.026000 0.007238 Median 0.110000 0.110000 0.020000 0.010000 0.010000 Maximum 0.510000 0.570000 0.620000 0.960000 0.180000 Minimum -0.380000 -0.380000 -0.270000 -0.350000 -0.160000 Standard Deviation 0.177426 0.203049 0.133627 0.183185 0.055131
Skewness -0.247029 -0.184646 0.663710 1.704195 -0.058101 Kurtosis 2.972500 2.575718 6.086779 9.529573 4.319608 Observations 105 105 105 105 105
II. Correlation Matrix (3 Asset Class)
Australian Stocks
Australian Bonds
Bills
Australian Stocks
1.0000
0.3389
0.2524
Australian
Bonds
0.3389
1.0000
0.6344
Bills
0.2524
0.6344
1.0000
III. Correlation Matrix (5 Asset Class)
Australian Stocks
US Stocks
Australian Bonds
US Bonds
Bills
Australian Stocks
1.0000
0.8217
0.3389
0.3010
0.2524
US Stocks
0.8217
1.0000
0.2698
0.6185
0.1252
Australian Bonds
0.3389
0.2698
1.0000
0.7403
0.6344
US Bonds
0.3010
0.6185
0.7403
1.0000
0.3787
Bills
0.2524
0.1252
0.6344
0.3787
1.0000
254
1947-2004 Data
I. Descriptive Statistics
Australian Stocks US Stocks
Australian Bonds US Bonds Bills
Mean 0.080517 0.089828 0.010862 0.021897 0.006207 Median 0.105000 0.120000 0.020000 0.020000 0.015000 Maximum 0.510000 0.510000 0.270000 0.340000 0.090000 Minimum -0.380000 -0.360000 -0.270000 -0.210000 -0.160000 Standard Deviation 0.210642 0.174170 0.114682 0.130914 0.050881 Skewness -0.140441 -0.233371 -0.464026 0.229548 -0.988497 Kurtosis 2.416410 2.804259 3.133224 2.346402 4.467748 Observations 58 58 58 58 58
II. Correlation Matrix (3 Asset Class)
Australian Stocks
Australian Bonds
Bills
Australian Stocks
1.0000
0.3237
0.2113
Australian Bonds
0.3237
1.0000
0.6406
Bills
0.2113
0.6406
1.0000
III. Correlation Matrix (5 Asset Class)
Australian Stocks
US Stocks
Australian Bonds
US Bonds
Bills
Australian Stocks
1.0000
0.4887
0.3237
0.2140
0.2113
US Stocks
0.4887
1.0000
0.2064
0.1679
0.0650
Australian Bonds
0.3237
0.2064
1.0000
0.6446
0.6406
US Bonds
0.2140
0.1679
0.6446
1.0000
0.3179
Bills
0.2113
0.0650
0.6406
0.3179
1.0000
255
1975-2004 Data
I. Descriptive Statistics
Australian Stocks US Stocks
Australian Bonds US Bonds Bills
Mean 0.109333 0.112667 0.049667 0.049000 0.032000 Median 0.115000 0.125000 0.090000 0.035000 0.030000 Maximum 0.510000 0.520000 0.270000 0.340000 0.090000 Minimum -0.230000 -0.280000 -0.190000 -0.180000 -0.060000 Standard Deviation 0.205358 0.233533 0.111308 0.142499 0.037637 Skewness 0.084032 0.067832 -0.414026 0.098392 -0.588575 Kurtosis 2.081935 1.910695 2.546260 2.025290 3.133234 Observations 30 30 30 30 30
II. Correlation Matrix (3 Asset Class)
Australian Stocks
Australian Bonds
Bills
Australian Stocks
1.0000
0.0542
-0.0671
Australian
Bonds
0.0542
1.0000
0.4207
Bills
-0.0671
0.4207
1.0000
III. Correlation Matrix (5 Asset Class)
Australian Stocks
US Stocks
Australian Bonds
US Bonds
Bills
Australian Stocks
1.0000
0.8519
0.0542
0.0178
-0.0671
US Stocks
0.8519
1.0000
-0.0601
0.3518
-0.1430
Australian Bonds
0.0542
-0.0601
1.0000
0.6102
0.4207
US Bonds
0.0178
0.3518
0.6102
1.0000
0.2041
Bills
-0.0671
-0.1430
0.4207
0.2041
1.0000
256
APPENDIX B: Nominal Returns Data for Australian Asset Classes (1900-2004)
1. Descriptive Statistics
Stocks Bonds Bills Mean 0.1329 0.0596 0.04629 Median 0.1400 0.0500 0.04000 Maximum 0.6700 0.5400 0.17000 Minimum -0.2700 -0.1900 0.01000 Standard Deviation 0.1800 0.1149 0.04022
Skewness 0.1677 0.6740 1.5183 Kurtosis 3.4080 4.9474 4.7790 Observations 105 105 105
2. Correlation Matrix
Stocks
Bonds
Bills
Stocks 1.000 0.199 0.044 Bonds 0.199 1.000 0.297 Bills 0.044 0.297 1.000
257
APPENDIX C: Nominal Returns Data for US Asset Classes (1900-2004)
1. Descriptive Statistics
Stocks Bonds Bills Mean 0.1162 0.05276 0.04057 Median 0.1400 0.04000 0.04000 Maximum 0.5800 0.40000 0.15000 Minimum -0.4400 -0.09000 0.00000 Standard Deviation 0.2000 0.08215 0.02875
Skewness -0.3177 1.5267 0.7212 Kurtosis 2.7793 6.6831 4.1836 Observations 105 105 105
2. Correlation Matrix
Stocks
Bonds
Bills
Stocks 1.000 0.102 -0.083 Bonds 0.102 1.000 0.213 Bills -0.083 0.213 1.000