Portfolio Performance Evaluation - Infoserver |...

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Diplomarbeit

zur Erlangung des akademischen Grades

Magister rerum socialium oeconomicarumque

(Mag. rer. soc. oec.)

Portfolio Performance Evaluation

Institut für Betriebswirtschaftslehre

Universität Wien

Studienrichtung: Internationale Betriebswirtschaft

o. Univ.-Prof. Dr. Josef Zechner

eingereicht von

Johann Aldrian

(Matr.nr.: 9501942)

Wien, 8. September 2000

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Eidesstattliche Erklärung

Ich erkläre hiermit an Eides statt, daß ich die vorliegende Arbeit selbständig und

ohne Benutzung anderer als der angegebenen Hilfsmittel angefertigt habe. Die

aus fremden Quellen direkt oder indirekt übernommenen Gedanken sind als

solche kenntlich gemacht.

Die Arbeit wurde bisher in gleicher oder ähnlicher Form keiner anderen

Prüfungsbehörde vorgelegt und auch nicht veröffentlicht.

Wien, 8. September 2000 ……………………….

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PortfolioPerformanceEvaluation

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TABLE OF CONTENT

1. INTRODUCTION 1

1.1. THE RELEVANCE OF PORTFOLIO-MANAGEMENT-EVALUATION 11.2. STRUCTURE OF THIS MASTER'S THESIS 2

2. TRADITIONAL MEASURES OF PORTFOLIO PERFORMANCEEVALUATION AND ITS IMPLICATIONS. 4

2.1. FUNDAMENTALS 42.1.1. THE CONCEPT OF EFFICIENT MARKETS 42.1.2. RETURN AND RISK AS DETERMINANTS OF THE MARKET 62.2. PORTFOLIO MANAGEMENT 82.2.1. ACTIVE PORTFOLIO MANAGEMENT 92.2.2. PASSIVE PORTFOLIO MANAGEMENT 122.2.3. WHAT INDEX TO USE 132.3. TRADITIONAL MEASURES OF PERFORMANCE 152.3.1. SECURITY-MARKET-LINE BASED PERFORMANCE MEASURES 152.3.2. CAPITAL-MARKET-LINE BASED PERFORMANCE MEASURES 182.4. WEAKNESSES OF TRADITIONAL MEASURES OF PERFORMANCE 21

3. ALTERNATIVE MEASURES OF PORTFOLIO PERFORMANCE 24

3.1. THE FAMA AND FRENCH THREE & FIVE FACTOR APT-MODEL 243.2. THE GRINBLATT & TITMAN NO BENCHMARK MODEL 273.3. THE SHARPE APPROACH: ASSET ALLOCATION AND STYLE ANALYSIS 313.3.1. DETERMINANTS OF THE MODEL 323.3.2. THE PROCEDURE 353.3.3. CRITICISMS AND IMPROVEMENTS 37

4. APPLIED STYLE ANALYSIS 40

4.1. THE DATA 404.1.1. AUSTRIAN INVESTMENT FUNDS 404.1.2. ASSET CLASSES 454.1.2.1. Equity Asset Classes 454.1.2.2. Fixed Income Asset Classes 474.1.2.3. Statistical Properties of the Employed Asset Classes 48

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4.2. DETERMINING THE FUNDS STYLE AND SELECTION RETURN 504.2.1. THE FUNDS AVERAGE COMPOSITION 504.2.2. ROLLING A WINDOW 554.2.3. COMPARISON OF REAL AND ESTIMATED STYLE WEIGHTS 614.2.4. CONTRIBUTION THROUGH SELECTION 634.2.5. SUMMARY OF FINDINGS 704.3. SOME ADDITIONAL INSIGHT USING US MUTUAL FUNDS 71

5. CONCLUSION AND FINAL REMARKS 79

DATA APPENDIX

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Abbreviations

Con: Constantia Privat Invest Fund

A 4: Appollo 4 Fund

Gen: Generali Mixfund

Rai: Raiffeisen Global Mix Fund

Ers: SparInvest Fund

Spa: Global Securities Trust Fund

EVALUE: European Value Stock Index Net Dividends Reinvested

EGROWTH: European Growth Stock Index Net Dividends Reinvested

ESTAND: European Composite Stock Index Net Dividends Reinvested

NAVALUE: North American Value Stock Index Net Dividends Reinvested

NAGROWTH: North American Growth Stock Index Net Dividends Reinvested

NASTAND: North American Composite Stock Index Net Dividends Reinvested

JPSTAND: Japanese Composite Stock Index Net Dividends Reinvested

ATX: Austrian Trading Index (Composite Stock Index)

G7GOV: Government Bond Index of the 7 Largest European Countries

API: Austrian Performance Index (Government Bond Index Interest Reinvested)

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1. Introduction

1.1. The Relevance of Portfolio-Management-Evaluation

Whenever an investor employs resources, be it in the form of hiring employees

for his company, establishing a charitable fund or investing money in an

investment fund he will want to measure the performance of his investment. In

any of the above named cases the investor will establish an evaluation system

that provides him with the feedback needed to determine whether the investment

generates the predetermined utility. In the case of the employee the investor will

demand from him the accomplishment of the agreed on work objectives. From

the manager of the charity fund he will demand evidence that the money was not

spent lavishly. Both times he will bind the executing subjects to some kind of

charta which was defined in advance. In the very same manner he will consider

the evaluation of the investment manager. The investment manager will be

bound to the investment policy and subject to a constant evaluation of his

achievements. His achievement will be the return on the capital the investor

provided.

At this point one will have to determine whether the achieved return was good or

poor and whether it was skill or luck?

This is the punchline investors are are always facing when entrusting their money

to an investment manager. The evaluation now boils down to two main

questions. The first question the investor will want to address is the question of

performance. What is good and what is poor performance and where is the line

in between - the benchmark - and what to take as the benchmark. Should we

employ the performance of a riskless asset e.g. a T-bond, a generic like the S&P

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500 or other portfolio manager's performance as the benchmark? Unfortunately,

these simplistic measures of performance generally do not produce the desired

degree of specification. The investor will also want to find out whether his

investment manager is skillful of fortunate through an evaluation process, which

can be applied to his manager and thereby finding what kind of constranints may

help to get the investment manager to achieve the goal set by the investor. In

answering how to destinct between a skilled and unskilled portfolio manager and

what is good and poor performance, I will address the question central to this

master's thesis. Can Sharpe's asset allocation model and resulting style analysis

be a useful tool in assessing an investment portfolio's performance and the level

of skill of its investment manager?

1.2. Structure of this master's thesis

The first chapter is devoted to the definition of the problem and its justification in

order to give the reader a general overview of this works content.

In chapter 2 CAPM implications on performance measurement are being

elaborated and conventional measures of performance are being discussed in a

critical context. The last part of Chapter 2 will emphasize on weaknesses and

critiques of traditional measures of performance. In Chapter 3 I will introduce

alternative measures of portfolio performance. The Fama & French Model, the

Grinblatt & Titman Model and Sharpe's Asset Allocation and Style Analysis

Model will be described. The Sharpe Model will then be explained in further

detail, as it will be the core subject of this master's thesis.

Chapter 4 will comprehend a regression analysis according to Sharpe's Model. It

will be performed on 6 Austrian investment funds. The investment funds will be:

Raiffeisen Global Mix Fund

Appollo 4 Fund

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SparInvest Fund

Generali Mixfund

Global Securities Trust Fund

Constantia Privat Invest Fund

Through constrained quadratic programming the composition of the specific

funds will be determined and the performance of each of them evaluated. In the

end of this chapter the findings will be compared to traditional measures of

performance and its influence on rankings illustrated.

In Chapter 5 I will conclude the findings of this work and critically evaluate the

initially addressed question, whether Sharpe's portfolio evaluation model is a

good and useful model in assessing a portfolio's performance based on evidence

from Austrian and US investment funds.

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2. Traditional measures of portfolio performanceevaluation and its implications.

2.1. Fundamentals

The traditional evaluation of investment management is based on a few key

concepts. In many cases the framework therefore is provided by the CAPM. In

some other cases it is the risk return relationship of an individual portfolio, its total

risk, that provides the environment for portfolio performance evaluation. On this

basis the essential concepts will be explained in this chapter, as they will be

indirectly relevant in applying and explaining some investment management

evaluation tools.

2.1.1. The Concept of Efficient Markets

The efficient market concept assumes that all investors have free access to

currently available information about the future. All investors are capable of

processing the information as well as adjusting their holdings according to the

information appropriately.1 This concept guarantees that security prices fully

reflect the investment value of the security. This further implies that there exists

no possibility to generate abnormal return - in a systematic way - with generally

available information. Eugene Fama2 classified the efficient market hypothesis

into 3 forms:

The weak form of market efficiency is defined by Fama as reflecting all

historical prices in the value of a security. According to this definition it should be

impossible for a technical analyst to systematically make profits by looking at

past prices.

1 SHARPE, ALEXANDER, BAILEY (1998), p. 932 FAMA (1970), p. 383 - 417

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The semi-strong form of market efficiency is defined as incorporating all

publicly available information. This is the form currently assumed to hold,

although there is a discussion if maybe only the weak form of market efficiency

may hold.

The strong form of market efficiency is defined as including all publicly and

privately available information. If this form of market efficiency held true one

could in no circumstances make abnormal profits by using either of the three

above mentioned sources of information.

Market efficiency is of importance to CAPM, because one of its underlying

assumptions is the competitive investor. This means that prices of securities are

in equilibrium and the expected security return tomorrow based on the

information today will be zero. Security price changes are assumed to follow a

random walk, as positive "surprises" are assumed to be as likely as negative

"surprises". If a pattern can be found to detect mispriced securities on a

systematic basis, it would mean that returns are not random walk any more and

that CAPM would not hold and therefore evaluation measures based on CAPM

would be inaccurate.

The paradox that arises with the efficient markets hypothesis is that if there aren't

investors that do not believe in the efficient market hypothesis, efficient markets

can not exist. If information is free for all participants in the market than none of

the participants has an incentive to gather information. But if no one gathers

information, the market price can not reflect the information. This problem can be

overcome if the cost of gathering information (supporting a squad of analysts) is

the same as the excess return generated through their analysis.3 The short

discussion above indicated the importance of efficient markets on portfolio

management and in the same way on its evaluation.

3 SHARPE, ALEXANDER, BAILEY (1998), p. 96

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2.1.2. Return and Risk as Determinants of the Market

Return can be defined as the rate of change in the value of an asset in a defined

time interval. The mean return, which is interesting if one looks at the prices of an

investment at the beginning and the end of the investment horizon, covers

several time periods and can be measured geometrically or arithmetically. Using

geometric mean calculation is preferable when the "calculation basis" is changing

and has the additional advantage of being additive in every case. Arithmetic

mean calculation is useful when the "calculation basis" remains constant during

the observation period. Arithmetic mean computation returns the average

increase in wealth of a constant investment and does not regard reinvestments of

its proceeds. When analyzing financial time series the basis often varies and

proceeds are reinvested and thus making geometrical mean calculation more

suitable.

Risk is the uncertainty in what a security price - and in consequence the return -

will be at a certain point in the future. Another term would be volatility. Volatility is

equal to the statistical measure of standard deviation. Generally one uses

historical volatility when introducing risk into a financial model. There is also an

alternative way to determine volatility - calculating it implicitly by using the Black-

Scholes Formula.4 The Chicago board of trade provides several implied volatility

indexes for different commodity futures and options. This should help market

participants formulating their trading strategies.

The entire CAPM universe is described by risk and return where risk is

characterized through variance. Through different combinations of risk and

return, the combination of securities with different risk - return characteristics, an

investor can reach every point on the security market line.5 These two

determinants are positively correlated in the CAPM-world. The more risk one

takes the more "reward" he should expect. The linear relationship between

systematic risk and return is at the core of the CAPM. The graph on the next 4 HULL (1997), p. 2465 REILLY, BROWN (1997), p. 24

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page shows the relationship between risk-return and the derivation of the security

market line. The formula for the CAPM is:

[ ] jfMfj rrErrE β⋅−+= )()(

E(rj) = Average expected return of security (j)

r(f) = Average risk free rate (f)

E(rM) = Average return of the market (m)

β (j) = Sensitivity of the expected return of security (j) to changes in the expected

return of the market (m)

Figure 1: Capital Market Line, Security Market Line and the linear risk return relationship

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The relationship between beta and the expected return is known as the SML.

The slope of the line is given by (Rm-Rf), in other words the units of return over

the risk-free rate per unit of systematic risk.

This linear relationship shows that an investor can increase his expected return

by increasing the risk as according to CAPM securities with higher risk must have

a higher return in order to compensate the investor for the risk. This goes along

with the risk aversion assumption put forth in the CAPM. The question of utility

functions of investors will not be treated here but it should be mentioned that

investors are assumed to have convex indifference curves. This means that for

the more risk they take they demand an even higher return.6 (The marginal rate

of substitution, return for risk, increases as risk increases.)

Another important outcome of CAPM for the risk return relationship is that the

risk for which the investor can demand to be rewarded is the systematic risk of a

security as the unsystematic risk can be diversified away. This systematic risk is

reflected in a securities beta i.e. a securities co-movements with the market. The

beta reflects the systematic risk for which the investor can expected to be

rewarded for through return. Questions concerning the validity and the testability

of CAPM shall not be addressed in this work as they are of minor importance to

the central object of this work - the evaluation of portfolio management through

Sharpes' asset allocation and style analysis framework.

2.2. Portfolio Management

Portfolio management or in other words investment management is the process

by which money is managed.7 The way portfolios are managed has severely

changed over the last 100 years. Traditionally portfolio management was strongly

based on fundamental analysis of securities or assets which were to be included

6 FISCHER (1996), p. 40 - 437 SHARPE, ALEXANDER, BAILEY (1998), p. 792

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in the portfolio.8 Fundamental analysis researches the capabilities of a company

to generate future cash flows. This system was by far not as elaborate in terms of

mathematical analysis as it is performed in modern portfolio management. Also

the belief in the possibility of "beating the market" had more acceptance than

today. With the tremendous rise in the US equity market in the nineties the issue

of beating the index (e.g. S&P 500) has become more and more difficult.9 The

controversy over the possibility to outperform the market through active portfolio

management has been reinforced.

2.2.1. Active Portfolio Management

Active portfolio management aims to beat an index by detecting securities that

are under-priced. Securities are under-priced to a certain investor who takes an

active position because his view about the future, his forecast of the securities

price in the future, differs from that of the market. This in turn implies that an

investor or portfolio manager of this sort disregards the conclusion of CAPM that

securities are priced accurately. Active portfolio management is only worthwhile if

the additional return realized through active management is higher than the cost

of maintaining the necessary staff. Costs incurred through active management

are manager fees, analyst reimbursement and higher turnover of securities held

in the portfolio. Manager fees are typically in a range from 0.2 - 1.5 % of the

assets under management.10 Another cost an active fund is more prone of is the

potentially higher turnover of investment managers who, if not reaching their

predetermined returns, are fired quickly. Different styles and beliefs of different

managers will cause (conditioned by high "manager turnover) additional turnover

cost. The cost of turnover depends on the size of the trade and the liquidity of a

title.

8 comp. GRAHAM (1949)9 SORENSON, MILLER, SAMAK (1998), p. 1810 SORENSON, MILLER, SAMAK (1998), p 18

10

Size of Trade

Number of $100 $300 $500Portfolio Universe Stocks Million MillionMillion

Salornon Smith Barney large-cap /growth 50 36 bps 53 bps 64 bpsSalomon Smith Barney large-cap/value 50 26 37 44Salomon Smith Barney small-cap /growth 50 131 196 246Salomon Smith Barney small-cap /value 50 113 183 239S&P large-cap /growth 162 27 38 45S&P large-cap/value 338 27 34 44S&P small-cap /growth 234 136 187 226S&P small-cap /value 366 132 189 234Note: Costs estimated at a point in time using Salomon Smith Barney's impact-cost model.

Figure 2: Typical turnover cost for different trade sizes and different asset classes

Active managers can be categorized in three groups: market timers, sector

selectors and security selectors.

Market timers change the beta of their portfolio according to their forecast on how

the market will do.11 Market timers will increase the beta on their portfolio above

the beta of the market portfolio if their forecast is bullish. Securities with a higher

beta than the market will result in the higher appreciation of the specific security

than the appreciation of the market. The reverse will be true if their forecast is

bearish. There were multiple tests on market timing ability. Treynor and Mazuy

conducted the first study on market timing.12 They found that the management of

mutual funds did not exhibit any market timing ability.

11 ELTON, GRUBER (1992), p. 70812 TREYNOR , MAZUY (1966), p. 131 - 136

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Figure 3: Characteristic line for a mutual fund that has outguessed the market.

Mutual fund managers with market timing ability show above than average

performance through detecting when the market will be bullish and when it will be

bearish. This is essentially what the graph above shows.

Further studies on market timing abilities of mutual fund managers were

conducted, showing little evidence of successful market timing.13

Sector Selectors increase their exposure to a certain sector when they believe it

will perform above average in the future and decrease their exposure to a sector

when their belief is that it will under-perform. Sectors can be classified by

industries, products, or particular perceived characteristics like size, cyclical,

growth etc. The sector selection idea is very prominent in the investment

industry. Investment managers often specialize in sectors. The investor in turn

can choose from different "specialists" and from a portfolio of managers that he

13 IPPOLITO, (1993), p. 46

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considers most appropriate for his investment strategy. Sector selection

additionally exerts influence on the later on of discussed style analysis.

The third type of active manager is the security selector. Security selection is the

most traditional form of active portfolio management. By security selection the

investment manager tries to identify securities with higher expected returns than

suggested by the market. By identifying and getting exposure to them the active

manager will realize a higher than market performance if his judgment was right.

Security selection, like all active strategies, neglects the concept of equilibrium

prices on CAPM. There are numerous tests on the ability of active managers to

detect mispriced securities and through that generating excess returns. Excess

return is the return realized above the one with the same risk predicted by

CAPM. An early and notable study on the performance of mutual funds was

conducted by William Sharpe.14 He concluded that mutual funds did not show

better performance than the Dow Jones Industrial Index and that corollary mutual

fund managers did not have stock picking ability. Jensen15 also conducted a

study on mutual fund performance and confirmed the findings of Sharpe. There

was positive evidence found in favor of stock picking by Grinblatt & Titman.16

After all it remains still an open issue if stock-picking ability exists.

2.2.2. Passive Portfolio Management

Index funds have seen a remarkable rise in the past five to seven years.17 Elton

& Gruber also aknowledged: "One of the major companies evaluating manager

performance estimated in 1989 that during the past 20 years the S&P 500 has

outperformed more than 80 % of active managers."18

Portfolio managers who try to replicate the return pattern of a predetermined

index are said to pursue passive portfolio management. The simplest way to

14 SHARPE, (1966), p. 119 - 13815 JENSEN, (1968), p. 389 - 41616 GRINBLATT, TITMAN (1989), p. 393 - 41617 SORENSON, MILLER, SAMAK (1998), p. 1818 ELTON, GRUBER (1992), p. 705

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follow passive portfolio management is to exactly replicate the index or

benchmark. Replicating an index can be very tricky and expensive. Replicating

the S&P 500 may still be feasible without incurring excessive cost but replicating

a Russell 3000 may almost be unfeasible due to excessive turnover cost and

little liquidity in small stocks. This highlights the tradeoff between accuracy and

turnover cost in duplicating an index for a passively managed portfolio.

There are two alternative ways to reproduce an index. By finding a

predetermined number of stock which best tracked the index historically or by

finding a set of stocks that represents all the industry segments in the portfolio in

the same portion as present in the index. A mixture of the three approaches may

very well be found as well as the benefits of the different methods can be

realized. The main benefit of exactly replicating the index is that the tracking error

will be relatively low compared to the other measures. In that sense an index

fund may hold exactly the same weight of large stocks in its fund as represented

in the index. Applying one of the alternative measures presented above,

therefore realizing the benefit of lower transaction cost can solve the problem

with small and illiquid stocks. Cash holdings caused by dividend payments and

cash inflows from investors will also make it harder to track an index due to the

different risk-return characteristics of cash compared to the index.

2.2.3. What Index to use

Portfolio performance evaluation traditionally involves the application of a

benchmark or index to which the portfolios return is compared. If indices are

used as benchmarks the method used to measure the market return needs to be

considered. Friend, Blume and Crockett found in their study that the average

performance of an equally weighted NYSE index differed from the one obtained

when applying a value weighted NYSE index by 2.5 %. The equal weighed

NYSE index yielded 12.4 % whereas the value weighed index yielded only 9.9 %

on average.19 The difference may be attributed to the size effect. The size effect

19 FRIEND, BLUME, CROCKETT (1970) in IPPOLITO (1993), p. 44

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or small firm effect states that small firms stocks tend to have higher returns than

large firms.

There are three commonly used weighting methods in computing a market index

the price weighting method, the value weighting method and the equal weighting

method.

A price-weighted index is computed by summing up the prices of the securities

that are included in the index and dividing them by a constant. This returns the

average price of the securities at time t and when divided by the average price at

time 0 and added to the base of the index, it will return the value of the index at

time t. In the case of stock splits, the constant is adjusted in order to reflect the

price changes due to the stock split. The prestigious Dow Jones Industrial

Average is a price weighted index.

The value weighting method is the most common. Indices like the S&P 500,

Russell 1000, Russell 3000 and the ATX are value weighted. In calculating the

index one simply takes the market value of the securities included in the index at

time t and divides it by the market value of the securities at time 0 and adds the

value to the index base at time 0.

An equal-weighted index is calculated by multiplying the level of the index at time

t-1 with the price relatives at time t. The price relatives are calculated by dividing

the price of every single security in the index at time t by its price at t-1 and then

dividing the sum these price relatives by the number of securities included

herein. An example for an equal weighted index would be the Value Line

Composite Index.

When evaluating the performance of a portfolio and applying an index as the

benchmark one has to make sure that the return measurement method for the

index is the same as for the portfolio under evaluation. Using general market

indices as benchmarks has been criticized as being to general and not

representative for a manager's "habitat" or his style. More elaborate and

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specialized measurements of portfolio performance have been developed. They

will be introduced in the following chapters.

2.3. Traditional Measures of Performance

The foundation of these performance measures is that the return of a portfolio is

adjusted for the risk it bore over the time period under consideration. Traditionally

the adjustment was either based on the security-market-line or on the capital

market line. The security market line based performance measures are Jensen's

Alpha and the Treynor Index. Traditional capital market line based measures of

portfolio performance are the Sharpe Ratio and the RAP (Risk-Adjusted

Performance) Ratio proposed by Modigliani. Morningstar's RAR (Risk-Adjusted

Rating) falls also into this category.

2.3.1. Security-Market-Line based performance measures

In 1965 Jack L. Treynor20 introduced a risk-adjusted measure to rank mutual fund

performance. As a measure of risk he used the beta. Beta reflects the non-

diversifiable portion of a securities total risk and can be calculated from CAPM.

The equation is the following:

)()()()(

pfRpRpTR

β−=

R(p) = Average return of portfolio (p)

R(f) = Average risk free rate (f)

β (p) = Sensitivity of portfolio (p) to market return changes

20 TREYNOR (1965), p. 63 - 75

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The Treynor Ratio gives the slope of the security market line. The higher the TR

the better a portfolio will rank. That can be seen if one introduces indifference

curves of a risk-averse investor. Through a greater TR higher indifference curves

of a risk-averse investor can be reached and the greater will be his utility.

Beta

Return

r2

r1

ß2 ß1

SML1SML2

rf

Beta

Return

r2

r1

ß2 ß1

SML1SML2

rf

Indifference Curves

Figure 4: Relationship between TR and an investors' utility.

The second measure that uses the CAPM as the underlying concept is Jensen's

Alpha.21 Jensen's Alpha measures the positive or negative abnormal return

relatively to the return predicted by the CAPM. With the subsequent formula the

value for Alpha can be calculated.

( )[ ])()()()()()( pfRmRfRpRp βα −+−=



R(m) = Average return of the market (m)

β (p) = Sensitivity of portfolio (p) to market return changes

21 JENSEN (1968), p. 389 - 416

17

Alpha represents the return differential between the return of the portfolio and the

return predicted by the CAPM adjusted for the systematic risk of portfolio (p). The

following table shows the popularity of Jensen's Alpha.

1971-75 1976-80 1981-85 1986-90 TotalSharpe 54 63 38 36 191Jensen 51 81 36 52 220Total 105 144 74 88 411Treynor-Mazuy 6 10 8 10 34Friend II 37 31 7 5 80Contradictory Studies* 0 11 11 21 43Grossman-Stiglitz 0 0 78 117 195Source: Institute for Scientific Informaion, Social Science Citation Index , annual.*Studies by McDonald (1974), Mains (1977), Kon and Jen (1979) and Shawky (1982)

Figure 5: Citations for the SR and the Jensen Alpha and some additional studies.

The Treynor Ratio and Jensen's Alpha are related to the systematic risk

component implied by the Sharpe-Lintner Model. There are 2 problems with the

application of these two performance measures:

1) Is the systematic risk the appropriate risk measure for an investor?

2) Does the Sharpe-Lintner Model regard all relevant information in predicting a

securities or portfolios expected return?

The answer to question 1 will depend on whether the investor holds a single

security or a portfolio of securities. In the case that he holds a portfolio of

securities the systematic risk may well be the relevant measure of risk. In the

case of holding a single security the total risk of the specific security will be the

just measure of risk.22 The second question will be addressed in point 2.4.

22 SARPE, ALEXANDER, BAILEY (1998), p. 835

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2.3.2. Capital-market-line based performance measures

When risk-adjusted portfolio performance measures are grounded on the capital-

market-line, the risk adjustment is accomplished by using the total risk of a

portfolio or security. The main difference to security-market-line based

performance measures is, that a capital asset pricing model is not required and

thus alleviating the problem of making assumptions concerning a certain model.

The sole measure of risk is total risk which is equivalent to the statistical measure

of standard deviation or σ. The two traditional measures based thereon are the

Sharpe Ratio and the RAP (Risk-Adjusted Performance) measure.

Another popular measure to rank investment funds in the United States is

Morningstar's RAR (Risk-Adjusted Rating) and as it is also based on a portfolios

total risk adjustment although using a special procedure to adjust for it, it will be

briefly described too.

The Sharpe Ratio23 essentially measures a portfolios average performance over

the risk-free rate per unit of total risk of the portfolio.

)()()()(

pfRpRpSR

σ−=



σ (p) = Ex post standard deviation of portfolio (p)

The Sharpe Ratio's simplicity may be of major appeal to ranking agencies. Even

the Austrian periodical "trendINVEST"24 reports the SR although the funds are

not ranked according to it. Modigliani & Modigliani mention it to be "probably the

23 SHARPE (1966), p. 119 - 13824 trendINVEST (2000), p. 56 - 90

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most popular measure of risk-risk adjusted return"25. Following SR the portfolio

with the highest SR can be considered to be performing best.

Franco Modigliani and Leah Modigliani26 propose a modified version of Sharpe's

measurement approach. They call the ratio they calculate RAP but it is also

referred to as M². In opposite to Sharpe who ranks funds according to the slope

of the capital market line, they lever or un-lever, depending if the sigma of the

portfolio is higher or lower than that of the market, the portfolios risk to equal the

market risk and present the resulting risk-adjusted return as the ranking variable.

This procedure produces the exact same ranking as obtained by applying the

Sharpe Ratio. They justify their approach with the argument that the average

investor who is not familiar with advanced finance techniques can easier

understand RAP. Analytically their approach is the following:

( ) )()()(*)()()( fRfRpR

pmpRAP +−=

σσ


R(f) = Average return of the risk-free rate (f)

σ (m) = Ex post standard deviation of market (m)

σ (p) = Ex post standard deviation of portfolio (p)

The relationship between SR and RAP can be shown to be the following:

)()(*)()( fRmpSRpRAP += σ

The benefit of RAP is that it can be readily compared to the market index yield.

The portfolio with the highest value of RAP is corollary the best performing one.

25 MODIGLIANI, MODIGLIANI (1997), p. 5126 MODIGLIANI, MODIGLIANI (1997), p. 45 - 54

20

Morningstar's risk-adjusted rating (RAR) is one of the most popular ratings in the

United States. 27 In 1995 90 % of new money invested in stock funds went into

four-star or five-star ratings awarded by Morningstar. I will not pursue the exact

procedure and its implications on traditional concepts in this project as it is very

complex and lengthy and therefore may be the subject of another work. Rather I

would like to mention the paper28 in which Sharpe analyzed RAR and summarize

his findings.

Sharpe compared the ranking of mutual funds calculated on the basis of RAR to

the ranking obtained through calculating the excess return sharpe ratio. The

excess return sharpe ratio takes the return of a portfolio over the risk free rate

and divides it by the standard deviation differential between the risk-free rate's

standard deviation and the portfolio's standard deviation. Sharpe finds that if

funds have good average historical returns the excess return sharpe ratio ERSR

and RAR are closely related with a correlation coefficient of 0.985.

Figure 6: Correlation between Morningstar's RAR and Excess Return Sharpe Ratio (ERSR).

27 SHARPE (1998), p. 2128 SHARPE (1998), p. 21 - 33

21

He further concludes that RAR should be view as an attempt to determine a best

single fund and assumes that the investor holds only one single fund. The

findings lay out that also in the case of poor overall market performance RAR is

appropriate in determining which fund is best performing assuming an investor

holds only one fund. The weakness Sharpe specifies is that RAR fails to capture

an important property of investors preferences - the desire for portfolios that are

neither the least nor most risky available. He finally concludes that if the only

choice for a measure by which to select funds is between RAR and ERSR, the

evidence favors selecting the ERSR but he acknowledges also that a more

appropriate choice would be to use either a different measure or none at all.

2.4. Weaknesses of Traditional Measures of Performance

The main problem with traditional performance measures is the usage of a

benchmark, especially in estimating the security market line. Whenever the

security market line is incorrectly estimated that means the market index is

inefficient, it can have severe impacts on the outcomes of the Treynor Index and

Jensen's Alpha. The incorrect positioning of the security market line can have

two reasons, neither of which is related to statistical variation:29

1) The true risk free return is different from the risk-free return used in the

model. This problem can be caused by the circumstance that the investor

under consideration can not borrow at the assumed risk-free rate used in the

model. This problem is not only limited to the Treynor Index and Jensen

Alpha as will be explained later on.

29 ROLL (1980), p. 5 - 12

22

2) A non-optimized market index has been employed that means an index

whose expected return differs from the expected return of the optimized index

appropriate for the true risk-free return.

These factors cause the security market line to be positioned incorrectly as

shown below.

Figure 7: Possible performance measurement errors due to mis-specification of the benchmark.

On the basis of these evaluations it can be seen that the Teynor Ratio and

Jensen's Alpha rate funds take on more risk relatively better compared to the

market. Lehmann and Modest30 concluded further that the application of a

specific factor model has major implication on the performance measures yielded

by benchmarks thus fueling the discussion over what is a proper model to

describe return characteristics of securities. At this point it becomes clear that the

relevant problem in determining performance of mutual funds is finding and

providing the correct input measures for the model and assumptions in models

about risk reflection parameters may often not be as clear cut as seeming.

The problem of defining the appropriate risk-free rate has also implications on the

Sharpe Ratio and therefore on RAP. The Sharpe ratio assesses performance in

assuming a linear relationship between total risk and excess return over the risk- 30 LEHMANN, MODEST (1987), p. 233 - 265

23

free rate. If an investor has to pay higher interest rates the higher the presumed

level of risk than that will also lead to a misclassification of funds as his

investment universe compared to the benchmark differs.

24

3. Alternative Measures of Portfolio Performance

Traditional measures have shown several points of concern when applied in

performance evaluation. In this chapter I will introduce alternative approaches to

determine a portfolios required return.

3.1. The Fama and French three & five Factor APT-Model

The Fama and French31 model is built on the Arbitrage Pricing Theory Model

developed by Ross in 1976.32 It states that in an equilibrium market the arbitrage

portfolio must be zero or in other words an arbitrage portfolio can not exist. If this

condition did not hold market participants would sell assets whose expected

return is lower than implied by the detected common risk factors of the market

and buy assets whose expected return is higher than implied by the risk factors.

This process of arbitrage ensures equilibrium market as market participants

engage in it until there is no further possibility in making a riskless profit through

trading one security for another.

On this basis Fama and French tried to define the factors which are relevant in

predicting a securities expected return. The equation to measure a security's

expected return is given below:

kiki FFiR λλλ +++= ...)( 110

R(i) = Return on security (i)

λ (0) = The risk-free rate or zero beta portfolio

λ (ik) = Factor sensitivity of security (i) to factor (k)

F(1-k) = Factors that explain a security's return

31 FAMA, FRENCH (1993), p. 3 - 5632 ROSS (1976), p. 341 - 360

25

Through regression analysis the factors responsible for a security's variation can

be detected. One setback of APT-model is that the model does not specify the

specific risk factors. Fama and French detected three risk factors for stock

portfolios and two risk factors for bond portfolios. The factors for stock portfolios

are

� The excess return of the market over the risk free rate

� The size of the firm

� The book-to-market equity ratio

and for bond portfolios they are

� The time to maturity

� The default risk premium

Fama and French propose their findings as being useful for portfolio performance

evaluation but did not pursue it per se.

Lehmann and Modest33 conducted an extensive study on different benchmarks.

They use the CRSP34 equally weighted and value weighted returns to construct

the different benchmarks. The number of securities they used in the construction

of their benchmarks was 750. The fund returns were taken from 130 mutual

funds over the period of 15 years that is from January 1968 to December 1982.

They compared the Sharpe-Lintner Model's excess return predictions with the

APT-Model's excess return predictions over the above mentioned time period.

They found that the Sharpe-Lintner model produces alphas that are less negative

and less statistically significant than the APT-Models alpha predictions. See table

below.

33 LEHMANN MODEST (1987), p. 233 - 26534 University of Chicago Center for Research in Security Prices (It's files contain complete data on NYSElisted stocks since July 1962)

26

Values in % except for t-value(absolute)

APT-M Alpha S-L-MAlpha

Difference APT - SLM Alpha

VWER EWAR VWERJan. 1968 to Dec. 1972 -4,85 -1,41 -0,15 -3,44(Standard deviation) 3,86 4,37 4,23(t-value) 14,33 3,68 0,40Jan. 1973 to Dec. 1977 -5,45 -0,79 -6,32 -4,66(Standard deviation) 3,6 4,54 4,91(t-value) 17,26 1,98 14,68Jan. 1978 to Dec. 1982 -3,85 1,4 -3,19 -5,25(Standard deviation) 3,3 3,98 3,27(t-value) 13,30 4,01 11,12Figure 8: S-L-M is the Sharpe-Lintner-Model. VWER denotes the excess return when using thevalue weighted CRSP and EWAR denotes the excess return when using the equally weightedCRSP as the benchmark. I calculated the t-value the following: α(i)/(σ(i)/²√130). 130 is thenumber of funds they used in their study.

They found that the Sharpe-Lintner model and APT benchmarks "differ more

than they agree on the Treynor-Black benchmarks over all three periods"35 (they

split the 15 year period in three 5-year periods). On the application of Jensen's

Alpha on the Sharpe-Lintner model benchmark they conclude that this is more

similar to no risk-adjustment at all than it is to the application on the APT

benchmark. The typical rank difference between the APT based Jensen Alpha

and no risk-adjustment was twenty two, nineteen and forty seven positions for

the three 5-year periods. In contrast, the typical rank difference between the

Sharpe-Lintner model based Jensen Alpha and no risk-adjustment are seven,

seven and twelve positions for the three 5-year periods. They conclude that

inferences about mutual fund performance are dramatically affected by the

choice between an APT model benchmark and a Sharpe-Lintner model

benchmark.

Their tests do not say anything about the basic validity of the Sharpe-Lintner

model and the APT mode. The explanation they give for the significant negative

abnormal returns is that their benchmarks, the Sharpe-Lintner model benchmark

35 LEHMANN, MODEST (1987), p. 260

27

and the APT model benchmark, are possibly not mean-variance efficient. They

further acknowledge that the APT model could explain anomalies involving

dividend yield and own variance but could not account for size-effect.

Beyond that they tested different numbers of factors in the APT-Model and found,

that between five, ten and fifteen factors the result-changes were very small. This

can be considered as support for the Fama-French APT approach using five

factors to represent market risk.

Kothari and Warner36 conducted another study that shows the difference in

Jensen Alphas when applying the Sharpe-Lintner model and APT-Model in

defining the benchmark. Kothari and Warner built a 50 stock portfolio through

randomly drawing from the population of the NYSE/AMEX securities. They

repeated this procedure at the beginning of every month over 336 month that is

from January 1964 to December 1991. The portfolio's returns were than tracked

for 36 months. This formed the basis for their benchmark. They found that when

they compared the performance of their randomly selected stock portfolios to a

Sharpe-Lintner model benchmark their random portfolios showed a Jensen Alpha

of over 3 %. The Fama-French APT model performed better as setting a

benchmark by which it only had a Jensen Alpha of -1.2 %. These empirical

results are very similar to the ones found in Lehmann and Modest as their

average performance difference was (3.44% + 4.66% + 5.25%)/3 that is -4.45 %

(APT-M minus SL-M). They conclude that standard mutual fund performance

measures are unreliable and mis-specified.

3.2. The Grinblatt & Titman no Benchmark Model

The encountered problems with benchmarks have led to alternative approaches

to determine a portfolio's performance. Grinblatt and Titman37 pursued one

36 KOTHARI, WARNER (1997), p. 1 - 4437 GRINBLATT, TITMAN (1993), p. 47 - 68

28

where no benchmark is needed and thus alleviating several problems associated

with the use of a benchmark. Their analysis in turn is only applicable if the

evaluator has knowledge about the exact composition of the portfolio under

evaluation. This is in strong contrast to the portfolio performance measures

introduced earlier since they allowed portfolio performance evaluation without

apprehending a portfolio's composition.

The underlying concept of their measure, they call it the "Portfolio Change

Measure"38, is that an informed investor will hold securities that will have a higher

return when they are included in the portfolio than when they are not included.

Further, an informed investor will tilt his portfolio weights towards assets with

expected returns higher than average and away from assets with expected

returns lower than average. This will cause a positive covariance between

portfolio weights and the return of a security for an informed investor whereas it

should not be any covariance between portfolio weights and the return of an

asset for the uninformed investor. The way Grinblatt and Titman propose to

measure this covariance is the following:

( )[ ] TwwRPCMN

j

T

tktjjtjt /

1 1,∑∑

= =−−=

PCM = Portfolio Change Measure

R(jt) = Return of security (j) at time (t)

w(jt) = Weight of security (j) at time (t)

w(j,t-k) = Weight of security (j) at time (t - k)

T = Number of time periods under consideration

38 GRINBLATT, TITMAN (1993), p. 51

29

Under the null hypothesis of no superior information, both current and past

weights are uncorrelated with current returns and thus the PCM measure should

be indistinguishable from zero.

Potential problems with this measure can arise from the violation of the key

assumption to this concept namely that mean returns of assets are constant over

the sample period. Portfolios that specialize in takeover targets or bankrupt

stocks will realize positive performance with this measure because they include

assets whose expected returns are higher than usual. The same holds true for

managers who are exploiting serial correlation in stock returns. One must also

keep in mind that this measure can only be applied if the evaluator knows the

exact composition of the portfolio over time, which may be the cause for its

sparse use.

Despite that the PCM approach overcomes the problems of measuring the SML

as described in 2.4.

Grinblatt and Titman applied the PCM measure on 155 mutual funds over a 10-

year time period from December 31st 1974 to December 31st 1984 on quarterly

holdings. On this basis they formed two portfolios, the first lagged one quarter

and the second lagged 4 quarters. These differenced weights where then

multiplied by CRSP monthly stock returns where the weights were held constant

over 3 months and therefore a time series of monthly portfolio returns was

created for the one quarter and four quarter lagged PCM. For example with the

one quarter lag, the April, May and June returns were multiplied by the difference

between the portfolio weights held on March 31st 1975 and the weights held on

December 31st 1974 and so forth.

They found that for the one quarter lagged PCM measure the value was

statistically indistinguishable from zero which indicates that informed investors

can not realize the benefits of their information in one quarter. The 4 quarters

lagged PCM showed statistically significant abnormal returns indicating that

investors do have superior information and that it is revealed with a one-year lag.

30

The average abnormal returns of the entire sample are about 2% per year. The

table below shows the abnormal returns for different mutual fund categories and

its level of significance.

Performance Measure

Lagged 1 Quarter Lagged 4 Quarters

No. of Mean Wilcoxon Mean Wilcoxon Funds Performance t-statistica Probabilityb Performance t_statistica Probabilityb

Total sample 155.37 1.47 .233 2.04 3.16* .004Aggressive growth funds 45 . 39 .98 .475 3.40 3.55* .004Balanced funds 10 -.48 -1.87 .057 .01 .03 .902Growth funds 44 .66 2.01* .017 2.41 2.94* .009Growth-income funds 37 .14 .61 .095 .83 1.75 .107Income funds 13 .54 1.54 .475 1.33 2.64* .002Special purpose funds 3 -.10 -.16 .233 .21 .19 .711Venture capital/special situation funds 3 1.26 1.07 .812 2.66 1.43 .035

Fl-statistic (Abnormal performance in every category = 0)

F = 3.1438*

Prob > F = .0028c

F2-statistic (Abnormal performance across categories is equal)

F ~ 3.6590*

Prob > F = .0014c

a) The mean over all months divided by the standard error of mean.b) The probability that the absolute value of the Wilcoxon-Mann-Whitney Rank z-statistic is greater than the absolute value of the

observed z-statistic under the null.c) The probability of the F-statistic being greater than the outcome shown, tinder the null hypothesis (Type 1 error).*) Type I error < .05.

Figure 9: Performance estimates for 155 surviving mutual funds grouped by investment objectivecategories (Return in % per year).

Grinblatt and Titman report that the PCM measure results in smaller standard

errors than approaches that use the security market line. They attribute the

increased estimation precision to the higher correlation between their

"benchmark" (the current returns of a funds historical portfolio) and the returns of

the current portfolio than any traditional benchmark portfolio.

31

Their final conclusion was that mutual funds on average achieved positive

abnormal performance during the 10-year period under estimation but that after

considering transaction cost and fund expenses the net abnormal average

performance is close to zero. They further conclude that traditional measures of

performance add noise to true performance and thus bias the measure towards

finding no performance. This is because outside evaluators are not measuring

the true performance of a fund but only the performance of some hypothetical

portfolio that is correlated with the fund instead of evaluating holdings that

correspond to each transaction. Consequently they found that managers who

performed well in one period were likely to do so in a following period thus

inferring manager skill.

3.3. The Sharpe Approach: Asset Allocation and StyleAnalysis

The portfolio evaluation models described in this master's thesis does not require

the knowledge of the exact composition of the portfolio except for the Grinblatt

and Titman model described in 3.2. For an outside evaluator this is of practical

importance as it is the condition for making portfolio evaluation feasible. The

inconvenience is that the resulting portfolio measures are of general nature. In

light of that Sharpe39 developed an "evaluation system" that reflects a higher

degree of specification and regards an investment manager's universe also

labeled his specific "investment style". He argued that it would be more adequate

to measure an investment manager by the asset class returns he invested in

instead of comparing his return to a universal benchmark. This idea of "grouping"

funds was put forth first time by LeClair40. Brinson, Hood and Beebower41 found

in their study in 1986 that the staggering part of the portfolio performance of 91

pension plans came from asset allocation. In 1988 Sharpe introduced a method

39 SHARPE (1992), p. 7 - 1940 LeCLAIR (1974), p. 220 - 22441 BRINSON, HOOD, BEEBOWER (1986), p. 39 - 44

32

to determine a funds "effective asset mix"42 through constrained regression

analysis and thereon he grounded his renowned paper of 1992 titled "Asset

Allocation: Management Style and Performance Measurement".

3.3.1. Determinants of the Model

The main input in Sharpe's asset class factor model is the single asset classes.

Sharpe defined certain standards that an asset class should meet in order to

assure the usefulness of the model. This is not found to be strictly necessary, but

it is desirable for the usefulness of the model. The qualitative exigencies on an

asset class are

1. Mutually exclusive

2. Exhaustive

3. Have returns that differ

The asset class should represent a capitalization-weighted portfolio of securities

in order to mimic return variation created by different weights of asset classes in

the returns of the portfolio under evaluation. Sharpe pointed out further that asset

class returns should either have low correlations with one another or, in cases

where correlations are high, different standard deviations.43 If independent

variables are highly correlated, as two indexes representing different approaches

to investing with the same asset class, the reliability of the estimated coefficients

in meaningfully describing the underlying relationship is very much in doubt.44

The problem of multicollinearity can reduce the explanatory power of a model

and therefore the asset classes should show low correlation, possibly none,

following Sharpe's qualification mentioned above.

The number of asset classes Sharpe uses in his proposed model is twelve. Each

of the twelve indexes is supposed to represent a strategy that could be followed 42 SHARPE (1988), p. 59 - 6943 SHARPE (1992), p. 843 LOBOSCO, DiBARTOLOMEO (1997), p. 80

33

passively and at low cost using an index fund. The possibility of investing in the

index at low cost is of importance as this is the alternative the manager is

measured against. If the benchmark we apply is not a feasible investment

alternative it will be a biased measure. The twelve classes he uses are

1. T-Bills Cash equivalents with less than 3 months to maturity. Index: Salomon

Brothers' 90-day Treasury Bill Index.

2. Intermediate-Term Government Bonds Government bonds with less than

10 years to maturity. Index: Lehman Brothers' Intermediate-Term Government

Bond Index

3. Long-Term Government Bonds Government bonds with more than 10

years to maturity. Index: Lehman Brothers' Long-Term Government Bond

Index

4. Corporate Bonds Corporate bonds with ratings at least Baa by Moody's or

BBB by Standard & Poor's. Index: Lehman Brothers' Corporate Bond Index

5. Mortgage Related Securities Mortgage-backed and related securities.

Index: Lehman Brothers' Mortgage-Backed Securities Index

6. Large-Capitalization Value Stocks Stocks in S&P 500 stock index with high

book-to-price ratios (50% of the stocks in the S&P 500 index). Index:

Sharpe/BARRA Value Stock Index

7. Large-Capitalization Growth Stocks Stocks in the S&P 500 stock index with

low book-to-price ratios (remaining 50% of the stocks in the S&P 500 index).

Index: Sharpe/BARRA Growth Stock Index

8. Medium-Capitalization Stocks Stocks in the top 80% of capitalization in the

US equity universe after the exclusion of stocks in the S&P 500 stock index.

Index: Sharpe/BARRA Medium Capitalization Stock Index

34

9. Small-Capitalization Stocks Stocks in the bottom 20% of capitalization in

the US equity universe after the exclusion of stocks in the S&P 500 stock

index. Index: Sharpe/BARRA Small Capitalization Stock Index

10. Non-US Bonds Bonds outside the US and Canada.

Index: Salomon Brothers' Non-US Government Bond Index

11. European Stocks European and non-Japanese Pacific Basin stocks.

Index: FTA Euro-Pacific Ex Japan Index

12. Japanese Stocks Index: FTA Japan Index

Every six months the equity categories are reclassified. The S&P 500 stocks are

reviewed and if the change in book-to-price ratios implies a change in the

classification, for example a stock that falls from the top 50% (relatively high

book-to-price ratio) into the bottom 50% (relatively low book-to-price ratio) than

the stock is regrouped. Non-S&P stocks, stocks in the medium-cap and small-

cap class, are classified in order that 80% of these stocks are in the medium-cap

class and 20% in the small-cap class. To avoid excessive turnover in the

composition of these indexes of relatively illiquid stocks and an associated high

cost for index tracking, any stock that has "recently crossed over the line"45 a

relatively small distance is allowed to remain in its former index. A relatively small

distance is defined with 20% within the boundary value. The remaining eight

asset classes are self-explanatory all together the twelve asset classes were

constructed to cover the investment universe from which portfolio managers

chose their assets.

The explained variables will be the individual fund returns, which can be

observed in newspapers or bought from specialized research companies.

45 SHARPE (1992), p. 9

35

3.3.2. The Procedure

After asset classes have been defined and the desired history of returns

corresponding to them has been obtained, data analysis is put to work. The

objective is to determine the weights of the previously defined asset classes in

the portfolio of an individual mutual fund through quadratic programming.

Quadratic programming is set to minimize the variance of the residuals under

certain constraints. The usefulness of minimizing the variance and not using

standard regression or constrained regression to determine a portfolios "asset

class exposures" can be seen in the table below.

Regression and Quadratic Programming ResultsTrustees' Commingled Fund-U.S. Portfolio

Januarv 1985 through December 1989Unconstrained

RegressionConstrainedRegression

QuadraticProgramming

Bills 14.69 42.65 0

Intermediate Bonds -69.51 -68.64 0

Long-Term Bonds -2.54 -2.38 0

Corporate Bonds 16.57 15.29 0

Mortgages 5.19 4.58 0

Value Stocks 109.52 110.35 69.81

Growth Stocks -7.86 -8.02 0

Medium Stocks -41.83 -43.62 0

Small Stocks 45.65 47.17 30.04

Foreign Bonds -1.85 -1.38 0

European Stocks 6.15 5.77 0.15

Japanese Stocks -1.46 -1.79 0

Total 72.71 100.00 100.00

R-squared 95.20 95.16 92.22Figure 10: Resulting asset class weights through unconstrained and constrained regression andthrough quadratic programming.

The constraints are that the sum of the weights of the different asset classes in

the portfolio must be 1 and that no short positions are allowed as common

36

mutual funds policies do not allow short positions46. Analytically, the program

looks the following:

[ ] iKikjiji

i

RwRwR

Var

FunctionObjective

ε

ε

+++=

→

⋅

...

)(min

:

10

1

:

1

≤≤

=

⋅

∑=

ij

K

jiK

w

w

tosubject

Var(ε (i)) = Variance of residuals of security (i)

R(i) = Return of portfolio (i)

R(j) = Return of asset class (j)

w(ij) = Weight of asset class (j) in portfolio (i)

ε (i) = Residual return of portfolio (i)

Sharpe defines the residual return of a portfolio as the portfolios "tracking error"

and its variance as the funds "tracking variance"47. In other words, it represents

the value contributed to the total return of a portfolio by a managers stock picking

ability. The other part is explained by the employed asset classes. The style

determined through this method can be regarded as an average of the potentially

changing styles over the examined period. This indicates that the longer the

examination period the more inaccurate this method becomes. To obtain a

46 SHARPE (1992), p. 1147 SHARPE (1992), p. 11

37

clearer picture and especially to see how a style changes over time one needs to

roll a time window over the examination and run the quadratic program for every

time window. The result will be a series of asset class weights that reflect if the

manager changed his "style" or if he kept weights constant over time.

The style weights can now be used to produce a time series of excess returns by

subtracting the "style benchmark" from the actual portfolio return at each single

point in time. The excess returns would be generated by the formula

[ ]tKtpKtjtpjtptp RwRwR ,,,,,, ... ++−=ε

ε (p,t) = Excess return or return due to selection of portfolio (p) at time (t)

R(p,t) = Absolute return of portfolio (p) at time (t)

R(j,t) = Return of asset class (j) at time (t)

w(p,t) = Weight of asset class (j) in portfolio (p) at time (t)

The method of separating a portfolios return in a "style return" and in a "selection

return" makes it possible to distinguish between the performance of the portfolio

manager and the investor. Knowing the styles of investment an investor can

create his individual asset class portfolio. The investment manager on the other

hand will be measured accordingly to his class benchmark and will not have to

bear responsibility for overall unsatisfying returns due to asset allocation.

3.3.3. Criticisms and Improvements

The basic style analysis model averages the styles of an investment manager

over the period under consideration and returns the estimated weights. If an

investment manager changes his investment styles, style analysis will return an

average of his styles and not the accurate composition of his investment portfolio

38

at a time.48 This problem can be overcome through rolling a window over the

period under consideration and thus partly offset the problem of changing styles

of the investment manager.49 Trzcinka50 acknowledges the problem of

inaccuracy but concludes that the strengths of Sharpe's style analysis are its

objectivity, low cost and its practical application.

Lobosco and DiBartolomeo51 have researched the problem of determining the

confidence intervals of Sharpe's style weights. They found that the confidence

interval for a style weight of a particular market index increases with the standard

error of the style analysis, decreases with the number of returns used in the style

analysis and also decreases with the "independence" of the market indexes used

in the analysis. The formula52 they derived to calculate the confidence intervals

is shown below:

1−−×=

knBi

awi σ

σσ

σ (wi) = Standard deviation of the amount of error in the estimate of the style

weight for index (i) through style analysis

σ (a) = Standard deviation of the residuals from determining the style weights

through quadratic programming

σ (Bi) = Standard deviation of the portion of return on index (i) not attributable to

other market indexes

n = Number of data points in the return time series

k = Number of market indexes with nonzero style weights

48 CHRISTOPHERSON (1995), p. 3849 SHARPE (1992), p. 1150 TRZCINKA (1995, p. 4651 LOBOSCO, DiBARTOLOMEO (1997), p. 80 - 8552 LOBOSCO, DiBARTOLOMEO (1997), p 84 -85

39

Through Monte Carlo simulations on a portfolio of market index weights with an

arbitrarily chosen value for the standard error they tried to approximate the true

index weights. The repetition of Monte Carlo simulation generated a probability

distribution for each of the style weights with the mean values showing

approximately the true values chosen in the beginning (before taking an arbitrary

value for the standard error and simulating the different outcomes of style

weights). Lobosco and DiBartolomeo concluded that the predicted values and the

simulated values converge. The confidence interval measure can help to

determine whether different asset classes should be used due to excessive

collinearity and for which situations style analysis through quadratic programming

may not be well suited. Furthermore they suggest using daily returns in order to

reduce the confidence intervals.

The problem of multicollinearity in the chosen asset classes can be coped with

by using less asset classes.53

53 LOBOSCO, DiBARTOLOMEO (1997), p. 82

40

4. Applied Style Analysis

4.1. The Data

4.1.1. Austrian Investment Funds

I will be evaluating six Austrian investment funds using style analysis. The six

funds I choose are all open-end funds. I selected them randomly from a list of

mixed international investment funds published in trendINVEST54. The reason for

choosing international funds was to examine the general validity of style analysis

for Austrian funds and not only for a specific subcategory like stock funds. The

larger number of funds in the international category proved also useful in regard

to obtaining sufficient historical data as such data is often not available. The

funds initially selected were:

Raiffeisen Global Mix Fd (Raiffeisen KAG)

Appollo 4 (Capital Invest KAG - BA)

SparInvest (Erste SparInvest KAG)

Gernerali Mixfond (3-Banken-Generali Invest)

Global Securities Trust (Carl Spängler KAG)

Constantia Privat Invest (Constantia Privatbank KAG)

Volksbanken Inter Invest (Volksbanken KAG)

Aquila International (Gutmann KAG)

The latter two asset management companies, Volksbanken KAG and Gutmann

KAG, did not provide any historical data, resulting in the elimination of these 54 trendINVEST (2000), p. 76 - 77

41

funds in my final "examination group". The return histories gathered from the

remaining asset management companies included reinvested dividends, thus

avoiding possible interruptions in fund return data due to dividend outpayments

made by the fund. The mutual fund data covers the period from 4/95 to 12/99.

Fund data for Austrian investment funds beyond a five-year history often does

not exist and in turn it was the main parameter for choosing an approximate five-

year history. The fact that there are only 56 monthly returns instead of 60, is due

to the data series of Constantia Privat Invest, which had only a history of 56

month by December 31st 1999.

Monthly return data was used to enhance the statistical significance compared to

quarterly data and constrained to the relatively short time period. Although daily

data would be preferable due to the previously mentioned statistical significance

of the estimated style weights55, it was not feasible as daily return histories for

the necessary asset classes could not be obtained. The advantage of this "data

tradeoff" is a reduced computation time especially when "rolling a window" as

described later in 4.2.2.

Returns were computed for all funds and asset classes using the natural

logarithm (ln). Exchange rate problems associated with investments in different

currency areas did not cause any specific difficulty as the individual asset

management companies provided fund return histories in local (Austrian)

currency terms. The returns were not corrected for management fees or any

other administrative cost incurred by the fund.

In the following the descriptive statistics of the investment funds are displayed.

By that a first glance may be gathered concerning the potential composition of a

particular investment fund.

Figure 12 shows the return history of Constantia Privat Invest. I will refer to it as

Con fund. The relatively low mean return of Con fund accompanied by an also

55 LOBOSCO, DiBARTOLOMEO (1997), p. 84

42

low standard deviation is characteristic to this fund indicating a high portion of

fixed income securities.

0

2

4

6

8

10

-0.01 0.00 0.01 0.02

Series: CONSSample 1995:05 1999:12Observations 56

Mean 0.005105Median 0.005561Maximum 0.027207Minimum -0.016894Std. Dev. 0.009842Skewness -0.116157Kurtosis 2.498004

Jarque-Bera 0.713930Probability 0.699797

Figure 12: Descriptive statistics of Constantia Privat Invest fund.

Figure 11 exhibits the descriptive statistics for Appollo 4. The descriptive

statistics reveal a moderate mean monthly return of 0.76% per month with a

relatively small standard deviation of 1.8%, potentially indicating a substantial

share of fixed income securities. The Jarque-Bera test indicates that we cannot

reject the null hypothesis of normal distribution for Appollo 4.

0

2

4

6

8

10

12

14

-0.04 -0.02 0.00 0.02 0.04

Series: A4Sample 1995:05 1999:12Observations 56



Figure11: Descriptive statistics of Appollo 4 fund

43

Below the descriptive statistics of Generali Mixfund, in short Gen fund, are

displayed. The histogram reflects a relatively larger range of realized returns

indicating greater volatility.

0

2

4

6

8

10

12

-0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08

Series: GENSample 1995:05 1999:12Observations 56



Figure 13: Descriptive statistics of Generali Mixfund.

The histogram in figure 14 reflects the realized returns of Raiffeisen Global Mix

Fund, referred to as Rai Fund. Distinct is the relatively high mean return.

0

2

4

6

8

10

12

-0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08

Series: RAISample 1995:05 1999:12Observations 56



Figure14: Descriptive statistics of Raiffeisen Global Mix fund.

The descriptive statistics of SparInvest from Erste Bank capital asset

management, denominated Ers, reveal a relatively high third and fourth moment

and are therefore at the 100 % level not normally distributed. The Jarque-Bera

44

test for normality follows a Chi-square statistic with two degrees of freedom and

is based on skewness and kurtosis. The high mean and standard deviation

indicate strong exposure to stocks and potentially derivative instruments.

0

2

4

6

8

10

-0.10 -0.05 0.00 0.05

Series: ERSSample 1995:05 1999:12Observations 56



Figure 15: Descriptive Statistics of SparInvest Fund.

In Figure 16 the descriptive statistics of Global Securities Trust from Carl

Spängler asset management (referred to as Spa) are exhibited. The relatively

low mean and standard deviation could indicate significant exposure to bonds.

0

2

4

6

8

10

-0.03 -0.02 -0.01 0.00 0.01 0.02 0.03 0.04

Series: SPASample 1995:05 1999:12Observations 56



Figure 16: Descriptive statistics of Global Securites Trust fund.

45

4.1.2. Asset Classes

The primary question I faced was how many asset classes to include in the

analysis and what markets to cover. Sharpe specifies that all markets should be

covered and that the resulting asset classes should be mutually exclusive56. It

was not feasible to obtain asset class data for all markets, especially concerning

bond asset classes. In trying to determine the investment universe from which a

typical Austrian investment fund selects its securities, I gathered fund

composition data from some of the funds under evaluation. The fund data

revealed that the funds showed strong exposure to European, US and Japanese

equities and to European bonds. Knowing the approximate exposure, a

restriction to lesser asset classes seemed feasible without endangering the

meaningfulness of the results.

4.1.2.1. Equity Asset Classes

Morgan Stanley Capital International (MSCI) provides historical data on

numerous equity asset classes. MSCI asset classes are constructed to cover at

least 60% of an entire equity market. Extended asset classes offered by MSCI

cover at least 70% of a specific market. The market is consequently split into

value and growth securities. The specification into value stocks or growth stocks

is subject to the Price/Book ratio of the specific security. Those 50% of securities

with the relatively higher Price/Book ratio are grouped into the growth stock class

and the remaining 50% with relatively lower Price/Book are grouped into the

value stock class. MSCI provides semi-annual re-balancing of the growth and

value categories. If Price/Book ratios change in a manner that they would qualify

for the other category, they would have to surpass the 50% separation line by

more than 10% before being reclassified in the other category. This policy

reduces asset turnover and consequently provides a more appropriate

benchmark.

56 SHARPE (1992), p. 8

46

MSCI selects stocks with sufficient liquidity until 60% of the market capitalization

is reached. The indexes are capital-weighted indexes using the Laspeyres price

index formula to calculate the price change.

Furthermore, these equity indexes are also calculated using net and gross

dividends reinvested. The constructed indexes reinvest dividends when they are

paid. The net dividend index seems more apt for investment fund evaluations as

it corrects for certain taxation aspects. MSCI subtracts from gross dividends any

withholding tax retained at the source for foreigners who do not benefit from a

double taxation treaty.57 MSCI indicates further that as withholding taxes may

vary according to the shareholders domicile the most conservative rates are

applied. This master's thesis will use net dividend reinvested indexes as equity

indexes representing the most viable investment alternative available and thus

alleviating some of the problems discussed in chapter 2.

To reflect investment alternatives, asset class indexes had to be converted into

local currency terms. To achieve this, I gathered the necessary exchange rate

data from the homepage of Österreichische Kontrollbank58. Converting the USD

indexes and the JPY index with the appropriate exchange rate series resulted in

the final asset class index of the applied foreign asset classes. Asset class

returns were calculated applying the natural logarithm. The formula for the return

calculation was rt = ln(Pt) - ln(Pt-1).

The equity asset classes employed in this master's thesis are:

Austrian Trading Index Source: Reuters

European Value Stocks Net Dividends Reinvested Source: MSCI Europe

Value Index.

57 INDEX CALCLATION (MSCI 2000), p. 4458 www.oekb.at, June 2000

47

European Growth Stocks Net Dividends Reinvested Source: MSCI Europe

Growth Index.

Japanese Standard Stocks Net Dividends Reinvested Source: MSCI Japan

Standard Index.

North America Standard Stocks Net Dividends Reinvested Source: MSCI

North America Standard Index.

The term "Standard" indicates that the Japanese equity universe was not split

into the subgroups value and growth hence the index represents 60% of the

Japanese equity universe.

Although Austrian stocks are already included in the European value and growth

index it seems useful to employ a separate asset class covering liquid Austrian

stocks. The problem of redundancy is of minor importance since Austrian

equities weight only 2.9 % in the MSCI Standard European Stock Index. In

addition this could only cause stronger collinearity, but could not result in a

biased estimation. The possible loss of information when evaluating Austrian

investment funds justifies this compromise. Besides there is the problem of

neglecting dividends paid when using the ATX as an asset class. The problem

would be especially severe if the funds under evaluation showed significant

exposure to the ATX asset class. It was found later that this was not the case

leading to the use of the ATX as an asset class that provides an interesting

insight in how much of an Austrian portfolio, classified as being internationally

diversified, is invested in Austrian securities. The problem is also partly mitigated

by using net dividends for reinvestment since the dividend-factor does not

influence the return history as severe as when gross dividends are used.

4.1.2.2. Fixed Income Asset Classes

Unfortunately, it was not possible to gather sufficient bond index data to cover

the entire bond universe. Thus resulting in an unsatisfying coverage of the bond

48

universe by only two indexes that could be obtained. Extensive bond indexes

with sufficient histories are generally provided by investment services. Unlike

equity indexes, fixed income indexes are not for free. The two fixed income asset

classes chosen are the following:

Austrian Government Bond Index Interest Reinvested Source:

Österreichische Kontrollbank.

European Government Bond Index Source: Salomon Brothers G7 Government

Bond Index.

The Austrian government bond index is called API59. This index includes all

Austrian government bonds and is also corrected for interest and bond discount

proceeds. These payments are reinvested. This property serves well for this work

as this property makes the index a potential investment alternative and thereby

reduces some of the inaccuracies of a benchmark. The data series was provided

by Österreichische Kontrollbank. The European Government Bond Index was

provided in the tutorial "Kapitalmarktforschung" at the University of Vienna.

Unfortunately, it does not incorporate interest and other proceeds provided by

bonds. The index represents the government bond market of the seven largest

European nations. I was not able to obtain data on European corporate bonds.

After contacting all renowned providers of such data no response was received.

Nevertheless it should not be crucial to this work either.

4.1.2.3. Statistical Properties of the Employed Asset Classes

Asset classes should be mutually exclusive, exhaustive and have returns that

differ60. The aspects of mutual exclusivity and exhaustiveness were discussed in

subchapters 4.1.2.1 and 4.1.2.2. The property of different returns will be

examined in this part. The asset-class return series descriptive statistics are

shown below.

59 Anleihen Performance Index60 SHARPE (1992), p. 8

49

API ATX EGROWTH EVALUE G7GOV JPSTAND NASTAND

Mean 0.0056 0.0040 0.0226 0.0222 0.0120 0.0074 0.0265 Median 0.0072 0.0129 0.0282 0.0277 0.0095 0.0138 0.0334 Maximum 0.0212 0.1241 0.1219 0.1161 0.0725 0.1553 0.1312 Minimum -0.0171 -0.1925 -0.1133 -0.1642 -0.0390 -0.1245 -0.1572 Std. Dev. 0.0082 0.0618 0.0484 0.0496 0.0272 0.0678 0.0545 Skewness -0.6088 -0.6526 -0.7907 -1.2184 0.2862 -0.0164 -0.8685 Kurtosis 2.7356 3.8168 3.7970 5.5491 2.3414 2.1438 4.0103

Jarque-Bera 3.62 5.53 7.32 29.02 1.78 1.71 9.42 Probability 0.1635 0.0629 0.0258 0.0000 0.4114 0.4246 0.0090

Observations 56 56 56 56 56 56 56Figure 17: Descriptive statistics of selected asset classes.

Figure 17 shows that except for the European growth asset class and the

European value asset class where the mean return is similar, the preferred

property of different returns is accomplished. Consequently standard deviations

also differ except for the above mentioned asset classes where they are very

close. For the remaining asset classes the problem of multicollinearity should not

be of major concern. One asset class could probably represent the European

growth and European value asset class but for the sake of possible additional

information, resulting from the constrained regression, they will be applied

individually. Intuitively one would expect correlations between the different asset

classes to be moderate except for the European value and growth classes.

Figure 18 displays the cross-correlations of the individual asset classes.

API ATX EGROWTH EVALUE G7GOV JPSTAND NASTANDAPI 1.00 0.09 0.20 0.18 0.48 0.07 0.28ATX 0.09 1.00 0.71 0.82 0.37 0.46 0.63EGROWTH 0.20 0.71 1.00 0.88 0.51 0.55 0.80EVALUE 0.18 0.82 0.88 1.00 0.48 0.56 0.79G7GOV 0.48 0.37 0.51 0.48 1.00 0.31 0.67JPSTAND 0.07 0.46 0.55 0.56 0.31 1.00 0.56NASTAND 0.28 0.63 0.80 0.79 0.67 0.56 1.00Figure 18: Cross-Correlations of selected asset classes.

50

The cross-correlogram shows the expected higher correlation between the

European growth and value asset classes and interestingly also a relatively high

correlation of these asset classes with the North American asset class. However

Sharpe mentions that in cases where correlations between asset classes are

high, these classes should have different standard deviations61 which is the case

when the European asset classes are compared to the North American asset

class.

4.2. Determining the Funds Style and Selection Return

4.2.1. The Funds Average Composition

The constrained regression procedure described in 3.3.2 was employed on the

return series introduced above. The calculation of style weights was performed in

Excel using Solver. This was necessary since EVIEWS does not allow

constrained regressions involving inequality parameters and does further not

include an explicitly addressable optimizer. Nevertheless it did not cause any

problem concerning the accuracy of the estimates as Solver computes the style

weights to the fourth decimal point.

Setting up a quadratic program in Excel is relatively uncomplicated. The

optimizer Solver in Excel can be used to solve three common optimization

problems: minimizing, maximizing and equalizing a certain parameter. In this

case the minimization feature is used.

61 SHARPE (1992), p. 8

51

Figure 19: Solver set-up to calculate Sharpe style weights.

Figure 19 displays the Solver mask programmed to calculate style weights for

Gen fund. The target is to minimize the variance of the residuals. Thus, one first

needs to calculate the residuals using arbitrary weights plugged into the fields

below the asset class line (C3:I3). Now the variance formula for the residuals can

be inserted into the target cell defined in Solver (in this case K3). The only task

left to calculate the style weights is defining of the constraints, which can be done

easily by clicking on the add button on the Solver surface.

In figure 20 style weights were calculated setting up Solver as described above

and using the selected asset classes.

52

Fund EVALUE EGROWTH NAVALUE NAGROWTH JPSTAND G7GOV API ATX R² adjusted R²Con 0% 1% 0% 0% 0% 3% 89% 7% 0.7899 0.7642A4 7% 16% 3% 1% 2% 13% 58% 0% 0.8221 0.8004Gen 4% 35% 0% 7% 0% 9% 38% 7% 0.8446 0.8256Rai 1% 8% 8% 2% 13% 32% 27% 8% 0.8247 0.8032Ers 0% 0% 0% 0% 0% 0% 88% 12% -0.0366 -0.1635Spa 0% 0% 0% 13% 2% 2% 75% 8% 0.5511 0.4961

Fund EVALUE EGROWTH NASTAND JPSTAND G7GOV API ATX R² adjusted R²Con 0% 1% 0% 0% 3% 89% 7% 0.7899 0.7642A4 8% 15% 4% 2% 13% 58% 0% 0.8218 0.8000Gen 3% 38% 5% 0% 10% 37% 6% 0.8418 0.8224Rai 3% 6% 10% 13% 32% 27% 9% 0.8243 0.8028Ers 0% 0% 0% 0% 0% 88% 12% -0.0366 -0.1635Spa 0% 0% 15% 3% 1% 75% 6% 0.5376 0.4809

Fund EVALUE EGROWTH NAVALUE JPSTAND G7GOV API R² adjusted R²Con 7% 1% 0% 0% 3% 89% 0.7164 0.6817A4 6% 17% 4% 2% 14% 58% 0.8219 0.8001Gen 11% 40% 2% 0% 12% 35% 0.8347 0.8144Rai 8% 9% 11% 13% 31% 27% 0.8150 0.7923Ers 11% 0% 0% 0% 0% 89% -0.0639 -0.1941Spa 0% 5% 13% 4% 3% 74% 0.4927 0.4305

Figure 20: Style weights using different asset classes.

The data above reveals that style weights do not differ significantly when the

North American asset class is split in a value and a growth class. Thus inferring

that a North American composite asset class is sufficient to explain variations in

the returns of the individual funds. Yet when dropping the ATX asset class

weights change notably. It can be regarded as evidence that the investment

funds under evaluation do have exposure to the ATX asset class and that

inclusion in the analysis is essential. The analysis shows that using the seven

asset classes introduced in 4.2.2.1 is reasonable. However, introducing a

European corporate bond asset class may have improved the results. This is

consistent with intuition that Austrian investment funds classified as "International

Mixfunds" should have at least exposure to the asset classes in the middle panel

of figure 20. Figure 15 reveals that Ers fund should be strongly invested in

stocks. The constrained regression analysis over the entire sample period

53

indicates no exposure to stocks at all. The results must be questioned and the

usefulness of a constrained regression for Ers fund is seriously in doubt62.

The R-squared values are reasonable except for Ers fund. The likely reasons are

missing asset classes, changes in style and/or a high asset turnover63. The

analysis of changing styles will be put forth at a later point. Besides, R-squared

values are relatively stable when using different combinations of asset classes.

Notwithstanding a notable difference exists in R-squared between the six asset-

class model and the seven and eight asset-class model thus favoring one of the

latter. It is useful to mention that the objective is not to maximize R-squared but

to infer as much as possible about the fund's exposures to variations in the

returns of asset classes during the period studied64.

According to the evidence the seven asset-class model will be used in the

subsequent analysis.

Residual Series AnalysisThe resulting residual series from the constrained regression performed on the

six investment funds using Solver were exported to EVIEWS and their statistical

properties examined. The accuracy of the following analysis is somewhat limited

due to the constraints employed in the regression analysis and thus may lead to

residual properties different to the ones from standard regression analysis.

However the analysis is performed in order to gather an approximation of the true

results. Plotting the residuals in a histogram and applying a Jarque-Bera test

revealed that most residuals were distributed normal at about the same level as

the underlying fund returns presented in figure 11 to 16. Jarque-Bera test

analysis for Ers fund's return distribution unveiled non-normality at the 100%

level. Residual analysis for normal distribution revealed the same result.

62 LOBOSCO, DiBARTOLOMEO (1997), p. 8463 comp. CHRISTOPERSON (1995), p. 32 - 4364 SHARPE (1992), p. 11

54

A Ljung-Box (LB) test was applied to test for auto-correlation in the residuals.

The LB test follows a Chi-square distribution with k degrees of freedom where

the k degrees of freedom are equal to the number of auto-correlations. The

analysis was performed on the first 10 lags but only results for the first lag are

reported, as probability values concerning auto-correlation at a greater lag were

less significant.

AC PAC Q-Stat ProbCon -0.218 -0.218 2.8098 0.094A4 -0.048 -0.048 0.1339 0.714Gen 0.045 0.045 0.117 0.732Rai -0.244 -0.244 3.5254 0.06Ers -0.167 -0.167 1.6458 0.2Spa 0.006 0.006 0.0024 0.961

Figure 21: Test statistic of first-lag auto-correlation of residuals.

The values in the probability column are all greater than 0.05 revealing no auto

correlation at a α level of 95%. The null hypothesis of the LB statistic is that the

time series is White Noise thus inferring that the regression residuals are White

Noise in regard to auto-correlation and the null can not be rejected at the 95%

significance level.

Finally the mean expected values of the residuals were tested for significance

from zero. This was accomplished with a standard t-test. The t-values are

displayed in figure 22.

E(resid) STDV(resid) t-valueCon -0.00055 0.00452 -0.91294A4 -0.00359 0.00766 -3.51108Gen -0.00276 0.01174 -1.75742Rai 0.00281 0.01190 1.77016Ers 0.00922 0.03257 2.11946Spa 0.00184 0.01136 1.20879

Figure 22: T-values of the estimated residual's mean value for selected Austrian investmentfunds.

55

The critical t-value at the 95% level is (+ -) 1.67 for an approximately normally

distributed variable with k-1 degrees of freedom. Figure 22 shows that residuals

of A4, Gen, Rai and Ers fund are statistically significantly different from zero at

the 95% level. The style analysis for Ers fund returned unlikely results,

consequently the t-value is likely improper. One should keep in mind that the

calculated style weights represent an average over the estimation period leading

to inaccuracies in cases where portfolio management changes its style and

securities are frequently turned over.

4.2.2. Rolling a Window

The problem of changing styles can be overcome by rolling a time window during

the estimation period. In the following, the impact of this operation on styles

estimated in 4.2.1 and the corresponding R-squared values will be disclosed. I

used a 20-month time window hence estimating the style composition of a

portfolio on 36 consequential periods. The resulting style changes are 20-month

average style changes.

Estimate 1: min → ε for the time interval t….t+20

Estimate 2: min → ε for the time interval t+1….t+21

�

Estimate 36: min → ε for the time interval t+35….t+55

Besides, the same procedure as described in 3.3.2 was applied for every single

estimate. In general the R-squared values increased, as one would expect due to

the shorter estimation periods. Con funds style changes from January 1997 to

December 1999 are shown below.

56

Con Style Changes

0%

20%

40%

60%

80%

100%

J-97 A-97 J-97 O-97 J-98 A-98 J-98 O-98 J-99 A-99 J-99 O-99

Months

Styl

e W

eigh

ts

API G7GOV ESTAND ATX

Figure 23: Style changes of Con fund.

When examining the return properties of Con fund in 4.1.1, a low mean return

and a low standard deviation were specific to it. The assumption that Con fund is

mainly invested in fixed income securities was confirmed. Striking 89% of the

funds assets are invested in Austrian government bonds. The style weights from

the 56-month constrained regression were 1% EGROWTH, 3% G7GOV, 89%

API and 7% for the ATX. The corresponding R-squared value was 79%. Thus

inferring that almost 80% of the return generated by Con fund are attributable to

the asset allocation decision of Con fund. The graph in figure 23 reveals no

material changes in the composition of the fund over the estimation period.

In the course of the analysis it turned out that the weights estimates for EVALUE

and EGROWTH were relatively small. Thus the European growth and value

index were combined in the graph for a better perception. The similar mean and

standard deviation of these two asset classes have occasionally caused slightly

erratic style weight allocations between the two asset classes. The problem was

of minor importance though. The combined index is termed ESTAND.

The only slightly higher R-squared of 82.4% when taking the average R-squared

of the 36 estimations compared to the 79% computed initially provides evidence

57

for a stable investment style of Con fund. When performing style change analysis

the R-squared value climbed to about 90 % for the period from April 98 to July 90

and fell to around 70% by December 99. This may either indicate superior

selection skill of the fund management or a shift in asset allocation towards an

asset class not represented in the analysis.

A4 Style Changes

0%

20%

40%

60%

80%

100%

J-97 A-97 J-97 O-97 J-98 A-98 J-98 O-98 J-99 A-99 J-99 O-99

Months

Styl

e W

eigh

ts

API G7GOV ESTAND NASTAND JPSTAND ATX

Figure 24: Style changes of A4 fund.

A4 fund kept a steady 70:30 allocation policy between fixed income assets and

equity assets. Austrian government bonds although were steadily replaced by

European government bonds, reaching about 20% by the end of 1999. The

composition of equity shows diversification to all four equity-classes applied. The

strongest equity exposure is to European stocks with about 15% of total fund

value. Interestingly ATX values were eliminated by the end of 1998 maybe

reflecting the inferior development of ATX-values compared to other asset

classes. Generally when looking at A4 funds descriptive statistics one would

have expected a relatively strong fixed income portion in the portfolio as the

mean return was around 9% and standard deviation was relatively low. These

58

expectations are confirmed here. The composition of the fund can be regarded

as stable and therefore making it especially suitable for the style analysis

approach put fourth by Sharpe.65 R-squared increased when using the 20-month

window technique to an average of about 89% compared to 82% computed

initially. Again, this reveals that rolling a window enhances the explanatory

power of style analysis.

Figure 25 shows the composition change for Gen fund.

Gen Style Changes

0%

20%

40%

60%

80%

100%

J-97 A-97 J-97 O-97 J-98 A-98 J-98 O-98 J-99 A-99 J-99 O-99

Months

Styl

e W

eigh

ts

API G7GOV ESTAND NASTAND ATX

Figure 25: Style changes of Gen fund.

Distinct is the large share of ATX securities in the beginning of the evaluation

period and its reduction to about zero by the end of 1997, in favor of European

stocks. Furthermore the stable split of about 45:55 between bonds and stocks is

striking. In the period form April 1998 to April 1999 the R-squared value was

approximately 95% indicating little asset rotation and/or the application of asset

classes resembling viable passive investment alternatives. The average R-

squared value using the window technique augmented by about 6%, in line with

the findings in the A4 fund analysis. The reduction in Austrian government bonds

65 CHRISTOPHERSON (1995), p. 41

59

in favor of European government bonds somewhat resembles the development

of the fixed income asset classes of A4 fund over the time period studied.

Rai Style Changes

0%

20%

40%

60%

80%

100%

J-97 A-97 J-97 O-97 J-98 A-98 J-98 O-98 J-99 A-99 J-99 O-99

Months

Styl

e W

eigh

ts


Figure 26: Style changes of Rai fund.

Remarkable for Rai fund is the abrupt change out of European stocks into

European government bonds and North American stocks in the third quarter of

1997. Rai fund splits its securities at a 55:45 ratio between fixed income

securities and equities. In contrary to Gen fund, Rai fund increased its exposure

to ATX-securities by the end of 1997 but steadily reduced it thereafter. The

cumulative return on the ATX from July 1997 until December 1998 was circa

negative 15%, marking a possible reason for the reduction in exposure to the

ATX. Overall the styles reflected in the graph above are relatively smooth except

for the significant changes in 1997.

The style weights estimated for Ers fund in figure 20 did not seem plausible

because of the almost 90% exposure to the Austrian government bond index. Ers

had an average return of around 17% over the estimation period compared to a

6% average return of the API over the same period thus indicating that the real

style weights are misrepresented. The negative R-squared value is further

60

evidence that the estimated style weights for Ers fund are not representative for

the true style weights. The reason for this severe mis-specification may be the

lack of specific asset classes. This example shows the indispensability of

representing the entire investment universe when selecting asset classes.

Notwithstanding the composition of Ers fund will be displayed below.

Ers Style Changes

0%

20%

40%

60%

80%

100%

J-97 A-97 J-97 O-97 J-98 A-98 J-98 O-98 J-99 A-99 J-99 O-99

Months

Styl

e W

eigh

ts

API G7GOV ESTAND ATX

Figure 27: Style changes of Ers fund.

The consecutive style estimates for Spa fund are exhibited in figure 28. With the

Spa fund the significant increase in R-squared is striking. Compared to the

estimation of style weights over 56 months, R-squared raised by 17% from about

53% to 70% when applying the 20-month time window over the estimation

period. This could reflect a relatively high asset class rotation that could not be

detected with the "static" model. The near disappearance of European bonds and

equities could be doubted and may be the result of a missing asset class.

Unfortunately Spa fund did not provide any composition data in order to confirm

the findings.

61

Spa Style Changes

0%10%20%30%40%50%60%70%80%90%

100%

J-97 A-97 J-97 O-97 J-98 A-98 J-98 O-98 J-99 A-99 J-99 O-99

Months

Styl

e W

eigh

ts


Figure 28: Style changes of Spa fund.

4.2.3. Comparison of real and estimated style weights

Raiffeisen capital asset management, Bank Austria capital asset management

and 3-Banken-Gernerali capital asset management provided detailed

composition data for the requested funds. The findings in the preceding analysis

will be compared to the "true" composition of the funds of these 3 asset

management services. The individual securities will be assigned to the

corresponding asset class used in the constrained regression analysis. Problems

arise with European corporate bonds and foreign bonds. European corporate

bonds were assumed in the G7GOV asset class, as a more specific index (asset

class) was unattainable. Therefore the G7GOV is assigned all European bonds -

corporate and government. Non-European bonds were classified according to

their country-assignment by the capital asset management company. Two asset

classes are added in figure 29 to represent the true exposure of the individual

funds to them. Rai fund split European stocks in the supplied composition data

into EUR for the participating Euro countries and the remaining European stocks

according to their country. Hence the explicit portion of ATX securities in the EUR

composite weight provided by Rai fund could not be determined and was set to

62

zero. The data was supplied for December 1999. When comparing the data one

must keep in mind that he will be comparing the "true" composition at the end of

December 1999 with the average composition of each fund over the 20-month

period from May 1998 to December 1999.

TRUE CALC TRUE CALC TRUE CALCESTAND 12% 22% 43% 48% 18% 4%NASTAND 16% 4% 10% 5% 25% 16%ATX 3% 0% 0% 0% 0% 8%JPSTAND 4% 1% 0% 0% 10% 10%API 19% 48% 10% 24% 0% 6%G7GOV 33% 25% 34% 23% 15% 55%NABOND 9% 0% 0% 0% 21% 0%JPBOND 0% 0% 0% 0% 8% 0%CASH 4% 0% 3% 0% 0% 0%

A4 Gen Rai

Figure 29: True and calculated weight comparison of A4, Gen and Rai fund.

Figure 29 unveils a relatively close estimation of Gen funds true weight

exposures. The application of the appropriate asset classes in the constrained

regression analysis may very well be the substantial contributor to this result.

Except for the lack of a non-European bond asset class and a European

corporate bond asset class the passive benchmark asset classes utilized were

exhaustive. The relatively stable style over the period from the end of 1997 to the

end of 1999 may have assisted the close estimation of the true style. These

points refer exactly to what was discussed in 4.1, namely the properties that

asset classes should be exhaustive, mutual exclusive and have low correlations.

The estimated style weights for A4 fund resemble the true allocations to fixed

income assets and to equities reasonably close. An estimated 73% invested in

fixed income assets and the remainder in equity compared to the true 65% in

fixed income assets and 35% invested in equities by December 1999. The style

weight allocations to the single equity asset classes and bond asset classes are

unsatisfactory. The lack of certain bond asset classes may cause significant

63

misallocations in the applied asset classes. For a similar discussion see

LOBOSCO and DiBARTOLOMEO (1997).

With Rai fund the problem is very much the same. Striking 29% of the funds total

asset value was not represented in the constrained regression analysis leading

to the previously discussed misallocations. Interestingly the JPSTAND asset

class was not affected by that problem. Possibly the low correlation of the

JPSTAND asset class with the other asset classes caused the stability of the

estimated weight despite the named obstacles. Now, at the latest, the importance

of carefully and exhaustively specified asset classes becomes evident.

4.2.4. Contribution through Selection

So far the discussion of style analysis revolved around defining an investment

funds style, neglected the skill evaluation of the individual portfolio manager.

Detecting superior and inferior performance will be at the core in this section.

Style analysis qualifies asset allocation performance as variance of portfolio

performance explained. By that means, the R-squared ratio determines the

amount of variance in the returns of a portfolio explained and attributable to asset

allocation. Thus an R-squared value of 80% suggests that 80% of a portfolio's

return is attributable to the asset allocation decision of the investor or the

investment manager. The remaining part (in this case 20%) is what the

investment manager contributed to the overall portfolio return through active

stock selection. In Sharpe's words: "A passive fund manager provides an

investor with an investment style, while an active manager provides both style

and selection."66 Hence, an active manager is only worth the money if his

contribution through stock selection exceeds the higher management fees. In the

following the cumulative selection returns for five of the six funds are displayed.

Ers fund was not considered due to the improper style weight estimates resulting

from the restricted number of asset classes.

66 SHARPE (1992), p. 16

64

Cumulative Excess Return of Con Fund

-0.04

-0.03

-0.02

-0.01

0.00

0.01

0.02

M-95 N-95 M-96 N-96 M-97 N-97 M-98 N-98 M-99 N-99Months

Cum

ulat

ive

Exce

ss

Ret

urn

Figure 30: Cumulative selection return of Con fund.

Asset allocation accounts for 79% of Con funds return. The rest is attributable to

the above displayed selection return, which is negative. The average selection

return for Con fund was negative 0.055% per month with a standard deviation of

0.452% per month. The corresponding t-value is -0.91. The graph reveals that

the investment management may not have been worth its money. Especially in

the first year and a half of the examination period the underperformance is

persistent. From the end of 1997, a more erratic pattern evolves resembling

white noise instead of skill. One drawback is that it was not possible to verify the

estimated style weights by actual composition data since Constantia asset

management did not provide the data. The possible lack of an asset class may

influence the analysis in this paragraph too. However, this has no impact on the

effectiveness of the residual evaluation provided style weights are estimated

correctly.

65

Cumulative Excess Return of A4 Fund

-0.23

-0.18

-0.13

-0.08

-0.03

0.02


Cum

ulat

ive

Exce

ss

Ret

urn

Figure 31: Cumulative excess return of A4 fund.

In opposition to Con fund A4 fund's performance is relatively stable but also

negative. The average under performance is negative 0.36% per month with a

standard deviation of 0.766% per month and a t-value of -3.51. The critical t-

value at the 95% level for 55 degrees of freedom is 1.67, thus indicating that the

under performance is significant. The contribution through security selection to

the overall return of A4 fund was a negative 18%. The return contribution through

asset allocation to the overall return was 82%. A4 funds management provided

composition data for 12/1998 and 12/1999. Subsequently the data will be used

and the weights and results will be referred to as "true".

The process applied was the following: The weights computed for A4 fund when

rolling the window, were roughly steady. It was assumed that the "true" average

portfolio weights would be stable in the same manner. Therefore, the supplied

composition data for December 1998 and December 1999 was averaged and the

resulting weights calculated. Since asset class data for US bonds and cash

holdings were not included in the analysis the average 11% US bonds between

December 1998 and December 1999 were split between the asset classes

G7GOV and API assuming that these two asset classes somewhat resemble the

US-bond market. The 4% average cash were assumed to behave similar to API

and attributed to it. Figure 32 displays the cumulative excess return using the

66

estimation residuals from style analysis termed "cumresestim" and the "true"

cumulative excess return applying the supplied data for A4 fund.

-0.35-0.30-0.25-0.20-0.15-0.10-0.050.000.05

M-95 N-95 M-96 N-96 M-97 N-97 M-98 N-98 M-99 N-99

Months

Cum

ulat

ive

Exce

ss R

etur

n

Cumrestrue Cumresestim

Figure 32: Comparison of performance development of A4 fund using "true" style weights andestimated style weights.

The average performance when utilizing "true" weights was -0.586% per month

with a standard deviation of 1.4% per month. In comparison, the average under

performance using estimated data was -0.36% per month with a standard

deviation of 0.77% per month. The t-values were -3.1 and -3.5 for the "true" and

the estimated weights hence both show statistical significance at the 95% level.

The comparison shows that in this case, although the estimated weights do not

exactly resemble "true" weights, the residual analysis still provides reasonable

approximations for the true performance.

67

Cumulative Excess Return of Gen Fund

-0.23

-0.18

-0.13

-0.08

-0.03

0.02

M-95 N-95 M-96 N-96 M-97 N-97 M-98 N-98 M-99 N-99

Months

Cum

ulat

ive

Exce

ss

Ret

urn

Figure 33: Cumulative excess return of Gen fund.

Gen fund shows an average negative performance of 0.276% per month.

Substantial under performance occurred between May 1995 and December1996.

The fund underperformed by approximately -15% cumulatively over that period.

From there on the under performance was not as severe but still present. The

monthly standard deviation for the overall period was 1.174% and the figure for

the t-value was -1,74. The computed style weights were shown to comply

especially well with what the fund really invested in. This is exhibited in figure 29.

Gen fund did provide composition data but only for December 1999, thus the

"true" composition of Gen fund can not be reasonably defined especially since

style changes occurred as revealed by rolling the 20-month window through the

estimation period. Furthermore figure 28 indicated that the style of Gen fund was

well estimated and thus the residuals plotted in figure 33 should be

representative.

Over the evaluation period 84% of Gen funds return was accounted for by asset

allocation. The remaining 16% were the selection return described above. The

data leads to the conclusion that the security selection ability of the fund

management is not sufficient to justify active asset management fees, even

worse, the contribution through active stock selection rather corresponds to a

negatively sloped trend line. An investor who invested the equivalent portions of

68

the portfolio in the overall index instead of selected securities of the index, would

have outperformed Gen fund's management by approximately 15.5% over the

56-month period.

Cumulative Excess Returns of Rai Fund

-0.05

0.00

0.05

0.10

0.15

0.20

M-95 N-95 M-96 N-96 M-97 N-97 M-98 N-98 M-99 N-99

Months

Cum

ulat

ive

Exce

ss

Ret

urn

Figure 34: Cumulative excess returns for Rai fund.

According to the initial style analysis Rai fund's overall return is to 82%

attributable to Rai fund's the asset allocation decision.

However, residual analysis for Rai fund unveils significant abnormal positive

returns, particularly over the last three years. The t-value for the entire sample

period is 1.75. The average excess return is 0.28% per month with a standard

deviation of 1.19% per month. These findings must be used cautiously. Figure 29

shows that by December 1999 Rai fund was invested in US and Japanese bonds

with 29% of its total fund value. These two asset classes were not represented in

the style analysis computations, hence style weights may be inaccurately

estimated. The relatively high mean return of Rai fund of 1.39% per month or

about 16% p.a. (see Figure 14) may indicate that the portion of fixed income

securities is not 59% but somewhat lower. This would mean that the cumulative

excess return plot is upward biased.

69

To see how sensitive Rai fund's cumulative excess return is to changes in the

style weights two additional residual series are generated using different weight

settings. The impacts are demonstrated in Figure 35.

-0.05

0.00

0.05

0.10

0.15

0.20

M-95 N-95 M-96 N-96 M-97 N-97 M-98 N-98 M-99 N-99

Months

Cum

ulat

ive

Exce

ss R

etur

n

Testres1 Testres2 Raires

Figure 35: Sensitivity of Rai fund's selection return to style weight changes.

Testres1 is the cumulative excess return of a conducted style analysis for Rai

fund reducing the initially calculated fixed income weights of G7GOV and API by

5% each and increasing ESTAND and NASTAND by 5% thus reducing fixed

income asset classes by 10% and increasing equity asset classes by 10%. It is

assumed that JPSTAND is stable due to the distinct mean and standard

deviation characteristics.

In Testres2 the style weight change between the fixed income asset classes and

the equity asset classes was set to 5%. The API asset class was reduced by 3%

and the G7GOV asset class by 2%, while ESTAND was increased by 2% and

NASTAND by 3%.

Even when fixed income asset classes are reduced by 10% in favor of equity

asset classes the valuation reveals above zero cumulative excess returns. The

average excess return for Testres1 is 0.1% per month with a standard error of

1.26%. Testres2 shows an average excess return of 0.17% and a standard

deviation of 1.21%. In both cases the t-statistic is not significant with a t-value

70

below 1.1 and it can not be concluded that Rai's fund management exhibits stock

selection skill.

For reasons stated earlier a more detailed analysis of this point is not possible.

Cumulative Excess Return of Spa Fund

-0.04

0.00

0.04

0.08

0.12

0.16


Cum

ulat

ive

Exce

ss

Ret

urn

Figure 36: Cumulative excess return of Spa fund.

Spa funds asset allocation accounted for only 54% of its overall return, which

may be an indicator for missing asset classes. The computed style weights in

turn are also seriously in doubt as European bonds and equities are estimated to

be zero. Nevertheless the average excess return estimated is 0.18% per month

with a standard error of 1.14% and a t-value of 1.2 thus inferring insignificance

from zero.

For Ers fund no residual analysis will be conducted as the estimated style

weights are unlikely to be good estimates of the "true" style weights.

4.2.5. Summary of Findings

A comparison of the findings obtained through style analysis to common

benchmark measures like the Jensen Alpha, the Sharpe Ratio or the Traynor

Ratio does not seem to be useful due to distinct differences. The previously

mentioned measures are all based on a single benchmark, contrary to style

71

analysis, which splits the benchmark in an asset allocation and a style selection

return. Style analysis is most suited to define a funds composition and an

investment management's stock picking abilities and thereby provides a more

confined and detailed analysis of how the overall return was obtained.

Comparing selection return findings with general return ratios would be

comparing two different sets of information and thus would not be appropriate.

Nevertheless a general overview of the findings is provided below.

56m CumR Avg TR/m SR Avg B/MR/m Avg SelR/m T-V SelR

Con Fund 28.59% 0.51% 0.42 0.57% -0.055% -0.91A 4 Fund 42.47% 0.76% 0.83 1.12% -0.360% -3.51Gen Fund 64.07% 1.14% 1.13 1.42% -0.276% -1.74Rai Fund 77.77% 1.39% 1.35 1.11% 0.280% 1.75Ers Fund 81.71% 1.46% 1.12Spa Fund 58.84% 1.05% 1.31 0.87% 0.180% 1.2

56m CumR: Cumulative total return over the observed 56 months

Avg TR/m: Average total return per month over the observed 56 months

SR: Sharpe Ratio from trendInvest for the last 36 months using the 12-months Euribor

of 3.459% p. a. Avg B/MR/m: Average benchmark return per month over the observed 56 months

Avg SelR/m: Average selection return per month over the observed 56 months

T-V SelR: T-value of the average selection return per month

Figure 37: Summary of findings for Austrian investment funds.

4.3. Some additional insight using US Mutual Funds

The analysis of Austrian investment funds disclosed some critical points, for

example the specification of asset classes or multicollinearity. Thus some

additional evidence is sought using a different investment universe: The US

investment world. Four US mutual funds are analyzed using style analysis. The

funds are displayed below.

72

Acorn FundDreyfuss Growth Opportunity FundFidelity Magellan Fund20th Century Ultra Investors Fund

Figure 38: Selected US mutual funds.

According to the denomination Dreyfuss Growth Opportunity fund should be

mainly invested in equities and Fidelity Magellan fund should have strong

exposure to equities too, if no sever change in style occurred since Sharpe's

analysis. Especially interesting is Fidelity Magellan Fund as its style analysis data

estimated by Sharpe for the period from January 1985 to December 1989 were

displayed in his paper.67 And the time period studied will be from January 1990 to

December 1995 thus revealing possible changes over the entire period.

Asset class data for the period under examination was supplied by the Carlson

School of Management and in particular by Professor Maheswaran. The returns

for the asset classes as well as for the above-mentioned funds were provided

monthly. The returns were computed geometrically. The asset classes are:

US Treasury bills (Cash equivalents with less than 3 month to maturity)

US Intermediate-term government bond. (Government bonds with less than 10

years to maturity)

US Long-term government bonds (Government bonds with more than 10 years

to maturity)

US Corporate bonds

US Value stocks (Russel 1000 value index)

US Growth stocks (Russel 1000 growth index) 67 SHARPE (1992), p. 7 - 19

73

US Small stocks (Russel 2000, which are the 2000 smallest stocks of Russel

3000)

To gather a comprehension of the level of the multicollinearity dimension a

correlation summary is shown.

CORPBDS GRSTCKS IMBDS LTBDS SMSTCKS TBILLS VLSTCKSCORPBDS 1.00 0.56 0.92 0.98 0.43 0.04 0.64GRSTCKS 0.56 1.00 0.41 0.53 0.82 0.05 0.87IMBDS 0.92 0.41 1.00 0.91 0.22 0.14 0.50LTBDS 0.98 0.53 0.91 1.00 0.37 0.01 0.62SMSTCKS 0.43 0.82 0.22 0.37 1.00 -0.15 0.82TBILLS 0.04 0.05 0.14 0.01 -0.15 1.00 -0.12VLSTCKS 0.64 0.87 0.50 0.62 0.82 -0.12 1.00

Figure 39: Correlogram of selected US asset classes.

Interestingly the correlation between US growth and value stocks is about the

same as between European growth and value stocks. A high correlation is also

striking between different bond asset classes. This is what one would anticipate

due to the common sensitivity to interest rate changes and maybe similar

duration characteristics. T-bills in turn almost indicate no correlation at all.

74

CORPBDS GRSTCKS IMBDS LTBDS SMSTCKS TBILLS VLSTCKS

Mean 0.0069 0.0083 0.0061 0.0070 0.0093 0.0039 0.0075 Median 0.0091 0.0073 0.0058 0.0067 0.0197 0.0034 0.0127 Maximum 0.0436 0.1413 0.0270 0.0581 0.1122 0.0069 0.0838 Minimum -0.0383 -0.0959 -0.0258 -0.0450 -0.1338 0.0021 -0.0879 Std. Dev. 0.0176 0.0406 0.0135 0.0230 0.0483 0.0015 0.0347 Skewness -0.3873 0.3758 -0.4347 -0.2582 -0.4443 0.6691 -0.2612 Kurtosis 2.8024 4.3267 2.4504 2.7475 3.1198 2.1130 3.0743

Jarque-Bera 1.60 5.81 2.64 0.83 2.01 6.44 0.70 Probability 0.4499 0.0547 0.2665 0.6616 0.3661 0.0399 0.7061

Observations 60 60 60 60 60 60 60

Figure 40: Descriptive statistics of selected US asset classes.

Asset classes used in the analysis of US mutual funds are shown above. The

mean return of the overall equity universe has sharply increased in the period

form January 1995 to December 1999 compared to the period from January

1990 to December 1994. If one looks at the average return of growths, value and

small stocks - representing the entire US equity universe - than the mean return

is somewhere between 0.75% per month to 0.93% per month for the 1990 to

1995 period. The analysis of the 1995 to 1999 period displayed in figure 17

shows a mean return for North American equities of about 2.65% per month

about three times the average return of the 1990 to 1995 period. Corporate

bonds and long-term bonds are the only two asset classes showing similar mean

returns but standard deviations are different. The correlogram in figure 38

already revealed this information. Striking is also the substantial difference

between median and mean for small and value stocks. For small stocks the

median is more than double the value of the mean marking fewer but larger

negative returns relatively to positive ones.

75

0.0% 20.0% 40.0% 60.0% 80.0% 100.0%

TBILLS

IMBDS

LTBDS

CORPBDS

VLSTCKS

GRSTCKS

SMSTCKS

R-squared

-0.2

-0.1

0

0.1

0.2

0.3

J-90 J-91 J-92 J-93 J-94

Cum

ulat

ive

Exce

ss R

etur

n

Figure 41: Style weights and cumulative selection contribution of Akorn fund.

Akorn fund returned on average 1.13% per month with a standard deviation of

4.41% per month. The asset allocation decision of the fund management

accounted for 88.2% of the overall return. Akorn fund experienced substantial

exposure to small stocks, which returned about 0.93% per month from January

1990 to December 1994 hence possibly revealing stock selection skill. The

volatility of small stocks over that period was 4.83% per month.

The residual analysis shows that Akorn's fund management did contribute value

through stock selection of approximately 0.24% per month and a standard

deviation of 1.51% per month over the studied period. These figures are not

significant at the 95% level as the t-value of 1.25 is below the required 1.67. The

Jarque-Bera test for normality is 0.7 with an associated 70% probability for the

normal distribution assumption under the null hypothesis of Jarque Bera.

76

0.0% 20.0% 40.0% 60.0% 80.0% 100.0%

TBILLS

IMBDS

LTBDS

CORPBDS

VLSTCKS

GRSTCKS

SMSTCKS

R-squared

-0.2

-0.1

0.0

0.1

J-90 J-91 J-92 J-93 J-94

Cum

ulat

ive

Exce

ss R

etur

nFigure 42: Style weights and cumulative selection contribution of Dreyfuss Growth OpportunityFund.

Dreyfuss Growth Opportunity fund's composition data unveils an almost sole

exposure to small and growth stocks. The fund's mean return was 0.53% per

month which somewhat pales when compared to the average returns of the two

asset classes of 0.93% per month for small stocks and 0.83% per month for

growth stocks. The standard deviation of Deryfuss Growth Opportunity fund's

return series is about 4.46% per month, slightly lower than that of small stocks of

4.83% and higher than the 4.1% of the growth stock asset class. About 81% of

Dreyfuss Growth Opportunity fund's return are attributable to asset allocation.

Stock selection accounted for 19% of Dreyfuss Growth Opportunity fund's return

- in this case a negative stock selection return averaging 0.31% per month with a

volatility of 1.94%. The erratic graph of the cumulative excess return suggests no

stock selection skill over the analyzed period. The adjacent t-value is negative

1.25 thus not significant at the 95%. A Jarque-Bera test returned a value of 0.16

with a probability for normal distribution of the residuals of 92%.

77

0.0% 20.0% 40.0% 60.0% 80.0% 100.0%

TBILLS

IMBDS

LTBDS

CORPBDS

VLSTCKS

GRSTCKS

SMSTCKS

R-squared

-0.05

0.00

0.05

0.10

0.15

0.20

J-90 J-91 J-92 J-93 J-94

Cum

ulat

ive

Exce

ss R

etur

nFigure 42: Style weights and cumulative selection contribution of Fidelity Magellan fund.

Fidelity Magellan Fund is substantially invested in value and growth stocks. This

is not surprising as the fund managed about $14 billion at the end of 1989,

making substantial investments in small stocks difficult.68 Sharpe found in his

study that the management of Fidelity Magellan fund reduced the portion of small

stocks successively from 1985 to about mid 1987 and kept it constant thereafter

at a 15 to 18 percent level. Sharpe found an R-squared for Fidelity Magellan fund

of 97.3% for the period from January 1985 to December 1989. The R-squared

value for the period studied here is 93.6% thus asset allocation accounted for

more than 90% of Fidelity Magellan fund's generated return of the last 10 years.

The mean return of Fidelity Magellan fund was 1.03% per month with a standard

deviation of 4.08%.

Remarkable is Magellan fund's stock selection contribution. Although only 6.4%

relative to its asset allocation decision but 0.23% per month in absolute terms

with a volatility of 1.04% per month. Over the period studied by Sharpe the

selection return was 0.57% per month with a standard deviation of 1.05% per

month. Testing the residuals for normality resulted in a 76% probability using the

Jarque Bera test. The t-value for this period was 1.7 indicating significant

68 SHARPE (1992), p. 13

78

outperformance and the t-value found by Sharpe was 3.76.69 This shows Fidelity

Magellan fund's remarkable performance.

0.0% 20.0% 40.0% 60.0% 80.0% 100.0%

TBILLS

IMBDS

LTBDS

CORPBDS

VLSTCKS

GRSTCKS

SMSTCKS

R-squared

-0.2

0

0.2

0.4

0.6

0.8

J-90 J-91 J-92 J-93 J-94C

umul

ativ

e Ex

cess

Ret

urn

Figure 43: Style weights and cumulative excess return of 20th Century Ultra Investors fund.

20th Century Ultra Investors fund generated a mean return of 1.71% per month

during the time period studied. This impressive return was achieved by taking on

substantial risk, namely 6.75% per month. Compared to the previous funds

asset allocation accounts for remarkable smaller part of the overall return. 73.7%

of the overall fund return are attributable to asset allocation.

Style analysis reveals significant stock picking skill of 20th Century Ultra Investors

management. The average excess return was 0.81% per month with a standard

deviation of 3.46. Although the excess return exhibits a considerable standard

deviation the t-value of 1.82 is significant at the 95% level. The fact that the

residuals are only normally distributed with a probability of 43% somewhat

mitigates the aptness of the t-value.

69 SHARPE (1992), p. 18

79

5. Conclusion and Final Remarks

Generally there are two broad ways to approach portfolio performance

evaluation. One is based on knowing the exact composition of the target

portfolio. If access to this information is provided the Grinblatt & Titman model

may be well suited to detect manager skill. Furthermore, the procedure will

produce very accurate results and conventional benchmark problems are

irrelevant, as no benchmark is needed.

The alternative is that no knowledge about an investment fund's composition

exists. This was the subject this master's thesis explored. The main problem

arising from the uncertainty of the investment funds composition is the selection

of an appropriate benchmark. Especially when asset allocation decisions of an

investment management are restricted by investment policies imposed by the

investor. In such cases a "generic" benchmark like the S&P 500 will be

notoriously non-reached by a fixed income fund but likely beaten by a fund taking

on sufficiently high risk like a small stock fund. Traditional measures of

performance do take risk into account but do not regard investment style and

reveal only a relatively small part of the information incorporated in the return

series of funds.

The analysis of six Austrian investment funds using style analysis unveiled

strength and weaknesses of style analysis. Most crucial for obtaining sound

results is the proper choice of asset classes. The fact that asset classes were not

exhaustive as required by Sharpe70 turned out to be very demonstrative in terms

of limitations of the model. When asset classes, the fund is invested in, are not

represented in the constrained regression analysis the estimated weights are

seriously in doubt. Furthermore asset classes with very similar return histories,

similar mean return and standard deviation are also prone to cause erratic style

weight estimates when rolling a time window over the sample period. This

70 SHARPE (1992), p. 8

80

problem was occasionally present with the EVALUE and EGROWTH asset

classes, but was of minor impact. This infers that a correlation of about 0.87 does

not pose a significant problem even when potential asset classes are missing.

Another point of concern is high asset turnover as well as high asset class

turnover because style weights may not be stable and be insufficient estimates of

the "true" style weights. However, rolling a window can mitigate this problem.

When asset classes are specified appropriately the information content revealed

with style analysis is remarkable. Particularly practical is the division of portfolio

returns into an asset allocation contribution and a security selection contribution.

By that, an active investment manager's skill can be isolated from obligations

imposed by an investment policy or independent asset allocation decisions made

by the manager. On this basis the investor has a tool to select a manager with a

style he considers apt for his investment strategy. Furthermore sufficiently large

investment funds can construct a "portfolio manager matrix". Thus hiring

investment managers for the asset allocation decision, who have shown to do

especially well in that field and stock selection managers who were detected to

do well in the stock selection field. An additional advantage of style analysis is its

cost effectiveness and simplicity. The sole input are return series.

One problem the style analysis approach developed by Sharpe does not solve

either is the benchmark problem. Style analysis breaks the benchmark down into

separate benchmarks for each asset class. By that the benchmark problem has

only been broken down into separate "smaller" benchmark inaccuracies, but the

initial problem persists namely that that a mispecified riskless rate and a

mispecified market portfolio (individual asset class portfolios) can lead to the

inaccuracies exhibited in Figure 7.

Overall it seems that style analysis is very useful in cases where composition

data for specific investment fund is not available. Thus, referring to the question

addressed in the beginning about the usefulness of Sharpe's style analysis

model for portfolio performance evaluation, the conclusion was reached that

81

when asset classes are specified carefully, impressive information can be

revealed. Furthermore portfolio evaluation can be very specific resulting in a fair

classification and evaluation of a portfolio management's performance.

I

Figures

Figure 1: Haugen Robert A., "Modern Investment Theory", Third Edition,

Prentice Hall/Upper Saddle River, NJ (1993), p. 207.

Figure 2: Sorenson Eric H., Miller Keith L., Samak Vele, "Allocating between

Active and Passive Management", Financial Analyst Journal, Sept./Oct. (1998),

p. 19.

Figure 3: Treynor Jack L., Mazuy Kay K., "Can Mutual Funds Outguess the

Market?", Harvard Business Review, July/Aug. (1966), p. 133.

Figure 4: "Relationship between the TR and an investors' utility", Created by

Johann Aldrian

Figure 5: Ippolito Richard A., "On Studies of Mutual Fund Performance, 1962 -

1991", Financial Analysts Journal, Jan./Feb. (1993), p. 44.

Figure 6: Sharpe William F., "Morningstar's Risk-Adjusted Ratings", Financial

Analyst Journal, July/Aug., (1998), p. 30.

Figure 7: Roll Richard, "Performance Evaluation and Benchmark Errors (I)", The

Journal of Portfolio Management, Summer (1980), p.6.

Figure 8: Lehmann Bruce N., Modest David M., "Mutual Fund Performance

Evaluation: A Comparison of Benchmarks and Benchmark Comparisons",

Journal of Finance, June, (1987), p. 251.

II

Figure 9: Grinblatt Mark, Titman Sheridan, "Performance Measurement without

Benchmarks: An Examination of Mutual Fund Returns", Journal of Business, vol.

66 no. 1, (1993), p. 56.

Figure 10: Sharpe, William F., "Asset Allocation: Management Style and

Performance Measurement", Journal of Portfolio Management, Winter (1992),

p.10.

Figure 11: Descriptive statistics of Appollo 4 fund.

Figure 12: Descriptive statistics of Constantia Privat-Invest fund.

Figure 13: Descriptive statistics of Generali Mixfund.

Figure 14: Descriptive statistics of Raiffeisen Global Mix fund.

Figure 15: Descriptive statistics of SparInvest fund.

Figure 16: Descriptive statistics of Spängler Securities Trust fund.

Figure 17: Descriptive statistics of selected asset classes.

Figure 18: Cross-Correlogram of selected asset classes.

Figure 19: Solver set-up to calculate Sharpe style weights.

Figure 20: Style weights using different asset classes.

Figure 21: Teststatistic of first-lag auto-correlation of residuals.

III

Figure 22: T-values of the estimated residual's mean value for selected Austrian

investment funds.

Figure 23: Style changes of Con fund.

Figure 24: Style changes of A4 fund.

Figure 25: Style changes of Gen fund.

Figure 26: Style changes of Rai fund.

Figure 27: Style changes of Ers fund.

Figure 28: Style changes of Spa fund.

Figure 29: True and calculated weight comparison of A4, Gen and Rai fund.

Figure 30: Cumulative selection return of Con fund.

Figure 31: Cumulative excess return of A4 fund.

Figure 32: Comparison of performance development of A4 fund using "true"

style weights and estimated style weights.

Figure 33: Cumulative excess return of Gen fund.

Figure 34: Cumulative excess return of Rai fund.

.

Figure 35: Sensitivity of Rai fund's selection return to style weight changes.

Figure 36: Cumulative excess return of Spa fund.

IV

Figure 37: Summary of findings for Austrian investment funds.

Figure 38: Selected US mutual funds.

Figure 39: Correlogram of US asset classes.

Figure 40: Descriptive statistics of US asset classes.

Figure 41: Style weights and cumulative selection contribution of Akorn fund.

Figure 42: Style weights and cumulative selection contribution of Dreyfuss

Growth Opportunity fund.

Figure 42: Style weights and cumulative selection contribution of Fidelity

Magellan fund.

Figure 43: Style weights and cumulative excess return of 20th Century Ultra

Investors fund.

V

References

Brinson Gary P., Hood Randolph L., Beebower Gilbert L., "Determinants of

Portfolio Performance", Financial Analysts Journal, July/August (1986).

Christopherson Jon A., "Equity Style Classifications", The Journal of Portfolio

Management, Spring (1995).

Elton Edwin J., Gruber Martin J., "Modern Portfolio Theory and Investment

Analysis", Fourth Edition, John Wiley & Sons Inc./NY (1992).

Fama Eugene F., French Kenneth R., "Common Risk Factors in the Returns on

Stocks and Bonds", Journal of Financial Economics, February, (1993).

Fama Eugene F., "Efficient Capital Markets: A Review of Theory and Empirical

Work", Journal of Finance, May (1970).

Fischer, Edwin O., "Finanzwirtschaft für Fortgeschrittene", Oldenburg Verlag,

Wien - München, (1996).

Friend Irwin, Blume Marshall E., Crockett Jean, "Mutual Funds and other

Institutional Investors", Mc Graw Hill/NY (1970).

Graham Benjamin, "The Intelligent Investor", HarperBusiness NY, (1949).

Grinblatt Mark, Titman Sheridan, "Performance Measurement without

Benchmarks: An Examination of Mutual Fund Returns", Journal of Business, vol.

66 no. 1, (1993).

VI

Grinblatt Mark, Titman Sheridan, "Mutual Fund Performance: An Analysis of

Quarterly Portfolio Holdings", Journal of Business, 62 (1989).

Hull John C., "Options Futures and other Derivatives", Third Edition, Prentice

Hall/Upper Saddle River, NJ (1997).

Ippolito Richard A., "On Studies of Mutual Fund Performance, 1962 - 1991",

Financial Analysts Journal, Jan./Feb. (1993).

Jensen Michael C., "The Performance of Mutual funds in the Period 1945 -

1964", Journal of Finance, May, (1968).

Kothari S. P., Warner Jerold B., "Evaluating Mutual Fund Performance",

Working Paper SLOAN School of Management (1997); MIT, 50 Memorial Drive,

Cambridge, MA 02142; email:[email protected].

LeClair Robert T., "Discriminant Analysis and the Classification of Mutual

Funds", Journal of Economics and Business, Spring (1974).

Lehmann Bruce N., Modest David M., "Mutual Fund Performance Evaluation: A

Comparison of Benchmarks and Benchmark Comparisons", Journal of Finance,

June, (1987).

Lobosco Angelo, DiBartolomeo Dan, "Approximating the Confidence Intervals

for Sharpe Style Weights", Financial Analysts Journal, July/August (1997).

Modigliani Franco, Modigliani Leah, "Risk-Adjusted Performance", The Journal

of Portfolio Management, Winter (1997).

MSCI, "Index Calculations", www.msci.com/cover/index.html, June 2000.

VII

Österreichische Kontrollbank, "Index Downloads", www.oekb.at, June 2000.

Roll Richard, "Performance Evaluation and Benchmark Errors (I)", The Journal

of Portfolio Management, Summer (1980).

Ross Stephen A., "The Arbitrage Theory of Capital Asset Pricing", Journal of

Economic Theory, December, (1976).

Sharpe William F., "Morningstar's Risk-Adjusted Ratings", Financial Analyst

Journal, July/Aug., (1998).

Sharpe William F., Alexander Gordon J., Bailey Jeffery V., "Investments",

Sixth Edition, Prentice Hall/Upper Saddle River, NJ (1998).

Sharpe, William F., "Asset Allocation: Management Style and Performance

Measurement", Journal of Portfolio Management, Winter (1992).

Sharpe William F., "Determining a Fund's Effective Asset Mix", Investment

Management Review, December (1988).

Sharpe William F., "Mutual Fund Performance", Journal of Business, January

(1966).

Sorenson Eric H., Miller Keith L., Samak Vele, "Allocating between Active and

Passive Management", Financial Analyst Journal, Sept./Oct. (1998).

trendINVEST, "Investment & Fonds", No. 1/Jänner 2000.

Treynor Jack L., Mazuy Kay K., "Can Mutual Funds Outguess the Market?",

Harvard Business Review, July/Aug. (1966).

VIII

Treynor Jack L., "How to Rate Management of Investment Funds", Harvard

Business Review, Jan./Feb., (1965).

Tzcinka Charles A., "Equity Style Classifications: Comment", The Journal of

Portfolio Management, Spring (1995).

IX

Monthly data with dividends reinvested of the analyzed Austrian investment funds in EUR.

Con BA Gen Rai Ers Spa

A-95 39.39 145.31 82.48 344.70 88.77 68.06M-95 40.48 148.51 86.33 353.58 91.03 69.89

J-95 40.48 147.79 85.09 351.13 93.20 72.20

J-95 40.79 150.19 86.55 359.51 93.17 73.14

A-95 41.00 151.71 86.11 370.61 96.02 75.53

S-95 41.14 151.23 84.95 363.28 97.25 75.62

O-95 41.07 150.75 82.77 360.55 98.65 75.84

N-95 41.91 152.66 85.97 373.79 98.49 77.67

D-95 42.44 153.51 87.22 382.20 101.65 76.98

J-96 43.46 156.48 93.25 394.66 104.35 79.55

F-96 43.07 155.97 93.32 392.08 107.55 80.70

M-96 43.31 157.30 93.57 396.83 106.59 82.30

A-96 43.63 160.53 93.99 410.08 108.53 85.23

M-96 43.84 160.89 93.89 412.06 111.17 87.10

J-96 43.70 160.41 92.95 411.52 112.59 86.82

J-96 43.46 157.81 90.48 395.97 113.69 84.62

A-96 43.95 159.91 91.70 400.76 109.06 85.62

S-96 44.54 162.81 93.24 415.57 110.29 88.50

O-96 44.86 163.07 93.37 416.79 115.12 87.67

N-96 45.52 166.59 96.11 439.02 116.96 89.51

D-96 45.94 167.84 97.95 445.54 123.51 90.20

J-97 46.43 173.02 101.76 465.60 123.13 93.21

F-97 47.10 177.11 105.43 485.84 128.59 95.26

M-97 46.68 176.01 105.84 481.12 131.22 95.43

A-97 46.61 178.69 107.47 489.77 130.37 96.68

M-97 47.03 182.78 109.68 512.75 134.76 98.20

J-97 47.52 189.14 114.39 531.22 139.24 99.77

J-97 48.54 199.13 121.18 572.65 147.52 103.64

A-97 47.87 192.24 115.28 558.34 156.04 101.24

S-97 48.54 194.34 119.18 555.36 146.60 102.04

O-97 47.87 187.67 114.13 526.10 152.57 100.01

N-97 48.12 191.34 117.09 530.21 146.39 102.10

D-97 48.68 194.55 120.10 535.73 149.16 102.19

J-98 49.41 198.38 123.19 558.00 154.88 104.53

F-98 49.94 202.42 127.73 575.30 159.03 107.34

M-98 50.57 206.40 133.87 589.90 167.59 107.86

A-98 50.39 204.37 131.65 583.96 175.09 106.53

M-98 51.13 203.89 133.42 580.17 175.36 106.58

J-98 51.38 207.16 137.75 584.84 173.39 108.09

J-98 51.66 207.47 137.24 574.19 175.32 107.62

A-98 51.94 201.41 128.84 547.19 175.87 104.48

S-98 51.83 196.99 123.89 533.62 158.00 105.45

X

Con BA Gen Rai Ers Spa

O-98 51.76 199.71 125.57 545.52 153.47 109.10N-98 52.50 208.91 133.57 579.48 161.16 111.17

D-98 52.88 207.39 135.21 576.47 171.93 113.39

J-99 53.58 211.01 135.14 601.91 174.97 116.31

F-99 53.58 208.64 134.89 613.58 179.13 117.80

M-99 53.34 209.52 135.64 636.46 179.04 119.67

A-99 54.39 213.93 137.93 667.54 187.04 120.90

M-99 53.48 212.35 134.85 655.00 195.58 117.97

J-99 53.34 213.73 138.01 680.58 190.54 119.74

J-99 53.06 210.67 133.48 671.50 196.12 119.14

A-99 52.95 214.08 136.58 685.09 191.35 120.20

S-99 52.39 209.56 133.53 672.57 190.99 119.37

O-99 52.15 210.51 138.45 675.95 186.23 120.09

N-99 52.57 218.79 148.91 724.56 192.34 122.29

D-99 52.43 222.21 156.53 750.20 200.97 122.60

XI

Asset class data with net dividends reinvested in USD applied in Austrian fund's style analysis.

ESTAND EVALUE EGROWTH NASTAND NAVALUE NAGROWTH JPSTAND G7GOV API

A-95 180 105

M-95 0.0203 0.0242 0.0163 0.0380 0.0391 0.0369 -0.0640 190 107

J-95 0.0094 -0.0040 0.0227 0.0235 0.0143 0.0327 -0.0490 186 107

J-95 0.0508 0.0515 0.0501 0.0322 0.0360 0.0282 0.0766 187 108

A-95 -0.0394 -0.0480 -0.0313 -0.0003 0.0074 -0.0082 -0.0410 200 109

S-95 0.0298 0.0279 0.0342 0.0410 0.0313 0.0505 0.0084 196 110

O-95 -0.0047 -0.0067 -0.0028 -0.0012 -0.0137 0.0108 -0.0576 196 111

N-95 0.0071 0.0113 0.0034 0.0423 0.0482 0.0366 0.0575 205 113

D-95 0.0312 0.0357 0.0276 0.0144 0.0212 0.0072 0.0499 205 115

J-96 0.0065 0.0010 0.0116 0.0355 0.0313 0.0395 -0.0132 214 116

F-96 0.0181 0.0183 0.0179 0.0090 0.0062 0.0119 -0.0180 209 115

M-96 0.0119 0.0100 0.0142 0.0102 0.0179 0.0025 0.0347 210 116

A-96 0.0072 0.0101 0.0037 0.0157 0.0150 0.0163 0.0553 218 117

M-96 0.0077 0.0079 0.0071 0.0255 0.0108 0.0402 -0.0528 218 118

J-96 0.0110 0.0083 0.0136 0.0038 -0.0034 0.0109 0.0053 220 117

J-96 -0.0126 -0.0101 -0.0150 -0.0446 -0.0445 -0.0444 -0.0458 213 118

A-96 0.0292 0.0322 0.0263 0.0229 0.0281 0.0174 -0.0457 215 119

S-96 0.0208 0.0145 0.0265 0.0534 0.0402 0.0662 0.0341 226 121

O-96 0.0230 0.0197 0.0254 0.0276 0.0369 0.0171 -0.0694 228 122

N-96 0.0494 0.0534 0.0458 0.0724 0.0732 0.0712 0.0189 236 124

D-96 0.0192 0.0221 0.0170 -0.0203 -0.0189 -0.0216 -0.0716 235 125

J-97 0.0027 0.0082 -0.0018 0.0650 0.0506 0.0792 -0.1152 252 126

F-97 0.0131 0.0210 0.0067 0.0059 0.0057 0.0062 0.0231 260 127

M-97 0.0318 0.0316 0.0320 -0.0464 -0.0364 -0.0567 -0.0335 255 126

A-97 -0.0050 -0.0029 -0.0070 0.0613 0.0394 0.0836 0.0356 268 127

M-97 0.0418 0.0491 0.0346 0.0562 0.0561 0.0562 0.1048 265 127

J-97 0.0488 0.0407 0.0568 0.0429 0.0355 0.0504 0.0721 274 129

J-97 0.0458 0.0465 0.0451 0.0752 0.0818 0.0686 -0.0309 295 130

A-97 -0.0588 -0.0579 -0.0597 -0.0611 -0.0482 -0.0745 -0.0907 288 129

S-97 0.0926 0.0929 0.0922 0.0510 0.0544 0.0475 -0.0152 287 130

O-97 -0.0504 -0.0322 -0.0670 -0.0289 -0.0259 -0.0320 -0.0978 282 130

N-97 0.0152 0.0167 0.0138 0.0433 0.0355 0.0513 -0.0633 291 131

D-97 0.0359 0.0362 0.0358 0.0149 0.0242 0.0054 -0.0589 299 132

J-98 0.0408 0.0391 0.0424 0.0112 -0.0103 0.0328 0.0855 307 134

F-98 0.0753 0.0685 0.0818 0.0682 0.0644 0.0720 0.0052 306 135

M-98 0.0688 0.0949 0.0438 0.0514 0.0493 0.0535 -0.0705 314 135

A-98 0.0192 0.0208 0.0176 0.0111 0.0204 0.0018 -0.0041 306 135

M-98 0.0201 0.0221 0.0181 -0.0201 -0.0248 -0.0152 -0.0565 307 137

J-98 0.0109 -0.0008 0.0222 0.0382 0.0071 0.0684 0.0139 313 138

J-98 0.0196 0.0324 0.0074 -0.0128 -0.0184 -0.0075 -0.0133 310 139

A-98 -0.1344 -0.1607 -0.1099 -0.1538 -0.1746 -0.1350 -0.1211 313 141

S-98 -0.0408 -0.0409 -0.0407 0.0620 0.0551 0.0690 -0.0277 304 143

O-98 0.0770 0.0683 0.0856 0.0751 0.0787 0.0715 0.1550 301 143

XII

ESTAND EVALUE EGROWTH NASTAND NAVALUE NAGROWTH JPSTAND G7GOV API

N-98 0.0518 0.0543 0.0494 0.0644 0.0529 0.0760 0.0447 308 144D-98 0.0428 0.0197 0.0648 0.0555 0.0262 0.0834 0.0380 302 145

J-99 -0.0065 -0.0183 0.0046 0.0433 0.0249 0.0597 0.0072 315 147

F-99 -0.0257 -0.0105 -0.0400 -0.0297 -0.0101 -0.0472 -0.0222 321 146

M-99 0.0109 0.0428 -0.0217 0.0404 0.0252 0.0555 0.1299 330 146

A-99 0.0294 0.0665 -0.0105 0.0375 0.0859 -0.0120 0.0409 339 149

M-99 -0.0492 -0.0589 -0.0385 -0.0240 -0.0201 -0.0282 -0.0580 342 147

J-99 0.0167 0.0175 0.0159 0.0517 0.0273 0.0775 0.0904 341 145

J-99 0.0092 0.0258 -0.0102 -0.0317 -0.0270 -0.0366 0.0952 328 144

A-99 0.0101 0.0053 0.0154 -0.0070 -0.0313 0.0177 -0.0070 332 143

S-99 -0.0077 -0.0110 -0.0042 -0.0282 -0.0463 -0.0109 0.0589 331 143

O-99 0.0361 0.0191 0.0540 0.0632 0.0528 0.0728 0.0420 336 142

N-99 0.0266 -0.0053 0.0594 0.0217 -0.0049 0.0451 0.0420 351 143

D-99 0.0976 0.0776 0.1168 0.0699 0.0202 0.1107 0.0602 352 143

XIII

Monthly exchange rate data from April 1995 to December 1999

ATS-JPY ATS-USD RetJPY RetUSD

A-95 11.549 9.707M-95 11.765 10.094 0.019 0.039

J-95 11.47 9.736 -0.025 -0.036

J-95 11.05 9.719 -0.037 -0.002

A-95 10.62 10.315 -0.040 0.060

S-95 10.127 9.976 -0.048 -0.033

O-95 9.742 9.944 -0.039 -0.003

N-95 9.94 10.065 0.020 0.012

D-95 9.842 10.088 -0.010 0.002

J-96 9.776 10.48 -0.007 0.038

F-96 9.87 10.335 0.010 -0.014

M-96 9.74 10.382 -0.013 0.005

A-96 10.3 10.757 0.056 0.035

M-96 9.964 10.801 -0.033 0.004

J-96 9.838 10.731 -0.013 -0.007

J-96 9.651 10.34 -0.019 -0.037

A-96 9.578 10.418 -0.008 0.008

S-96 9.652 10.747 0.008 0.031

O-96 9.376 10.649 -0.029 -0.009

N-96 9.496 10.801 0.013 0.014

D-96 9.423 10.954 -0.008 0.014

J-97 9.466 11.495 0.005 0.048

F-97 9.872 11.905 0.042 0.035

M-97 9.583 11.819 -0.030 -0.007

A-97 9.61 12.166 0.003 0.029

M-97 10.272 11.962 0.067 -0.017

J-97 10.739 12.283 0.044 0.026

J-97 11.068 12.99 0.030 0.056

A-97 10.615 12.634 -0.042 -0.028

S-97 10.25 12.436 -0.035 -0.016

O-97 10.12 12.148 -0.013 -0.023

N-97 9.748 12.418 -0.037 0.022

D-97 9.767 12.633 0.002 0.017

J-98 10.117 12.837 0.035 0.016

F-98 10.094 12.729 -0.002 -0.008

M-98 9.777 13.001 -0.032 0.021

A-98 9.548 12.627 -0.024 -0.029

M-98 9.02 12.552 -0.057 -0.006

J-98 9.093 12.732 0.008 0.014

J-98 8.692 12.531 -0.045 -0.016

A-98 8.811 12.488 0.014 -0.003

S-98 8.675 11.803 -0.016 -0.056

XIV

ATS-JPY ATS-USD RetJPY RetUSD

O-98 9.97 11.616 0.139 -0.016

N-98 9.758 11.995 -0.021 0.032

D-98 10.290 11.747 0.053 -0.021

J-99 10.417 12.087 0.012 0.029

F-99 10.478 12.489 0.006 0.033

M-99 10.766 12.810 0.027 0.025

A-99 10.843 12.985 0.007 0.014

M-99 10.820 13.160 -0.002 0.013

J-99 11.024 13.323 0.019 0.012

J-99 11.170 12.867 0.013 -0.035

A-99 11.911 13.015 0.064 0.011

S-99 12.213 12.902 0.025 -0.009

O-99 12.556 13.164 0.028 0.020

N-99 13.360 13.628 0.062 0.035

D-99 13.395 13.697 0.003 0.005

XV

Monthly US Mutual fund data from January 1990 to December 1994

20th cent. Ultra Investor Akorn Dreyfuss Fidelity MagellanJ-90 -0.11020 -0.06480 -0.04640 -0.06450

F-90 0.03690 0.01250 0.01240 0.02050

M-90 0.03680 0.03030 0.02150 0.02560

A-90 -0.02450 -0.02890 -0.02910 -0.02530

M-90 0.17090 0.07130 0.07840 0.08890

J-90 0.01610 0.01630 -0.00190 0.00430

J-90 -0.02530 -0.01440 -0.01050 -0.01130

A-90 -0.08880 -0.13460 -0.08910 -0.09800

S-90 -0.05590 -0.10630 -0.05850 -0.06350

O-90 -0.02640 -0.02350 0.00960 -0.01240

N-90 0.13200 0.03970 0.04300 0.07570

D-90 0.06610 0.03310 0.01480 0.03100

J-91 0.15270 0.05960 0.04260 0.06990

F-91 0.08210 0.08170 0.07540 0.08680

M-91 0.12840 0.04050 0.04770 0.03400

A-91 -0.05120 0.03220 -0.02790 0.00370

M-91 0.08370 0.04710 0.04210 0.05700

J-91 -0.08770 -0.04310 -0.04860 -0.05880

J-91 0.12540 0.04620 0.07710 0.06210

A-91 0.06010 0.03790 0.03670 0.03070

S-91 -0.00610 0.00090 0.00180 -0.00380

O-91 0.06660 0.03160 0.04940 0.01340

N-91 -0.04570 -0.02840 -0.01400 -0.04940

D-91 0.17000 0.09670 0.15620 0.11800

J-92 0.01730 0.05360 -0.02040 0.00040

F-92 -0.01640 0.03640 -0.01860 0.02030

M-92 -0.06970 -0.00710 -0.05300 -0.02710

A-92 -0.07370 -0.03030 -0.04800 0.01480

M-92 0.02470 0.00430 0.02610 0.00960

J-92 -0.06270 -0.02440 -0.05000 -0.01760

J-92 0.05710 0.03760 0.05260 0.02810

A-92 -0.05140 -0.01600 -0.02290 -0.02170

S-92 0.02360 0.01770 0.01170 0.01150

O-92 0.04880 0.05280 0.02150 0.00710

N-92 0.07700 0.05800 0.05600 0.02530

D-92 0.05470 0.04140 0.01080 0.01940

J-93 0.02790 0.04300 -0.00080 0.02630

F-93 -0.07590 -0.00280 -0.07010 0.02090

M-93 0.05160 0.05410 0.01060 0.03670

A-93 -0.01770 -0.02510 -0.04380 0.00980

M-93 0.11670 0.08240 0.06860 0.03940

J-93 0.03950 0.01140 -0.00240 0.01390

J-93 -0.00850 -0.00510 -0.00400 0.01100

XVI

20th cent. Ultra Investor Akorn Dreyfuss Fidelity MagellanA-93 0.08120 0.06600 0.06070 0.05880

S-93 0.02850 0.02920 0.03690 0.01080

O-93 -0.02000 0.03810 -0.00870 0.00070

N-93 -0.05090 -0.03780 -0.04660 -0.03290

D-93 0.04290 0.03720 0.02700 0.02990

J-94 0.05940 0.00500 0.02610 0.03950

F-94 -0.01240 -0.01210 -0.01090 -0.00730

M-94 -0.06170 -0.04840 -0.06970 -0.04640

A-94 -0.00570 0.00830 0.00690 0.01000

M-94 -0.02920 -0.01130 0.00980 -0.01150

J-94 -0.04980 -0.03420 -0.02720 -0.04340

J-94 0.01140 0.03230 0.01790 0.03350

A-94 0.05850 0.04610 0.02250 0.04740

S-94 -0.01790 -0.01250 -0.01440 -0.02600

O-94 0.04490 -0.00370 0.01550 0.03380

N-94 -0.04060 -0.03890 -0.05000 -0.05480

D-94 0.01560 -0.00360 0.01320 0.01410

XVII

Monthly US asset class returns from January 1990 to December 1994

Tbills IMBDS LTBDS CORPBDS VLSTCKS GRSTCKS SMSTCKSJ-90 0.0057 -0.0105 -0.0343 -0.0191 -0.0623 -0.0804 -0.0873

F-90 0.0057 0.0007 -0.0025 -0.0012 0.0252 0.0071 0.0310

M-90 0.0064 0.0002 -0.0044 -0.0011 0.0102 0.0398 0.0392

A-90 0.0069 -0.0077 -0.0202 -0.0191 -0.0390 -0.0130 -0.0327

M-90 0.0068 0.0261 0.0415 0.0385 0.0830 0.1039 0.0708

J-90 0.0063 0.0151 0.0230 0.0216 -0.0227 0.0108 0.0026

J-90 0.0068 0.0174 0.0107 0.0102 -0.0087 -0.0091 -0.0438

A-90 0.0066 -0.0092 -0.0419 -0.0292 -0.0879 -0.0959 -0.1338

S-90 0.0060 0.0094 0.0117 0.0091 -0.0484 -0.0539 -0.0889

O-90 0.0068 0.0171 0.0215 0.0132 -0.0137 0.0040 -0.0611

N-90 0.0057 0.0193 0.0402 0.0285 0.0693 0.0674 0.0763

D-90 0.0060 0.0161 0.0187 0.0167 0.0254 0.0354 0.0393

J-91 0.0052 0.0107 0.0130 0.0150 0.0450 0.0512 0.0901

F-91 0.0048 0.0048 0.0030 0.0121 0.0665 0.0794 0.1122

M-91 0.0044 0.0023 0.0038 0.0108 0.0148 0.0394 0.0701

A-91 0.0053 0.0117 0.0140 0.0138 0.0074 -0.0047 -0.0026

M-91 0.0047 0.0059 0.0000 0.0039 0.0373 0.0446 0.0476

J-91 0.0042 -0.0023 -0.0063 -0.0018 -0.0421 -0.0474 -0.0578

J-91 0.0049 0.0129 0.0157 0.0167 0.0419 0.0536 0.0350

A-91 0.0046 0.0247 0.0340 0.0275 0.0182 0.0334 0.0369

S-91 0.0046 0.0216 0.0303 0.0271 -0.0074 -0.0174 0.0078

O-91 0.0042 0.0134 0.0054 0.0043 0.0166 0.0156 0.0264

N-91 0.0039 0.0128 0.0082 0.0106 -0.0513 -0.0255 -0.0463

D-91 0.0038 0.0265 0.0581 0.0436 0.0838 0.1413 0.0800

J-92 0.0034 -0.0195 -0.0324 -0.0173 0.0016 -0.0242 0.0811

F-92 0.0028 0.0022 0.0051 0.0096 0.0245 0.0015 0.0292

M-92 0.0034 -0.0079 -0.0094 -0.0073 -0.0145 -0.0273 -0.0338

A-92 0.0032 0.0098 0.0016 0.0016 0.0431 0.0072 -0.0351

M-92 0.0028 0.0222 0.0243 0.0254 0.0050 0.0074 0.0133

J-92 0.0032 0.0177 0.0200 0.0156 -0.0062 -0.0252 -0.0470

J-92 0.0031 0.0242 0.0398 0.0308 0.0386 0.0448 0.0348

A-92 0.0026 0.0150 0.0067 0.0090 -0.0306 -0.0122 -0.0283

S-92 0.0026 0.0194 0.0185 0.0099 0.0138 0.0116 0.0230

O-92 0.0023 -0.0182 -0.0198 -0.0156 0.0009 0.0150 0.0316

N-92 0.0023 -0.0084 0.0010 0.0069 0.0328 0.0435 0.0766

D-92 0.0028 0.0146 0.0246 0.0228 0.0238 0.0100 0.0348

J-93 0.0023 0.0270 0.0280 0.0250 0.0290 -0.0115 0.0338

F-93 0.0022 0.0243 0.0354 0.0256 0.0352 -0.0158 -0.0231

M-93 0.0025 0.0043 0.0021 0.0025 0.0295 0.0193 0.0324

A-93 0.0024 0.0088 0.0072 0.0052 -0.0128 -0.0400 -0.0275

M-93 0.0022 -0.0009 0.0047 0.0020 0.0201 0.0350 0.0442

J-93 0.0025 0.0201 0.0449 0.0293 0.0221 -0.0092 0.0062

J-93 0.0024 0.0005 0.0192 0.0100 0.0112 -0.0179 0.0138

XVIII

Tbills IMBDS LTBDS CORPBDS VLSTCKS GRSTCKS SMSTCKSA-93 0.0025 0.0223 0.0434 0.0287 0.0361 0.0410 0.0432

S-93 0.0026 0.0056 0.0005 0.0043 0.0016 -0.0075 0.0282

O-93 0.0022 0.0018 0.0096 0.0051 -0.0007 0.0278 0.0258

N-93 0.0025 -0.0093 -0.0259 -0.0188 -0.0206 -0.0066 -0.0326

D-93 0.0023 0.0032 0.0020 0.0067 0.0190 0.0173 0.0342

J-94 0.0025 0.0138 0.0257 0.0202 0.0378 0.0231 0.0313

F-94 0.0021 -0.0258 -0.0450 -0.0286 -0.0342 -0.0182 -0.0036

M-94 0.0027 -0.0257 -0.0395 -0.0383 -0.0372 -0.0483 -0.0527

A-94 0.0027 -0.0105 -0.0150 -0.0097 0.0192 0.0048 0.0059

M-94 0.0032 -0.0002 -0.0082 -0.0062 0.0115 0.0151 -0.0113

J-94 0.0031 -0.0028 -0.0101 -0.0081 -0.0240 -0.0295 -0.0337

J-94 0.0028 0.0169 0.0363 0.0309 0.0311 0.0342 0.0164

A-94 0.0037 0.0026 -0.0086 -0.0031 0.0287 0.0557 0.0557

S-94 0.0037 -0.0158 -0.0331 -0.0265 -0.0332 -0.0137 -0.0034

O-94 0.0038 -0.0023 -0.0025 -0.0050 0.0139 0.0236 -0.0040

N-94 0.0037 -0.0070 0.0066 0.0018 -0.0404 -0.0320 -0.0404

D-94 0.0044 0.0053 0.0161 0.0157 0.0115 0.0168 0.0268

Date post:	18-May-2018
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