An Age-Based, Three Dimensional, Universal Distribution ...€¦ · Investment Research for the...

An Age-Based, Three Dimensional, Universal Distribution Model Incorporating Sequence and Longevity Risks

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Presented at Academy of Financial Services Las Vegas NV October 23, 2011 Session A1: 8:00 – 9:15 am, Retirement Planning I

Larry R Frank Sr., Registered Investment Adviser (California) Better Financial Education

1100 Melody Lane Suite 134 Roseville, CA 95678

Corresponding author: [email protected] (916) 773-3509

John B. Mitchell, Department of Finance and Law

328 Sloan Hall Central Michigan University

Mt. Pleasant, MI 48859 [email protected]

(989) 774-3651

David M. Blanchett, Director – Consulting and Investment Research Unified Trust Company, NA 2353 Alexandria Drive, Suite 100

Lexington, KY 40504 [email protected]

(859) 296-4407 x 222 Larry R. Frank, Sr., MBA, CFP®, a Registered Investment Advisor and author, lives in Rocklin, California. He has combined an MBA with a finance concentration from the University of South Dakota, with a BS cum laude Physics from the University of Minnesota, to bring the time dimension into the dynamics of retirement distributions in personal finance.

John B. Mitchell, DBA, is Professor of Finance at Central Michigan University. His research focuses include simulation-based retirement planning models, the statistical properties of financial time series, assessment of learning, and derivatives strategies. David M. Blanchett, MBA, CFP®, CLU, AIFA®, QPA, CFA, is the Director of Consulting and Investment Research for the Retirement Plan Consulting Group at Unified Trust Company in Lexington, KY. He recently completed his MBA at the University of Chicago, Booth School of Business in Chicago, Illinois. He won the Journal of Financial Planning’s 2007 Financial Frontiers Award with a paper titled “Dynamic Allocation Strategies for Distribution Portfolios: Determining the Optimal Distribution Glide Path.”


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Abstract

The authors develop an Age-Based Three Dimensional Distribution Model that illustrates a retiree transition from early retirement into later retirement, including superannuated years for the long-lived who continue to survive. The model for this concept development simultaneously: 1) Establishes an age-based distribution model. 2) Incorporates current age life expectancy directly into the model. 3) Addresses survivorship into superannuated ages. 4) Addresses sequence risk to incorporate decisions due to market changes as the retiree ages. What is new? This is a concept development paper. Rather than generic distribution periods non-correlated with retirement age, the authors have developed an age-based model that uses expected longevity to define the length of the current distribution period (DP). The current DP changes dynamically each year 1) as the retiree ages and 2) by adjusting for the percentage of those statistically expected to outlive the current age’s expected longevity. Finally, market sequence risk is evaluated to confirm a decision rule from prior research for withdrawal amount adjustments based on either poor or good market sequences. Brief Overview.

This paper’s objective is to develop an Age-Based Three Dimensional Distribution Model for Retirement. The model consists of plotting the results of many simulations relative to each other, where each simulation represents a Transitory State that a retiree may pass through as time and portfolio values change. A persistent distribution problem is the lack of a specific distribution period based on the retiree’s current age. The authors also evaluate the transition between “early” retiree ages with those corresponding expected longevities, to “older” retiree ages (superannuated); specifically how outliving early/younger Distribution Period estimates affects later/older distribution feasibility. A sustainable withdrawal rate (WR%) depends on a number of factors. The withdrawal rate itself is a time dependent variable. Thus, longevity is a very important variable to determine proper age specific distribution periods. This paper is based on U.S. expected longevity. For application of withdrawal rate research in any given country, the expected longevity of the population of that country needs to be substituted. Additionally, rather than any given country trying to sustain distributions using their own market exclusively as studied by Pfau (2010), the authors suggest that a globally diversified portfolio be used regardless of what country a retiree lives in. A need exists for a more comprehensive distribution model. First, making decisions based on a single simulation, or a series of simulations, is essentially a reactive form of decision making based on a single Transitory State, i.e., results of a single simulation on a single set of temporary conditions. Proactive, or strategic, decision making requires a larger context of how a decision to solve one issue, e.g., longevity risk, may affect another issue, e.g., sequence risk, vice versa, and may need to include other factors relevant to overall strategic decisions such as asset allocation, time frame, etc.; all of which come from within a model and methodology to evaluate choices. In


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other words, how do a multitude of possible Transitory States relate to each other? Second, models can be developed, using a consistent methodology, to compare strategies, e.g., comparing different retrenchment strategy models to the baseline model (the model without any strategic changes), or comparing allocation change strategy models to the baseline model. Finally, the methodology should be consistent throughout all models and include the three dimensions of distributions (allocation, withdrawal rate, time) with a focus on Probability of Failure (POF) which is a time independent variable (Frank, Mitchell & Blanchett (2010)). The model and methodology in this paper extends the work of Mitchell (2009) and (2010). This paper also combines Mitchell’s work with the methodology first developed by Frank, Mitchell, & Blanchett (2010) to address the following issues simultaneously: 1) applying expected longevity as the distribution period to an age-specific model; 2) evaluating sequence risk as the retiree ages through this model; and 3) developing a method to address, early on, the effect of a retiree continuing to survive beyond longevity estimates, i.e., development of a method to address survivor superannuation. The objective is to develop a more complete model and methodology that addresses all phases and issues of distributions. Using the model developed in this paper the reader may ask, “What is the effect on WR%, more importantly POF, of continuing to serially survive into the “next” Distribution Period (DP) where the DP is the current life expectancy for the current retiree’s age?” The model dynamically adjusts as the retiree ages through rolling distribution periods that decrease slightly in length each year. The authors’ hypothesis is that Sequence Risk occurs more often, earlier, and throughout retirement, relative to the occurrence of longevity risk; hence the POF-based techniques that manage exposure to Sequence Risk simultaneously manage aging into and through superannuation. The DP used in this paper for each retiree age is the expected longevity corresponding to that current age and sex. Joint couples are assumed to be the same age for concept development purposes. The overall effect of using joint data initially is for longer DPs in the model, thus making the model more conservative than would be the case for either single female or single male situations. Further model development and research is needed for situations of females only or males only, although rationally the effect would be slightly shorter DPs compared to joint data which would result in slightly higher WR% for single sex situations. Future research using the methodology in this paper is also needed to explore iterations of age differences. The use of life expectancy as the current DP as the retirees dynamically age will be discussed below in methodology. A data cross-section (Table 1) for the DPs is extracted from the latest (2006) Social Security Period Life Table. Life Expectancy is used as the DP for each current retiree age in the model. The authors’ model proposal no longer shows generic distribution periods without reference to a specific retirement age. We introduce here a model that is age-based on current retiree age with their specific life expectancy as the DP adjusted for the percentage who may outlive that life expectancy. The authors combine male and female and assume independence to determine joint probabilities. For


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Period Life Table, 2006

Exact

age

Male Female

Death

probability a

Number

of

lives b

Life

expectancy

Death

probability a

Number

of

lives b

Life

expectancy

50 0.005660 92,041 28.78 0.003275 95,460 32.49

55 0.007936 89,037 24.66 0.004640 93,659 28.07

60 0.011599 85,026 20.70 0.007219 91,109 23.78

65 0.017161 79,354 17.00 0.011009 87,217 19.72

70 0.026212 71,586 13.55 0.017646 81,571 15.90

75 0.041267 60,942 10.46 0.028247 73,134 12.43

80 0.066266 47,073 7.78 0.046337 61,289 9.33

85 0.107951 30,778 5.56 0.079984 45,395 6.68

90 0.177636 15,051 3.84 0.138938 26,608 4.62

95 0.277945 4,445 2.67 0.226885 10,324 3.20

100 0.371724 657 2.01 0.317702 2,223 2.35

105 0.474424 46 1.51 0.425157 241 1.70

110 0.605499 1 1.11 0.568956 9 1.19

115 0.772787 0 0.78 0.761392 0 0.79.

a Probability of dying within one year. b Number of survivors out of 100,000 born alive

Table 1. Extracted from Social Security Period Life Table, 2006 example, if the probability of a 65 year old male living to age 85 is approximately 40% and the probability of a 65 year old female living to age 85 is approximately 50%, the probability that either or both would live to that age would be 1 minus the probability that both are dead, which would be 70% (1- ((1-.4)*(1-.5))). In this manner specific ages are combined with specific life expectancy to move away from generic distribution periods in order to develop an Age-Based Distribution Model. Various thresholds of life expectancy are used in this paper, i.e., 75% are expected to outlive the life expectancy, 50% outlive, and 25% outlive, in order to evaluate directly how longevity impacts the model. Asset classes.


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Returns for the analysis are based on five assets. Returns are from January 1926 until December 2010. All returns are converted into “real returns” (i.e., are adjusted for inflation), where the definition of inflation is the increase in the Consumer Price Index for Urban Consumers, data obtained from the Bureau of Labor Statistics. Cash: 30 Day T-bill Bonds: Ibbotson Associates Long-term Corporate Bond Index Domestic Large Equity: S&P 500 Domestic Small Cap Equity: Ibbotson Associates US Small Stock Index International Large Equity: Global Financial Data Global ex USA Index from January 1926 until December 1969 and then the MSCI EAFE from January 1970 until December 2010. The portfolios for the analysis are made of two primary components: a Cash/Fixed piece; and an Equity piece. The Cash/Fixed piece is 25% Cash and 75% Bond. The Equity piece is 50% Domestic Large Equity, 25% Domestic Small Equity and 25% International Large Equity. For example, a 60/40 portfolio (60% Equity and 40% Cash/Fixed) would have a 30% Domestic Large Equity allocation, 15% Domestic Small Equity allocation, 15% International Large Equity allocation, 10% Cash allocation, and a 30% Bond allocation. Time sequencing and simulation periods. The research in this paper is divided through the perspective of time, both time sequencing and simulation periods. Time sequencing refers to the stochastic generation of returns. Simulation periods refer to the length of time each stochastic simulation is run. The authors have used a 3D method of graphing to illustrate the concept of transitory states where each data point represents a possible withdrawal state for a retiree at any point in time and how that transitory state may relate to other possible transitory states the retiree may experience given changing market return sequences, retiree withdrawals, and/or asset allocation. For Step 1, a 10,000 run Monte Carlo generator was built in Microsoft Excel. The distribution is assumed to be taken from the portfolio at the beginning of each year. All returns are in “real” (inflation-adjusted) terms, so that a constant withdrawal amount is assumed to be taken from the portfolio during each year in retirement. Returns are generated assuming a normal distribution based on the average historical annual real returns and standard deviation, i.e. not the "actual" historical series and not bootstrapped. The “success” of a portfolio or withdrawal is calculated by determining how many portfolios had positive values at the end of the year. A positive value would indicate the portfolio was successful for that year. Withdrawal rates are tested in .05% increments from 0% to 25%, in .10% increments from 25% to 50%, and in .25% increments from 50% to 100%. The simulation period is based on a time period dependent on the retiree/s probability of outliving the distribution period as described for Table 1 above. Phase I


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Rather than illustrate distribution periods on a figure’s time-axis, this paper introduces the retirees age on the time-axis with each simulation distribution period from the expected longevity for each retiree age from Table 1 above.

Figure 1. 3D Probability of Failure Landscape (5% POF and 50% POF) The model (Figure 1) in this phase most closely represents how advisers envision retirement withdrawals, with the exception of being 3D. However, once the distribution is started, few advisers adjust the distribution period dynamically as the retiree ages. The distribution period (DP) selected in Figure 1 represents the estimated expected longevity of the retiree where 50% outlive the expected value. The withdrawal rate at the beginning of each DP represents the initial withdrawal rate for that DP. The fundamental difference for this paper is the adjustment of the


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distribution period each year the retiree ages, i.e., rolling DPs (decreasing lengths) as retiree ages each year. Finally, multiple possible transient states exist between the 5% POF landscape and the 50% POF landscape which describe not only the current transient state of the retiree, but also describe other alternative transient states should the retiree change their allocation or withdrawal amount (note that time and market return effects on the portfolio are outside the retiree’s control). This observation provides the adviser with insight into strategy while working with retiree distributions.


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Figure 2. Three Time/Age slices through Figure 1 landscapes (data Appendix 2). Figure 2 represents time/age slices, or planes, through Figure 1. Most advisers think in terms of constant asset allocation and illustrate their figures along the asset allocation plane. The authors


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show time slices to demonstrate how the withdrawal rate is actually a time-dependent variable and also show that the time-independent variable is the Probability of Failure (POF). See Appendices 1, 2 and 3 for 75%, 50% and 25% %Outlive data respectively. Appendix 1 data is derived where 75% of the people are expected to outlive Table 1 expected longevity; App. 2 data assumes 50% are expected to outlive; and App. 3 assumes 25%. Appendices 4 and 5 show the differences between data sets, i.e., 75% minus 50% expected to outlive (EO) values (75%EO – 50%EO), and 50% minus 25% (50%EO – 25%EO) respectively. Note that the similar POF landscapes shift the withdrawal rates up between 25%EO and 50%EO; and the withdrawal rates shift up yet again between 50%EO and 75%EO. This shift suggests an additional avenue to explore when evaluating the POF rates; i.e., in addition to changing the distribution dollar amounts to manage retiree exposure to POF, the relative exposure to expectation of outliving expected longevity may also be evaluated and managed. This will be conceptually developed in Phase II of this paper. Phase I Observations

Withdrawal rates change naturally across asset allocations as the retiree ages. Thus, a set withdrawal rate, e.g. 4%, is not optimal for all retirees because not all retirees are the same age.

Dispersion of POF in Figure 2 appears to be a function of volatility where POF dispersion is “narrow” for low equity allocations and “wider” for higher equity allocations. This is an area for further research.

Of interest: the differences between Outliving Expected Longevity increases as the retiree ages (appendices 4 and 5).

The last observation will be the focus of strategy application in Phase II, where the %Outlive Life Expectancy age variable will also be dynamically altered during simulations. Phase II When the distribution period used is expected longevity, the questions then arise; “What happens when the retiree continues to survive? What happens to retiree withdrawal values when the retiree continues to live beyond expected longevity? Phase II seeks to answer this fundamental problem where it is uncertain which retirees among the population will experience superannuation. Clearly, those who are already ill are unlikely to outlive expected longevity at some point in time. What about those who exhibit no sign of illness currently? Phase II of this project evaluates how the methodology applies to a retiree who continues to “age through” the Period Life Table. Cash flow values are expressed in real terms, thus representing the same level of income replacement when factoring inflation.


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Data tables in this paper are based on joint starting ages with the probability of either alive dynamically changing; further research may be performed to separate out differences between single male or single female retirees. Klinger (2007, 2010) researched higher WR% early in retirement and reducing them later in retirement. This paper suggests a method to do this, however within the constraints of also evaluating the percent who may outlive expected longevity. The methodology employed here is to utilize DPs based on the length of lifetimes as adjusted by a dynamic change to the percentage of the population expected to outlive expected longevity. The effect is to shorten the DPs, thus increasing WR% relative to static DPs, and providing a rational method to assign DPs to specific retiree ages. The result: an Age- Based model.

Figure 3. Retiree Cash flows ages 60, 70, 80 & 90 (data Appendices 6 through 9). Figure 3 reflects the range of cash flow percentiles as snap shots of a retiree aging while utilizing the %Outlive expectation to establish the length of the DP, which then determines an optimal WR% based on setting the expected %POF at 10% (the percent of simulations that “fail” with the given parameters). The 5th and 25th percentiles represent the "good" market sequence cash flows and the 75th and 95th percentiles represent the "bad" market sequence cash flows, all from static starting parameters (transient states). Frank, Mitchell & Blanchett (2010) demonstrate how using POF in a 3D model assists in evaluating exposure to sequence risk and when to make a decision about changing the withdrawal amount. A single asset allocation (60%) was used for Figure 3; however similar results emerge with any other allocation with only differences in cash flow amounts.

Retiree Age 60 Cash Flows (Percentiles) Retiree Age 70 Cash Flows (Percentiles)

Retiree Age 80 CashFlows (Percentiles)



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“Consumption-oriented” retiree. A “consumption-oriented” retiree can be demonstrated through the interaction and utility of %Outlive for planning purposes through the 75% expected to outlive expected longevity as an initial variable for a 60 year old retiree. De-cumulation should be viewed as a dynamic, rather than set-and-forget, exercise. This paper explores the interaction between DP and %Outlive. The DP for expecting 75% of the retirees to outlive the time horizon based on expected longevity results in a higher WR% since the DP is shorter relative to 50%Outlive, which is again shorter relative to 25%Outlive. The shorter DP results in a higher possible relative WR% with the same POF (e.g., POF 10% in the appendices). Note, as the retiree ages, the %Outlive is reduced, thus extending the DP. This is a dynamic, rolling adjustment that slowly extends the DP so the retiree has a lesser probability to outlive the DP from their current retirement age when their transient state is reevaluated. This method is thus a longevity-based methodology that investigates how to achieve Klinger’s objective where retirees begin with higher WR% and adjust the WR% as they age. Also note, the %Outlive reduction is an example for concept demonstration purposes, not as a single solution. A “consumption-oriented” retiree may find they are “unlucky” and find market returns under the 50th percentile. These retirees would need to adjust their withdrawal dollar amounts down. Alternatively, a retiree may choose lower %Outlive values, where the impact will be to extend the DP, thus reducing the WR% with the same target POF% (e.g., 10%POF). The effect on WR% is the same, however the methodology present here adjusts WR% rationally. Alternatively, a retiree may choose to be more conservative from the very beginning of retirement so that more of their portfolio value extends into their later years. This is accomplished by low %Outlive values (e.g., 10%POF). The authors label such a retiree “inheritance-oriented” which is illustrated in Figure 4. Note that a retiree may experience “good” markets to be above the 50th percentile during one period of time (e.g., age 60 simulation) and experience “bad” markets to be below the 50th percentile during another period of time (e.g., age 62, or any subsequent age simulation) because sequence risk is ever present during de-cumulation years. The POF function is best used as a method to evaluate exposure to sequence risk based on the paper Frank, Mitchell & Blanchett (2010), which finds if %POF increases, then the withdrawal dollar amount should be adjusted to reduce the probability of exhausting the portfolio within the current DP; and vice versa if %POF declines (adjustments made at threshold limits). %POF begins to compress above 30% where this compression increases the possibility the retiree will get into a probability of failure too quick to be able to make adjustments, thus resulting in even more drastic adjustments. “Inheritance-oriented” retiree.


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Figure 4 illustrates a low, constant, 10% %Outlive with data for each age in Appendix 10 for an “inheritance-oriented” retiree. The %Outlive variability may be used to evaluate where the retiree is in between either objective. Note that the cash flows are shifted towards later retirement ages as compared to the “consumption-oriented” use of %Outlive above.

Figure 4. Retiree Cash flows ages 60, 70, 80 & 90 (data Appendix 10). Phase II combines uncertain market returns (Probability of the Portfolio) with uncertain longevity (Probability of the Person) into one Age-Based Distribution Model that is also three dimensional when asset allocation and Probability of Failure are incorporated as demonstrated in Phase I. Phase II Observations

Utilizing higher %Outlive values, and moving towards lower values as the retiree ages, tends to maximize the distributions over the retirees lifetime. This is through shorter DPs initially, and then extending the DPs relative to expected life expectancy as the retiree ages. This is an example of using longevity %Outlive values for a consumption-oriented retiree.

Frank and Blanchett (2010) found that exposure to sequence risk never goes away. The results from the methodology in this paper also support this observation where percentile ranges at all ages had either “good” or “bad” cash flow values regardless of the retiree’s age.

The later retirement age cash flows reduce primarily due to the effect of ever-shorter DPs due to fewer years for life expectancy. Further research should look specifically at

Retiree Age 60 Cash Flows (Percentiles)



Retiree Age 70 Cash Flows (Percentiles)


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developing methods to evaluate later-age cash flow strategies according to retiree goal (consumption vs. estate/inheritance).

Sequence Risk How does sequence risk, with subsequent adjustment to the withdrawal amount, affect the distributions for retirees who continue to live beyond expected longevity? Frank, Mitchell, & Blanchett (2010) applied a Probability of Failure (POF) approach to address market sequence risk as the retiree ages. Failure in this paper is defined as running out of money while either member of the couple is still alive. Which one is alive is random chance according to the generator (based on the respective probabilities in the life table). Since withdrawal rate percentages (WR%) naturally increase for retirees as they age due to the effect of a decreasing DP, it is difficult to separate out an increasing WR% due to the aging effect from bad market sequence effect. WR% also is affected to some degree by asset allocation. Since market values change more rapidly relative to aging, the sequence risk effect is observed more often. Frank, Mitchell, & Blanchett (2010) decision rule to reduce the dollar amount withdrawn as POF approaches or exceeds 30% appears to remain an applicable decision rule when applied to an Age-Based model as described in this paper. Overall Conclusions The development of an Age-Based model is more meaningful than generic distribution period analysis since an Age-Based model incorporates life expectancy uncertainty in addition to stochastic returns. This is a concept development paper demonstrating a methodology to unify into a single model the various factors that affect de-cumulation.

The concept of transitory states suggests a dynamic process of change that the retiree's de-cumulation goes through over time and market changes. A retiree moves between the POF landscapes with every market move and every change in time. The simulation that tells us where the retiree is within the landscapes is but for that brief moment for those initial conditions, i.e., a transitory state. Redo the simulation again at a later time with a different portfolio value and you arrive at a different place in the landscapes. Most of the positions are okay to be in. As they approach the 30%POF boundary (poor markets or large lump sum withdrawal) where compression of the POF landscapes occurs (Frank, Mitchell & Blanchett 2010, then a decision should be made to pull them away from that boundary; vice versa: as they move away from that boundary they are better off (good markets). Pulling them away from a high POF boundary may be done by reducing the withdrawal dollar amount or by reducing the %Outlive value).

The Distribution Period (DP) may be dynamically managed, as the retiree ages, through the application of varying the percentage who outlive expected longevity (%Outlive). Shorter DPs result in higher withdrawal rates (WR%), and by evaluation of the %Outlive, distribution periods lengths may change dynamically. %Outlive is a useful “lever” to manage distribution periods.


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Probability of Failure (%POF) remains a useful metric to evaluate exposure to sequence risk in order to adjust withdrawal dollar amounts based on the market effects on portfolio values. A POF based decision rule standardizes for both the asset allocation effect and age effect on WR%.

Mitchell (2010) demonstrates that the uncertainty of remaining lifespan increases as the retiree ages even though there is a reduction in the number of expected remaining years. Both “consumption-” and “inheritance-oriented” type retirees experienced a decreasing cash flow in the superannuated years as a result of the higher withdrawal rates associated with such short DPs corresponding to very short expected longevity. Further research into how to manage de-cumulation during uncertain remaining lifespan is needed to rationally address this high-WR%-short-DP effect, specifically in the de-cumulation ages 90 and older.

Single simulations represent a single transitory state of the simulation's initial parameters. A compilation of simulations develops a model from which decisions may be made.

The DP is not a fixed period; it may be changed dynamically as the retiree ages through changing the longevity value %Outlive. %Outlive is also not a fixed value; it too may be changed dynamically as the retiree ages. The %POF is best used as a measure of exposure to sequence risk. This paper, combined with Frank, Mitchell & Blanchett (2010) demonstrates that WR% is a dynamic function of other variables, including portfolio allocation, each of which should be evaluated three dimensionally in relation to each other to access the current transitory state of a retiree during de-cumulation years. Researchers have sought a single withdrawal rate that would last the retiree's entire lifetime from initial retirement to death. The authors suggest a more dynamic model should be used where the author’s prior work demonstrates that a retiree's transient state is in constant flux due primarily to market sequences. The model in this, and the authors’ prior paper, develops a methodology to monitor, evaluate and react as necessary to those transient states as well as base the model on age specific expected longevity rather than generic, ageless or unanchored, distribution periods. References: Frank, L. R. and Blanchett, D. M. (2010). The dynamic implications of sequence risk on a distribution portfolio. Journal of Financial Planning, 23, 52-61. Frank, L. R., Mitchell, J.B. & Blanchett, D. M. (2010). Sequence Risk: Managing Retiree Exposure to Sequence Risk Through Probability of Failure Based Decision Rules. Presented at Academy of Financial Services, Denver, CO, Oct 2010, and submitted to Financial Services Review. Available at SSRN: http://ssrn.com/abstract=1849868. Klinger, W. (2007). Using Decision Rules to Create Retirement Withdrawal Profiles. Journal of Financial Planning, 20, 60-67. Klinger, W. (2010). Creating Safe, Aggressive Retirement Income Profiles. Journal of Financial Planning, 23, 44-53.


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Mitchell, J. B., (2009). Withdrawal rate strategies for retirement portfolios: Preventive reductions and risk management. Presented at Academy of Financial Services, Anaheim, CA, Available at SSRN: http://ssrn.com/abstract=1489657. Forthcoming, Financial Services Review. Mitchell, J. B. (2010). A modified life expectancy approach to withdrawal rate management. Presented at Academy of Financial Services, Denver, CO. Available at SSRN: http://ssrn.com/abstract=1703948. Pfau, W.D., (2010). An International Perspective on Safe Withdrawal Rates: The Demise of the 4 Percent Rule? Journal of Financial Planning, 23, 52-61. Social Security (2006) Period Life Table (available at http://www.ssa.gov/OACT/STATS/table4c6.html).


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Appendix 1 (75% Outlive Expected Longevity) 75% Outlive (Shorter Longevity = Shorter DP)

Joint Age 60

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

0% 3.20% 3.30% 3.25% 3.00% 2.70% 2.35% 2.00% 1.65% 1.35% 1.05% 0.70%

5% 4.10% 4.35% 4.45% 4.45% 4.35% 4.25% 4.05% 3.85% 3.65% 3.35% 3.00%

10% 4.25% 4.55% 4.65% 4.70% 4.70% 4.60% 4.50% 4.35% 4.15% 3.95% 3.60%

15% 4.40% 4.65% 4.80% 4.90% 4.90% 4.90% 4.80% 4.70% 4.55% 4.35% 4.05%

20% 4.50% 4.80% 4.95% 5.05% 5.15% 5.15% 5.10% 5.00% 4.90% 4.75% 4.50%

25% 4.60% 4.90% 5.10% 5.25% 5.30% 5.35% 5.35% 5.35% 5.25% 5.15% 4.90%

30% 4.70% 5.00% 5.20% 5.40% 5.50% 5.60% 5.60% 5.60% 5.55% 5.45% 5.25%

35% 4.75% 5.05% 5.30% 5.50% 5.65% 5.75% 5.85% 5.85% 5.85% 5.80% 5.60%

40% 4.85% 5.15% 5.40% 5.65% 5.80% 5.95% 6.05% 6.10% 6.15% 6.10% 5.95%

45% 4.90% 5.25% 5.50% 5.75% 6.00% 6.15% 6.30% 6.40% 6.45% 6.45% 6.30%

50% 5.00% 5.30% 5.60% 5.90% 6.15% 6.35% 6.50% 6.60% 6.70% 6.75% 6.65%

Joint Age 65

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

0% 4.05% 4.15% 4.05% 3.80% 3.40% 3.00% 2.60% 2.20% 1.80% 1.45% 1.00%

5% 5.00% 5.20% 5.30% 5.25% 5.15% 5.00% 4.80% 4.55% 4.30% 4.05% 3.65%

10% 5.20% 5.45% 5.55% 5.55% 5.50% 5.40% 5.30% 5.10% 4.90% 4.65% 4.30%

15% 5.30% 5.55% 5.70% 5.80% 5.80% 5.75% 5.65% 5.50% 5.35% 5.15% 4.80%

20% 5.45% 5.70% 5.85% 5.95% 6.00% 6.00% 5.95% 5.85% 5.70% 5.55% 5.25%

25% 5.55% 5.80% 6.00% 6.15% 6.20% 6.25% 6.20% 6.15% 6.05% 5.95% 5.70%

30% 5.65% 5.90% 6.10% 6.30% 6.40% 6.45% 6.50% 6.45% 6.40% 6.30% 6.05%

35% 5.70% 6.00% 6.25% 6.40% 6.55% 6.65% 6.70% 6.75% 6.70% 6.65% 6.45%

40% 5.80% 6.10% 6.35% 6.55% 6.75% 6.85% 6.95% 7.00% 7.00% 7.00% 6.80%

45% 5.90% 6.20% 6.45% 6.70% 6.90% 7.05% 7.20% 7.25% 7.30% 7.35% 7.20%

50% 5.95% 6.25% 6.55% 6.80% 7.05% 7.25% 7.40% 7.50% 7.60% 7.65% 7.55%

Joint Age 70

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

0% 5.30% 5.35% 5.20% 4.80% 4.35% 3.85% 3.35% 2.90% 2.40% 2.00% 1.50%

5% 6.50% 6.75% 6.75% 6.70% 6.55% 6.35% 6.10% 5.85% 5.55% 5.25% 4.80%

10% 6.75% 6.95% 7.05% 7.05% 6.95% 6.85% 6.65% 6.45% 6.20% 5.95% 5.55%

15% 6.90% 7.15% 7.25% 7.30% 7.25% 7.20% 7.05% 6.90% 6.70% 6.50% 6.15%

20% 7.00% 7.25% 7.40% 7.50% 7.50% 7.45% 7.40% 7.30% 7.10% 6.95% 6.65%

25% 7.15% 7.40% 7.55% 7.65% 7.70% 7.70% 7.65% 7.60% 7.50% 7.35% 7.10%

30% 7.25% 7.50% 7.70% 7.85% 7.90% 7.95% 7.95% 7.95% 7.85% 7.75% 7.55%

35% 7.35% 7.60% 7.80% 8.00% 8.10% 8.20% 8.20% 8.25% 8.20% 8.15% 7.95%

40% 7.40% 7.70% 7.95% 8.15% 8.30% 8.40% 8.45% 8.50% 8.50% 8.50% 8.30%

45% 7.50% 7.80% 8.05% 8.25% 8.45% 8.60% 8.70% 8.80% 8.85% 8.85% 8.70%

50% 7.60% 7.90% 8.15% 8.40% 8.60% 8.80% 8.95% 9.05% 9.15% 9.20% 9.10%

Joint Age 75

Equity Allocation

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

0% 6.60% 6.65% 6.40% 5.95% 5.40% 4.80% 4.20% 3.60% 3.05% 2.50% 1.95%

5% 8.05% 8.25% 8.25% 8.15% 8.00% 7.75% 7.45% 7.15% 6.80% 6.45% 5.95%

10% 8.30% 8.50% 8.60% 8.55% 8.45% 8.30% 8.10% 7.85% 7.55% 7.30% 6.85%

15% 8.50% 8.70% 8.80% 8.80% 8.75% 8.65% 8.55% 8.35% 8.15% 7.90% 7.50%

20% 8.60% 8.85% 9.00% 9.05% 9.00% 8.95% 8.90% 8.75% 8.60% 8.40% 8.05%

25% 8.75% 8.95% 9.10% 9.20% 9.25% 9.25% 9.20% 9.10% 8.95% 8.80% 8.50%

30% 8.85% 9.10% 9.30% 9.40% 9.45% 9.50% 9.50% 9.45% 9.35% 9.25% 9.00%

35% 8.95% 9.20% 9.40% 9.55% 9.65% 9.75% 9.75% 9.75% 9.75% 9.65% 9.45%

40% 9.05% 9.30% 9.55% 9.70% 9.85% 9.95% 10.00% 10.05% 10.05% 10.00% 9.85%

45% 9.15% 9.40% 9.65% 9.85% 10.05% 10.15% 10.25% 10.35% 10.40% 10.40% 10.25%

50% 9.25% 9.50% 9.80% 10.00% 10.20% 10.40% 10.55% 10.65% 10.70% 10.75% 10.65%

Joint Age 80

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

0% 9.10% 9.15% 8.85% 8.30% 7.65% 6.95% 6.20% 5.50% 4.75% 4.10% 3.35%

5% 10.70% 10.85% 10.85% 10.70% 10.50% 10.20% 9.90% 9.50% 9.10% 8.70% 8.15%

10% 10.95% 11.15% 11.20% 11.10% 10.95% 10.75% 10.55% 10.25% 9.95% 9.65% 9.15%

15% 11.15% 11.35% 11.40% 11.40% 11.30% 11.20% 11.00% 10.80% 10.55% 10.30% 9.90%

20% 11.30% 11.50% 11.60% 11.65% 11.60% 11.55% 11.40% 11.25% 11.05% 10.85% 10.50%

25% 11.40% 11.65% 11.80% 11.85% 11.85% 11.80% 11.75% 11.65% 11.50% 11.35% 11.05%

30% 11.55% 11.75% 11.95% 12.00% 12.05% 12.05% 12.05% 12.00% 11.90% 11.75% 11.50%

35% 11.65% 11.90% 12.10% 12.20% 12.30% 12.35% 12.35% 12.30% 12.25% 12.20% 11.95%

40% 11.75% 12.00% 12.20% 12.35% 12.50% 12.60% 12.65% 12.65% 12.65% 12.60% 12.45%

45% 11.85% 12.15% 12.35% 12.55% 12.70% 12.80% 12.90% 13.00% 13.05% 13.05% 12.90%

50% 11.95% 12.25% 12.50% 12.70% 12.90% 13.05% 13.20% 13.30% 13.40% 13.45% 13.35%

Joint Age 85

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

0% 13.90% 13.85% 13.40% 12.65% 11.75% 10.75% 9.75% 8.70% 7.70% 6.70% 5.65%

5% 16.00% 16.15% 16.05% 15.85% 15.55% 15.20% 14.80% 14.35% 13.90% 13.40% 12.75%

10% 16.30% 16.45% 16.45% 16.35% 16.15% 15.90% 15.60% 15.25% 14.90% 14.50% 13.95%

15% 16.50% 16.70% 16.75% 16.65% 16.55% 16.35% 16.10% 15.85% 15.60% 15.25% 14.80%

20% 16.70% 16.85% 16.95% 16.90% 16.85% 16.70% 16.55% 16.40% 16.15% 15.90% 15.50%

25% 16.80% 17.05% 17.15% 17.15% 17.10% 17.05% 16.95% 16.80% 16.65% 16.45% 16.10%

30% 16.95% 17.15% 17.30% 17.35% 17.35% 17.35% 17.30% 17.20% 17.10% 16.95% 16.70%

35% 17.10% 17.30% 17.45% 17.55% 17.60% 17.65% 17.65% 17.60% 17.55% 17.45% 17.25%

40% 17.20% 17.45% 17.65% 17.75% 17.85% 17.95% 17.95% 17.95% 17.95% 17.90% 17.75%

45% 17.35% 17.60% 17.80% 17.95% 18.10% 18.20% 18.30% 18.35% 18.40% 18.40% 18.25%

50% 17.45% 17.70% 17.95% 18.15% 18.35% 18.50% 18.60% 18.70% 18.80% 18.85% 18.80%

Equity Allocation

Probability of Failure

Equity Allocation





Equity Allocation

Equity Allocation


Equity Allocation


17

Appendix 2 (50% Outlive Expected Longevity) "50% Outlive"

Joint Age 60

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

0% 2.70% 2.85% 2.80% 2.60% 2.30% 2.00% 1.70% 1.45% 1.15% 0.90% 0.60%

5% 3.60% 3.85% 3.95% 4.00% 3.90% 3.80% 3.65% 3.45% 3.25% 3.00% 2.65%

10% 3.80% 4.05% 4.20% 4.25% 4.25% 4.20% 4.10% 3.95% 3.75% 3.60% 3.25%

15% 3.90% 4.15% 4.35% 4.45% 4.45% 4.45% 4.40% 4.30% 4.15% 3.95% 3.65%

20% 4.00% 4.30% 4.45% 4.60% 4.65% 4.70% 4.65% 4.60% 4.50% 4.35% 4.10%

25% 4.10% 4.40% 4.60% 4.75% 4.85% 4.90% 4.90% 4.90% 4.85% 4.70% 4.45%

30% 4.15% 4.45% 4.70% 4.90% 5.00% 5.10% 5.15% 5.15% 5.10% 5.05% 4.80%

35% 4.25% 4.55% 4.80% 5.00% 5.20% 5.30% 5.40% 5.40% 5.40% 5.35% 5.15%

40% 4.30% 4.65% 4.90% 5.15% 5.35% 5.50% 5.60% 5.65% 5.65% 5.65% 5.50%

45% 4.40% 4.70% 5.00% 5.25% 5.50% 5.65% 5.80% 5.90% 5.95% 5.95% 5.85%

50% 4.45% 4.80% 5.10% 5.40% 5.65% 5.85% 6.00% 6.15% 6.25% 6.30% 6.20%

Joint Age 65

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

0% 3.35% 3.45% 3.35% 3.15% 2.80% 2.45% 2.10% 1.75% 1.40% 1.10% 0.75%

5% 4.25% 4.50% 4.60% 4.55% 4.50% 4.35% 4.20% 4.00% 3.75% 3.50% 3.10%

10% 4.45% 4.70% 4.80% 4.85% 4.80% 4.75% 4.65% 4.45% 4.30% 4.05% 3.70%

15% 4.55% 4.80% 4.95% 5.05% 5.05% 5.05% 4.95% 4.85% 4.70% 4.50% 4.15%

20% 4.65% 4.95% 5.10% 5.20% 5.25% 5.25% 5.25% 5.15% 5.05% 4.90% 4.60%

25% 4.75% 5.05% 5.25% 5.40% 5.45% 5.50% 5.50% 5.45% 5.40% 5.25% 5.00%

30% 4.85% 5.15% 5.35% 5.55% 5.65% 5.70% 5.75% 5.75% 5.70% 5.60% 5.40%

35% 4.90% 5.20% 5.45% 5.65% 5.80% 5.90% 6.00% 6.00% 6.00% 5.95% 5.75%

40% 5.00% 5.30% 5.55% 5.80% 5.95% 6.10% 6.20% 6.25% 6.30% 6.25% 6.10%

45% 5.05% 5.40% 5.70% 5.90% 6.15% 6.30% 6.45% 6.50% 6.55% 6.60% 6.45%

50% 5.15% 5.45% 5.80% 6.05% 6.30% 6.50% 6.65% 6.75% 6.85% 6.90% 6.80%

Joint Age 70

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

0% 4.05% 4.15% 4.05% 3.80% 3.40% 3.00% 2.60% 2.20% 1.80% 1.45% 1.00%

5% 5.00% 5.20% 5.30% 5.25% 5.15% 5.00% 4.80% 4.55% 4.30% 4.05% 3.65%

10% 5.20% 5.45% 5.55% 5.55% 5.50% 5.40% 5.30% 5.10% 4.90% 4.65% 4.30%

15% 5.30% 5.55% 5.70% 5.80% 5.80% 5.75% 5.65% 5.50% 5.35% 5.15% 4.80%

20% 5.45% 5.70% 5.85% 5.95% 6.00% 6.00% 5.95% 5.85% 5.70% 5.55% 5.25%

25% 5.55% 5.80% 6.00% 6.15% 6.20% 6.25% 6.20% 6.15% 6.05% 5.95% 5.70%

30% 5.65% 5.90% 6.10% 6.30% 6.40% 6.45% 6.50% 6.45% 6.40% 6.30% 6.05%

35% 5.70% 6.00% 6.25% 6.40% 6.55% 6.65% 6.70% 6.75% 6.70% 6.65% 6.45%

40% 5.80% 6.10% 6.35% 6.55% 6.75% 6.85% 6.95% 7.00% 7.00% 7.00% 6.80%

45% 5.90% 6.20% 6.45% 6.70% 6.90% 7.05% 7.20% 7.25% 7.30% 7.35% 7.20%

50% 5.95% 6.25% 6.55% 6.80% 7.05% 7.25% 7.40% 7.50% 7.60% 7.65% 7.55%

Joint Age 75

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

0% 5.00% 5.10% 4.90% 4.60% 4.15% 3.70% 3.20% 2.75% 2.30% 1.90% 1.45%

5% 6.15% 6.35% 6.40% 6.35% 6.20% 6.00% 5.80% 5.55% 5.25% 4.95% 4.50%

10% 6.35% 6.55% 6.65% 6.65% 6.60% 6.50% 6.30% 6.15% 5.90% 5.65% 5.25%

15% 6.50% 6.75% 6.85% 6.90% 6.90% 6.80% 6.70% 6.55% 6.35% 6.15% 5.80%

20% 6.60% 6.85% 7.00% 7.10% 7.10% 7.10% 7.00% 6.90% 6.75% 6.60% 6.30%

25% 6.75% 7.00% 7.15% 7.30% 7.35% 7.35% 7.30% 7.25% 7.15% 7.00% 6.75%

30% 6.85% 7.10% 7.30% 7.45% 7.55% 7.60% 7.60% 7.55% 7.50% 7.40% 7.15%

35% 6.90% 7.20% 7.40% 7.60% 7.70% 7.80% 7.85% 7.85% 7.80% 7.75% 7.55%

40% 7.00% 7.30% 7.55% 7.75% 7.90% 8.00% 8.10% 8.15% 8.15% 8.10% 7.95%

45% 7.10% 7.40% 7.65% 7.85% 8.05% 8.20% 8.35% 8.40% 8.45% 8.45% 8.30%

50% 7.20% 7.50% 7.75% 8.00% 8.20% 8.40% 8.55% 8.65% 8.75% 8.80% 8.70%

Joint Age 80

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

0% 6.60% 6.65% 6.40% 5.95% 5.40% 4.80% 4.20% 3.60% 3.05% 2.50% 1.95%

5% 8.05% 8.25% 8.25% 8.15% 8.00% 7.75% 7.45% 7.15% 6.80% 6.45% 5.95%

10% 8.30% 8.50% 8.60% 8.55% 8.45% 8.30% 8.10% 7.85% 7.55% 7.30% 6.85%

15% 8.50% 8.70% 8.80% 8.80% 8.75% 8.65% 8.55% 8.35% 8.15% 7.90% 7.50%

20% 8.60% 8.85% 9.00% 9.05% 9.00% 8.95% 8.90% 8.75% 8.60% 8.40% 8.05%

25% 8.75% 8.95% 9.10% 9.20% 9.25% 9.25% 9.20% 9.10% 8.95% 8.80% 8.50%

30% 8.85% 9.10% 9.30% 9.40% 9.45% 9.50% 9.50% 9.45% 9.35% 9.25% 9.00%

35% 8.95% 9.20% 9.40% 9.55% 9.65% 9.75% 9.75% 9.75% 9.75% 9.65% 9.45%

40% 9.05% 9.30% 9.55% 9.70% 9.85% 9.95% 10.00% 10.05% 10.05% 10.00% 9.85%

45% 9.15% 9.40% 9.65% 9.85% 10.05% 10.15% 10.25% 10.35% 10.40% 10.40% 10.25%

50% 9.25% 9.50% 9.80% 10.00% 10.20% 10.40% 10.55% 10.65% 10.70% 10.75% 10.65%

Joint Age 85

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

0% 9.10% 9.15% 8.85% 8.30% 7.65% 6.95% 6.20% 5.50% 4.75% 4.10% 3.35%

5% 10.70% 10.85% 10.85% 10.70% 10.50% 10.20% 9.90% 9.50% 9.10% 8.70% 8.15%

10% 10.95% 11.15% 11.20% 11.10% 10.95% 10.75% 10.55% 10.25% 9.95% 9.65% 9.15%

15% 11.15% 11.35% 11.40% 11.40% 11.30% 11.20% 11.00% 10.80% 10.55% 10.30% 9.90%

20% 11.30% 11.50% 11.60% 11.65% 11.60% 11.55% 11.40% 11.25% 11.05% 10.85% 10.50%

25% 11.40% 11.65% 11.80% 11.85% 11.85% 11.80% 11.75% 11.65% 11.50% 11.35% 11.05%

30% 11.55% 11.75% 11.95% 12.00% 12.05% 12.05% 12.05% 12.00% 11.90% 11.75% 11.50%

35% 11.65% 11.90% 12.10% 12.20% 12.30% 12.35% 12.35% 12.30% 12.25% 12.20% 11.95%

40% 11.75% 12.00% 12.20% 12.35% 12.50% 12.60% 12.65% 12.65% 12.65% 12.60% 12.45%

45% 11.85% 12.15% 12.35% 12.55% 12.70% 12.80% 12.90% 13.00% 13.05% 13.05% 12.90%

50% 11.95% 12.25% 12.50% 12.70% 12.90% 13.05% 13.20% 13.30% 13.40% 13.45% 13.35%


Equity Allocation


Equity Allocation


Equity Allocation


Equity Allocation


Equity Allocation


Equity Allocation


18

Appendix 3 (25% Outlive Expected Longevity) "25% Outlive" (Higher Longevity=Longer DP)

Joint Age 60

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

0% 2.40% 2.55% 2.50% 2.30% 2.10% 1.80% 1.50% 1.25% 1.00% 0.75% 0.45%

5% 3.15% 3.40% 3.55% 3.55% 3.55% 3.45% 3.30% 3.10% 2.90% 2.65% 2.30%

10% 3.35% 3.60% 3.75% 3.85% 3.85% 3.80% 3.70% 3.60% 3.45% 3.25% 2.90%

15% 3.45% 3.75% 3.90% 4.05% 4.05% 4.05% 4.00% 3.90% 3.75% 3.60% 3.30%

20% 3.55% 3.85% 4.05% 4.20% 4.25% 4.30% 4.30% 4.25% 4.15% 4.00% 3.70%

25% 3.60% 3.90% 4.15% 4.30% 4.45% 4.50% 4.55% 4.50% 4.45% 4.35% 4.10%

30% 3.70% 4.00% 4.25% 4.45% 4.60% 4.70% 4.75% 4.75% 4.70% 4.65% 4.40%

35% 3.75% 4.10% 4.35% 4.60% 4.75% 4.90% 4.95% 5.00% 5.00% 4.95% 4.75%

40% 3.85% 4.15% 4.45% 4.70% 4.90% 5.05% 5.15% 5.25% 5.25% 5.25% 5.10%

45% 3.90% 4.25% 4.55% 4.80% 5.05% 5.25% 5.40% 5.50% 5.55% 5.55% 5.40%

50% 3.95% 4.30% 4.65% 4.95% 5.20% 5.40% 5.60% 5.75% 5.85% 5.85% 5.75%

Joint Age 65

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

0% 2.70% 2.85% 2.80% 2.60% 2.30% 2.00% 1.70% 1.45% 1.15% 0.90% 0.60%

5% 3.60% 3.85% 3.95% 4.00% 3.90% 3.80% 3.65% 3.45% 3.25% 3.00% 2.65%

10% 3.80% 4.05% 4.20% 4.25% 4.25% 4.20% 4.10% 3.95% 3.75% 3.60% 3.25%

15% 3.90% 4.15% 4.35% 4.45% 4.45% 4.45% 4.40% 4.30% 4.15% 3.95% 3.65%

20% 4.00% 4.30% 4.45% 4.60% 4.65% 4.70% 4.65% 4.60% 4.50% 4.35% 4.10%

25% 4.10% 4.40% 4.60% 4.75% 4.85% 4.90% 4.90% 4.90% 4.85% 4.70% 4.45%

30% 4.15% 4.45% 4.70% 4.90% 5.00% 5.10% 5.15% 5.15% 5.10% 5.05% 4.80%

35% 4.25% 4.55% 4.80% 5.00% 5.20% 5.30% 5.40% 5.40% 5.40% 5.35% 5.15%

40% 4.30% 4.65% 4.90% 5.15% 5.35% 5.50% 5.60% 5.65% 5.65% 5.65% 5.50%

45% 4.40% 4.70% 5.00% 5.25% 5.50% 5.65% 5.80% 5.90% 5.95% 5.95% 5.85%

50% 4.45% 4.80% 5.10% 5.40% 5.65% 5.85% 6.00% 6.15% 6.25% 6.30% 6.20%

Joint Age 70

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

0% 3.35% 3.45% 3.35% 3.15% 2.80% 2.45% 2.10% 1.75% 1.40% 1.10% 0.75%

5% 4.25% 4.50% 4.60% 4.55% 4.50% 4.35% 4.20% 4.00% 3.75% 3.50% 3.10%

10% 4.45% 4.70% 4.80% 4.85% 4.80% 4.75% 4.65% 4.45% 4.30% 4.05% 3.70%

15% 4.55% 4.80% 4.95% 5.05% 5.05% 5.05% 4.95% 4.85% 4.70% 4.50% 4.15%

20% 4.65% 4.95% 5.10% 5.20% 5.25% 5.25% 5.25% 5.15% 5.05% 4.90% 4.60%

25% 4.75% 5.05% 5.25% 5.40% 5.45% 5.50% 5.50% 5.45% 5.40% 5.25% 5.00%

30% 4.85% 5.15% 5.35% 5.55% 5.65% 5.70% 5.75% 5.75% 5.70% 5.60% 5.40%

35% 4.90% 5.20% 5.45% 5.65% 5.80% 5.90% 6.00% 6.00% 6.00% 5.95% 5.75%

40% 5.00% 5.30% 5.55% 5.80% 5.95% 6.10% 6.20% 6.25% 6.30% 6.25% 6.10%

45% 5.05% 5.40% 5.70% 5.90% 6.15% 6.30% 6.45% 6.50% 6.55% 6.60% 6.45%

50% 5.15% 5.45% 5.80% 6.05% 6.30% 6.50% 6.65% 6.75% 6.85% 6.90% 6.80%

Joint Age 75

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

0% 4.05% 4.15% 4.05% 3.80% 3.40% 3.00% 2.60% 2.20% 1.80% 1.45% 1.00%

5% 5.00% 5.20% 5.30% 5.25% 5.15% 5.00% 4.80% 4.55% 4.30% 4.05% 3.65%

10% 5.20% 5.45% 5.55% 5.55% 5.50% 5.40% 5.30% 5.10% 4.90% 4.65% 4.30%

15% 5.30% 5.55% 5.70% 5.80% 5.80% 5.75% 5.65% 5.50% 5.35% 5.15% 4.80%

20% 5.45% 5.70% 5.85% 5.95% 6.00% 6.00% 5.95% 5.85% 5.70% 5.55% 5.25%

25% 5.55% 5.80% 6.00% 6.15% 6.20% 6.25% 6.20% 6.15% 6.05% 5.95% 5.70%

30% 5.65% 5.90% 6.10% 6.30% 6.40% 6.45% 6.50% 6.45% 6.40% 6.30% 6.05%

35% 5.70% 6.00% 6.25% 6.40% 6.55% 6.65% 6.70% 6.75% 6.70% 6.65% 6.45%

40% 5.80% 6.10% 6.35% 6.55% 6.75% 6.85% 6.95% 7.00% 7.00% 7.00% 6.80%

45% 5.90% 6.20% 6.45% 6.70% 6.90% 7.05% 7.20% 7.25% 7.30% 7.35% 7.20%

50% 5.95% 6.25% 6.55% 6.80% 7.05% 7.25% 7.40% 7.50% 7.60% 7.65% 7.55%

Joint Age 80

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

0% 5.30% 5.35% 5.20% 4.80% 4.35% 3.85% 3.35% 2.90% 2.40% 2.00% 1.50%

5% 6.50% 6.75% 6.75% 6.70% 6.55% 6.35% 6.10% 5.85% 5.55% 5.25% 4.80%

10% 6.75% 6.95% 7.05% 7.05% 6.95% 6.85% 6.65% 6.45% 6.20% 5.95% 5.55%

15% 6.90% 7.15% 7.25% 7.30% 7.25% 7.20% 7.05% 6.90% 6.70% 6.50% 6.15%

20% 7.00% 7.25% 7.40% 7.50% 7.50% 7.45% 7.40% 7.30% 7.10% 6.95% 6.65%

25% 7.15% 7.40% 7.55% 7.65% 7.70% 7.70% 7.65% 7.60% 7.50% 7.35% 7.10%

30% 7.25% 7.50% 7.70% 7.85% 7.90% 7.95% 7.95% 7.95% 7.85% 7.75% 7.55%

35% 7.35% 7.60% 7.80% 8.00% 8.10% 8.20% 8.20% 8.25% 8.20% 8.15% 7.95%

40% 7.40% 7.70% 7.95% 8.15% 8.30% 8.40% 8.45% 8.50% 8.50% 8.50% 8.30%

45% 7.50% 7.80% 8.05% 8.25% 8.45% 8.60% 8.70% 8.80% 8.85% 8.85% 8.70%

50% 7.60% 7.90% 8.15% 8.40% 8.60% 8.80% 8.95% 9.05% 9.15% 9.20% 9.10%

Joint Age 85

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

0% 6.60% 6.65% 6.40% 5.95% 5.40% 4.80% 4.20% 3.60% 3.05% 2.50% 1.95%

5% 8.05% 8.25% 8.25% 8.15% 8.00% 7.75% 7.45% 7.15% 6.80% 6.45% 5.95%

10% 8.30% 8.50% 8.60% 8.55% 8.45% 8.30% 8.10% 7.85% 7.55% 7.30% 6.85%

15% 8.50% 8.70% 8.80% 8.80% 8.75% 8.65% 8.55% 8.35% 8.15% 7.90% 7.50%

20% 8.60% 8.85% 9.00% 9.05% 9.00% 8.95% 8.90% 8.75% 8.60% 8.40% 8.05%

25% 8.75% 8.95% 9.10% 9.20% 9.25% 9.25% 9.20% 9.10% 8.95% 8.80% 8.50%

30% 8.85% 9.10% 9.30% 9.40% 9.45% 9.50% 9.50% 9.45% 9.35% 9.25% 9.00%

35% 8.95% 9.20% 9.40% 9.55% 9.65% 9.75% 9.75% 9.75% 9.75% 9.65% 9.45%

40% 9.05% 9.30% 9.55% 9.70% 9.85% 9.95% 10.00% 10.05% 10.05% 10.00% 9.85%

45% 9.15% 9.40% 9.65% 9.85% 10.05% 10.15% 10.25% 10.35% 10.40% 10.40% 10.25%

50% 9.25% 9.50% 9.80% 10.00% 10.20% 10.40% 10.55% 10.65% 10.70% 10.75% 10.65%

Equity Allocation


Equity Allocation


Equity Allocation


Equity Allocation


Equity Allocation


Equity Allocation



19

Appendix 4. 75% Expected to Outlive Life Expectancy minus 50% Expected to Outlive Life Expectancy

75% ‐ 50% Outlive (Difference)

Joint Age 60

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

0% 0.50% 0.45% 0.45% 0.40% 0.40% 0.35% 0.30% 0.20% 0.20% 0.15% 0.10%

5% 0.50% 0.50% 0.50% 0.45% 0.45% 0.45% 0.40% 0.40% 0.40% 0.35% 0.35%

10% 0.45% 0.50% 0.45% 0.45% 0.45% 0.40% 0.40% 0.40% 0.40% 0.35% 0.35%

15% 0.50% 0.50% 0.45% 0.45% 0.45% 0.45% 0.40% 0.40% 0.40% 0.40% 0.40%

20% 0.50% 0.50% 0.50% 0.45% 0.50% 0.45% 0.45% 0.40% 0.40% 0.40% 0.40%

25% 0.50% 0.50% 0.50% 0.50% 0.45% 0.45% 0.45% 0.45% 0.40% 0.45% 0.45%

30% 0.55% 0.55% 0.50% 0.50% 0.50% 0.50% 0.45% 0.45% 0.45% 0.40% 0.45%

35% 0.50% 0.50% 0.50% 0.50% 0.45% 0.45% 0.45% 0.45% 0.45% 0.45% 0.45%

40% 0.55% 0.50% 0.50% 0.50% 0.45% 0.45% 0.45% 0.45% 0.50% 0.45% 0.45%

45% 0.50% 0.55% 0.50% 0.50% 0.50% 0.50% 0.50% 0.50% 0.50% 0.50% 0.45%

50% 0.55% 0.50% 0.50% 0.50% 0.50% 0.50% 0.50% 0.45% 0.45% 0.45% 0.45%

Joint Age 65

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

0% 0.70% 0.70% 0.70% 0.65% 0.60% 0.55% 0.50% 0.45% 0.40% 0.35% 0.25%

5% 0.75% 0.70% 0.70% 0.70% 0.65% 0.65% 0.60% 0.55% 0.55% 0.55% 0.55%

10% 0.75% 0.75% 0.75% 0.70% 0.70% 0.65% 0.65% 0.65% 0.60% 0.60% 0.60%

15% 0.75% 0.75% 0.75% 0.75% 0.75% 0.70% 0.70% 0.65% 0.65% 0.65% 0.65%

20% 0.80% 0.75% 0.75% 0.75% 0.75% 0.75% 0.70% 0.70% 0.65% 0.65% 0.65%

25% 0.80% 0.75% 0.75% 0.75% 0.75% 0.75% 0.70% 0.70% 0.65% 0.70% 0.70%

30% 0.80% 0.75% 0.75% 0.75% 0.75% 0.75% 0.75% 0.70% 0.70% 0.70% 0.65%

35% 0.80% 0.80% 0.80% 0.75% 0.75% 0.75% 0.70% 0.75% 0.70% 0.70% 0.70%

40% 0.80% 0.80% 0.80% 0.75% 0.80% 0.75% 0.75% 0.75% 0.70% 0.75% 0.70%

45% 0.85% 0.80% 0.75% 0.80% 0.75% 0.75% 0.75% 0.75% 0.75% 0.75% 0.75%

50% 0.80% 0.80% 0.75% 0.75% 0.75% 0.75% 0.75% 0.75% 0.75% 0.75% 0.75%

Joint Age 70

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

0% 1.25% 1.20% 1.15% 1.00% 0.95% 0.85% 0.75% 0.70% 0.60% 0.55% 0.50%

5% 1.50% 1.55% 1.45% 1.45% 1.40% 1.35% 1.30% 1.30% 1.25% 1.20% 1.15%

10% 1.55% 1.50% 1.50% 1.50% 1.45% 1.45% 1.35% 1.35% 1.30% 1.30% 1.25%

15% 1.60% 1.60% 1.55% 1.50% 1.45% 1.45% 1.40% 1.40% 1.35% 1.35% 1.35%

20% 1.55% 1.55% 1.55% 1.55% 1.50% 1.45% 1.45% 1.45% 1.40% 1.40% 1.40%

25% 1.60% 1.60% 1.55% 1.50% 1.50% 1.45% 1.45% 1.45% 1.45% 1.40% 1.40%

30% 1.60% 1.60% 1.60% 1.55% 1.50% 1.50% 1.45% 1.50% 1.45% 1.45% 1.50%

35% 1.65% 1.60% 1.55% 1.60% 1.55% 1.55% 1.50% 1.50% 1.50% 1.50% 1.50%

40% 1.60% 1.60% 1.60% 1.60% 1.55% 1.55% 1.50% 1.50% 1.50% 1.50% 1.50%

45% 1.60% 1.60% 1.60% 1.55% 1.55% 1.55% 1.50% 1.55% 1.55% 1.50% 1.50%

50% 1.65% 1.65% 1.60% 1.60% 1.55% 1.55% 1.55% 1.55% 1.55% 1.55% 1.55%

Joint Age 75

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

0% 1.60% 1.55% 1.50% 1.35% 1.25% 1.10% 1.00% 0.85% 0.75% 0.60% 0.50%

5% 1.90% 1.90% 1.85% 1.80% 1.80% 1.75% 1.65% 1.60% 1.55% 1.50% 1.45%

10% 1.95% 1.95% 1.95% 1.90% 1.85% 1.80% 1.80% 1.70% 1.65% 1.65% 1.60%

15% 2.00% 1.95% 1.95% 1.90% 1.85% 1.85% 1.85% 1.80% 1.80% 1.75% 1.70%

20% 2.00% 2.00% 2.00% 1.95% 1.90% 1.85% 1.90% 1.85% 1.85% 1.80% 1.75%

25% 2.00% 1.95% 1.95% 1.90% 1.90% 1.90% 1.90% 1.85% 1.80% 1.80% 1.75%

30% 2.00% 2.00% 2.00% 1.95% 1.90% 1.90% 1.90% 1.90% 1.85% 1.85% 1.85%

35% 2.05% 2.00% 2.00% 1.95% 1.95% 1.95% 1.90% 1.90% 1.95% 1.90% 1.90%

40% 2.05% 2.00% 2.00% 1.95% 1.95% 1.95% 1.90% 1.90% 1.90% 1.90% 1.90%

45% 2.05% 2.00% 2.00% 2.00% 2.00% 1.95% 1.90% 1.95% 1.95% 1.95% 1.95%

50% 2.05% 2.00% 2.05% 2.00% 2.00% 2.00% 2.00% 2.00% 1.95% 1.95% 1.95%

Joint Age 80

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

0% 2.50% 2.50% 2.45% 2.35% 2.25% 2.15% 2.00% 1.90% 1.70% 1.60% 1.40%

5% 2.65% 2.60% 2.60% 2.55% 2.50% 2.45% 2.45% 2.35% 2.30% 2.25% 2.20%

10% 2.65% 2.65% 2.60% 2.55% 2.50% 2.45% 2.45% 2.40% 2.40% 2.35% 2.30%

15% 2.65% 2.65% 2.60% 2.60% 2.55% 2.55% 2.45% 2.45% 2.40% 2.40% 2.40%

20% 2.70% 2.65% 2.60% 2.60% 2.60% 2.60% 2.50% 2.50% 2.45% 2.45% 2.45%

25% 2.65% 2.70% 2.70% 2.65% 2.60% 2.55% 2.55% 2.55% 2.55% 2.55% 2.55%

30% 2.70% 2.65% 2.65% 2.60% 2.60% 2.55% 2.55% 2.55% 2.55% 2.50% 2.50%

35% 2.70% 2.70% 2.70% 2.65% 2.65% 2.60% 2.60% 2.55% 2.50% 2.55% 2.50%

40% 2.70% 2.70% 2.65% 2.65% 2.65% 2.65% 2.65% 2.60% 2.60% 2.60% 2.60%

45% 2.70% 2.75% 2.70% 2.70% 2.65% 2.65% 2.65% 2.65% 2.65% 2.65% 2.65%

50% 2.70% 2.75% 2.70% 2.70% 2.70% 2.65% 2.65% 2.65% 2.70% 2.70% 2.70%

Joint Age 85

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

0% 4.80% 4.70% 4.55% 4.35% 4.10% 3.80% 3.55% 3.20% 2.95% 2.60% 2.30%

5% 5.30% 5.30% 5.20% 5.15% 5.05% 5.00% 4.90% 4.85% 4.80% 4.70% 4.60%

10% 5.35% 5.30% 5.25% 5.25% 5.20% 5.15% 5.05% 5.00% 4.95% 4.85% 4.80%

15% 5.35% 5.35% 5.35% 5.25% 5.25% 5.15% 5.10% 5.05% 5.05% 4.95% 4.90%

20% 5.40% 5.35% 5.35% 5.25% 5.25% 5.15% 5.15% 5.15% 5.10% 5.05% 5.00%

25% 5.40% 5.40% 5.35% 5.30% 5.25% 5.25% 5.20% 5.15% 5.15% 5.10% 5.05%

30% 5.40% 5.40% 5.35% 5.35% 5.30% 5.30% 5.25% 5.20% 5.20% 5.20% 5.20%

35% 5.45% 5.40% 5.35% 5.35% 5.30% 5.30% 5.30% 5.30% 5.30% 5.25% 5.30%

40% 5.45% 5.45% 5.45% 5.40% 5.35% 5.35% 5.30% 5.30% 5.30% 5.30% 5.30%

45% 5.50% 5.45% 5.45% 5.40% 5.40% 5.40% 5.40% 5.35% 5.35% 5.35% 5.35%

50% 5.50% 5.45% 5.45% 5.45% 5.45% 5.45% 5.40% 5.40% 5.40% 5.40% 5.45%


Equity Allocation


Equity Allocation


Equity Allocation


Equity AllocationProbability of Failure

Equity Allocation


Equity Allocation


20

Appendix 5. 50% Expected to Outlive Life Expectancy minus 25% Expected to Outlive Life Expectancy

50% ‐ 25% Outlive (WR% Difference)

Joint Age 60

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

0% 0.30% 0.30% 0.30% 0.30% 0.20% 0.20% 0.20% 0.20% 0.15% 0.15% 0.15%

5% 0.45% 0.45% 0.40% 0.45% 0.35% 0.35% 0.35% 0.35% 0.35% 0.35% 0.35%

10% 0.45% 0.45% 0.45% 0.40% 0.40% 0.40% 0.40% 0.35% 0.30% 0.35% 0.35%

15% 0.45% 0.40% 0.45% 0.40% 0.40% 0.40% 0.40% 0.40% 0.40% 0.35% 0.35%

20% 0.45% 0.45% 0.40% 0.40% 0.40% 0.40% 0.35% 0.35% 0.35% 0.35% 0.40%

25% 0.50% 0.50% 0.45% 0.45% 0.40% 0.40% 0.35% 0.40% 0.40% 0.35% 0.35%

30% 0.45% 0.45% 0.45% 0.45% 0.40% 0.40% 0.40% 0.40% 0.40% 0.40% 0.40%

35% 0.50% 0.45% 0.45% 0.40% 0.45% 0.40% 0.45% 0.40% 0.40% 0.40% 0.40%

40% 0.45% 0.50% 0.45% 0.45% 0.45% 0.45% 0.45% 0.40% 0.40% 0.40% 0.40%

45% 0.50% 0.45% 0.45% 0.45% 0.45% 0.40% 0.40% 0.40% 0.40% 0.40% 0.45%

50% 0.50% 0.50% 0.45% 0.45% 0.45% 0.45% 0.40% 0.40% 0.40% 0.45% 0.45%

Joint Age 65

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

0% 0.65% 0.60% 0.55% 0.55% 0.50% 0.45% 0.40% 0.30% 0.25% 0.20% 0.15%

5% 0.65% 0.65% 0.65% 0.55% 0.60% 0.55% 0.55% 0.55% 0.50% 0.50% 0.45%

10% 0.65% 0.65% 0.60% 0.60% 0.55% 0.55% 0.55% 0.50% 0.55% 0.45% 0.45%

15% 0.65% 0.65% 0.60% 0.60% 0.60% 0.60% 0.55% 0.55% 0.55% 0.55% 0.50%

20% 0.65% 0.65% 0.65% 0.60% 0.60% 0.55% 0.60% 0.55% 0.55% 0.55% 0.50%

25% 0.65% 0.65% 0.65% 0.65% 0.60% 0.60% 0.60% 0.55% 0.55% 0.55% 0.55%

30% 0.70% 0.70% 0.65% 0.65% 0.65% 0.60% 0.60% 0.60% 0.60% 0.55% 0.60%

35% 0.65% 0.65% 0.65% 0.65% 0.60% 0.60% 0.60% 0.60% 0.60% 0.60% 0.60%

40% 0.70% 0.65% 0.65% 0.65% 0.60% 0.60% 0.60% 0.60% 0.65% 0.60% 0.60%

45% 0.65% 0.70% 0.70% 0.65% 0.65% 0.65% 0.65% 0.60% 0.60% 0.65% 0.60%

50% 0.70% 0.65% 0.70% 0.65% 0.65% 0.65% 0.65% 0.60% 0.60% 0.60% 0.60%

Joint Age 70

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

0% 0.70% 0.70% 0.70% 0.65% 0.60% 0.55% 0.50% 0.45% 0.40% 0.35% 0.25%

5% 0.75% 0.70% 0.70% 0.70% 0.65% 0.65% 0.60% 0.55% 0.55% 0.55% 0.55%

10% 0.75% 0.75% 0.75% 0.70% 0.70% 0.65% 0.65% 0.65% 0.60% 0.60% 0.60%

15% 0.75% 0.75% 0.75% 0.75% 0.75% 0.70% 0.70% 0.65% 0.65% 0.65% 0.65%

20% 0.80% 0.75% 0.75% 0.75% 0.75% 0.75% 0.70% 0.70% 0.65% 0.65% 0.65%

25% 0.80% 0.75% 0.75% 0.75% 0.75% 0.75% 0.70% 0.70% 0.65% 0.70% 0.70%

30% 0.80% 0.75% 0.75% 0.75% 0.75% 0.75% 0.75% 0.70% 0.70% 0.70% 0.65%

35% 0.80% 0.80% 0.80% 0.75% 0.75% 0.75% 0.70% 0.75% 0.70% 0.70% 0.70%

40% 0.80% 0.80% 0.80% 0.75% 0.80% 0.75% 0.75% 0.75% 0.70% 0.75% 0.70%

45% 0.85% 0.80% 0.75% 0.80% 0.75% 0.75% 0.75% 0.75% 0.75% 0.75% 0.75%

50% 0.80% 0.80% 0.75% 0.75% 0.75% 0.75% 0.75% 0.75% 0.75% 0.75% 0.75%

Joint Age 75

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

0% 0.95% 0.95% 0.85% 0.80% 0.75% 0.70% 0.60% 0.55% 0.50% 0.45% 0.45%

5% 1.15% 1.15% 1.10% 1.10% 1.05% 1.00% 1.00% 1.00% 0.95% 0.90% 0.85%

10% 1.15% 1.10% 1.10% 1.10% 1.10% 1.10% 1.00% 1.05% 1.00% 1.00% 0.95%

15% 1.20% 1.20% 1.15% 1.10% 1.10% 1.05% 1.05% 1.05% 1.00% 1.00% 1.00%

20% 1.15% 1.15% 1.15% 1.15% 1.10% 1.10% 1.05% 1.05% 1.05% 1.05% 1.05%

25% 1.20% 1.20% 1.15% 1.15% 1.15% 1.10% 1.10% 1.10% 1.10% 1.05% 1.05%

30% 1.20% 1.20% 1.20% 1.15% 1.15% 1.15% 1.10% 1.10% 1.10% 1.10% 1.10%

35% 1.20% 1.20% 1.15% 1.20% 1.15% 1.15% 1.15% 1.10% 1.10% 1.10% 1.10%

40% 1.20% 1.20% 1.20% 1.20% 1.15% 1.15% 1.15% 1.15% 1.15% 1.10% 1.15%

45% 1.20% 1.20% 1.20% 1.15% 1.15% 1.15% 1.15% 1.15% 1.15% 1.10% 1.10%

50% 1.25% 1.25% 1.20% 1.20% 1.15% 1.15% 1.15% 1.15% 1.15% 1.15% 1.15%

Joint Age 80

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

0% 1.30% 1.30% 1.20% 1.15% 1.05% 0.95% 0.85% 0.70% 0.65% 0.50% 0.45%

5% 1.55% 1.50% 1.50% 1.45% 1.45% 1.40% 1.35% 1.30% 1.25% 1.20% 1.15%

10% 1.55% 1.55% 1.55% 1.50% 1.50% 1.45% 1.45% 1.40% 1.35% 1.35% 1.30%

15% 1.60% 1.55% 1.55% 1.50% 1.50% 1.45% 1.50% 1.45% 1.45% 1.40% 1.35%

20% 1.60% 1.60% 1.60% 1.55% 1.50% 1.50% 1.50% 1.45% 1.50% 1.45% 1.40%

25% 1.60% 1.55% 1.55% 1.55% 1.55% 1.55% 1.55% 1.50% 1.45% 1.45% 1.40%

30% 1.60% 1.60% 1.60% 1.55% 1.55% 1.55% 1.55% 1.50% 1.50% 1.50% 1.45%

35% 1.60% 1.60% 1.60% 1.55% 1.55% 1.55% 1.55% 1.50% 1.55% 1.50% 1.50%

40% 1.65% 1.60% 1.60% 1.55% 1.55% 1.55% 1.55% 1.55% 1.55% 1.50% 1.55%

45% 1.65% 1.60% 1.60% 1.60% 1.60% 1.55% 1.55% 1.55% 1.55% 1.55% 1.55%

50% 1.65% 1.60% 1.65% 1.60% 1.60% 1.60% 1.60% 1.60% 1.55% 1.55% 1.55%

Joint Age 85

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

0% 2.50% 2.50% 2.45% 2.35% 2.25% 2.15% 2.00% 1.90% 1.70% 1.60% 1.40%

5% 2.65% 2.60% 2.60% 2.55% 2.50% 2.45% 2.45% 2.35% 2.30% 2.25% 2.20%

10% 2.65% 2.65% 2.60% 2.55% 2.50% 2.45% 2.45% 2.40% 2.40% 2.35% 2.30%

15% 2.65% 2.65% 2.60% 2.60% 2.55% 2.55% 2.45% 2.45% 2.40% 2.40% 2.40%

20% 2.70% 2.65% 2.60% 2.60% 2.60% 2.60% 2.50% 2.50% 2.45% 2.45% 2.45%

25% 2.65% 2.70% 2.70% 2.65% 2.60% 2.55% 2.55% 2.55% 2.55% 2.55% 2.55%

30% 2.70% 2.65% 2.65% 2.60% 2.60% 2.55% 2.55% 2.55% 2.55% 2.50% 2.50%

35% 2.70% 2.70% 2.70% 2.65% 2.65% 2.60% 2.60% 2.55% 2.50% 2.55% 2.50%

40% 2.70% 2.70% 2.65% 2.65% 2.65% 2.65% 2.65% 2.60% 2.60% 2.60% 2.60%

45% 2.70% 2.75% 2.70% 2.70% 2.65% 2.65% 2.65% 2.65% 2.65% 2.65% 2.65%

50% 2.70% 2.75% 2.70% 2.70% 2.70% 2.65% 2.65% 2.65% 2.70% 2.70% 2.70%


Equity Allocation


Equity Allocation


Equity Allocation


Equity Allocation


Equity Allocation


Equity Allocation


21

Appendix 6. Retiree Cash flows and Portfolio Values; Age 60 Cash Flow Distribution Portfolio Value Distribution End of Year

Male Age 60 Retire Yr POF Outlive% Years Left Withdraw% Either Alive% CF Yr Age 95th 75th 50th 25th 5th Age 95th 75th 50th 25th 5th

Female Age 60 1 10.00% 75% 25 4.50% 100.00% 1 61 $45,000 $45,000 $45,000 $45,000 $45,000 61 $818,462 $931,975 $1,007,684 $1,084,669 $1,194,775

2 10.00% 75% 24 4.65% 99.99% 2 62 $38,058 $43,337 $46,857 $50,437 $55,557 62 $755,589 $899,280 $1,007,124 $1,122,840 $1,292,659

Equity% 60% 3 10.00% 75% 23 4.75% 99.96% 3 63 $35,890 $42,716 $47,838 $53,335 $61,401 63 $712,399 $875,395 $1,006,357 $1,148,455 $1,378,005

4 10.00% 75% 22 4.90% 99.91% 4 64 $34,908 $42,894 $49,312 $56,274 $67,522 64 $679,488 $854,948 $1,003,424 $1,168,258 $1,439,481

Start Value $1,000,000 5 10.00% 65% 23 4.75% 99.83% 5 65 $32,276 $40,610 $47,663 $55,492 $68,375 65 $647,616 $836,767 $998,987 $1,189,155 $1,501,734

6 10.00% 65% 22 4.90% 99.71% 6 66 $31,733 $41,002 $48,950 $58,269 $73,585 66 $617,609 $823,012 $993,667 $1,204,611 $1,565,702

7 10.00% 65% 21 5.10% 99.56% 7 67 $31,498 $41,974 $50,677 $61,435 $79,851 67 $591,675 $807,495 $994,095 $1,224,495 $1,608,821

Min Max Outlive% 8 10.00% 65% 20 5.30% 99.36% 8 68 $31,359 $42,797 $52,687 $64,898 $85,267 68 $568,278 $787,345 $985,598 $1,229,535 $1,668,176

0 4 75% 9 10.00% 65% 19 5.50% 99.09% 9 69 $31,255 $43,304 $54,208 $67,624 $91,750 69 $546,121 $770,643 $981,185 $1,240,176 $1,719,269

5 9 65% 10 10.00% 55% 20 5.30% 98.76% 10 70 $28,944 $40,844 $52,003 $65,729 $91,121 70 $523,945 $756,738 $972,430 $1,246,700 $1,753,558

10 14 55% 11 10.00% 55% 19 5.50% 98.35% 11 71 $28,817 $41,621 $53,484 $68,568 $96,446 71 $505,326 $745,736 $967,056 $1,259,069 $1,792,340

15 19 50% 12 10.00% 55% 18 5.75% 97.83% 12 72 $29,056 $42,880 $55,606 $72,396 $103,060 72 $490,255 $727,809 $960,867 $1,259,086 $1,834,712

20 24 40% 13 10.00% 55% 17 6.00% 97.20% 13 73 $29,415 $43,669 $57,652 $75,545 $110,083 73 $472,549 $707,016 $952,815 $1,258,308 $1,864,665

25 29 30% 14 10.00% 55% 17 6.00% 96.43% 14 74 $28,353 $42,421 $57,169 $75,498 $111,880 74 $459,736 $694,540 $934,723 $1,252,914 $1,885,965

30 34 20% 15 10.00% 50% 17 6.00% 95.50% 15 75 $27,584 $41,672 $56,083 $75,175 $113,158 75 $441,113 $674,458 $919,898 $1,250,583 $1,939,027

35 39 10% 16 10.00% 50% 16 6.30% 94.41% 16 76 $27,790 $42,491 $57,954 $78,787 $122,159 76 $420,686 $653,907 $907,647 $1,248,321 $1,942,077

40 44 10% 17 10.00% 50% 15 6.65% 93.12% 17 77 $27,976 $43,485 $60,359 $83,013 $129,148 77 $404,267 $631,911 $890,237 $1,238,765 $1,942,191

45 49 10% 18 10.00% 50% 14 7.05% 91.60% 18 78 $28,501 $44,550 $62,762 $87,333 $136,924 78 $384,921 $613,824 $868,882 $1,223,651 $1,958,187

50 100 10% 19 10.00% 50% 13 7.50% 89.82% 19 79 $28,869 $46,037 $65,166 $91,774 $146,864 79 $364,968 $592,124 $840,399 $1,198,423 $1,928,992

20 10.00% 40% 14 7.05% 87.76% 20 80 $25,730 $41,745 $59,248 $84,489 $135,994 80 $349,461 $573,033 $820,327 $1,186,372 $1,936,042

21 10.00% 40% 13 7.50% 85.39% 21 81 $26,210 $42,977 $61,525 $88,978 $145,203 81 $330,796 $557,128 $803,483 $1,159,130 $1,929,304

Min Max POF% 22 10.00% 40% 13 7.50% 82.68% 22 82 $24,810 $41,785 $60,261 $86,935 $144,698 82 $312,649 $538,575 $777,539 $1,138,211 $1,898,431

0 4 10% 23 10.00% 40% 12 8.10% 79.60% 23 83 $25,325 $43,625 $62,981 $92,195 $153,773 83 $295,318 $516,526 $754,832 $1,107,652 $1,868,193

5 9 10% 24 10.00% 40% 11 8.75% 76.13% 24 84 $25,840 $45,196 $66,048 $96,920 $163,467 84 $274,342 $489,658 $723,233 $1,068,199 $1,835,957

10 14 10% 25 10.00% 30% 12 8.10% 72.26% 25 85 $22,222 $39,662 $58,582 $86,524 $148,713 85 $261,516 $472,381 $696,812 $1,043,640 $1,816,333

15 19 10% 26 10.00% 30% 11 8.75% 67.99% 26 86 $22,883 $41,333 $60,971 $91,319 $158,929 86 $247,175 $448,590 $669,688 $1,011,064 $1,740,277

20 24 10% 27 10.00% 30% 10 9.55% 63.33% 27 87 $23,605 $42,840 $63,955 $96,557 $166,196 87 $225,877 $421,178 $637,880 $963,572 $1,711,428

25 29 10% 28 10.00% 30% 10 9.55% 58.31% 28 88 $21,571 $40,222 $60,918 $92,021 $163,441 88 $214,185 $401,050 $606,755 $923,303 $1,661,231

30 34 10% 29 10.00% 30% 9 10.55% 52.98% 29 89 $22,596 $42,311 $64,013 $97,408 $175,260 89 $197,498 $372,521 $567,566 $873,765 $1,585,248

35 39 10% 30 10.00% 20% 10 9.55% 47.43% 30 90 $18,861 $35,576 $54,203 $83,445 $151,391 90 $186,769 $351,535 $542,511 $834,607 $1,557,460

40 44 10% 31 10.00% 20% 9 10.55% 41.74% 31 91 $19,704 $37,087 $57,235 $88,051 $164,312 91 $171,812 $329,299 $512,092 $798,546 $1,498,051

45 49 10% 32 10.00% 20% 9 10.55% 36.04% 32 92 $18,126 $34,741 $54,026 $84,247 $158,044 92 $159,814 $310,039 $481,046 $749,178 $1,419,341

50 100 10% 33 10.00% 20% 8 11.75% 30.49% 33 93 $18,778 $36,430 $56,523 $88,028 $166,773 93 $143,358 $284,233 $447,266 $701,938 $1,353,064

34 10.00% 20% 8 11.75% 25.20% 34 94 $16,845 $33,397 $52,554 $82,478 $158,985 94 $130,389 $259,342 $413,228 $657,415 $1,271,130

35 10.00% 10% 9 10.55% 20.33% 35 95 $13,756 $27,361 $43,596 $69,357 $134,104 95 $120,980 $243,263 $390,835 $625,071 $1,217,236

36 10.00% 10% 8 11.75% 15.97% 36 96 $14,215 $28,583 $45,923 $73,446 $143,025 96 $110,821 $223,239 $364,586 $579,573 $1,146,022

37 10.00% 10% 8 11.75% 12.20% 37 97 $13,021 $26,231 $42,839 $68,100 $134,658 97 $102,123 $205,635 $339,742 $543,933 $1,084,330

38 10.00% 10% 8 11.75% 9.08% 38 98 $11,999 $24,162 $39,920 $63,912 $127,409 98 $92,552 $190,840 $313,433 $508,271 $1,020,561

39 10.00% 10% 7 13.40% 6.57% 39 99 $12,402 $25,573 $42,000 $68,108 $136,755 99 $83,235 $172,727 $286,798 $469,297 $949,897

40 10.00% 10% 7 13.40% 4.64% 40 100 $11,154 $23,145 $38,431 $62,886 $127,286 100 $75,453 $155,492 $261,033 $432,279 $884,794

41 10.00% 10% 6 15.60% 3.19% 41 101 $11,771 $24,257 $40,721 $67,435 $138,028 101 $65,557 $137,370 $231,745 $388,275 $805,743

42 10.00% 10% 6 15.60% 2.14% 42 102 $10,227 $21,430 $36,152 $60,571 $125,696 102 $56,990 $122,080 $206,932 $348,719 $719,487

43 10.00% 10% 6 15.60% 1.40% 43 103 $8,890 $19,044 $32,281 $54,400 $112,240 103 $49,821 $107,840 $184,417 $315,067 $656,920

44 10.00% 10% 5 18.70% 0.88% 44 104 $9,317 $20,166 $34,486 $58,917 $122,844 104 $42,312 $92,268 $157,734 $270,499 $575,626

45 10.00% 10% 5 18.70% 0.54% 45 105 $7,912 $17,254 $29,496 $50,583 $107,642 105 $35,795 $78,694 $134,552 $234,231 $504,664

46 10.00% 10% 5 18.70% 0.32% 46 106 $6,694 $14,716 $25,161 $43,801 $94,372 106 $30,021 $68,014 $116,155 $201,005 $436,185

47 10.00% 10% 5 18.70% 0.18% 47 107 $5,614 $12,719 $21,721 $37,588 $81,567 107 $25,249 $57,681 $99,868 $175,115 $383,142

48 10.00% 10% 5 18.70% 0.10% 48 108 $4,722 $10,786 $18,675 $32,747 $71,648 108 $21,528 $49,243 $85,864 $151,443 $336,309

49 10.00% 10% 5 18.70% 0.05% 49 109 $4,026 $9,208 $16,057 $28,320 $62,890 109 $18,083 $41,978 $74,109 $130,266 $293,376

50 10.00% 10% 5 18.70% 0.02% 50 110 $3,382 $7,850 $13,858 $24,360 $54,861 110 $15,466 $36,001 $63,373 $112,726 $259,785

POF For Years Left

Outlive % for # of Years in Retirement


22



Female Age 70 1 10.00% 55% 19 5.50% 100.00% 1 71 $53,350 $53,350 $53,350 $53,350 $53,350 71 $784,208 $894,316 $967,754 $1,042,429 $1,149,232

2 10.00% 55% 18 5.75% 99.95% 2 72 $45,092 $51,423 $55,646 $59,940 $66,081 72 $715,317 $853,100 $956,535 $1,067,647 $1,230,756

Equity% 60% 3 10.00% 55% 17 6.00% 99.80% 3 73 $42,919 $51,186 $57,392 $64,059 $73,845 73 $665,170 $819,599 $943,847 $1,078,524 $1,296,599

4 10.00% 55% 17 6.00% 99.52% 4 74 $39,910 $49,176 $56,631 $64,711 $77,796 74 $627,349 $791,219 $930,533 $1,085,154 $1,340,373

Start Value $970,000 5 10.00% 50% 17 6.00% 99.08% 5 75 $37,641 $47,473 $55,832 $65,109 $80,422 75 $589,711 $764,506 $914,814 $1,091,131 $1,381,390

6 10.00% 50% 16 6.30% 98.46% 6 76 $37,152 $48,164 $57,633 $68,741 $87,028 76 $554,343 $741,146 $896,788 $1,089,959 $1,420,690

7 10.00% 50% 15 6.65% 97.63% 7 77 $36,864 $49,286 $59,636 $72,482 $94,476 77 $522,124 $715,652 $883,109 $1,090,997 $1,438,238

Min Max Outlive% 8 10.00% 50% 14 7.05% 96.56% 8 78 $36,810 $50,453 $62,259 $76,915 $101,396 78 $492,346 $685,146 $860,109 $1,076,614 $1,466,289

0 4 55% 9 10.00% 50% 13 7.50% 95.19% 9 79 $36,926 $51,386 $64,508 $80,746 $109,972 79 $463,040 $656,788 $838,965 $1,064,302 $1,481,092

5 9 50% 10 10.00% 40% 14 7.05% 93.52% 10 80 $32,644 $46,304 $59,147 $75,033 $104,417 80 $435,805 $633,072 $816,747 $1,050,934 $1,486,802

10 14 40% 11 10.00% 40% 13 7.50% 91.49% 11 81 $32,685 $47,480 $61,256 $78,820 $111,510 81 $411,236 $611,420 $795,677 $1,039,929 $1,488,727

15 19 30% 12 10.00% 40% 13 7.50% 89.06% 12 82 $30,843 $45,856 $59,676 $77,995 $111,655 82 $392,102 $585,993 $777,312 $1,021,957 $1,497,499

20 24 20% 13 10.00% 40% 12 8.10% 86.19% 13 83 $31,760 $47,465 $62,962 $82,778 $121,297 83 $369,313 $556,951 $754,180 $1,000,499 $1,491,215

25 29 10% 14 10.00% 40% 11 8.75% 82.86% 14 84 $32,315 $48,733 $65,991 $87,544 $130,481 84 $348,840 $531,231 $718,316 $968,953 $1,464,901

30 34 10% 15 10.00% 30% 12 8.10% 79.03% 15 85 $28,256 $43,030 $58,184 $78,485 $118,657 85 $327,233 $504,415 $691,590 $946,468 $1,477,229

35 39 10% 16 10.00% 30% 11 8.75% 74.72% 16 86 $28,633 $44,136 $60,514 $82,816 $129,257 86 $304,191 $476,920 $665,938 $920,941 $1,442,537

40 44 10% 17 10.00% 30% 10 9.55% 69.92% 17 87 $29,050 $45,546 $63,597 $87,950 $137,762 87 $283,581 $446,677 $633,984 $887,282 $1,402,917

45 49 10% 18 10.00% 30% 10 9.55% 64.65% 18 88 $27,082 $42,658 $60,545 $84,735 $133,979 88 $262,690 $422,951 $602,050 $854,291 $1,379,665

50 100 10% 19 10.00% 30% 9 10.55% 58.98% 19 89 $27,714 $44,621 $63,516 $90,128 $145,555 89 $240,688 $394,838 $564,373 $809,816 $1,317,327

20 10.00% 20% 10 9.55% 52.99% 20 90 $22,986 $37,707 $53,898 $77,337 $125,805 90 $224,623 $372,265 $536,088 $782,029 $1,286,161

21 10.00% 20% 9 10.55% 46.79% 21 91 $23,698 $39,274 $56,557 $82,504 $135,690 91 $205,035 $350,253 $508,246 $739,268 $1,243,604

Min Max POF% 22 10.00% 20% 9 10.55% 40.52% 22 92 $21,631 $36,952 $53,620 $77,993 $131,200 92 $188,139 $327,683 $476,960 $704,331 $1,186,682

0 4 10% 23 10.00% 20% 8 11.75% 34.36% 23 93 $22,106 $38,503 $56,043 $82,759 $139,435 93 $170,442 $302,617 $445,601 $658,884 $1,124,206

5 9 10% 24 10.00% 20% 8 11.75% 28.46% 24 94 $20,027 $35,557 $52,358 $77,419 $132,094 94 $153,423 $276,991 $413,339 $615,649 $1,070,446

10 14 10% 25 10.00% 10% 9 10.55% 22.99% 25 95 $16,186 $29,223 $43,607 $64,951 $112,932 95 $142,373 $260,647 $388,138 $585,786 $1,035,628

15 19 10% 26 10.00% 10% 8 11.75% 18.08% 26 96 $16,729 $30,626 $45,606 $68,830 $121,686 96 $129,928 $239,585 $360,770 $551,255 $960,471

20 24 10% 27 10.00% 10% 8 11.75% 13.83% 27 97 $15,267 $28,151 $42,391 $64,772 $112,855 97 $116,195 $219,486 $336,447 $513,263 $921,796

25 29 10% 28 10.00% 10% 8 11.75% 10.29% 28 98 $13,653 $25,790 $39,533 $60,308 $108,311 98 $107,303 $204,520 $311,626 $479,806 $874,731

30 34 10% 29 10.00% 10% 7 13.40% 7.45% 29 99 $14,379 $27,406 $41,758 $64,294 $117,214 99 $95,988 $183,895 $283,152 $439,719 $809,788

35 39 10% 30 10.00% 10% 7 13.40% 5.26% 30 100 $12,862 $24,642 $37,942 $58,922 $108,512 100 $86,773 $166,016 $259,474 $403,686 $763,936

40 44 10% 31 10.00% 10% 6 15.60% 3.62% 31 101 $13,537 $25,899 $40,478 $62,975 $119,174 101 $75,490 $147,572 $231,770 $364,661 $696,683

45 49 10% 32 10.00% 10% 6 15.60% 2.42% 32 102 $11,776 $23,021 $36,156 $56,887 $108,682 102 $66,007 $131,211 $205,790 $325,105 $625,222

50 100 10% 33 10.00% 10% 6 15.60% 1.58% 33 103 $10,297 $20,469 $32,103 $50,716 $97,535 103 $56,995 $115,095 $183,344 $291,626 $570,562

34 10.00% 10% 5 18.70% 1.00% 34 104 $10,658 $21,523 $34,285 $54,534 $106,695 104 $47,716 $97,144 $156,604 $252,359 $496,547

35 10.00% 10% 5 18.70% 0.61% 35 105 $8,923 $18,166 $29,285 $47,191 $92,854 105 $40,333 $82,812 $135,408 $219,622 $436,268

36 10.00% 10% 5 18.70% 0.36% 36 106 $7,542 $15,486 $25,321 $41,069 $81,582 106 $34,183 $69,961 $116,762 $188,348 $380,240

37 10.00% 10% 5 18.70% 0.20% 37 107 $6,392 $13,083 $21,834 $35,221 $71,105 107 $29,030 $59,732 $100,161 $163,718 $333,308

38 10.00% 10% 5 18.70% 0.11% 38 108 $5,429 $11,170 $18,730 $30,615 $62,329 108 $24,317 $51,236 $85,561 $141,510 $291,899

39 10.00% 10% 5 18.70% 0.06% 39 109 $4,547 $9,581 $16,000 $26,462 $54,585 109 $20,499 $43,729 $73,905 $123,279 $255,359

40 10.00% 10% 5 18.70% 0.03% 40 110 $3,833 $8,177 $13,820 $23,053 $47,752 110 $17,422 $36,945 $63,326 $106,743 $224,537

POF For Years Left



23



Female Age 80 1 10.00% 40% 13 7.50% 100.00% 1 81 $61,500 $61,500 $61,500 $61,500 $61,500 81 $646,539 $739,620 $801,701 $864,828 $955,115

2 10.00% 40% 13 7.50% 99.69% 2 82 $48,490 $55,471 $60,128 $64,862 $71,634 82 $578,538 $692,494 $778,291 $870,321 $1,005,946

Equity% 60% 3 10.00% 40% 12 8.10% 98.71% 3 83 $46,862 $56,092 $63,042 $70,496 $81,482 83 $525,756 $650,455 $751,697 $861,067 $1,038,960

4 10.00% 40% 11 8.75% 96.98% 4 84 $46,004 $56,915 $65,773 $75,343 $90,909 84 $480,872 $610,368 $719,891 $842,540 $1,045,774

Start Value $820,000 5 10.00% 30% 12 8.10% 94.44% 5 85 $38,951 $49,440 $58,311 $68,246 $84,708 85 $441,819 $576,400 $692,433 $829,455 $1,055,497

6 10.00% 30% 11 8.75% 91.02% 6 86 $38,659 $50,435 $60,588 $72,577 $92,356 86 $404,643 $544,562 $662,037 $808,442 $1,059,698

7 10.00% 30% 10 9.55% 86.72% 7 87 $38,643 $52,006 $63,225 $77,206 $101,201 87 $369,216 $509,721 $632,608 $785,498 $1,042,199

Min Max Outlive% 8 10.00% 30% 10 9.55% 81.55% 8 88 $35,260 $48,678 $60,414 $75,015 $99,530 88 $338,440 $475,503 $600,036 $754,721 $1,035,850

0 4 40% 9 10.00% 30% 9 10.55% 75.54% 9 89 $35,705 $50,166 $63,304 $79,623 $109,282 89 $308,134 $441,197 $566,738 $723,492 $1,015,473

5 9 30% 10 10.00% 20% 10 9.55% 68.81% 10 90 $29,427 $42,134 $54,123 $69,093 $96,978 90 $282,191 $413,941 $537,548 $696,250 $992,764

10 14 20% 11 10.00% 20% 9 10.55% 61.51% 11 91 $29,771 $43,671 $56,711 $73,454 $104,737 91 $257,683 $387,062 $507,165 $667,349 $964,449

15 19 10% 12 10.00% 20% 9 10.55% 53.85% 12 92 $27,186 $40,835 $53,506 $70,405 $101,749 92 $237,316 $359,214 $479,848 $635,350 $940,563

20 24 10% 13 10.00% 20% 8 11.75% 46.08% 13 93 $27,885 $42,208 $56,382 $74,654 $110,516 93 $214,746 $328,058 $447,972 $599,069 $903,311

25 29 10% 14 10.00% 20% 8 11.75% 38.46% 14 94 $25,233 $38,547 $52,637 $70,391 $106,139 94 $196,642 $302,905 $413,378 $561,887 $860,488

30 34 10% 15 10.00% 10% 9 10.55% 31.26% 15 95 $20,746 $31,956 $43,611 $59,279 $90,781 95 $179,634 $279,867 $387,782 $535,478 $846,516

35 39 10% 16 10.00% 10% 8 11.75% 24.70% 16 96 $21,107 $32,884 $45,564 $62,919 $99,466 96 $161,413 $256,500 $361,366 $505,239 $799,611

40 44 10% 17 10.00% 10% 8 11.75% 18.95% 17 97 $18,966 $30,139 $42,460 $59,366 $93,954 97 $146,876 $234,381 $336,330 $475,129 $759,748

45 49 10% 18 10.00% 10% 8 11.75% 14.13% 18 98 $17,258 $27,540 $39,519 $55,828 $89,270 98 $132,912 $216,728 $311,842 $446,540 $729,095

50 100 10% 19 10.00% 10% 7 13.40% 10.24% 19 99 $17,810 $29,042 $41,787 $59,836 $97,699 99 $117,500 $196,188 $283,049 $410,586 $677,425

20 10.00% 10% 7 13.40% 7.23% 20 100 $15,745 $26,289 $37,929 $55,018 $90,775 100 $105,336 $177,495 $258,191 $380,476 $634,765

21 10.00% 10% 6 15.60% 4.97% 21 101 $16,432 $27,689 $40,278 $59,354 $99,023 101 $90,656 $157,501 $231,585 $340,304 $582,177

Min Max POF% 22 10.00% 10% 6 15.60% 3.33% 22 102 $14,142 $24,570 $36,127 $53,087 $90,820 102 $78,760 $139,434 $205,557 $307,486 $525,710

0 4 10% 23 10.00% 10% 6 15.60% 2.17% 23 103 $12,287 $21,752 $32,067 $47,968 $82,011 103 $68,246 $123,430 $184,273 $275,357 $478,132

5 9 10% 24 10.00% 10% 5 18.70% 1.37% 24 104 $12,762 $23,081 $34,459 $51,492 $89,411 104 $56,771 $104,569 $157,994 $238,061 $422,435

10 14 10% 25 10.00% 10% 5 18.70% 0.83% 25 105 $10,616 $19,554 $29,545 $44,517 $78,995 105 $47,812 $89,269 $135,309 $207,091 $371,575

15 19 10% 26 10.00% 10% 5 18.70% 0.49% 26 106 $8,941 $16,693 $25,303 $38,726 $69,484 106 $40,197 $75,952 $116,019 $180,293 $321,834

20 24 10% 27 10.00% 10% 5 18.70% 0.28% 27 107 $7,517 $14,203 $21,695 $33,715 $60,183 107 $33,208 $64,217 $100,149 $155,764 $284,826

25 29 10% 28 10.00% 10% 5 18.70% 0.15% 28 108 $6,210 $12,009 $18,728 $29,128 $53,262 108 $28,149 $55,287 $85,869 $134,953 $250,820

30 34 10% 29 10.00% 10% 5 18.70% 0.08% 29 109 $5,264 $10,339 $16,057 $25,236 $46,903 109 $23,665 $46,803 $73,287 $116,154 $220,306

35 39 10% 30 10.00% 10% 5 18.70% 0.04% 30 110 $4,425 $8,752 $13,705 $21,721 $41,197 110 $20,062 $39,787 $63,230 $100,427 $195,580

40 44 10% 31 10.00% 10% 5 18.70% 0.02% 31 111 $3,752 $7,440 $11,824 $18,780 $36,573 111 $16,836 $33,977 $54,458 $87,436 $171,556

45 49 10% 32 10.00% 10% 5 18.70% 0.01% 32 112 $3,148 $6,354 $10,184 $16,351 $32,081 112 $14,229 $29,136 $46,693 $75,466 $149,431

50 100 10% 33 10.00% 10% 5 18.70% 0.00% 33 113 $2,661 $5,448 $8,732 $14,112 $27,944 113 $11,813 $24,665 $40,196 $64,924 $130,991

POF For Years Left



24



Female Age 90 1 10.00% 20% 9 10.55% 100.00% 1 91 $54,333 $54,333 $54,333 $54,333 $54,333 91 $390,350 $448,810 $487,800 $527,447 $584,152

2 10.00% 20% 9 10.55% 97.53% 2 92 $41,182 $47,349 $51,463 $55,646 $61,628 92 $337,418 $406,332 $458,502 $514,657 $597,381

Equity% 60% 3 10.00% 20% 8 11.75% 90.80% 3 93 $39,647 $47,744 $53,874 $60,472 $70,192 93 $294,073 $366,623 $426,055 $490,395 $595,283

4 10.00% 20% 8 11.75% 80.95% 4 94 $34,554 $43,078 $50,061 $57,621 $69,946 94 $260,068 $333,143 $395,158 $464,873 $580,959

Start Value $515,000 5 10.00% 10% 9 10.55% 69.24% 5 95 $27,437 $35,147 $41,689 $49,044 $61,291 95 $232,407 $306,400 $370,493 $446,177 $572,052

6 10.00% 10% 8 11.75% 56.87% 6 96 $27,308 $36,002 $43,533 $52,426 $67,216 96 $205,933 $280,070 $342,576 $421,662 $557,013

7 10.00% 10% 8 11.75% 44.92% 7 97 $24,197 $32,908 $40,253 $49,545 $65,449 97 $183,168 $256,042 $320,045 $399,963 $535,690

Min Max Outlive% 8 10.00% 10% 8 11.75% 34.19% 8 98 $21,522 $30,085 $37,605 $46,996 $62,944 98 $163,915 $233,218 $296,595 $375,806 $519,863

0 4 20% 9 10.00% 10% 7 13.40% 25.13% 9 99 $21,965 $31,251 $39,744 $50,358 $69,662 99 $144,777 $209,684 $271,488 $349,364 $495,549

5 9 10% 10 10.00% 10% 7 13.40% 17.88% 10 100 $19,400 $28,098 $36,379 $46,815 $66,404 100 $126,915 $188,662 $246,967 $322,458 $464,741

10 14 10% 11 10.00% 10% 6 15.60% 12.35% 11 101 $19,799 $29,431 $38,527 $50,303 $72,500 101 $109,195 $166,489 $220,393 $293,000 $427,243

15 19 10% 12 10.00% 10% 6 15.60% 8.28% 12 102 $17,034 $25,972 $34,381 $45,708 $66,650 102 $95,038 $146,100 $197,217 $264,017 $395,861

20 24 10% 13 10.00% 10% 6 15.60% 5.39% 13 103 $14,826 $22,792 $30,766 $41,187 $61,754 103 $82,529 $127,713 $176,768 $238,547 $365,096

25 29 10% 14 10.00% 10% 5 18.70% 3.39% 14 104 $15,433 $23,882 $33,056 $44,608 $68,273 104 $69,353 $108,709 $150,665 $207,381 $323,005

30 34 10% 15 10.00% 10% 5 18.70% 2.06% 15 105 $12,969 $20,329 $28,174 $38,780 $60,402 105 $57,645 $91,576 $129,023 $180,835 $291,601

35 39 10% 16 10.00% 10% 5 18.70% 1.21% 16 106 $10,780 $17,125 $24,127 $33,816 $54,529 106 $47,606 $77,491 $111,256 $157,718 $255,461

40 44 10% 17 10.00% 10% 5 18.70% 0.68% 17 107 $8,902 $14,491 $20,805 $29,493 $47,771 107 $39,941 $65,500 $95,663 $137,668 $224,692

45 49 10% 18 10.00% 10% 5 18.70% 0.37% 18 108 $7,469 $12,249 $17,889 $25,744 $42,017 108 $33,302 $55,812 $81,871 $119,481 $200,364

50 100 10% 19 10.00% 10% 5 18.70% 0.19% 19 109 $6,227 $10,437 $15,310 $22,343 $37,468 109 $27,645 $47,531 $70,121 $103,450 $175,168

20 10.00% 10% 5 18.70% 0.09% 20 110 $5,170 $8,888 $13,113 $19,345 $32,756 110 $23,290 $40,641 $60,085 $90,334 $154,463

21 10.00% 10% 5 18.70% 0.04% 21 111 $4,355 $7,600 $11,236 $16,892 $28,885 111 $19,386 $34,756 $51,983 $78,189 $137,197

Min Max POF% 22 10.00% 10% 5 18.70% 0.02% 22 112 $3,625 $6,499 $9,721 $14,621 $25,656 112 $16,253 $29,657 $44,582 $68,109 $120,058

0 4 10% 23 10.00% 10% 5 18.70% 0.01% 23 113 $3,039 $5,546 $8,337 $12,736 $22,451 113 $13,509 $25,263 $38,542 $58,789 $104,829

5 9 10% 24 10.00% 10% 5 18.70% 0.00% 24 114 $2,526 $4,724 $7,207 $10,994 $19,603 114 $11,307 $21,420 $33,106 $50,857 $92,521

10 14 10% 25 10.00% 10% 5 18.70% 0.00% 25 115 $2,114 $4,006 $6,191 $9,510 $17,301 115 $9,521 $18,315 $28,303 $44,126 $81,636

15 19 10% 26 10.00% 10% 5 18.70% 0.00% 26 116 $1,780 $3,425 $5,293 $8,252 $15,266 116 $8,024 $15,575 $24,232 $38,432 $70,411

20 24 10% 27 10.00% 10% 5 18.70% 0.00% 27 117 $1,500 $2,913 $4,531 $7,187 $13,167 117 $6,637 $13,191 $20,952 $33,195 $62,317

25 29 10% 28 10.00% 10% 5 18.70% 0.00% 28 118 $1,241 $2,467 $3,918 $6,207 $11,653 118 $5,644 $11,352 $18,004 $28,775 $54,782

30 34 10% 29 10.00% 10% 5 18.70% 0.00% 29 119 $1,055 $2,123 $3,367 $5,381 $10,244 119 $4,736 $9,611 $15,313 $24,783 $47,949

35 39 10% 30 10.00% 10% 5 18.70% 0.00% 30 120 $886 $1,797 $2,864 $4,634 $8,967 120 $4,041 $8,167 $13,251 $21,347 $42,520

40 44 10% 31 10.00% 10% 5 18.70% n/a 31 121 $756 $1,527 $2,478 $3,992 $7,951 121 $3,378 $6,988 $11,381 $18,622 $37,546

45 49 10% 32 10.00% 10% 5 18.70% n/a 32 122 $632 $1,307 $2,128 $3,482 $7,021 122 $2,856 $6,005 $9,795 $16,068 $32,399

50 100 10% 33 10.00% 10% 5 18.70% n/a 33 123 $534 $1,123 $1,832 $3,005 $6,059 123 $2,383 $5,095 $8,405 $13,842 $28,491

POF For Years Left



25

Appendix 10. Retiree Cash flows and Portfolio Values - Age 60; “Inheritance-oriented” Retiree Cash Flow Distribution Portfolio Value Distribution End of Year


Female Age 60 1 10.00% 10% 37 3.55% 100.00% 1 61 $35,500 $35,500 $35,500 $35,500 $35,500 61 $827,962 $941,475 $1,017,184 $1,094,169 $1,204,275

2 10.00% 10% 36 3.60% 99.99% 2 62 $29,807 $33,893 $36,619 $39,390 $43,354 62 $773,390 $918,419 $1,027,336 $1,144,131 $1,315,585

Equity% 60% 3 10.00% 10% 35 3.65% 99.96% 3 63 $28,229 $33,522 $37,498 $41,761 $48,019 63 $737,403 $904,212 $1,038,025 $1,182,938 $1,417,095

4 10.00% 10% 34 3.70% 99.91% 4 64 $27,284 $33,456 $38,407 $43,769 $52,433 64 $712,271 $894,107 $1,047,634 $1,217,482 $1,496,661

Start Value $1,000,000 5 10.00% 10% 33 3.80% 99.83% 5 65 $27,066 $33,976 $39,810 $46,264 $56,873 65 $685,857 $883,571 $1,052,789 $1,251,035 $1,576,209

6 10.00% 10% 32 3.85% 99.71% 6 66 $26,405 $34,017 $40,532 $48,165 $60,684 66 $661,370 $878,194 $1,058,217 $1,280,533 $1,660,283

7 10.00% 10% 31 3.90% 99.56% 7 67 $25,793 $34,250 $41,270 $49,941 $64,751 67 $641,336 $872,469 $1,071,699 $1,317,206 $1,725,895

Min Max Outlive% 8 10.00% 10% 30 4.00% 99.36% 8 68 $25,653 $34,899 $42,868 $52,688 $69,036 68 $624,755 $861,915 $1,076,492 $1,339,128 $1,812,871

0 4 10% 9 10.00% 10% 29 4.10% 99.09% 9 69 $25,615 $35,339 $44,136 $54,904 $74,328 69 $609,194 $856,336 $1,087,060 $1,370,548 $1,892,729

5 9 10% 10 10.00% 10% 29 4.10% 98.76% 10 70 $24,977 $35,110 $44,569 $56,192 $77,602 70 $591,832 $851,007 $1,089,761 $1,393,242 $1,953,192

10 14 10% 11 10.00% 10% 28 4.20% 98.35% 11 71 $24,857 $35,742 $45,770 $58,516 $82,034 71 $578,621 $849,731 $1,098,307 $1,425,848 $2,020,740

15 19 10% 12 10.00% 10% 27 4.30% 97.83% 12 72 $24,881 $36,538 $47,227 $61,311 $86,892 72 $569,372 $841,395 $1,107,257 $1,446,691 $2,099,324

20 24 10% 13 10.00% 10% 26 4.40% 97.20% 13 73 $25,052 $37,021 $48,719 $63,654 $92,370 73 $558,728 $831,433 $1,115,848 $1,468,831 $2,167,149

25 29 10% 14 10.00% 10% 25 4.50% 96.43% 14 74 $25,143 $37,414 $50,213 $66,097 $97,522 74 $552,290 $828,974 $1,112,196 $1,484,714 $2,225,160

30 34 10% 15 10.00% 10% 24 4.65% 95.50% 15 75 $25,681 $38,547 $51,717 $69,039 $103,470 75 $537,465 $816,676 $1,108,928 $1,501,977 $2,318,493

35 39 10% 16 10.00% 10% 23 4.75% 94.41% 16 76 $25,530 $38,792 $52,674 $71,344 $110,128 76 $520,320 $804,902 $1,111,750 $1,522,160 $2,357,157

40 44 10% 17 10.00% 10% 22 4.90% 93.12% 17 77 $25,496 $39,440 $54,476 $74,586 $115,501 77 $509,922 $791,595 $1,109,723 $1,538,685 $2,396,701

45 49 10% 18 10.00% 10% 21 5.10% 91.60% 18 78 $26,006 $40,371 $56,596 $78,473 $122,232 78 $495,342 $784,771 $1,105,131 $1,548,884 $2,464,012

50 100 10% 19 10.00% 10% 20 5.30% 89.82% 19 79 $26,253 $41,593 $58,572 $82,091 $130,593 79 $480,924 $774,093 $1,093,499 $1,552,275 $2,479,707

20 10.00% 10% 19 5.50% 87.76% 20 80 $26,451 $42,575 $60,142 $85,375 $136,384 80 $467,153 $761,487 $1,084,257 $1,560,941 $2,530,872

21 10.00% 10% 19 5.50% 85.39% 21 81 $25,693 $41,882 $59,634 $85,852 $139,198 81 $451,607 $756,539 $1,084,231 $1,556,603 $2,571,010

Min Max POF% 22 10.00% 10% 18 5.75% 82.68% 22 82 $25,967 $43,501 $62,343 $89,505 $147,833 82 $435,370 $743,846 $1,068,715 $1,554,661 $2,577,648

0 4 10% 23 10.00% 10% 17 6.00% 79.60% 23 83 $26,122 $44,631 $64,123 $93,280 $154,659 83 $420,244 $729,559 $1,059,305 $1,546,027 $2,588,478

5 9 10% 24 10.00% 10% 16 6.30% 76.13% 24 84 $26,475 $45,962 $66,736 $97,400 $163,074 84 $400,958 $709,103 $1,041,556 $1,528,917 $2,603,302

10 14 10% 25 10.00% 10% 15 6.65% 72.26% 25 85 $26,664 $47,155 $69,263 $101,673 $173,120 85 $387,481 $694,490 $1,017,935 $1,516,946 $2,613,030

15 19 10% 26 10.00% 10% 15 6.65% 67.99% 26 86 $25,767 $46,184 $67,693 $100,877 $173,766 86 $375,606 $674,715 $999,771 $1,500,440 $2,562,447

20 24 10% 27 10.00% 10% 14 7.05% 63.33% 27 87 $26,480 $47,567 $70,484 $105,781 $180,653 87 $352,296 $650,325 $978,190 $1,467,217 $2,579,708

25 29 10% 28 10.00% 10% 13 7.50% 58.31% 28 88 $26,422 $48,774 $73,364 $110,041 $193,478 88 $341,888 $632,328 $950,979 $1,437,492 $2,558,729

30 34 10% 29 10.00% 10% 12 8.10% 52.98% 29 89 $27,693 $51,219 $77,029 $116,437 $207,257 89 $323,188 $602,812 $913,621 $1,394,146 $2,508,248

35 39 10% 30 10.00% 10% 12 8.10% 47.43% 30 90 $26,178 $48,828 $74,003 $112,926 $203,168 90 $309,368 $578,162 $885,152 $1,354,144 $2,498,866

40 44 10% 31 10.00% 10% 11 8.75% 41.74% 31 91 $27,070 $50,589 $77,451 $118,488 $218,651 91 $290,811 $551,050 $851,389 $1,317,624 $2,448,328

45 49 10% 32 10.00% 10% 10 9.55% 36.04% 32 92 $27,772 $52,625 $81,308 $125,833 $233,815 92 $273,483 $525,644 $809,031 $1,251,097 $2,342,253

50 100 10% 33 10.00% 10% 10 9.55% 30.49% 33 93 $26,118 $50,199 $77,262 $119,480 $223,685 93 $251,668 $492,936 $769,993 $1,198,859 $2,288,753

34 10.00% 10% 9 10.55% 25.20% 34 94 $26,551 $52,005 $81,234 $126,480 $241,463 94 $231,790 $456,019 $720,536 $1,140,399 $2,177,114

35 10.00% 10% 9 10.55% 20.33% 35 95 $24,454 $48,110 $76,017 $120,312 $229,686 95 $214,598 $427,564 $682,377 $1,082,815 $2,087,845

36 10.00% 10% 8 11.75% 15.97% 36 96 $25,215 $50,239 $80,179 $127,231 $245,322 96 $197,818 $391,866 $636,085 $1,002,403 $1,968,340

37 10.00% 10% 8 11.75% 12.20% 37 97 $23,244 $46,044 $74,740 $117,782 $231,280 97 $181,577 $361,564 $591,993 $940,377 $1,856,167

38 10.00% 10% 8 11.75% 9.08% 38 98 $21,335 $42,484 $69,559 $110,494 $218,100 98 $164,481 $335,439 $546,604 $880,252 $1,749,718

39 10.00% 10% 7 13.40% 6.57% 39 99 $22,040 $44,949 $73,245 $117,954 $234,462 99 $148,080 $303,457 $499,647 $813,672 $1,629,331

40 10.00% 10% 7 13.40% 4.64% 40 100 $19,843 $40,663 $66,953 $109,032 $218,330 100 $133,875 $272,564 $455,557 $747,892 $1,515,450

41 10.00% 10% 6 15.60% 3.19% 41 101 $20,884 $42,520 $71,067 $116,671 $236,410 101 $115,977 $241,151 $404,150 $673,076 $1,383,139

42 10.00% 10% 6 15.60% 2.14% 42 102 $18,092 $37,620 $63,047 $105,000 $215,770 102 $101,055 $214,274 $360,569 $603,829 $1,234,127

43 10.00% 10% 6 15.60% 1.40% 43 103 $15,765 $33,427 $56,249 $94,197 $192,524 103 $88,402 $189,451 $321,692 $544,388 $1,127,946

44 10.00% 10% 5 18.70% 0.88% 44 104 $16,531 $35,427 $60,156 $101,801 $210,926 104 $74,975 $161,728 $274,814 $469,615 $988,066

45 10.00% 10% 5 18.70% 0.54% 45 105 $14,020 $30,243 $51,390 $87,818 $184,768 105 $63,680 $138,265 $234,915 $405,936 $867,541

46 10.00% 10% 5 18.70% 0.32% 46 106 $11,908 $25,856 $43,929 $75,910 $162,230 106 $53,592 $119,255 $202,304 $348,058 $748,886

47 10.00% 10% 5 18.70% 0.18% 47 107 $10,022 $22,301 $37,831 $65,087 $140,042 107 $44,582 $101,183 $173,962 $304,062 $656,999

48 10.00% 10% 5 18.70% 0.10% 48 108 $8,337 $18,921 $32,531 $56,860 $122,859 108 $38,073 $86,735 $150,087 $262,600 $576,007

49 10.00% 10% 5 18.70% 0.05% 49 109 $7,120 $16,219 $28,066 $49,106 $107,713 109 $32,030 $73,559 $129,247 $225,487 $505,397

50 10.00% 10% 5 18.70% 0.02% 50 110 $5,990 $13,755 $24,169 $42,166 $94,509 110 $27,331 $63,205 $110,461 $195,001 $447,781

POF For Years Left


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