Your mileage may vary

Manoj Athavalea*, Stephen Avilaa, Joseph Goebela

aDepartment of Finance and Insurance, Ball State University, 2000 West University Avenue, Muncie,

IN 47306, USA

Abstract

The traditional model of retirement planning centers around the accumulation of a portfolio dur-

ing the earning years followed by a drawdown from this portfolio after retirement. This drawdown is

intended to support a desired retirement lifestyle, and central to a successful retirement is the sustain-

ability of the retirement portfolio over the expected planning horizon. We define portfolio success to

mean the ability of the retirement portfolio to sustain a desired retirement lifestyle over the desired

planning horizon, and use simulations and logistic regressions to evaluate the impact of asset alloca-

tion, the profile of portfolio returns, the withdrawal rate, and the length of the planning horizon on

portfolio success. Our analysis shows that the likelihood of success is inversely related to withdrawal

rate, retirement horizon, and portfolio risk increase, and directly related to portfolio return, allocation

aggressiveness, and early experience. The analysis also indicates that portfolio success is highly sen-

sitive to withdrawal rates, with conservative allocations exhibiting greater variation in portfolio out-

comes and aggressive allocations providing more dependable portfolio outcomes for retirees who

desire higher withdrawal rates. © 2022 Academy of Financial Services. All rights reserved.

JEL classifications: G51; G53

Keywords: Retirement planning; Portfolio success; Retirement income; Withdrawal rate; Sequence risk

1. Introduction

In the process of building wealth and trying to ensure a financially secure retirement, indi-

viduals typically go through two distinct phases: an accumulation phase over the course of

their career, and a postretirement drawdown or withdrawal phase. These withdrawals from

*Corresponding author: Tel.: +1-765-285-5200; fax: +1-765-285-4314.

E-mail address: athavale@bsu.edu

1057-0810/22/$ – see front matter © 2022 Academy of Financial Services. All rights reserved.

Financial Services Review 30 (2022) 125–143



the accumulated retirement portfolio are intended to sustain the desired lifestyle over the

retired lifetime. Traditionally, retirees typically relied on Social Security, pension benefits,

and personal savings to sustain their retirement lifestyle. Social security benefits in the

United States are designed to only partially replace earnings that workers lose when they

retire, and average only about 40% of total retirement income (Biggs & Springstead, 2008).

Further, employer-sponsored defined-benefit pension plans have been declining over the

years, and are being replaced by defined-contribution pension plans. The prospective retiree

has to rely on social security retirement income and their retirement portfolio comprised of

the defined-contribution plan balance and personal savings.

The cash flow characteristics of each source of retirement income is different. Social se-

curity retirement income is similar to a defined-benefit plan with fixed inflation-indexed pay-

ments over the life of the retiree with some survivor benefits and no potential for a bequest.

The traditional defined-contribution plan requires the retiree to take minimum distributions

(RMD) that fluctuate every year based on the actual plan balance and the relevant life ex-

pectancy factor for that year. A retiree who lives longer than expected may face a substan-

tially depleted plan balance and reduced cash flow towards the later retirement years, while

a retiree who dies earlier than expected may leave a large bequest. Elective withdrawals can

be made from Roth defined-contribution plans and from personal savings, and any balance

remaining in either is available for a bequest. These elective withdrawals serve to supple-

ment retirement income available from other sources. An additional consideration affecting

retirement cash flows is the different tax implications of each of these sources.

An important financial issue that most prospective retirees contend with, and has been

extensively examined by financial planners and in the financial planning literature is: “How

much can I spend each year from the retirement portfolio without completely depleting the

retirement portfolio?” The most common response to this question is the “4% rule” which in

its most general form, suggests that a retiree with a diversified portfolio could make infla-

tion-adjusted annual withdrawals equal to 4% of the initial portfolio balance with a low

chance of depleting the retirement portfolio over a 30-year retirement horizon. While it is

popularly termed a rule, both financial planners and the academic literature understand that

it is a guideline, a starting point for discussion, and that the safe withdrawal rate (SWR)

should be modified based on individual circumstances.

This discussion suggests that the ability of the retirement portfolio to successfully sustain

the desired lifestyle would depend on various factors such as asset allocation, portfolio

return characteristics, the desired retirement horizon, and of course the desired withdrawal

rate. While the literature suggests that retirees remain flexible to individual circumstances,

there is very little guidance about the manner in which these factors impact portfolio suc-

cess. All retirees do not make the same retirement portfolio choices and consequently may

face very different retirement outcomes. We create plausible retirement scenarios and simu-

late variations in these factors to determine portfolio success or failure. We then use logistic

regression to measure the impact that these factors have had in determining portfolio

success.

Unlike previous studies, we define portfolio outcome as a binary variable and use logistic

analysis to highlight the likelihood of portfolio success as a function of five retirement plan-

ning horizons, three asset allocation strategies, and five fixed real withdrawal rates to arrive

126 M. Athavale et al. / Financial Services Review 30 (2022) 125–143



at 75 plausible unique retirement scenarios. For each scenario, we use four distinct monthly

return generating distributions and run 100 simulations to arrive at 30,000 portfolio outcomes

and use these in a logistic regression to examine the determinants of portfolio success or fail-

ure. We show that the probability of portfolio success is inversely related to withdrawal rate,

retirement horizon, and portfolio risk, and directly related to portfolio return, allocation

aggressiveness, and the returns experience in the five years immediately after retirement.

This paper is important because it applies an interesting methodology to a large number of

retirement scenarios and portfolio outcomes to enable a retiree better understand how their

unique set of circumstances and choices impact retirement success. The rest of this article is

organized as follows: We begin by reviewing some of the relevant literature to provide the

necessary context for the current research. We then present the empirical design of our

research, data definitions, sample statistics, and the results of our regression analysis. Finally,

we present our conclusions, practical implications, and suggestions for future research.

2. Background and literature review

The traditional view of retirement is that in the early years people earn, save and invest (the

“accumulation” stage) to subsequently retire and withdraw from their retirement portfolio to

finance consumption over their retirement horizon (the “decumulation” or “asset distribution”

stage). In the decumulation stage, individuals balance the competing goals of maintaining con-

sumption in retirement without prematurely depleting their retirement portfolio.

One of the early solutions to the problem of creating retirement cash inflows was the state

retirement pension program created in 1889 by Chancellor Bismark of Germany that pro-

vided a pension starting at age 70 when life expectancy was merely an additional two years.

However, with improved working conditions and increased life expectancy, the amount of

time spent in retirement today is now both longer and also a larger proportion of total life ex-

pectancy. Retirement income is now needed for a few decades rather than a few years.

The reduction in the number of defined-benefit plans and an increase in defined-contribu-

tion plans, transfers risk from the employer to the retirement saver. Employees are now re-

sponsible for the saving decision, the asset allocation decision, and the asset withdrawal

decision, while simultaneously accepting the real danger of premature retirement portfolio

depletion (“portfolio failure”).

The determination of a sustainable withdrawal rate that would reduce the probability of

portfolio failure has been addressed in a number of prior studies generally using the overlap-

ping periods methodology or simulation methodology. A historical analysis of the overlap-

ping retirement experiences of individuals retiring between 1926 and 1980 led to the early

consensus that a retiree with a diversified portfolio could make inflation-adjusted annual

withdrawals equal to 4% of the initial portfolio balance with a low chance of depleting the

retirement portfolio over a 30-year retirement horizon. This 4% rule refers to the popular

withdrawal rate that originated from studies like Bierwirth (1994), Bengen (1994), and

Cooley, Hubbard, and Walz (1998) that were meant to dispel the notion that higher

M. Athavale et al. / Financial Services Review 30 (2022) 125–143 127



withdrawal rates that matched the historic average real returns on a diversified portfolio

(between 5% to 6%) were sustainable over the retirement horizon.

Saving for retirement is challenging, and most employees have little training upon which

to draw in making the relevant decisions (Benartzi & Thaler, 2007, p.102). Similarly, most

retirees lack the skills required to manage their retirement portfolio successfully, highlight-

ing the need for practical and easily understood solutions to generating sustainable retire-

ment income (or, alternately, the need for an experienced and reputable financial advisor).

Merton (2014, p.1408) states that requiring people to save for retirement is reasonable, but

expecting them to acquire the expertise necessary to make investment and withdrawal deci-

sions is not reasonable. Further, cognitive functions may decline in retirement (Bonsang,

Adam, & Perelman, 2012) and while the portfolio decisions of older investors may reflect

greater knowledge about investing, their investment skill does deteriorate with age due to

the adverse effects of cognitive aging (Korniotis & Kumar, 2011).

This is where retirees may find the 4% rule to be useful, and it is certainly a reasonable

and intuitive starting point in the retirement planning process. Indeed, Cooley, Hubbard, and

Walz (1998, p.16) argue that individual experiences may vary due to personal behavioral

traits, circumstances, and goals, and that no single rate appears appropriate for every inves-

tor. Moreover, the finding of a 4% SWR itself has been subject to various challenges. Pfau

(2010) contends that the early consensus may be an artifact of the data used in the analysis

for a couple of reasons. First, the use of rolling 30-year periods emphasizes data from the

middle of the period and hence introduces temporal bias in these analyses. Second, from an

international perspective, a 4% real withdrawal rate would have been “safe” in only four of

17 developed countries. These results are consistent with Dimson, Marsh and Staunton

(2004) who explained that the United States has had higher real returns and lower market

volatility during the 1900 to 2002 period when compared with many other countries. These

results are also consistent with Estrada (2018, p. 62) who examined the retirement experi-

ence across 21 countries and 115 years using 11 asset allocations. Using equally weighted

returns to a balanced portfolio across all countries in the sample, they find that a retiree with

a 30-year retirement horizon would face a 50% probability of failure with a 4.8% withdrawal

rate and could only withdraw 2.6% if a 5% probability of failure was desired. Further, the

maximum withdrawal rate varied substantially, leading them to conclude that individuals

who retired in some countries or at certain points in time had vastly different standards of

living than those who retired in other countries or at other points in time.

The success of any retirement portfolio certainly depends on the expected return assump-

tions used in the analysis. Pye (2000) showed that 4% withdrawals from an equity portfolio

with 8% real return and 18% standard deviation could be sustained for 35 years with an 81%

chance of success, but a higher 4.5% withdrawal rate could be achieved by allocating 60%

of the portfolio to Treasury Inflation Protected Securities (TIPS) assuming a certain 3.7%

real return. Finke, Pfau, and Blanchett (2013) used simulations to review the safe withdrawal

rate in the current low-yield environment to conclude that a 30-year retirement portfolio

would have a failure rate of 18% if yields revert to their historic mean in 5 years. Similarly,

Blanchett, Finke, and Pfau (2014) test the sustainable withdrawal rate in a low bond-yield

environment and use a drift model of bond yields to show that a 4% initial withdrawal rate

has just a 50% probability of success over a 30-year retirement horizon.

128 M. Athavale et al. / Financial Services Review 30 (2022) 125–143



Thus, there is some evidence that the demonstrated success of the 4% rule is partly an

anomaly of historic U.S. market returns and assumptions of expected returns. The implica-

tion from these studies is that the historical asset returns used in the overlapping periods

model are not suitable for forward-looking forecasts on which retirement withdrawal strat-

egies should be based. Further, asset returns experienced in the last decade appear to have

disrupted the conventional thinking about the safe withdrawal rate, and Athavale and

Goebel (2011) reinforced the notion that the 4% rule constitutes a probabilistic model and

past success does not guarantee future success.

In addition to returns, there is some evidence that the standard deviation of returns and

the sequence of returns may impact the success of a retirement portfolio. Blanchett and

Blanchett (2008) investigate the relative importance of portfolio return and standard devia-

tion on portfolio success using the standard 4% withdrawal rate over a 30-year period. They

find that a 1% reduction in returns is likely to result in an increase in the probability of fail-

ure that is approximately four times greater than a 1% increase in portfolio standard devia-

tion, leading them to conclude that portfolio returns have greater impact on the probability

of portfolio success compared with standard deviation. Clare, Seaton, Smith, and Thomas

(2017, 2021) suggest that the sequence of returns matters in both the accumulation and decu-

mulation stages, and show that a portfolio-timing strategy using the cyclically adjusted

price-to earnings (CAPE) ratio can help investors mitigate sequence risk and achieve higher

withdrawal rates.

In addition to the overlapping periods model and the simulations model, researchers have

explored the use of other sophisticated models to design withdrawal strategies. For example,

Milevsky and Robinson (2005) use investment risk and return, mortality estimates, and

spending rates in a stochastic present value framework to investigate the relationship

between withdrawal rates and the probability of portfolio failure. They find that 4% with-

drawals by a 65-year old retiree invested in a balanced portfolio has a 9% chance of portfolio

failure, and a 3.24% withdrawal rate has a 5% chance of portfolio failure, leading them to

conclude that payout ratios should be lower than generally recommended. Scott, Sharpe, and

Watson (2009) suggest a strategy that includes buying and selling 30-year European call

options on the market portfolio over the planning horizon to replicate the traditional 4%

withdrawals, but acknowledge that many practical issues remain to be addressed before this

utility maximizing methodology can be incorporated in retirement planning.

Recent studies have focused on dynamic rule-based multi-asset allocation and liquidation

strategies, and switching from fixed withdrawals to variable withdrawals to improve the

probability of portfolio success. A case study of the retirement experience of a 1973 retiree

invested in a balanced multi-asset portfolio led Guyton (2004) to conclude that systematic

decision rules and some restriction on subsequent inflation adjustments could allow for a

5.8% initial withdrawal rate.

Other examples of dynamic withdrawal strategies include adjusting the withdrawal rate

based on portfolio performance and remaining life expectancy to improve retirement portfo-

lio success and average lifetime withdrawal rates (Stout & Mitchell, 2006); using a multi-

asset portfolio with periodic adjustments to the asset mix and a “bonds first” withdrawal

strategy that mitigates the higher volatility in equity returns (Liu, Chang, De Jong, &

M. Athavale et al. / Financial Services Review 30 (2022) 125–143 129



Robinson, 2009); and calculating the probability of portfolio failure each year and changing

the withdrawal rate based on decision rules (Blanchett & Frank, 2009).

The importance of analyzing portfolio success rates in determining withdrawal rates has

previously been emphasized by Cooley, Hubbard, and Walz (2011). They assert that changes

should be made to withdrawal rates in response to unexpected changes in financial market

conditions, and use the overlapping periods methodology to present portfolio success rate

tables for various combinations of withdrawal rates, portfolio compositions, and payout

periods.

Dynamic adjustment strategies have been shown to be relevant in both the accumulation

stage (Estrada, 2019) and in the drawdown stage (Estrada, 2020) of the retirement portfolio.

Specifically, Estrada (2020) shows that dynamic strategies outperform a static strategy of

sticking to the plan, and periodic adjustments to the withdrawal rate is superior to adjusting

portfolio asset allocations. Similarly, Robinson and Tahani (2010) treat portfolio return, lon-

gevity, and consumption as stochastic variables and use an analytical model to conclude that

changing consumption to match changes in wealth could reduce the risk of portfolio failure.

These dynamic withdrawal strategies do have intuitive appeal. It is logical to calibrate

asset allocations and withdrawals to changing circumstances and economic realities. An

unresolved question is whether retirees would have the discipline to follow decision rules

and would have the flexibility to reduce consumption. These strategies are still in the early

stages of their development and we need a better understanding of the manner in which rele-

vant variables impact portfolio success (DeJong & Robinson, 2017). Retirees may become

better equipped to make these changes if they understand the implications of economic cir-

cumstances and their actions on the probability of portfolio success. Our current research,

therefore, is an effort to better understand the determinants of retirement portfolio success.

3. Hypothesis development and empirical design

Each individual entering retirement has to decide about the asset allocation for their

retirement portfolio, the expected retirement horizon, and the desired withdrawal rate from

their retirement portfolio. In making these decisions, the retiree faces the tradeoff between

maximizing consumption during retirement while minimizing the probability of prematurely

exhausting the retirement portfolio.

In this context it is important to understand the composition of the retirement portfolio. As

previously described, the retirement portfolio may comprise some proportion of the traditional

defined-contribution plan balance, the Roth defined-contribution plan balance, and personal

savings. Each of these is taxed differently; consequently, a million dollars in a traditional

retirement account is not equivalent to a million dollars in personal savings which, in turn, is

not equivalent to a million dollars in a Roth retirement account. Generally, withdrawals from

the traditional plan balance are taxable as ordinary income; the capital gains arising from

assets liquidated from personal savings prior to withdrawal are taxable at a reduced capital-

gains rate; and withdrawals from Roth plan balances are not taxable. Therefore, all references

to a retirement portfolio should be on a tax-equivalent basis, and for the purpose of this

130 M. Athavale et al. / Financial Services Review 30 (2022) 125–143



research, to avoid the differential effect of taxes on retirement withdrawals, we implicitly

assume that the retirement portfolio referenced here has been aggregated on an after-tax basis.

It is also necessary to differentiate between the terms withdraw and consume. While the

purpose of withdrawals is to finance a desired level of consumption, RMD rules may result

in a withdrawal different from that necessary to finance that level of consumption. In the

event RMD rules require a withdrawal greater than that needed for a desired lifestyle, we im-

plicitly assume that the prudent retiree would reinvest the excess so as to reduce the risk of

premature portfolio depletion.

Prior research has documented that the probability of portfolio success is impacted by

withdrawal rates, asset allocation, retirement horizon, and measures of actual portfolio per-

formance, including return, standard deviation of returns, and the sequence of returns. The

retiree makes decisions about the withdrawal rate, the planning horizon, and the asset alloca-

tion for the retirement portfolio. However, the retirement portfolio will be affected by eco-

nomic circumstances and chance, factors which are outside the retiree’s control, but which

will nevertheless affect the actual return, standard deviation, and sequence of returns that the

retirement portfolio may experience.

We define a retirement portfolio to be a success if the portfolio can sustain a specified

level of withdrawal over the entire retirement horizon. Conversely, a portfolio that is fully

consumed within the retirement horizon is a “failure.” Retirees need to be cognizant of the

factors that can lead to portfolio failure, and while some of these factors cannot be con-

trolled, other factors (most commonly, the withdrawal rate) can be managed to mitigate the

risk of portfolio failure.

While financial planners and prior academic research encourage retirees to remain flexi-

ble with their retirement expenditures, retirees may not be aware of the impact that these

variables may have on the probability of a successful retirement and may therefore be ill-

equipped to make these decisions or respond to circumstances. We seek to identify those

factors that contribute to portfolio success, and measure the impact that each of these factors

will have on the probability of portfolio success.

Portfolio success lies at the intersection of the planning horizon, asset allocation, and

withdrawal strategy (Collins, Lam, & Stampfli, 2015, p.194), and the probability of portfolio

failure (also called “ruin”) is a useful risk metric that can help retirees understand the link

between their withdrawal strategy, planning horizon, and the asset allocation of their retire-

ment portfolios (Milevsky & Robinson, 2005, p. 99). We use portfolio success as the de-

pendent variable in our analysis.

We model the retirement experience as a sequence of annual adjustments, with the initial

retirement portfolio growing or shrinking according to the portfolio returns in the first year

followed by a withdrawal at the end of the year to finance retirement expenditures. The

remaining portfolio balance then grows or shrinks according to the portfolio returns in the

second year followed by an inflation-indexed withdrawal, and this progression continues

over the duration of the retirement.

The decisions that the retiree makes about asset allocation, the retirement horizon, and

the desired withdrawal rate are used as inputs in our analysis. We assume that the retiree pre-

fers fixed real withdrawal rates as they are easy to understand and provide the retiree with

constant purchasing power. Annual portfolio returns and standard deviation are a function of

M. Athavale et al. / Financial Services Review 30 (2022) 125–143 131



the selected asset allocation but reflect the uncertain external environment, and are deter-

mined by simulation. The simulated annual portfolio returns also determine if the retirement

portfolio encounters an unfortunate sequence of negative returns during the early retirement

years. The early sequence of negative returns may decimate the portfolio and significantly

impair the portfolio’s ability to grow and generate income, decreasing the probability of a

successful retirement (Blanchett et al., 2014, p. 55).

Evaluation of retirement strategies involves the consideration of a large number of simu-

lated or historical retirement periods and the subsequent estimation of their failure rate. The

use of simulations in retirement planning has both proponents and opponents, and Sandidge

(2020) explains that that simulations are ineffective because most people lack the numeric

skills needed to assess probability. Collins, Lam, and Stampfli (2015) reviewed retirement

income modeling strategies and state that the simulation methodology overcomes the limita-

tion of relying on past returns as the basis of potential outcomes, thus allowing for a much

greater range of potential outcomes. However, the inputs that drive these models need to be

realistic. Cooley, Hubbard, and Walz (2003, p. 128) find that success rates differ when using

Monte Carlo simulation methodology compared with the overlapping periods methodology,

and recommend the use of simulation methodology for the longer payout periods which are

important in retirement planning. We intend to simulate a large number of scenarios repre-

senting the wide spectrum of possible retirement experiences. We then follow the previously

described sequence of annual adjustments over the retirement horizon to determine the out-

come of each scenario, that is, whether each of the scenarios ends in portfolio success or

portfolio failure. And finally, we will model the portfolio outcome (success or failure) using

a logistic regression that generally takes the form:

Ln
p

1� p

� �
¼ a þob iXi þ «

where p is the probability of portfolio success, and the left-hand term is the log-odds. The

explanatory variables include the retiree choice variables (withdrawal rate, asset allocation,

and retirement horizon) and the chance variables (return, risk, and the early returns experi-

ence). These variables are defined in Table 1.

The binary logistic regression is typically preferred when modeling a dichotomous out-

come variable. We intend to use a logit model because the dependent variable is a binary

categorical variable, equaling one when the portfolio successfully sustains the desired with-

drawal rate over the entire retirement horizon, and zero when the outcome is portfolio fail-

ure. The logistic regression allows us to identify and analyze the impact of factors that

influence portfolio success in a multivariate setting.

4. Data and method

At the start of the retirement period, individuals can make choices about the retirement

planning horizon, asset allocation, and the withdrawal rate. Individuals retiring today are liv-

ing longer than prior generations and spending longer periods of time in retirement. For the

132 M. Athavale et al. / Financial Services Review 30 (2022) 125–143



T
ab
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1
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).

M. Athavale et al. / Financial Services Review 30 (2022) 125–143 133



average American, life expectancy for males, females, and married couples is 82, 85, and

89, respectively, and the probability that one member of a married couple will live to age 95

is 18% (Browning, 2016, p.51). The problem with determining the correct retirement hori-

zon is that retirees do not know precisely when they will die. Further, while in theory a

retirement portfolio is meant for consumption, in practice most retirees will feel comfortable

under-consuming the retirement portfolio and planning for a long retirement rather than risk-

ing portfolio failure (longevity risk). Our analysis assumes that retirees will select one of

five retirement planning horizons (23, 26, 29, 32, or 35 years) based on their health and life-

style. Our analysis recognizes that each retirement situation is different and this uniqueness

is captured through the intentional use of a wide range of values for the independent varia-

bles, allowing the analysis to apply to many retirement scenarios. For example, assuming

life expectancy of 90 years, our choice of planning horizon is wide enough to cover both the

traditional age 67 retiree and with a 23-year retirement horizon and the age 55 early retiree

with a 35-year retirement horizon.

Our analysis also assumes that a retiree will select one of three asset allocation strategies

(a conservative strategy with an emphasis on fixed-income investments, with expected real

return of approximately 3.1% and standard deviation of 8%, a balanced strategy with

expected real return of 5.1% and standard deviation of 12%, and an aggressive strategy with

an emphasis on equity investments, with expected real return of 7.1% and standard deviation

of 16%) based on their personal risk tolerance. These numbers reflect the approximate aver-

ages of the mean real return and standard deviation reported in prior research referenced in

this paper. Finally, our analysis also assumes that a retiree will select one of five fixed real

withdrawal rates (2.5%, 3.25%, 4%, 4.75%, and 5.5%) based on their consumption needs.

The use of a range of annual withdrawal rates, retirement planning horizons, and stock allo-

cations, is consistent with Cooley et al. (1998). These three decisions about Retirement

Horizon, Asset Allocation, and Withdrawal Rate result in 5 � 3 � 5 = 75 unique retirement

scenarios.

The next step in the analysis is to consider likely outcomes for each of these scenarios.

For example, does a 2.5% withdrawal rate from a conservative portfolio sustain the retire-

ment portfolio over a 23-year retirement horizon? While we know that our conservative

portfolio will average annual returns of approximately 3.1% and have a standard deviation

of 8% over long periods of time, returns in any particular year can fluctuate away from the

average with a wide range of uncertain values. The standard methodology in such cases

draws random returns for each year of the retirement horizon from a theoretical distribution.

We should test our hypothesis by drawing random annual returns for the first year, making

2.5% withdrawals, noting the portfolio balance at the end of the year, and if the portfolio has

not been depleted, continuing this exercise for a total of 23 years.

Drawing random annual returns to the retirement portfolio requires us to impose a priori

assumptions about the functional form of the distribution of expected returns, and a standard

assumption is that returns are characterized by the normal distribution. This assumption,

though convenient, was empirically challenged by Fama (1965) who found that the distribu-

tion of monthly stock returns belonged to a non-normal member of the stable class of distri-

butions. Subsequently, Officer (1972) confirmed that the distribution of stock returns has fat-

tails, and Gray and French (1990) confirmed that the distribution of stock index returns also

134 M. Athavale et al. / Financial Services Review 30 (2022) 125–143



deviates from the normal distribution. The preponderance of empirical evidence finds that

return distributions are not normally distributed (Kring, Rachev, Höchstötter, Fabozzi, &

Bianchi, 2009, p. 272), and have rejected the normal distribution in favor of either a skewed

distribution or a fat-tailed distribution (Levy & Duchin, 2004 p. 48). We relax the assump-

tion that returns follow any single distribution and use four different continuous probability

distributions (Beta, Kumaraswamy, Pert, and Triangular) from which to draw random annual

returns. In the absence of theoretical arguments or empirical evidence to guide our selection

of the appropriate distribution, we selected four continuous distributions which allowed neg-

ative returns, allowed us to specify bounds, and displayed skewness and fat tails. The param-

eters of the distributions were set to ensure consistency with the desired mean and standard

deviation, and reasonable boundaries were established. Thus, each of the 75 previously men-

tioned scenarios were tested using four different returns distributions.

Continuing our prior example, we define a retirement portfolio to be a success if 2.5%

withdrawals from a conservative portfolio could be sustained over a 23-year retirement hori-

zon, when realized returns followed the Beta distribution. In such cases we assign

Outcome = 1, and in cases where the retirement portfolio is prematurely depleted before the

end of the retirement horizon, we assign Outcome= 0. This gives us a total of 75 � 4 = 300

retirement experiences, reflecting both the choices the retiree has made and the returns

uncertainty that impacts portfolio outcomes.

Another returns uncertainty that we considered in the analysis is that portfolio outcomes

may also be impacted by the sequence of returns obtained. A sequence of large negative

returns early in the retirement period may hasten portfolio depletion. Sequence risk (or serial

returns risk) refers to the risk of premature portfolio depletion caused by a combination of

withdrawals and significant negative returns early in retirement. We proxy for sequence risk

by constructing an Early Experience variable, defined as:

Early Experience ¼ Observed Balance 5, 2:5%, 3:1%, 12%ð Þ
Expected Balance 5, 2:5%, 3:1%, 0%ð Þ

where, the numerator is the observed portfolio balance at the end of the fifth year after 2.5%

withdrawals each year from a conservative portfolio earning 3.1% average real returns that

follow the Beta distribution with a standard deviation of 12%, while the denominator is what

the balance would be assuming certainty in portfolio returns. A better Early Experience

implies a greater probability of portfolio success, and we would expect a positive relation

between the Early Experience variable and the Outcome variable. The observed portfolio

balance at the end of the fifth year and the value of the Early Experience variable at the end

of the fifth year are presented in Table 2.

The process described above was repeated 100 times. Thus, the 300 retirement experien-

ces simulated 100 times each gives us 300 � 100 = 30,000 portfolio outcomes. Another way

of thinking about this is that the simulations are a way of testing the retirement scenarios to

see the potential outcome of many possible trajectories and to gauge how vulnerable the sce-

narios are to portfolio failure. Our model is consistent with Pfau (2012) in that portfolio suc-

cess is dependent on the interaction of withdrawal rates, capital market conditions,

retirement durations, and asset allocation, and the Spitzer, Strieter, and Singh (2007)

M. Athavale et al. / Financial Services Review 30 (2022) 125–143 135



assertion that a blanket four percentage withdrawal rule may be an oversimplification of a

complex set of circumstances.

5. Descriptive statistics and empirical results

The frequency of success (Outcome= 1) or failure (Outcome= 0) among the 30,000 port-

folio outcomes described in the previous section is presented in Table 3.

Portfolio success occurred 83.3% (24,989 of 30,000) of the time among the observed

portfolio outcomes. The aggressive portfolio had an average success rate of 87.83% (8,783

of 10,000) while the conservative portfolio has a success rate of 76.34%. As expected, the

portfolio with a 2.50% withdrawal rate had an average success rate of 99.13% (5,948 of

6,000) while the portfolio with a 5.50% withdrawal rate had a success rate of 59.08%. And

finally, as expected, the portfolio with a 23-year planning horizon had an average success

rate of 91.3% (5,478 of 6,000) while the portfolio with a 35-year horizon had a success rate

of 75.73%.

We had previously indicated that the retiree decides about portfolio allocation (based on

risk tolerance), withdrawal rate (based on consumption needs), and retirement horizon

(based on expected life expectancy and lifestyle choice), and we can disaggregate the

observed portfolio success rates using these variables. These disaggregated observed portfo-

lio success rates are presented in Table 4.

Table 2 The early (returns) experience

Portfolio
allocation

Withdrawal
rate

Average portfolio
balance

Early experience

Mean Minimum Maximum

Conservative 2.50% 1,033,998 100.20 47.78 170.27
3.25% 994,054 100.20 46.39 172.39
4.00% 954,110 100.21 44.89 174.71
4.75% 914,166 100.21 43.26 177.23
5.50% 874,222 100.22 41.47 179.97

Balanced 2.50% 1,145,076 100.10 38.63 206.12
3.25% 1,103,597 100.10 37.27 208.77
4.00% 1,062,118 100.11 35.80 211.64
4.75% 1,020,638 100.12 34.21 214.73
5.50% 979,159 100.13 32.48 218.10

Aggressive 2.50% 1,284,861 101.56 22.52 274.61
3.25% 1,241,476 101.61 21.20 278.86
4.00% 1,198,091 101.65 19.77 283.43
4.75% 1,154,706 101.70 18.25 288.35
5.50% 1,111,322 101.75 16.59 293.65

Note. This table presents information about the observed portfolio balance at the end of the fifth year and the

value of the early experience variable. The early experience variable is a proxy for sequence risk which refers to

the risk of premature portfolio depletion caused by a combination of fixed withdrawals and significant negative

returns in the early years of retirement. There are 2,000 observations in each of the 15 combinations of portfolio

allocation and withdrawal rate for a total of 30,000 observations.

136 M. Athavale et al. / Financial Services Review 30 (2022) 125–143



A few observations are notable. A withdrawal rate of 2.5% can largely be sustained irre-

spective of portfolio allocation and retirement horizon. However, higher withdrawal rates

(5.5%) over longer retirement horizons (35 years) have a success rate of 65.5% with an

Table 3 Frequency table of observed portfolio outcomes

Failure Success

By portfolio allocation Conservative 2,366 7,634
Balanced 1,428 8,572
Aggressive 1,217 8,783

5,011 24,989
By withdrawal rate 2.50% 52 5,948

3.25% 253 5,747
4.00% 731 5,269
4.75% 1,520 4,480
5.50% 2,455 3,545

5,011 24,989
By retirement horizon 23 Years 522 5,478

26 Years 750 5,250
29 Years 1,004 4,996
32 Years 1,279 4,721
35 Years 1,456 4,544

5,011 24,989

Note. N= 30,000 portfolio outcomes. This table presents the number of successes (or failures) among the

30,000 portfolio outcomes in our sample, aggregated by portfolio allocation, or withdrawal rate, or retirement

horizon. These numbers suggest that conservative portfolios, higher withdrawal rates, and longer retirement

planning horizons increase the chance of portfolio failure.

Table 4 Observed portfolio success rates

Portfolio allocation Withdrawal rate Retirement horizon

23 Years 26 Years 29 Years 32 Years 35 Years

Conservative 2.50% 100.00% 100.00% 99.50% 99.75% 99.00%
3.25% 99.75% 98.75% 96.00% 95.75% 91.25%
4.00% 96.00% 93.00% 83.25% 79.50% 71.00%
4.75% 88.25% 76.75% 59.75% 50.25% 37.25%
5.50% 66.50% 47.75% 38.75% 23.50% 17.25%

Balanced 2.50% 99.75% 99.50% 99.75% 98.50% 99.00%
3.25% 99.25% 97.50% 96.00% 94.50% 93.25%
4.00% 95.50% 92.75% 90.50% 84.50% 84.00%
4.75% 86.50% 83.50% 83.00% 73.50% 68.25%
5.50% 77.25% 70.75% 65.50% 56.75% 53.75%

Aggressive 2.50% 98.75% 99.00% 98.00% 98.50% 98.00%
3.25% 96.50% 96.00% 94.75% 94.00% 93.50%
4.00% 94.50% 92.50% 88.50% 84.50% 87.25%
4.75% 89.25% 86.00% 82.25% 77.75% 77.75%
5.50% 81.75% 78.75% 73.50% 69.00% 65.50%

Note. This table allows us to evaluate the simultaneous impact of portfolio allocation, withdrawal rate, and

retirement horizon on portfolio success rates. Portfolio success occurs in 24,989 of the 30,000 portfolio

outcomes.

M. Athavale et al. / Financial Services Review 30 (2022) 125–143 137



aggressive portfolio allocation, but only 53.75% with a balanced portfolio allocation and

17.25% with a conservative portfolio allocation. A withdrawal rate of 4% over a 29-year ho-

rizon has a success rate of 90.50% with a balanced portfolio allocation, 88.50% with an

aggressive portfolio allocation and 83.25% with a conservative portfolio allocation. And

finally, a conservative portfolio exhibits wide variations in outcomes ranging from 100% to

17.25%, while an aggressive portfolio allocation exhibits variations ranging from 99.00% to

65.50%. These results confirm that aggressive portfolios improve the probability of portfolio

success for higher withdrawal rates.

We next use regression analysis to analyze the impact of factors which influence portfolio

success in a multivariate setting. Our variable of interest is portfolio success that is a binary

dependent variable. In such cases, the ordinary least squares technique can be nonconform-

ing and the estimates of the dependent variable can go out of bounds (0, 1). The logistic

regression technique is well suited to examining the relation between portfolio success and

the predictor variables as it keeps the predicted values of the dependent variable within

expected bounds.

At the start of the retirement period, the retiree makes decisions about the withdrawal

rate, the planning horizon, and the asset allocation for the retirement portfolio. The retire-

ment portfolio will also be affected by actual returns, standard deviation, and sequence of

returns that the retirement portfolio may experience. While these factors are outside the retir-

ee’s control and will nevertheless impact portfolio outcome, the retiree may be able to

observe and act on any early unfavorable sequence of returns that the portfolio may experi-

ence. These then, are the explanatory variables used in the analysis.

The logistic function is used to estimate, as a function of unit changes in the independent

variables, the probability that the event of interest will occur. Our logistic model provides a

good fit for the data if we can demonstrate an improvement over the intercept-only model,

and we check this using the Akaike Information Criterion and the Schwarz Criterion. We

also note that the Cox and Snell R2 is 46%, Nagelkerke’s rescaled R2 is 78%, and

McFadden’s pseudo R2 is 69%. In addition, the maximum likelihood coefficient estimates

are all individually significant at 1% using the Wald x2 test.

Direct interpretation of the logistic regression coefficients is difficult since coefficient

estimates are in terms of log-odds. The estimated coefficients do not represent the marginal

effects of the independent variables on the probability of portfolio success. Instead of the

coefficients being the rate of change in the dependent variable as the independent variable

changes, a coefficient derived from a logistic regression is interpreted as the rate of change

in the log-odds as the independent variable changes. Exponentiating the coefficient gives us

the odds ratio, which can range from 0 to infinity, and which allows for somewhat easier

interpretation. The model coefficients and the odds ratio are presented in Table 5.

While the odds ratio is somewhat easier to interpret than the coefficients of the logistic

regression, neither is as useful as the traditional marginal effect. Unlike a linear regression,

the marginal effect is not constant across the entire range of values of the explanatory vari-

able, and hence the marginal effect is calculated at each observation in the dataset, and then

averaged. This average marginal effect indicates expected changes in the predicted probabil-

ity of portfolio success as a function of a change in an explanatory variable while keeping

138 M. Athavale et al. / Financial Services Review 30 (2022) 125–143



other covariates constant. The average marginal effect for each explanatory variable is also

presented in Table 5.

The marginal effect of the Withdrawal Rate variable indicates that the probability of port-

folio success changes by �0.1311 for a 1-level change in the Withdrawal Rate. Similarly,

the marginal effect of the Retirement Horizon variable indicates that the probability of port-

folio success changes by �0.0154 for a 1-level change in the Retirement Horizon. Early

Experience is a continuous variable and hence the marginal effect is defined as the partial

derivative of the probability of portfolio success with respect to Early Experience. Similarly,

higher levels of Return increase the probability of portfolio success while higher levels of

Risk decrease the probability of portfolio success, and this is consistent across all alloca-

tions. Finally, an Aggressive Allocation changes the probability of portfolio success by

0.1142 compared with a Balanced Allocation, and a Conservative Allocation changes the

probability of portfolio success by �0.0993 compared with a Balanced Allocation.

Table 5 Determinants of portfolio success

Coefficient Wald
v2

Odds ratio Marginal effect

Intercept 18.4342
(0.6080)

919.2899

Withdrawal rate �3.1056
(0.0552)

3161.9001 0.045 �0.1311

Allocation aggressive 2.7052
(0.7069)

14.6443 14.957 0.1142

Allocation conservative �2.3530
(0.5821)

16.3402 0.095 �0.0993

Horizon �0.3638
(0.00870)

1746.6138 0.695 �0.0154

Return � Allocation Conservative 1.5348
(0.0412)

1384.7595 4.641 0.0648

Return � Allocation Balanced 1.3722
(0.0358)

1466.0887 3.944 0.0579

Return � Allocation Aggressive 1.2288
(0.0320)

1477.4365 3.417 0.0519

Risk � Allocation Conservative �2.648
(0.0424)

38.9240 0.767 �0.0112

Risk � Allocation Balanced �0.3202
(0.0377)

72.1836 0.726 �0.0135

Risk � Allocation Aggressive �0.4087
(0.0317)

166.5041 0.664 �0.0173

Early experience 0.0781
(0.00178)

1916.2730 1.081 0.0033

R2 69%

Note. N= 30,000. Standard errors are placed below the coefficient. All coefficients are significant at the 1%

level. This table presents the results of the logistic regression analysis used to model the probability of portfolio

success, where portfolio success is defined as the ability of a retirement portfolio to sustain a desired lifestyle

over a desired retirement horizon.

M. Athavale et al. / Financial Services Review 30 (2022) 125–143 139



We also analyzed the determinants of portfolio success by partitioning the data based on

Allocation. This facilitates validation of the full-sample results and also allows for easier

interpretation of the results. The results of this analysis are presented in Table 6.

As before, retiree-determined variables (Withdrawal Rate and Retirement Horizon) are

significant across all three values of Allocation, as are the chance variables (Early

Experience, Return, and Risk). The negative sign on withdrawal rate indicates a lower prob-

ability of portfolio success at higher withdrawal rates. This effect is most pronounced for the

conservative portfolio allocation—the probability of portfolio success changes by �0.1962

for a 1-level change in Withdrawal Rate. Retirees who select a conservative portfolio alloca-

tion will find that the probability of portfolio success is more sensitive to the determinants of

portfolio success, as compared with selecting a conservative or aggressive allocation.

6. Concluding comments

This analysis has examined the impact of various retiree-determined and chance variables

on the probability of portfolio success. The results of this analysis provide retirees with spe-

cific information about the impact their actions may have on the probability of portfolio suc-

cess. While the chance variables, by definition cannot be controlled, retirees may be able to

mitigate the risk of portfolio failure by using intermediate targets like Early Experience to

determine the need for midterm corrections to the retirement plan.

The results of the analysis confirm that portfolio success is impacted by both retiree-deter-

mined variables (Allocation, Withdrawal Rate, and Planning Horizon) and chance variables

(the profile of portfolio returns includes Return, Risk, and Early Experience). However, the

relative impact of each of these variables differs. Withdrawal Rate is the most significant

driver of portfolio success, and though relevant, Early Experience is not as significant.

Retirees who select a conservative portfolio allocation will find that their portfolio success is

much more sensitive to the explanatory variables, when compared with retirees who select

other allocations. Conservative portfolio allocations also result in wide variations in portfolio

success outcomes, while aggressive portfolio allocations result in relatively narrow variations

Table 6 Determinants of portfolio success (partitioned by portfolio allocation)

Aggressive Balanced Conservative

Coefficient Marginal effect Coefficient Marginal effect Coefficient Marginal effect

Intercept 14.62 16.12 24.98
Withdrawal rate �2.11 �0.0814 �2.84 �0.1137 �4.62 �0.1962
Horizon �0.26 �0.0101 �0.32 �0.0126 �0.55 �0.0232
Early experience 0.06 0.0023 0.07 0.0030 0.11 0.0045
Return 0.93 0.0360 1.26 0.0506 2.18 0.0926
Risk �0.31 �0.0120 �0.29 �0.0117 �0.38 �0.0163
R2 66% 68% 75%

Note. N= 10,000 for each of the three partitions. All coefficients are significant at the 1% level. This table

presents the results of the logistic regressions (sample partitioned by portfolio allocation) analyzing the impact

of the explanatory variables on the probability of portfolio success.

140 M. Athavale et al. / Financial Services Review 30 (2022) 125–143



across different withdrawal rates. These results are consistent with the Ho, Milevsky, and

Robinson (1994) assertion that equity should have a bigger role in retirement portfolios than

is recommended by most financial planners. The actual return to a particular retiree may differ

from that suggested by the portfolio allocation. Both Return and Risk are significant in the

analysis suggesting that asset selection within a portfolio is important to mitigating any

adverse effect that these variables would have on portfolio success. The Early Experience

variable could serve as an early indicator of the need for midterm course corrections to the

retirement plan with the withdrawal rate serving as the transmission mechanism for portfolio

success.

Planning for success in sustaining a retirement portfolio would be incomplete without

also discussing other issues which arise even in the event of portfolio success. In the event

of portfolio success, by definition, there is a residual (unconsumed) portfolio balance. This

reduced consumption over the retirement horizon is the prudent reality of dealing with an

uncertain future in the absence of well-accepted instruments that can capture the value of a

potential future surplus. Another issue is the possibility of the retiree living beyond the

planned retirement horizon. While any unconsumed portfolio balance may serve to mitigate

longevity risk, longevity insurance is also available in the form of a single-premium deferred

inflation-indexed fixed life annuity, and this could allow real consumption at the same level

as that experienced during the expected retirement years. And finally, many financial plan-

ners recommend that retirees maintain a cash bucket outside their invested portfolio as part

of their overall strategy. This cash bucket is intended to meet unexpected consumption

needs, reduce the need to liquidate portions of the invested portfolio during market down-

turns, and finance any mismatch in the timing of cash flows.

When it comes to retirement planning, the cost of failure is high. Nevertheless, most retir-

ees lacking the knowledge and tools, engage in wishful thinking rather than structured plan-

ning. Retirement planning is complex and has inherently uncertain outcomes. This analysis

is a simple and imperfect representation of the complex realities of retirement planning.

Although the analyses are simplistic, the results provide guidance to the manner in which

various retiree-determined and chance variables impact portfolio success. The research pro-

posed in this study is a topic of active policy debate, and may serve as a baseline for addi-

tional research and sophisticated and dynamic models for generating lifetime income for

retirees, pension funds, endowments, and managed payout mutual funds.

This research also has various limitations. The simulation methodology requires us to

specify the unknown future distribution from which returns might obtain, and the expected

parameters of that distribution. We have assumed that the retiree makes withdrawals at the

end of every year, and have not considered monthly or quarterly withdrawals. We have also

implicitly assumed that the retire may engage in additional retirement planning outside the

invested portfolio (e.g., bequests, longevity insurance, and a cash bucket for liquidity) and

that retirees desire a constant level of real consumption over the retirement horizon. And

finally, our analysis examines portfolio success as a binary (success/failure) variable but

does not consider the size of the bequest or the timing of the portfolio failure as measures of

the extent of success or failure (Estrada and Kritzman, 2019).

There is no “one size fits all” single right answer when it comes to addressing the various

tradeoffs and interactions associated with retirement planning, and outcomes will vary based

M. Athavale et al. / Financial Services Review 30 (2022) 125–143 141



on retiree choices, economic circumstances, and chance. It is nevertheless important to under-

stand them so that a realistic initial plan and consumption target can be established, and mid-

term adjustments can be initiated if necessary. Just be aware that your mileage may vary.

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