Selecting a Social Security age to balance consumption

and risk

Barry R. Cobb, Jeffrey S. Smith*

Virginia Military Institute, Department of Economics and Business, Lexington, VA 24450, USA

Abstract

This article uses Monte Carlo simulation to determine the maximum consumption given retire-

ment at age 62, initial wealth, risk tolerance, and Social Security take decision. Coile et al. (2002)

argue for a delay, because the payment increases seven percent for each year. Focusing on maximiz-

ing the expected present value of benefits may be misguided. This article shows that, conditional on

retirement at age 62, initial consumption is always maximized by taking Social Security no later

than age 63; it also results in the highest simulated ending wealth at death, and the lowest amount of

simulated time (if any) living on just Social Security. © 2020 Academy of Financial Services. All

rights reserved.

Keywords: Social Security; Consumption; Monte Carlo simulation

1. Introduction

Everyone is faced with several major questions in life, such as: which college to attend,

who to choose as a spouse, when to have children, and of course, when to take Social

Security? Unlike many of life’s other choices, the decision about when to claim Social

Security is irrevocable; therefore, it is one that fills people with much uncertainty. This arti-

cle will attempt to guide future retirees in their choices of when to begin receiving Social

Security benefits and how much to consume throughout their retirement. Building upon the

insights provided by Alderson and Betker (2017), this article uses a Monte Carlo simulation

model to show that the decisions regarding when to claim Social Security and how much to

consume during retirement are ultimately questions of risk tolerance. To be more specific,

*Corresponding author. Tel.: +1-540-464-7542; fax: +1-540-464-7005.

E-mail address: smithjs@vmi.edu (J. S. Smith)

1057-0810/20/$ – see front matter © 2020 Academy of Financial Services. All rights reserved.

Financial Services Review 28 (2020) 201–221



“What level of confidence does a person require as it pertains to the possibility of exhausting

their wealth before they die?” The answer to this question affects the level of consumption

that a person can pursue in their retirement years, how much wealth they possess when they

die, and how long they may have to live at a minimal consumption level if their savings is

exhausted.

Alderson and Betker (2017), in keeping with Modigliani’s (1966) theory of consumption

smoothing, presume that individuals want to maintain constant real consumption across their

lifetime. They asked the question, “Does a person that postpones taking Social Security get

adequately compensated for doing so?” To answer this question, they calculated the proba-

bility of exhausting tax-deferred savings given a person’s retirement age and the age they

decide to take Social Security. This article addresses a fundamentally different, but similar

question: “What is the maximum amount of real consumption a person can choose, given

their risk tolerance and the age at which they take Social Security?” Monte Carlo simulation

helps to reveal the maximum amount of consumption that is consistent with a person’s risk

tolerance.

The questions posed by Alderson and Betker (2017) and this article are different than pre-

vious research. Heretofore, most research that focused on when to claim Social Security did

so with the intent to maximize the expected present value of the stream of benefits. Coile,

Diamond, Gruber, and Jousten (2002) use simulations to show the optimal delay for both

individuals and one-earner married couples using both the expected present value under

financial calculations and a utility maximization model. They find that it is optimal to post-

pone, with delay times that ranged from months to years, in a large number of circumstan-

ces. Docking, Fortin, and Michelson (2012) solve for the optimal retirement age given

gender and race for single individuals. They find the decision is invariant to race and gender;

individuals should either retire at age 64 if they retire early, or they should retire at age 67.

Similarly, Shoven and Slavov (2014a) calculate expected present value of benefits for a

number of different situations and find that individuals who expected to live according to the

average mortality tables should delay taking Social Security past their full retirement age

unless the real interest rate is four percent (or higher). Shoven and Slavov (2014b) show that

the benefit from delaying Social Security has risen over time, with someone born in 1951

(close to the baseline for this article) gaining 12.7% if they delay claiming until age 69.

There is lots of evidence to suggest delaying receipt of Social Security; the popular press

would summarize by saying, “wait as long as you can.”

Munnell and Chen (2015) report that, in 2013, after adjusting for growing changes in the

size of Social Security cohorts, 36% of men who claim Social Security benefits are aged 62.

Shoven, Slavov, and Wise (2018) conduct a survey to assess people’s attitudes pertaining to

their decision to claim Social Security. Seventy seven percent are happy with their decision

to claim at age 62, while 90% are happy with their decision to claim at the full retirement

age. The main reason cited for claiming before the full retirement age is a need for the

money, and 23% of respondents state they use savings to finance the gap between retirement

expenditures and Social Security income (61% stated they relied upon an employer-spon-

sored pension). This article aims to guide the decision regarding when to collect Social

Security, as well as how much to spend during retirement, given an individual’s risk toler-

ance for failure. Here it is important to stress the definition of failure. Failure is defined as

202 B.R. Cobb, J.S. Smith / Financial Services Review 28 (2020) 201–221



fully exhausting the initial stock of wealth such that the individual must live only on their

Social Security benefits. According to a report by the U.S. Government Accountability

Office (GAO) (2019), 48% of households aged 55 and over have no retirement savings, but

may have a defined benefit plan. Twenty nine percent of households have neither. The GAO

gathered this information from the 2016 Survey of Consumer Finances. Thus, in this model,

failure is defined in accordance with the state of wealth accumulation that is consistent with

almost a third of American households, and possibly as many as 50% of households.

2. The model

The basic decision is a function of gender, wealth, annual level of consumption, the age

at which an individual begins collecting Social Security, the portfolio’s asset allocation, and

the annual return an asset earns. Gender is not a factor in the model; results are simulated for

males and females separately. Thus, gender affects the probability of death. A retiree’s

wealth, Wt, is modeled in year t as

Wt ¼ Wt�1 þ Pt � Ctð Þ � 1þ aEt þ 1� að ÞBtð Þ (1)

where Pt is the Social Security payment in year t; Ct is the consumption in year t; a is the

percentage invested in stocks, with stock (equity) and bond returns denoted by Et and Bt,

respectively. Fig. 1 depicts the structure of the simulation model utilized to evaluate the

retirement portfolio that includes Social Security payments.

The elements of the model and the components of (Eq. 1) are described in the remainder

of this section.

Fig. 1. Structure of the retirement portfolio model.

B.R. Cobb, J.S. Smith / Financial Services Review 28 (2020) 201–221 203



2.1. Stochastic assumptions

The retiree divides wealth among investments in stocks and bonds. Total returns from the

S&P 500 are used to model stock returns, and total returns on 10-year Treasury Bonds repre-

sent the bond returns. Both series range from 1928 to 2018 and were retrieved from

Professor Aswath Damodaran’s website (Damodaran, 2019). The article uses this site due to

the long history and the singular source. These data span the Great Depression, several wars

including World War II, and several extremely volatile periods for stocks. Additionally,

accurate total return series for bonds are hard to access, especially across such a long history.

Professor Damodaran calculates the price return for a 10-year Treasury Bond and adds that

to the coupon received for the 10-year Treasury Bond. Therefore, these data give us average

returns for both series and good correlation between the two.

Random variables are established by creating probability distributions for annual stock

and bond returns, and these returns are correlated within each year. Stock returns in each

year are modeled as normally distributed with a mean of 11.5% and a standard deviation of

19.6%. Bond returns are normally distributed with a mean of 5.2 percent and a standard

deviation of 7.7 percent. Returns are uncorrelated across years, but the stock and bond

returns within each year are modeled with a correlation coefficient of –0.0276.

Alderson and Betker (2017) use a bootstrapping approach and randomly sample an actual

observation of investment returns to calculate the simulated returns for a given year (e.g., for

year one their simulation might randomly select the historical return from 2010, in which

case their model will use the total return for stock and bonds from 2010). In contrast, the

portfolio model in this study defines the distributional parameters and then uses Monte Carlo

simulation to sample both stock and bond total returns.

Inflation is estimated using the difference between the yield to maturities for Treasury

Inflation-Protected Securities (TIPS) and the yield to maturity for similarly dated Treasury

securities matched for maturity dates from 2019 through 2029, with the smallest one-year

difference being 1.705 percentage points and the largest being 1.959 percentage points.

These inflation estimates from 2019 through 2029 are used to develop a normally distributed

variable with a mean (1.88 percent) and standard deviation (0.277 percent) that follows from

the projected inflation rate across these 11 years. Correlation between inflation and bond and

stock returns is estimated by calculating the correlation between the Consumer Price Index

(CPI) and bond and stock returns across the entire time period of the sample. This inflation

rate is used to maintain constant real consumption for an individual, while also adjusting the

level of Social Security benefits that will be paid in the future.

On each simulation trial, a random number of years (L) until death is selected. This ran-

dom variable is created using current Social Security life span assumptions. This is accom-

plished by running 10,000 simulation trials from the Actuarial Life Table (Social Security

Administration, 2018) and then compiling results for conditional remaining life span given

that an individual (male or female, as appropriate) obtains age 62. At the age of 62, a female

is projected to live 2.82 years longer than a male. The average male life expectancy in the

model is 19.44 years, which would suggest that a male that retires at age 62 will live to be

approximately 81.44 years old, while a female will live to be approximately 84.26 years old

after an average life expectancy of 22.26 years. The oldest person in any simulation was

204 B.R. Cobb, J.S. Smith / Financial Services Review 28 (2020) 201–221



108. These numbers are in line with, but longer than, the Cohort Life Expectancy published

by the Social Security Administration in Table 5.A5 of the 2019 Annual Report of the Board

of Trustees of the Old Age and Survivors Insurance and Federal Disability Insurance Trust

Funds (2019). Using calendar year 1955 (one year before the latest birth year of 1956),

males are expected to live an additional 13.1 years past 65 (78.1 years), while females are

expected to live 16.7 years past 65 (81.7 years).

2.2. Social security benefit payments

The retirement portfolio model assumes that an individual retires at the earliest opportunity

to claim Social Security, which is currently age 62. Unlike in Alderson and Betker (2017),

who use the online Social Security benefits estimator, the model calculates the Social Security

benefit using the process in Appendix D from the Annual Statistical Supplement to the Social

Security Bulletin for 2018, released May 2019 (Social Security Administration, 2019). The

model assumes that an individual who begins working at age 18 and works until age 62 earns

at least the maximum amount of income that is subject to Social Security tax in the highest

35 years of their working life. The initial benefit SA is then estimated to coincide with the age,

A, at which they start to collect Social Security. The benefit is adjusted for stochastic inflation,

It, in each year so that the Social Security payment Pt in each year is determined as

Pt ¼ R � SA �
Yt�1

u¼1

1 þ Iuð Þ (2)

where R is an indicator variable that is equal to 1 if t<A–61 and 0 otherwise. For simplicity,

it is assumed that someone turning 62 will retire and begin collecting benefits at some point

in the following month; however, someone choosing their benefits at the age of 70 will have

stopped working eight years earlier.

This monthly retirement benefit is based on income earned through the end of 2018.

Individuals experience a reduction in the full benefit for taking their Social Security bene-

fit before they reach their maximum retirement age. For example, the person that turns 70

(born in 1948) would experience a 25% reduction to their monthly benefit, while a person

that turns 62 (born in 1956) would experience a 26.67% reduction. Thus, the monthly ben-

efit ranges from SA ¼ $2,150 for a 62-year old to SA ¼ $3,565 for a 70-year old. An indi-

vidual would need to earn $128,400 in 2018 to earn the maximum income that is subject

to Social Security taxation; as of tax filing year 2017, the latest statistics released by the

IRS (2019), only 17.1% of households earned more than $100,000 in Adjusted Gross

Income. Purcell (2018) shows that the mean and median wage for males between 25 and

59 years old, in 2014 dollars, are $64,200 and $45,000, respectively. Much like the IRS

data, a male earning above $100,000 would put them somewhere in the upper teens in

terms of percentile earners. To increase applicability, the model is also used for an indi-

vidual that only earned half of the maximum income ($64,200 in 2018) that is subject to

Social Security taxation. These payments range from SA ¼ $1,552 for a 62-year old or

SA ¼ $2,538 for a 70-year old.

B.R. Cobb, J.S. Smith / Financial Services Review 28 (2020) 201–221 205



Similar to Alderson and Betker (2017), the model considers accumulated initial wealth

(W0) in $100,000 increments up to $1,000,000; thus, the results apply to retirees at a wide

range of savings levels. Because individuals are assumed to retire and stop saving at age 62,

waiting longer to claim Social Security does not directly, positively affect your accumulated

wealth in the model, though it would add to the possible Social Security benefit.

2.3. Decision variables

The retiree makes two choices in the model: (1) the age, A, to begin Social Security pay-

ments, and (2) the percentage of the portfolio allocated to stocks, a. Consumption, C1, in the

first year of retirement is maximized subject to these choices. Dimmock, Wang, and Yang

(2019) derive, using values attributed to the U.S. stock market, how Modern Portfolio

Theory can justify a 60/40 split between stocks and bonds, typically used to represent

endowments. This model, similar to Alderson and Betker (2017), sets a ¼ 60% for stocks

and 1–a ¼ 40% for bonds, acknowledging that this allocation might expose individuals to

an unacceptable level of Beta risk as they age. Someone in their Seventies may be comforta-

ble with a 25% chance of outliving their wealth, but uncomfortable with the possibility of

losing significant wealth in any given year. Since 1928, there have been 24 years with nega-

tive returns, and the average negative return is (13.7%). An individual with a 60% allocation

is risking almost 10% of their portfolio in any given year based on historical data. To

account for potential risk in the 60/40 allocation, this article also considers the “Rule of

Thumb” portfolio (ROT), where an individual allocates 120 minus their current age as the

percentage invested in stocks.

One other portfolio allocation considered is the “Bridge fund” portfolio. An investor who

decides to delay taking their Social Security benefit until after age 62 may want to limit the

exposure of some portion of their wealth to the risk from bonds only. The portion of wealth

for the Bridge fund is calculated as the present value of a growing annuity, where the annuity

is the annual payment to fund the foregone Social Security and the growth is equal to the

expected inflation rate. This present value is invested only in bonds and is “used” to fund

consumption until the individual begins drawing Social Security. At that time, any funds

remaining in the Bridge fund are then invested at the allocation rate for the portfolio, either

60/40 or the ROT. It should be noted that it is also possible that the Bridge fund will be ex-

hausted before the individual begins to draw Social Security, as bond returns are stochastic.

Consumption adapts throughout the investor’s life to stay constant in real terms because

the initial consumption, C1, adjusts with the stochastic inflation rate (It) each year. Thus,

consumption in year t is defined as

Ct ¼ C1 �
Yt�1

u¼1

I þ Iuð Þ (3)

for year 2 and beyond. Based on these choices, the model simulates a distribution of results

for the retiree’s ending wealth at death, and the average years the retiree lives after exhaust-

ing all savings.

206 B.R. Cobb, J.S. Smith / Financial Services Review 28 (2020) 201–221



2.4. Solution process

The objective of this study is to advise a potential retiree on a consumption amount that

is consistent with their risk tolerance. The investor chooses as a requirement of the portfolio

that “failure” only occurs a set percentage of the time – the Maximum Failure Rate. Failure

in this context means that savings are exhausted and the individual lives on Social Security

payments alone. In contrast, Alderson and Betker (2017) consider a number of consumption

strategies: (1) a retiree who chooses to spend 1/N of their accumulated wealth, where N is

the median number of years remaining in their life, plus the projected Social Security bene-

fit for the age at which they take the benefit, all adjusted for inflation; (2) a retiree who fol-

lows a similar strategy but sets N as the number of remaining years until they are 100 years

old; (3) a retiree that purchases longevity insurance; and (4) a retiree that sets aside the

equivalent amount spent on longevity insurance, excluding it from accumulated wealth

when calculating consumption (i.e., somewhat analogous to the current model’s Bridge

fund).

It is important to emphasize the difference between the approach in this study and the one

that Alderson and Betker (2017) pursue. The previous study calculates the probability of

failure given the age at which you select Social Security and the method of consumption an

individual pursues. Alderson and Betker (2017) realize this on page 43 when they note that

“The spending strategy with the lowest failure probability was not necessarily the “optimal”

strategy . . . . Any given retiree might well prefer a higher failure rate when balanced against

higher consumption today.” Given this admission, this model considers failure rates of five

percent and 25% for both males and females, and determines the highest level of annual con-

sumption that meets those failure rates, conditional on the age at which an individual takes

Social Security and their initial level of wealth. This allows the individual to select, within

some parameters, their comfort level, their consumption level, and the age at which they

take Social Security.

3. Results

The case of selecting sustainable consumption at an acceptable level of risk is considered.

For a 62-year old with tax-deferred savings of between $100,000 and $1,000,000, the retire-

ment portfolio is simulated for beginning Social Security ages of 62 through 70 in one-year

increments for male individuals and female individuals. We do not pursue joint decisions for

married couples due to the number of simplifying assumptions required. The goal is to maxi-

mize current beginning consumption, while still meeting the failure threshold. Charnes

(2012) finds that much of the reduction in the standard error of estimates in Monte Carlo

simulation models occurs when utilizing at least 2,000 simulation trials. In keeping with this

convention, the model uses 2,000 simulation trials for each combination to identify the com-

binations that achieve the maximum consumption without exceeding the maximum allow-

able rate of failure for the portfolio, and the model simulates results for approximately 130

possible consumption levels for each Social Security age and initial wealth before there was

no improvement in consumption. Failure is defined as the percentage of time the retirement

B.R. Cobb, J.S. Smith / Financial Services Review 28 (2020) 201–221 207



portfolio is exhausted before death, thus resulting in the investor living strictly on Social

Security income for the remainder of his or her lifetime.

The solution process is applied to scenarios for each combination of assumptions as

depicted in Fig. 2, which also lists the tables at the end of the article where numerical results

are reported. Maximum consumption for males and females when considering a five percent

failure rate is determined for the 60/40 and ROT portfolios assuming an individual earned

100% of the maximum income for Social Security. Each of these scenarios is also consid-

ered in combination with an initial Bridge fund. Results of these simulations are reported for

all initial wealth levels in Tables 1 through 4.

Results corresponding to those in Tables 1 through 4 for a 25% required failure rate are

only reported for an individual (male or female) that has $500,000 in initial wealth. Full

results are omitted because they do not differ meaningfully in consumption, ending wealth,

or the unconditional number of years a person may fall short with the results in Tables 1

through 4; however, these results are available upon request. Similarly, when considering an

individual that earned 50% of the maximum income for Social Security, we show the 60/40

allocation, both with and without the Bridge fund, for males and females with $500,000 in

initial wealth in the summary tables, but only for a five percent required failure rate.

3.1. Results for maximum social security income without Bridge fund

Table 1 considers a male who has earned the maximum amount of income subject to

Social Security taxation throughout his working life. Given a five percent chance of failure,

Table 1 displays the age at which an individual takes Social Security and the initial wealth

they possess when they retire. Keep in mind the assumption that everyone retires at age 62.

The table reports the maximum initial consumption values, the median ending wealth at

Fig. 2. Scenarios considered in the simulation results.

208 B.R. Cobb, J.S. Smith / Financial Services Review 28 (2020) 201–221



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6

B.R. Cobb, J.S. Smith / Financial Services Review 28 (2020) 201–221 209



T
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3

210 B.R. Cobb, J.S. Smith / Financial Services Review 28 (2020) 201–221



T
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3
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4

B.R. Cobb, J.S. Smith / Financial Services Review 28 (2020) 201–221 211



T
ab
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4
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1

212 B.R. Cobb, J.S. Smith / Financial Services Review 28 (2020) 201–221



death associated with that decision, and the average length of time that someone who does

fail would need to live on their Social Security benefits alone. Consider the specific example

of a 62-year old with $500,000 in tax-deferred savings. An initial consumption value of

$52,000 is the maximum initial payout that allows the male investor to meet the five percent

failure rate on average, and this occurs when starting Social Security payments as early as

age 63. Fifty-two thousand dollars is only the initial consumption at age 63; this amount is

indexed by inflation in each subsequent year.

While maximum initial consumption is the same when beginning Social Security pay-

ments at either age 63 or 64, the amount “left on the table” in median ending wealth differs

between these two possible alternatives, with the male investor ending with about $44,000

in additional wealth when payments begin at age 63 as opposed to age 64. Acknowledging

that median ending wealth is a tertiary goal, it should be viewed as a tiebreaker when consid-

ering similar consumption levels and rates of failure. Shoven, Slavov, and Wise (2018) iden-

tify reasons why an individual might claim immediately that generally center around the

desire to retire coupled with a lack of liquidity. The results in Table 1 suggest that it may be

a consumption-maximizing decision. Table 2 displays the results for a female investor.

Much like males, females maximize their consumption by claiming as early as age 63.

Starting Social Security payments at age 63 also maximizes median ending wealth relative

to all other claiming ages with the same level of consumption.

These results differ from traditional research regarding when to take Social Security bene-

fits. Many previous studies are concerned with ensuring the individual (or couple) maxi-

mizes the expected present value of their Social Security benefits. Coile, Diamond, Gruber,

and Jousten (2002) answer this question and find that a male that retires at age 62 with

$200,000 in initial wealth should wait three years to earn almost $11,000 (in 1992 dollars,

which would be just over $20,000 in today’s dollars using the change in CPI over this time

period) in expected present value. Table 1 above shows that a male with $200,000 that waits

three years to claim Social Security instead of claiming at age 62, assuming a five percent

risk of failure, would be able to consume the same amount, $36,000, but they would die

with about $112,000 less in median ending wealth. Consider that Dushi, Iams, and

Trenkamp (2017) use data from the redesigned CPS survey and find that half of all people

aged 65 or older use Social Security for at least 50% of their family income and almost 25%

of the population used Social Security for 90% of their income (the percentages are slightly

lower for males only, which would be the most directly comparable to this scenario). They

compare this to spending from assets (public and private pensions as well as IRAs), which

only represent 21% of income. Table 1 confirms that delaying Social Security does not

increase consumption; it only lowers ending median wealth. Thus, delaying Social Security

to collect an additional $11,000 in expected present value is not a utility-maximizing

decision.

Considering the risk-averse individual, the tables also identify the implications of the five

percent failure rate, as they provide the mean amount of time a person would need to live on

just their Social Security payment. This is calculated by taking the conditional number of

years short times the probability of actually falling short. The individuals (male and female)

possessing $500,000 in initial wealth that retire at age 62, begin consuming $52,000 (male)

or $50,000 (female) a year, and begin drawing Social Security at age 63 will fail, or draw

B.R. Cobb, J.S. Smith / Financial Services Review 28 (2020) 201–221 213



down their initial wealth, five percent of the time. On average, the individual spends just

over one-fourth of the last year of their life living solely on their Social Security payment,

and is most likely to die with assets totaling either $811,858 (male) or $1,059,723 (female).

Specifically, for the male retiree, there is a 95% probability that wealth is not exhausted

before death; whereas on the five percent of trials that failure occurs, this person spends an

average of 5.2 years living strictly on Social Security (for an average years short of 5.2 times

five percent, or 0.26 years). For this retiree, the first year spent living on Social Security pay-

ments typically occurs at age 84 years.

3.2. Results for maximum social security income with Bridge fund

How does the possibility of contributing to the Bridge fund change the results? Table 3

reports the results for a male that earns 100% of the Social Security income requirement, has

a risk tolerance level that supports a five percent failure rate, and maintains a 60/40 portfolio

allocation. Notice that consumption guidance is virtually unchanged, with maximum con-

sumption still occurring at age 63 for initial wealth levels of $300,000 and above. Ending

wealth is slightly lower when using the Bridge fund when Social Security payments are

delayed until age 64 or beyond.

This pattern is repeated for female investors as displayed in Table 4. When establishing a

Bridge fund, females also maximize consumption at age 63 ($50,000) with no decrease in

ending median wealth. The considerable wealth remaining at death, whether or not an indi-

vidual establishes a Bridge fund, is primarily due to precautionary consumption to ensure

that their savings is only exhausted five percent of the time.

The fact that consumption and ending median wealth do not change by establishing the Bridge

fund suggests that individuals could conceivably consider less risk and still achieve their goals.

This pattern does not hold as the time between retirement and Social Security claiming increase.

A male with $500,000 in initial wealth who retires at age 62 and claims Social Security at age 70

will have $230,000 less in median ending wealth, while a female under the same assumption will

have $261,000 less. The Bridge fund supports the same or slightly higher consumption, but the

lower portfolio return while the Bridge fund is active generates significantly less wealth.

3.3.Results for additional scenarios

To illustrate the effect of varying portfolio allocations and failure requirements, a male

(Table 5) or a female (Table 6) that has $500,000 in initial wealth is considered. For these

investors, maximum consumption is determined in the following scenarios: (1) Bridge fund

and no Bridge fund versions of the ROT portfolio allocation at the five percent level of fail-

ure; (2) Bridge fund and no Bridge fund versions of the 60/40 allocation at the 25% level of

failure; (3) Bridge fund and no Bridge fund versions of the ROT allocation at the 25% level

of failure; and finally (4) Bridge fund and no Bridge fund versions of the 60/40 allocation,

assuming the investor earns only 50% of the maximum Social Security income across their

lifetime, with a five percent probability of failure. These results allow a comparison with the

same individual, the retiree with $500,000 in initial wealth, across a wide variety of differing

214 B.R. Cobb, J.S. Smith / Financial Services Review 28 (2020) 201–221



T
ab
le

5
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6
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6
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7
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1
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B
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9

B.R. Cobb, J.S. Smith / Financial Services Review 28 (2020) 201–221 215



T
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9

216 B.R. Cobb, J.S. Smith / Financial Services Review 28 (2020) 201–221



scenarios. Some scenarios introduce more risk of failure, such as the 25% maximum failure

rate, while others exhibit more risk-averse behavior (ROT allocation). In all cases for both

males and females, consumption is maximized no later than age 63, and sometimes as early

as age 62, with no loss of ending median wealth and no significant increase in the number of

years short.

Two examples illustrate the effect of changing these assumptions. A female that accepts a

25% probability of failure who does not establish a Bridge portfolio and maintains a 60/40

allocation can maximize initial consumption at $59,000 by claiming Social Security at age

63. She will still have a median ending wealth of $460,737, and she would accept the possi-

bility of living an average of 2.18 years on just her Social Security payments (there is no

shortage with 75% probability, with an average of 8.72 years short on the trials where failure

occurs). As noted earlier (U.S. Government Accountability Office, 2019), at least 29% of

households live entirely on Social Security throughout retirement, and there are likely a

much larger percentage without personal savings that live entirely on Social Security plus

defined benefit pension plans. The same male could consume $61,000 and would possess

$391,000 in ending median wealth, with less time on Social Security if he fails (1.9 years;

there is no shortage with 75% probability, with an average of 7.6 years short on the trials

where failure occurs). The other example includes a male and female with $500,000 in ini-

tial wealth that earn just 50% of the maximum Social Security income. Assuming a five per-

cent probability of failure and a 60/40 allocation, a male would maximize consumption of

$44,000 by claiming at their retirement age of 62. Similarly, a female would maximize con-

sumption of $43,000 also by claiming at age 64.

4. Conclusions

When examining the results of the study, some general trends emerge. Once past the

lower levels of wealth accumulation (starting at $300,000), delaying receipt of Social

Security payments beyond age 63, for both male and female, only decreases median ending

wealth at death with effectively the same level of consumption in nearly all scenarios, and it

has virtually no effect on the average years spent living on Social Security if you fail. The

conclusion is that an individual that retires at age 62 should draw Social Security almost as

soon as they retire. Because of this, when an individual takes Social Security has far less im-

portance in terms of how much they can consume as compared with how much wealth they

possess when they retire. At a five percent chance of failure, each additional $100,000 means

$5,000 in additional initial annual consumption for both males and females.

The reason for this must be emphasized. If an individual retires and delays taking Social

Security, then they obviously make sizable withdrawals from their initial wealth to fund

their current consumption. Unlike Alderson and Betker (2017), who assume a constant level

of consumption equal to the individual’s initial wealth divided by their life expectancy,

which is then added to their Social Security benefit, this article solves for the maximum

amount of consumption that only exhausts the initial wealth level consistent with the chosen

probability of failure. Using Alderson and Betker’s formula, an individual that retires at age

62 with $500,000 in initial wealth would have initial consumption equal to approximately

B.R. Cobb, J.S. Smith / Financial Services Review 28 (2020) 201–221 217



$50,948. This model has a consumption level that roughly matches Alderson and Betker’s

consumption level assuming five percent failure; however, consumption is equal to $61,000

at a 25% level of failure.

At lower levels of income, the previous conclusion about when an individual should take

their Social Security payment is magnified. An individual that retires at age 62 that has not

accumulated much wealth must take their Social Security within the first few years of eligi-

bility or else they must be willing to constrain their consumption to very small levels. For

example, a male that has $100,000 in wealth that maximized their Social Security contribu-

tions that waits to take Social Security until age 67 can only safely consume $18,000 a year

if they accept a five percent chance of failure and do not establish a Bridge fund. This is con-

sistent with the evidence provided by Shoven, Slavov, and Wise (2018) that indicates a pri-

mary reason for starting early Social Security payments is the need to consume more than

the income earned from a retirement nest egg. This individual would be able to consume

considerably more by establishing the Bridge fund ($32,000), albeit with over $730,000 less

in median ending wealth. While the individual fails five percent of the time, the average

number of years that the male would fall short is very low, because consumption is severely

restricted.

Adopting a more conservative allocation strategy such that the percentage invested in

stocks is 120 minus an individual’s current age did not meaningfully affect the results.

Initial consumption was either the same or less under the “rule of thumb” portfolio across

both five percent and 25% failure probabilities, and there was no discernable pattern in end-

ing wealth or unconditional years short.

For any level of initial wealth beyond $300,000, the age Social Security payments begin

does not meaningfully change the maximum level of consumption at the five percent level

of failure; at the 25% level of failure, it only changes consumption by $5,000. Beyond an ini-

tial wealth level of $300,000, a $100,000 increase in your initial wealth level changes initial

consumption by as much, if not more, than taking Social Security at the earliest opportunity.

This suggests that advisors must continue to emphasize that it is as much about how much

an individual chooses not to spend before retirement as it is about how much an individual

makes in any given year.

The included tables help determine the amount of consumption a person can afford given

their wealth and the tolerance for risk. While it is unlikely that an individual would com-

pletely maximize their Social Security income, using either Table 5 (males) or Table 6

(females) can help guide an individual. Once an individual has determined which scenario

applies by matching their earnings profile to either of the two scenarios, the maximum

income or 50% of maximum income, they can determine levels of consumption associated

with their choice of establishing a Bridge fund, their asset allocation, and their accepted

probability of failure. The respective table demonstrates the resulting levels of wealth and

amount of time associated with failure. Thus, an individual can see the difference. For exam-

ple, assuming maximum income earnings is the baseline, an individual that has $500,000 in

retirement assets with no Bridge fund and a ROT allocation can take Social Security at 63

and consume, in real terms, $51,000 a year, assuming a five percent level of failure; this

individual will likely die with almost $770,000 dollars in wealth. If this does not match the

individual’s needs (or wants) for current consumption compared with ending wealth, they

218 B.R. Cobb, J.S. Smith / Financial Services Review 28 (2020) 201–221



can choose to accept a higher level of risk (25%) and take Social Security at age 62 and

begin consuming $60,000 a year. The results suggest they will most likely still have

$438,000 in wealth at death. Comparing the tradeoffs between consumption, Bridge fund,

ending wealth, and possible years of failing will help form opinions about the relative risk

aversion for each individual.

Simulations also show that the standard 60/40 endowment allocation provides results that

are as good or better than a model that adjusts allocation as a client ages, when it comes to

initial level of real consumption and ending wealth. There is a slight increase in the amount

of time the average person that fails will live only on Social Security, but it is measured in

days not month or years (at the five percentage level). This suggests, though it warrants fur-

ther investigation, that it is the flow of funds into and out of the investment account, as

opposed to making fine tuning adjustments to the asset allocation of the portfolio, that matter

for retirement consumption. Likewise, a male investor that believes an average death at 81 is

too young could always make their choices from the respective female table. Doing so

would add approximately 2.75 years, or an additional 10% of years beyond the statistical

death table for males.

Limitations

There are some limitations that must be identified. First and foremost, this article assumes

that an individual retires at age 62. As reported by Munnell and Chen (2015), the current

trend is to work longer. Also, the model uses Social Security actuarial tables, randomly sam-

pling the age of death; however, many financial planners allow for gradients of life past the

standard statistical tables. For instance, current financial planning software allows for a

10%, 20%, and 30% longer life span than projected by the Social Security tables, given a

certain age. For this model, the average life expectancy is 19.47 years; extending this by

30% would add an additional 5.84 years of Social Security benefits, as well as consumption.

We also only consider single individuals, although a reasonable way to follow the advice

provided in this article would be to pool the couple’s initial wealth and use guidance from

the female results to select an appropriate consumption level.

For each age and wealth combination, approximately 130 simulations of various levels of

initial consumption were attempted, each with 2,000 trials, before the highest consumption

value where the failure requirement was met was assumed to be the optimal solution. There

is no guarantee the solution is optimal, but all results presented are consistent with experi-

ments where more simulation trials were used for comparison. Additionally, the selected

returns for either stocks or bonds in actuality may not resemble the returns used in the simu-

lations, or that the long-run correlation used in this simulation will hold going forward.

The model in this article assumes constant, real consumption. Both Social Security pay-

ments and consumption are indexed by inflation and the market’s estimate of inflation may

not be realized. Some retirees may wish to front-load their consumption while they are

healthy enough to enjoy it. Additionally, some retirees will still have some expenses such as

remaining house payments, and so forth, in the first few years of retirement. At a certain

point, as mobility begins to decline and adverse health conditions start to increase, it is

B.R. Cobb, J.S. Smith / Financial Services Review 28 (2020) 201–221 219



reasonable to expect spending to become less on discretionary items such as travel and more

on nondiscretionary, such as health care. Thus, a non-linear consumption pattern may be

more realistic and is worthy of further research. A retiree who anticipates this type of spend-

ing pattern could potentially increase the maximum failure rate (say from five percent to

25%) because Social Security payments would remain for the last few years of the person’s

life in the event savings is exhausted.

Finally, this research does not account for the effect of taxes. Geisler and Hulse (2018)

look at the implications associated with portfolio drawdown strategies when including

Social Security benefits pertaining to efforts to extend the life of the portfolio. They show

that drawdown strategies do matter and can impact the life of the portfolio. However, as

their research shows, assumptions must be made regarding the split between tax-advantaged

accounts and those that are fully taxable, marital status, and deduction status (itemized vs.

standard).

Acknowledgments
We thank three anonymous reviewers for comments and suggestions which greatly improved the article.

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