Coping with Sequence Risk: How Variable Withdrawal and Annuitization Improve Retirement Outcomes
Both the level and the sequence of investment returns will have a big impact on retirement outcomes. Poor returns during the early years of retirement are bad news. However, the particular withdrawal strategy used affects sequence risk, and an approach where withdrawals are variable and respond to portfolio performance can improve retirement outcomes. I’ll examine the evidence and then use my own modeling to show how a strategy that combines variable withdrawals with partial annuitization using a singlepremium immediate annuity (SPIA) maximizes the cash available for consumption.
Key aspects
To gain a better understanding of sequence risk, I strongly recommend a series of five posts produced in 2013 by Dirk Cotton on his “Retirement Cafe” blog. The third post, “Sequence of Returns Risk and Payouts” delves into the impact of switching from fixed withdrawals set at the beginning of retirement to a variable approach where annual withdrawals are based on current portfolio values. The classic example of a fixed strategy is the 4% rule, where withdrawals are set at 4% of the initial portfolio and adjusted each year for inflation (i.e., fixed in real terms). The particular variable approach that Cotton used for comparison is known as the endowment method, where each year’s withdrawal is X% of the current portfolio.
Cotton developed an example where he took six recent annual stock market returns, rearranged them into 720 possible sequences, and then tested a fixed withdrawal strategy ($25,000 per year from an initial $1 million portfolio) on each of the 720 sequences. He showed that, even though the same six returns were used in all 720, the terminal values at the end of six years differed considerably. This is the essence of sequence risk – same returns, different sequences but different outcomes.
He then used the same 720 possible sequences, but changed to a withdrawal approach where annual withdrawals were 2.5% of the existing portfolio. He demonstrated the surprising result that, even though the portfolio values followed a variety of different paths over the six years, all 720 ended up at exactly the same amount. A quick reaction to this result might be that variable withdrawals eliminated sequence risk – but, as Cotton has illustrated, there is more to the story.
Switching to variable withdrawals does, indeed, dramatically reduce the variability of terminal or bequest values. However, it does this by adjusting the withdrawals. A “bad” sequence – poor returns in the early retirement years – will generate lower average withdrawals than a “good” sequence. So changing from fixed to variable withdrawals doesn’t eliminate sequence risk; it transforms a bequest risk into a payout risk.
But then we are left with the question, “Is it better to take bequest risk or payout risk?” For clients who are wealthy enough it may simply be a matter of priorities; do they care more about consumption or the size of their future bequest? However, for more constrained clients, analysis of potential outcomes is required.
Monte Carlo analysis
A popular research approach for testing the sustainability of retirement withdrawal strategies involves using Monte Carlo simulations. The random generation of annual investment returns will produce some “bad” sequences, some “good” sequences, and others that are more average. This is the approach I will use to test fixed versus variable withdrawal strategies. However, to provide supplementary information on sequence risk, I’ll also run Monte Carlo simulations where I tilt the return generation toward good and bad sequences, but keep the lifetime average returns about the same.
Other key aspects of my modeling approach are:
 The assumption of lowerthanhistorical returns for both stocks and bonds
 Stochastic mortality to generate a randomized year of death for each Monte Carlo run rather than assuming a fixed retirement period
The modeling approach and assumptions are described in detail in the Appendix.
The particular example I use is for a 65yearold female with a remaining life expectancy of 25 years. I assume she has $1 million in retirement savings allocated 50/50 stock/bond and will be receiving $30,000 per year from Social Security. I assume her essential living expenses are $50,000 per year, so she needs to generate at least an additional $20,000 per year from her savings portfolio to avoid plan failure. Her primary goal is to generate retirement income; leaving a bequest is of secondary importance. The analysis is pretax, and all dollar figures are in 2017 real dollars.
Variable versus fixed withdrawals
The chart below compares performance measures for the 4% rule (fixed) and an endowment approach (variable) based on withdrawing 4.9% of the portfolio at the beginning of each year. I highlight in bold what I consider to be the three key measures of outcomes. I show the comparison for normal sequences using the standard Monte Carlo approach as well as where the return generation has been tilted toward bad and good sequences.
Sequence of returns analysis 

Withdrawal method 
Average consumption 
Average CE consumption 
Average bequest 
Average shortfall 
Failure percent 
Normal sequences 

4% Rule 
$67,534 
$63,201 
$517,962 
$40,239 
28.2% 
4.9% Endowment 
$67,484 
$64,582 
$517,787 
$3,331 
3.7% 
Bad sequences 

4% Rule 
$65,967 
$59,822 
$378,194 
$64,580 
39.3% 
4.9% Endowment 
$63,791 
$61,092 
$493,929 
$6,163 
5.9% 
Good sequences 

4% Rule 
$68,550 
$65,607 
$670,272 
$24,049 
20.2% 
4.9% Endowment 
$71,641 
$68,029 
$544,510 
$2,413 
3.2% 
Average bequests are essentially the same for the two withdrawal strategies. What is dramatically different between the two strategies is the average shortfall, which measures the combined impact of the percentage of Monte Carlo simulations that fail to cover essential expenses and the dollar magnitude of such failures. The shortfalls are roughly 10times worse under the 4% rule, and this is true for normal, good, and bad sequences. What’s happening here is that the 4% rule is generating retirement withdrawals that ignore what’s happening with the underlying portfolio. So if things are going badly, withdrawals continue at the same real level until the portfolio is depleted. With the endowment withdrawals, when things go so badly the dollar amount of withdrawals is reduced, there is less lateinlife shock.
Based on these measures, I reach the same conclusion as Cotton that variable beat fixed withdrawals. There are other takeaways from the chart.
The good and bad sequences were calibrated to produce the same average lifetime returns, but there is a clear difference in outcomes for bad sequences with lower early returns than for good sequences. This is simply another way of demonstrating that for retirement outcomes both the level of returns and the sequence matter.
The general superiority of variable over fixed withdrawals applies regardless of the type of sequence – normal, bad, or good. The only exception is in the bequests where, as Cotton also demonstrated, variable withdrawals produce a tighter distribution of bequests. As a result, the good sequences average bequest is less for the endowment approach.
Cotton noted that the variable approach resulted in more yeartoyear variability in withdrawals. Although not shown in the chart, I measured variability – for the normal sequences it was 0.6% for the 4% rule and 4.6% for the endowment approach. One might wonder why the 4% rule with steadier withdrawals produced an inferior CE. The answer is that 28.2% of the Monte Carlo simulations ran out of money, causing a steady $70,000 of annual real consumption ($30,000 plus 4% of $1 million) to drop precipitously to $30,000. This resulted in a greater CE penalty than endowment withdrawals bouncing around from yeartoyear in a narrower range.
Improving on the endowment method
Lifecycle economics is allied with the concept of utility maximization via consumption smoothing. For retirement withdrawals this means spreading consumption over the expected remaining lifetime, or in very approximate terms determining consumption by dividing savings by expected remaining life. Since expected remaining life shortens as one ages, this implies a path of increasing withdrawal rates, rather than the level percentage under the endowment method. One can attempt exact calculations using an appropriate actuarial table and assumed investment returns, or a simpler approach is to rely on the IRS requires minimum distribution (RMD) tables. Utilizing the table that applies for most individuals, the withdrawal rate is 3.65% at age 70, 5.35% at age 80, 8.77% at age 90 and tops out at over 50% at extremely advanced ages.
In the following chart, I compare outcomes under endowment and RMD approaches.
Sequence of returns analysis 

Withdrawal method 
Average consumption 
Average CE consumption 
Average bequest 
Average shortfall 
Failure percent 
Normal sequences 

5.2% Endowment 
$68,583 
$65,238 
$484,015 
$4,498 
5.0% 
RMDs 
$68,636 
$65,985 
$462,818 
$2,251 
3.4% 
Bad sequences 

5.2% Endowment 
$64,882 
$61,803 
$460,688 
$6,550 
6.2% 
RMDs 
$64,721 
$62,527 
$430,678 
$3,278 
3.8% 
Good sequences 

5.2% Endowment 
$72,914 
$68,862 
$512,729 
$2,720 
4.3% 
RMDs 
$73,435 
$69,622 
$506,288 
$2,267 
4.1% 
For this comparison I raised the endowment percentage to 5.2% to roughly match average consumption under normal sequences. The results we see are a slight increase in CEs and slight decreases in average bequests – favorable if the retiree’s main focus is consumption. But the biggest differences are in the average shortfalls and these strongly favor RMDs, particularly for normal and bad sequences. (I should note that this is a single test with one endowment percentage and one asset allocation, so further testing would be needed for a full comparison of RMDs versus the endowment approach.)
Substitution of SPIAs for bonds
In the chart below, I show the results of purchasing an inflationadjusted SPIA at age 65 to produce $20,000 of annual income to fill the gap between Social Security and essential expenses. Based on pricing from the annuity information service CANNEX, such a SPIA would cost $468,384, and doing a fixed income substitution of the SPIA for bonds would use up most of the 50% bond allocation on the $1 million of savings. RMDs were applied to remaining savings.
Sequence of returns analysis 

Withdrawal method 
Average consumption 
Average CE consumption 
Average bequest 
Average shortfall 
Failure percent 
Normal sequences 

RMDs 
$68,636 
$65,985 
$462,818 
$2,251 
3.4% 
Include SPIA 
$77,196 
$72,855 
$390,202 
$0 
0.0% 
Bad sequences 

RMDs 
$64,721 
$62,527 
$430,687 
$3,278 
3.8% 
Include SPIA 
$72,297 
$68,918 
$350,504 
$0 
0.0% 
Good sequences 

RMDs 
$73,435 
$69,622 
$506,288 
$2,267 
4.1% 
Include SPIA 
$84,305 
$77,412 
$452,847 
$0 
0.0% 
With the SPIA purchase we significantly increase consumption and CEs while bringing down average bequests. Again, if the client’s primary focus is consumption, this is a positive change. We are able to push bequest money into consumption and accomplish this while eliminating the negative outcomes. We get these positive results regardless of the sequence of return scenario.
Final word
Besides demonstrating how variable withdrawals can mitigate sequence of returns risk, I’ve shown that the choice of variable approach and annuitization can make a significant improvement. There a lot of variable approaches that researchers have proposed, so it would be worth further testing, particularly under bad sequences, to see which variable approaches perform best.
Joe Tomlinson, an actuary and financial planner, is managing director of Tomlinson Financial Planning, LLC in Greenville, Maine. Most of his current work involves research and writing on financial planning and investment topics.
Appendix
This modeling is based on a 65yearold retired female with a remaining life expectancy of 25 years and $1 million in savings that she can dedicate to generating retirement income. Her basic living expenses are $50,000 per year, increasing with inflation, and she will receive an inflationadjusted $30,000 annually from Social Security. She will utilize withdrawals from savings to cover the gap between basic living expenses and guaranteed lifetime income and additional withdrawals can be used for discretionary spending. The analysis is pretax.
Investment assumptions: For the Monte Carlo analysis, stocks are assumed to earn an arithmetic average real return of 5% with a 20% standard deviation, and bonds (TIPS) are assumed to earn 0% with a 7% standard deviation. These returns are significantly lower than historical averages, reflecting current interest rates and a lowerthanhistorical equity risk premium. The modeling assumes a 50/50 stock/bond mix, and allocations are rebalanced annually to maintain this allocation.
Modeling sequence of returns risk: I compare “bad” sequences to “good” sequences. I create bad sequences by subtracting 5% from the Monte Carlo generated firstyear stock return and grade this reduction to zero at half of life expectancy and then grade up from there to a 5% addition at life expectancy. The good sequences are the mirror image. The basic idea was to create bad and good sequences that produced similar average returns over expected lifetimes, but with markedly different tilts.
Withdrawal methods: I test following approaches to generate funds for retirement consumption:

 The venerable 4% rule, where the initial annual withdrawal is set at 4% of the initial savings portfolio
 An approach with annual withdrawals equal to 4.9% of the current portfolio (with the 4.9% chosen to produce roughly the same lifetime average annual withdrawals as the 4% rule)
 An approach with annual withdrawals equal to 5.2% of the current portfolio (with the 5.2% chosen to produce roughly the same lifetime average annual withdrawals as IRS required minimum distributionsRMDs)
 An approach where withdrawals equal RMDs (and withdrawals prior to age 70 at the age70 percentage – 3.65%)
Modeling methodology: For each retirement income approach that I model, I generate 10,000 simulated retirements. Withdrawals each year are determined based on the particular withdrawal approach being modeled. Investment returns for each year are generated randomly based on average return and standard deviation characteristics. The date of death for each of the 10,000 simulations is randomly determined based on the Gompertz mortality function.
Although methods that determine withdrawals as a percentage of the current portfolio balance will never completely deplete savings, I use a slightly different approach. If calculated consumption is not sufficient to cover basic living expenses but there are remaining savings, I take from the savings to cover the expense gap until savings are depleted. This way I can determine the percentage of simulations where savings are depleted.
Performance measures
Average consumption: Consumption equals Social Security income ($30,000) plus annual withdrawals and SPIA payments, if any. For each of the 10,000 simulations, I compute the lifetime average of the annual consumption amounts and then take the average of these averages.
Average CE consumption: This certainty equivalent (CE) measure is based on an economic utility calculation that converts variable yearbyyear consumption into a level amount that the recipient would view as equivalent. The CE amount depends on what economists refer to as the recipient’s level of risk aversion. For example, if annual consumption bounced around randomly between $60,000 and $80,000, an individual with low risk aversion would demand close to $70,000 if offered a trade to level consumption. A highly risk averse individual would be willing to accept an amount closer to $60,000.
For this analysis, I have assumed a medium aversion to variable consumption – an individual would be willing to accept annual consumption of a level $66,600 in trade for consumption that bounced around randomly between $60,000 and $80,000. This translates to a risk aversion coefficient of 5 based on a CRRA utility function of the form U = (1/(1RA))*C^(1RA) to convert consumption into utility. For each of the 10,000 Monte Carlo iterations, I convert each year’s consumption into utility, average the utilities based on the number of years in each iteration and convert to a CE using the inverse of the utility function.
Average bequest: Each of the 10,000 simulations produces a remaining savings at time of death, which can be zero or a positive amount. I show the average of the 10,000 bequest amounts.
Average shortfall: For each simulation that “fails,” I calculate the amount of additional funds that would have been needed to pay for basic living expenses until the end of life. The sum of these amounts is divided by 10,000 to determine an average shortfall for all the simulations (including those with zero shortfall). This is a more useful failure measure than failure percentage, because it incorporates both frequency and magnitude. However, I also show failure percentage because it is a more commonly used measure.
Failure percentage: This represents the percentage of the 10,000 simulations where savings are insufficient to fully pay for the assumed $50,000 of basic living expenses.