The Best Approach to Adjustable Retirement Withdrawals

The modeling

I base this example on a 65-year-old female with a 25-year life expectancy and $1 million in retirement savings. Her basic living expenses are $50,000 increasing with inflation each year, and she will receive $35,000 as annual Social Security and other lifetime income. She needs to fill a gap of $15,000 in real dollars to pay for basic living expenses; additional withdrawals can be used for discretionary spending. I limit her investments to stocks and bonds to keep the analysis manageable – no annuities, although annuities could be used to improve results further. The analysis is pre-tax and future dollar figures are discounted for inflation and stated in real terms.

I start with a portfolio invested 50% in stocks, apply the ARVA method for determining each year’s withdrawals, do 10,000 Monte Carlo retirement simulations and assess retirement performance using a number of different measures related to income generated, bequests and plan failure.

Next I run simulations where I apply smoothing to the ARVA approach. First I keep the 50% stock portfolio, calculate ARVA withdrawals and then adjust the withdrawals to reduce the yearly change by 40%. Then I test the Waring/Siegel recommended approach to reduce withdrawal volatility by reducing the stock allocation to 30%, which has the effect of reducing the portfolio standard deviation by 40%. The chart below shows the outcomes.

Smoothing versus reduced stock allocation--Monte Carlo

Source: Author’s calculations

The top two rows are upside measures, and 40% smoothing produces better outcomes than reducing the stock allocation. The next two rows relate to plan failure, and the more meaningful metric is the average shortfall because it incorporates both the probability and magnitude of failure. This measure shows some deterioration when we move away from the base case, slightly more for 40% smoothing. The consumption change percent measures the average absolute value of changes in consumption expressed as a percentage of total consumption. We see a reduction in consumption volatility when we apply smoothing and a slightly greater reduction by reducing the stock allocation.

The CE (certainty equivalent) measure applies an economic utility calculation that converts variable year-by-year consumption into a level amount that the recipient would view as equivalent. Although this measure is the most complicated to calculate and explain (see appendix), it is the most comprehensive performance measure because it recognizes three income measures: level, volatility and sustainability. We see that the smoothing approach in the middle column wins out over the stock-reduction approach in the right column.

In determining an overall evaluation of income generation, pay attention to both the CE consumption and consumption-change percent. The latter measure places additional emphasis on year-to-year consumption change, whereas the CE measure assumes each year’s consumption utility is independent of prior consumption. 

Guyton/Klinger

In this section I test the Guyton/Klinger decision rules approach and compare it to the smoothed version of ARVA. I use the same 50% stock allocation.

Guyton/Klinger smoothing, 5.25% initial withdrawal rate

Source: Author’s calculations

The middle column of this chart shows that the Guyton/Klinger approach generates lower average consumption but higher bequest values than the smoothed ARVA method. The shortfall measure is slightly worse for Guyton/Klinger, but the consumption volatility improves. The CE consumption measure, which combines the key income aspects, falls slightly below smoothed ARVA. I chose the 5.25% initial withdrawal rate for the Guyton/Klinger test because that generated the highest CE consumption.

In the rightmost column I show the results for a fixed 5.25% withdrawal rate, and this demonstrates the beneficial impact of applying the Guyton/Klinger decision rules. Without the decision rules, the failure outcomes turn nightmarish. Consumption volatility is low, but that sends a false signal. Consumption stays level at $87,500 until the plans fail in more than half of the simulations. It then drops to $35,000 and remains at that level until death.  The impact of the failures does get picked up in the CE consumption measure.

Using historical returns

As an additional test, I did the same analysis as before, but switched from randomly generated returns (Monte Carlo simulations) to historical returns. I wanted to test the impacts of historical year-to-year correlations in stock and bond returns and the interaction between the two asset classes.

I ran 10,000 simulations with returns obtained by “bootstrapping” – building retirement return sequences by randomly selecting two 20-year blocks of returns for each simulation. I also scaled down the returns to produce the same stock and bond average returns used for the randomly generated returns in the earlier simulations.

Historical data--bootstrapped returns

Source: Author’s calculations, Ibbotson®

The results for the three methods tested are remarkably close to the results with randomly generated returns, with a slight worsening of the failure measures. Incorporating historical return relationships didn’t significantly change the outcomes.

Conclusion

This analysis has been based on a single client scenario and one set of investment assumptions, so caution needs to be applied before stating general conclusions. However, the results caution against following the Waring/Siegel advice and rejecting smoothing. The ARVA approach that they recommend produces excellent results in generating retirement income, but adding smoothing further improves the approach. The analysis of the Guyton/Klinger approach also indicates that methods that anchor to an initial withdrawal rate may also produce good results. There is more work to be done to sort out retirement income strategies.

Joe Tomlinson, an actuary and financial planner, is managing director of Tomlinson Financial Planning, LLC in Greenville, Maine. His practice focuses on retirement planning. He also does research and writing on financial planning and investment topics.
 

Appendix

Client assumptions: 65-year-old 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 $20,000 annually from Social Security and an additional inflation-adjusted $15,000 from a source such as a pension or a SPIA. She will utilize withdrawals from savings to cover the $15,000 gap between basic living expenses and guaranteed lifetime income, and take additional withdrawals for discretionary spending. Her goals are to generate sustainable retirement income and maintain liquidity and flexibility (not a candidate for additional annuity purchase). Leaving a bequest is of secondary importance.   

Investment assumptions: For the Monte Carlo analysis in the first part of the article, 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 zero standard deviation (bond ladder approach). These returns are significantly lower than historical averages, reflecting current interest rates and a lower-than-historical equity risk premium.

For the historical return analysis later in the article, I use a “bootstrapping” technique where I build retirement return sequences by randomly selecting blocks of 20-year stock and bond real returns from Ibbotson® data for large-cap stocks and intermediate-term government bonds. Again, I run 10,000 simulations. This approach captures historical serial correlation (if any) within each of the two asset classes and correlation between stock and bonds. (Bonds now behave more like a TIPS fund than a TIPS ladder.) I also scale back stock and bond returns in the historical data to match the average real returns assumed for the Monte Carlo simulations.

In both approaches, allocations are rebalanced annually to maintain the initial allocation.

The ARVA method: This approach, developed by Waring and Siegel, can be described based on the Excel PMT function. The maximum allowable withdrawal is recalculated each year as a function of the current portfolio balance, estimated remaining longevity, and expected investment returns. I change the method slightly from that described by the authors, by updating the estimated remaining longevity each year based on a mortality table. For a return assumption, I use my estimated TIPS yield, to be conservative, even though my assumed portfolios contain both stocks and TIPS. The key difference between the ARVA method and traditional approaches like the 4% rule is that ARVA adjusts withdrawals each year to reflect emerging investment experience, whereas traditional approaches determine the pattern of future withdrawals at the start of retirement. 

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 retirement income approach being modeled. Investment returns for each year are generated randomly based on average return and standard deviation characteristics or derived from historical data if bootstrapping is used. The date of death for each of the 10,000 simulations is randomly determined based on a Gompertz mortality function calibrated to a life expectancy of age 90 for a 65-year-old.

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 guaranteed income ($35,000) plus annual withdrawals. 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 bequest: Each of the 10,000 simulations produces a remaining savings at time of death, which can be zero or a positive amount. I calculate the average of the 10,000 bequest amounts.

Failure percentage: Represents the percentage of the 10,000 simulations where savings are insufficient to fully pay for the assumed $50,000 of basic living expenses.

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, but I also show failure percentage because it is a more commonly used measure.

Consumption change percent: This measures the degree of smoothing by calculating the absolute value of the change in consumption from year to year, averaging these for each of the 10,000 simulations and then averaging these averages.

Average CE consumption: This certainty equivalent (CE) measure is based on an economic utility calculation that converts variable year-by-year 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 $50,000 and $70,000, an individual with low risk aversion would demand close to $60,000 if offered a trade to level consumption. A highly risk averse individual would be willing to accept an amount closer to $50,000.

For this analysis, I have assumed a medium/high aversion to variable consumption – that an individual would be willing to accept annual consumption of a level $55,500 in trade for consumption that bounced around randomly between $50,000 and $70,000. This translates to a risk aversion coefficient of 6 based on a CRRA utility function of the form U = (1/(1-RA))*C^(1-RA) 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.

Guyton/Klinger decision rules: These authors start with a fixed initial withdrawal rate similar to the classic 4% rule, but vary future withdrawals to respond to future investment experience. However, they use the initial withdrawal rate as an anchor when making future adjustments. They set outer boundaries for withdrawals based on two rules: the “prosperity rule” and the “capital preservation rule.” The “prosperity rule” increases withdrawals by 10% in any year that the current withdrawal rate falls to 20% less than its initial level. The “capital preservation rule” applies during the first 15 years of retirement and cuts withdrawals by 10% if the current withdrawal rate rises to be more than 20% above its initial level. Within these boundaries, the decision rules take away the annual planned inflation adjustment if the prior year’s investment return was negative and the withdrawal rate based on the current portfolio level is higher than the initial withdrawal rate. Otherwise withdrawals increase with inflation each year as under the 4% (or X %) rule.    

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