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Retirement-Withdrawal Strategies Quantified

According to a new Morningstar metric, the best approach incorporates portfolio value and life expectancy.

David Blanchett, CFA, 10/19/2012

This article originally appeared in the October/November 2012 issue of MorningstarAdvisor magazine.  To subscribe, please call 1-800-384-4000. 

A significant amount of research has been devoted to determining how much a retiree can afford to withdraw from a retirement portfolio, but surprisingly little work has been done on comparing the efficiency of different types of retirement-withdrawal strategies.

Our study establishes a framework to evaluate the efficiency of several withdrawal strategies. We also use that framework, in conjunction with Monte Carlo simulations, to determine the most optimal strategies for different retirement scenarios.

To establish the framework, we introduce a new metric, the Withdrawal Efficiency Rate. WER compares the withdrawals received by a retiree who followed a specific strategy to what the retiree could have been obtained if he or she had “perfect information” at the beginning of retirement. This measure allows us to quantify the appeal of each retirement withdrawal approach. It thus creates a framework to determine how best to generate income from a portfolio.

Because maximizing retirees’ withdrawals, subject to their budget constraints, is a critical aspect of building a successful retirement plan, this framework should help both retirees and their advisors determine a more secure foundation for retirement spending. In particular, we will show that spending plans that dynamically adjust for changes in both market and mortality uncertainties outperform the more traditional approaches to retirement.

Building the New Framework
Most research on retirement-portfolio-withdrawal strategies has centered on the ability of a portfolio to maintain a constant withdrawal rate or constant dollar amount (either in real or in nominal terms) for some fixed period, such as 30 years. The annual withdrawal is commonly assumed to increase annually for inflation. Bengen (1994) is widely regarded as the first person to study the sustainable real withdrawal rates from a financial-planning perspective. He found that a “first-year withdrawal rate of 4%, followed by inflation adjusted withdrawals in subsequent years, should be safe.” This is commonly referred to as the “4% rule.”

Many experts and practitioners think that the 4% rule is rather naïve, as it ignores the dynamic nature of market and portfolio returns. More-recent research has sought to determine the optimal withdrawal strategy by dynamically adjusting to market and portfolio conditions. These approaches can offer a more realistic path for retirees to follow because they continually “adapt” to the returns of the portfolio. Up until this point, however, there has been no measure to evaluate the effectiveness of these withdrawal strategies (other than probability of failure, which has significant limitations).

Another common assumption in retirement research is the notion of a fixed retirement period, which is typically based on some life-expectancy percentile. For example, if we have a male and female couple, both age 65, the probability of either (or both) member of the couple living 35 more years, past age 100, is roughly 14%, based on the 2000 Annuity Mortality Table. If 14% was determined to be an acceptable probability of outliving the retirement period for modeling purposes, 35 years would be selected as the retirement duration. The fixed-period approach essentially assumes retirees will live through the period without dying. In other words, this approach ignores another important dynamic a retiree faces: the mortality probability. Assuming a fixed retirement period and then selecting a withdrawal rate based on that period is an incomplete methodology because this approach ignores the dynamic nature of mortality.

Possessing Perfect Information
Retirees face two unknowns when determining the best strategy to withdraw from a retirement portfolio to fund retirement: the future returns of their portfolio and the duration of the retirement period. If retirees knew their future returns and the years they will live—if they had “perfect information”—they would be able to determine the precise amount of income that could be generated from the portfolio for life, eliminating any uncertainty about a shortfall (running out of money before death) or surplus (not spending all the money during the lifetime).

As we mentioned, both a constant-withdrawal rate approach and fixed horizon planning— the most common approaches to assessing retirement withdrawal—leave out important aspects of what is relevant to a real failure or success of the retirement-spending decision. In general, determining the optimal withdrawal strategy is complicated because there are two unknown random variables—life expectancy and portfolio returns—that will have a dramatic effect on how much retirement income will be available.

Because of this, no single comparison metric has emerged to compare the competing methodologies of the different strategies. This puts the retiree and financial planner in a quandary because there are a number of strategies retirees can choose among to draw retirement income. Common rules include “draw X% of your initial savings pool,” or “draw Y% of your current, and constantly changing, account balance,” or “draw the inverse of your life expectancy.”

The new WER measure can be used to evaluate different withdrawal strategies and thus determine the optimal income maximizing strategy for a retiree. The main idea behind WER is the calculation of how well, on average, a given withdrawal strategy compares with what the retiree could have withdrawn if he or she possessed perfect information on both the portfolio’s market returns and the precise time of death. It is intuitively clear that, given a choice between two withdrawal strategies, the one that on average captures a higher percentage of what was feasible in a perfect-foresight world should be preferred.

How We Calculate WER
To calculate the WER, we first need to calculate the Sustainable Spending Rate under perfect information of market returns and life expectancy. (We use Monte Carlo simulations to generate both portfolio returns and the times of death.) For each simulation path, the SSR is the maximum constant income a retiree could have realized from the portfolio had he or she known the duration of the retirement period and annual returns as they were to be experienced in retirement, such that it depletes the portfolio to zero at time of death.

The SSR is the denominator for the WER equation; it is the constant amount that is feasible to withdraw for a given combination of market returns and death scenarios. (We disregard the bequest motive, which is secondary for most retirees.) To calculate the numerator for the WER equation, we first need to address the problem that most strategies will produce cash flows that fluctuate over time. Even a constant-withdrawal-rate approach may be subject to one dramatic fluctuation when a retiree happens to outlive his or her assets. Therefore, for each series of changing cash flows, we calculate the Certainty Equivalent Withdrawal, based on a standard Constant Relative Risk Aversion utility function:

We assume a risk-aversion coefficient— gamma—of four to better reflect the riskaverse nature of the retirement planning where failure is penalized more heavily than success. The CEW is the constant payment amount that a retiree would accept such that its utility (their sum, to be precise) would equal the utility of the actual cash flows realized on a given simulation path. The sum of all the CEW payments is smaller than the sum of all the realized cash flows—by the nature of the CRRA utility function, a retiree would give up some of the potential cash flow amount to ensure a stream of unchanging cash flows.

This process generates an equal-utility constant withdrawal amount for a given strategy (even if the strategy involves nonconstant cash flows), so the constant-amount equivalent of actual cash flows can be meaningfully compared against the constant cash flows achievable had the retiree had perfect information. Therefore, the per-path WER can be expressed as:

The metric we are going to use is the average of per-path WERs. The higher the average WER, the better the withdrawal strategy. We shall see that for plausible withdrawal strategies the average values of WER typically range between 50% and 80%.

Analyzing Five Withdrawal Strategies
For the analysis, a Monte Carlo simulation is created where life expectancies and returns are randomized. Returns are based on a lognormal return distribution. The values are based on the historical returns of the Ibbotson Associates S&P 500 and U.S. Intermediate Government Inflation Adjusted Total Return indexes. For conservative forecasting purposes, the portfolio return was reduced by 50 basis points and the standard deviations were increased by 200 basis points. Four equity allocations were considered for the analysis: 0% equities, 20% equities, 40% equities, and 60% equities; 40% equities was considered for base case scenarios. Life expectancies for males and females are based on the Annuity 2000 Mortality Table. The primary simulation will be based on the joint life expectancy of a couple, male and female, where the couple is assumed to be the same age, 65, and where the probability of each dying within a given year is independent. The retirement period is assumed to be “active” so long as either member of the couple (or both) is still living.

The five withdrawal strategies reviewed for the analysis were:

1 Constant Dollar
Otherwise known as the “4% Rule.” In the first year of retirement, a fixed amount (for example, 4%) is withdrawn from the portfolio. The dollar amount remains constant in subsequent years, adjusted only for inflation.

2 Endowment
A fixed percentage of the portfolio value is withdrawn every year.

3 Constant Failure Percentage
The withdrawal amount is based on maintaining a constant probability of failure over the expected fixed retirement period, so as to not bring the portfolio to ruin.

4 Required Minimum Distribution Method
The IRS method: Withdrawal amount is determined by annually dividing 1 by remaining life expectancy.

5 Mortality Updating Failure
Amount withdrawn is determined every year based on two variables: remaining life expectancy and portfolio value.

And the Winner Is…
Using WER, we contrasted the efficiency of the five withdrawal strategies. The results are shown in Exhibit 1. Among the strategies and for each of the four different portfolios, the fifth strategy, the Mortality Updating Failure approach, was the optimal withdrawal strategy. For three out of four equity allocations, the Constant Dollar strategy—the 4% rule— was the worst. The RMD Method was better than the Constant Dollar and Endowment approaches in equity allocations up to 40%.

The results make intuitive sense. Because market returns and mortality are stochastic variables, an approach that incorporates both into the withdrawal strategy should be expected to produce results that dominate strategies that focus on one variable, or none.

Additional Scenarios
The primary test case for this analysis was a male and female couple, both age 65. Tests for other age combinations of retired couples and for single retirees of various ages confirm this ranking of the efficiency of different withdrawal strategies. The Mortality Updating Failure approach was the most efficient approach for retirees ranging from age 60 to age 80 for males, females, and joint couples (male and female assumed to be the same age). Constant Dollar was the least efficient. The difference in the efficiency of the approaches, however, decreased at older ages (Exhibit 2).

To guide investors and advisors on what “levers” they should use for the Mortality Updating Failure approach, we reviewed the results for the different test combinations (male/female/joint, and ages 60/65/70/75/80). For couples 70 and younger, we suggest that they use a distribution period in which they have a 10% chance of outliving. For couples older than 70, we suggest a probability of 25%. Once that period is determined, retirees should generally withdraw an amount that has a 50% probability of failure.

The initial withdrawal percentages as a percentage of the portfolio balance for the 40% equity portfolios are included in Exhibit 3.

A Better Way
This paper introduced a framework to determine the efficiency of withdrawal strategies based on “perfect information.” WER measures the percentage of what was feasible given perfect foresight that the withdrawal strategy in question captures. We tested WER across five strategies through simulation analysis. The results suggest that the method employed by many practitioners, in which a constant real-dollar amount is withdrawn from the portfolio until it “fails,” was often the least efficient approach to maximizing lifetime income for a retiree.

The optimal withdrawal strategy points to approaches that incorporate mortality probability. In our study, the projected distribution period was updated based on the mortality experience of the retirees, and the withdrawal percentage was determined based on maintaining constant probability of failure. This approach best replicates how a financial planner should determine the available income from a portfolio for each year during retirement. As a practical matter, for retirees who can’t replicate these results, the RMD Method emerges as a reasonable alternative to the more common Constant Dollar and Endowment strategies.

 

This article is based on a longer research paper by the authors, titled “Optimal Withdrawal Strategy for Retirement Income Portfolios,” which is available on the Morningstar corporate website.

References
Bengen, William P. (1994), “Determining Withdrawal Rates Using Historical Data,” Journal of Financial Planning, vol. 7, no. 1 (January): 14–24.

Milevsky, M. A. and Robinson, C. (2005), “A Sustainable Spending Rate without Simulation,” Financial Analysts Journal, vol. 61, No.6.

Williams, Duncan and Finke, Michael S. (2011), “Determining Optimal Withdrawal Rates: An Economic Approach,” The Retirement Management Journal, vol. 1, no.2.

David Blanchett, CFA is Director of Retirement Research with Morningstar Investment Management.  

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