Joint Effect of Random Years of Longevity and Mean Reversion in Equity Returns on the Safe Withdrawal Rate in Retirement

23 Pages Posted: 7 Oct 2018 Last revised: 16 Oct 2018

Date Written: September 29, 2018


Using historical data on inflation-adjusted total equity returns (price change plus dividend) from the S&P 500 from 1926 to 2017, this paper develops a simulation-based model to determine the safe, inflation-adjusted withdrawal rate from a portfolio of assets. The model, named the Realistic Retirement Simulator (RRS), improves upon other simulation models by directly addressing two factors that significantly affect the safe withdrawal rate: (1) uncertainty about the number of years of retirement, i.e., at what age will the retiree die; and (2) mean reversion in equity returns. RRS models the number of years in retirement as a random factor based on the Social Security Administration’s 2015 Actuarial Life Table. The mean-reverting stock return model within RRS is statically calibrated to the 1926 to 2017 S&P 500 data. With these two key factors addressed and assuming future equity returns follow the historical record, RRS shows that a 65-year-old male retiree can withdraw 6% of the starting portfolio balance each year from a 100% stock portfolio with a 90% success rate; a 4% withdrawal rate is 99% successful. A simulation model that does not address these two key factors—and the author is not aware of single model that addresses both factors—shows that a 4% withdrawal rate results in a 90% success rate for a retirement lasting 30 years. At the 90% success level, about half of the increase from 4% to 6% comes from treating the length of the retirement as a random factor and other half comes from the mean-reverting model. Many scenarios are run to show how the success rate changes when RRS input assumptions are changed, e.g., age of retiree or stock/bond mix of retiree’s portfolio. Of particular importance is the assumption that future equity returns will repeat the historical record. If the future, long-run trend for equity returns is a 4% compound annual growth rate (CAGR) instead of the 6.93% observed in the historical data, RRS shows that a withdrawal rate of 4% has a success rate of 95%. Regardless of the assumption about future equity returns, directly modeling uncertainty in the length of retirement and mean reversion in equity returns results in more accurate and higher estimates of the safe withdrawal rates compared to models that do not directly address these factors.

Keywords: Safe Withdrawal Rate, Retirement, Mean Reversion, Stock Market

JEL Classification: G11, C53

Suggested Citation

Rosenthal, Donald, Joint Effect of Random Years of Longevity and Mean Reversion in Equity Returns on the Safe Withdrawal Rate in Retirement (September 29, 2018). Available at SSRN: or

Donald Rosenthal (Contact Author)

DHR Risk Consulting, LLC ( email )

United States

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