### Retirement Withdrawal Modeling with Actuarial Longevity and Stock Market Mean Reversion

**November 1, 2018** - Bonds, Equity Premium, Strategic Allocation

How does use of actuarial estimates of retiree longevity and empirical mean reversion of stock market returns affect estimated retirement portfolio success rates? In the October 2018 revision of his paper entitled “Joint Effect of Random Years of Longevity and Mean Reversion in Equity Returns on the Safe Withdrawal Rate in Retirement”, Donald Rosenthal presents a model of safe inflation-adjusted retirement portfolio withdrawal rates that addresses: (1) uncertainty about the number of years of retirement (rather than the commonly assumed 30 years); and, (2) mean reversion in annual U.S. stock market returns (rather than a random walk). He estimates retirement longevity as a random input based on the Social Security Administration’s 2015 Actuarial Life Table. He estimates stock market real returns and measures their mean reversion using S&P 500 Index inflation-adjusted total annual returns during 1926 through 2017. He models real bond returns using 10-year U.S. Treasury note (T-note) total annual returns during 1928 through 2017. He applies Monte Carlo simulations (3,000 trials for each scenario) to assess retirement portfolio performance by:

- Assuming an initial retirement portfolio either 100% invested in stocks or 60%/40% in stocks/T-notes (rebalanced at each year-end).
- Debiting the portfolio each year-end by a fixed, inflation-adjusted percentage of the initial amount.
- Calculating percentage of simulation trials for which the portfolio is not exhausted before death (success) and average portfolio terminal balance for successful trials.

He considers two benchmarks: (1) no stock market mean reversion (random walk) and fixed 30-year retirement; and, (2) no stock market mean reversion and actuarial estimate of retirement duration. He also runs sensitivity tests to see how changes in assumptions affect success rate. Using the specified data, *he finds that:*