A Mean-Variance Approach to Withdrawal Rate Management: Theory and Simulation

Abstract

Withdrawal rate management of retirement portfolios (decumulation) is explored in a traditional mean-variance context. The paper demonstrates that improvements in the composition of portfolios and in the management of withdrawal rates can both be thought of as increasing the opportunity cost price of annuitizing and reducing the optimal risk of portfolios. Increases in age are shown to have three separate components: decreasing remaining expected lifespan; decreasing variability of remaining lifespan; and increasing variability of returns over remaining holding period. The difficulty of employing a mean-variance approach when a portion of the variation in returns is absorbed by variation in the ending portfolio is noted.

The second portion of the paper demonstrates these principles with simulation analysis. A zero-tolerance (MAXSAFE) approach, as proposed by Bengen, is combined with a multiple-factor withdrawal management strategy, as developed by Stout and Mitchell, to generate a series of risk-return frontiers based on data from 1926-2008.

Improvements in risk-return relationships are found using more restrictive withdrawal rate management approaches than previously reported in the literature. Restricting withdrawal rates when retirees no longer have 1.45 times the present value of their expected withdrawals combined with limitations on withdrawal rate increases allow most retirees to experience average withdrawal rates in excess of 5.5% with average withdrawal rates in excess of 6% and with only a .1% chance of ruin before death.

Keywords: Retirement Planning, Withdrawal Rate Management

JEL Classification: G11, C15, I12, J26