Measuring and Controlling Shortfall Risk in Retirement

Abstract

A key challenge for retired investors is determining the stock-bond asset allocation that, for a given spending rate, provides an acceptable probability of shortfall—having real wealth drop below a specified floor during the investor's lifetime. Standard portfolio analysis yields the well known tradeoff between risk and return described by the Markowitz frontier. For retirement planning, we reconceptualize this as a tradeoff between shortfall probability (risk) and the median value of terminal wealth (return). For specified assumptions, there is a stock-bond asset allocation that minimizes shortfall risk. Portfolios with more stocks increase the median values of terminal wealth, but at the expense of higher shortfall risk. Portfolios with fewer stocks are inferior in that they decrease the median value of terminal wealth and increase shortfall risk. We find that for a variety of plausible assumptions about asset returns, investment strategies, and what constitutes a shortfall, the minimum-risk portfolio generally has between 50 and 70% stocks.