Spending Retirement on Planet Vulcan: The Impact of Longevity Risk Aversion on Optimal Withdrawal Rates (corrected July 2011)

Recommendations from the media and financial planners regarding retirement spending rates deviate considerably from utility maximization models. This study argues that wealth managers should advocate dynamic spending in proportion to survival probabilities, adjusted up for exogenous pension income and down for longevity risk aversion. In our study, we attempted to derive, analyze, and explain the optimal retirement spending policy for a utility-maximizing consumer facing (only) a stochastic lifetime. We deliberately ignored financial market risk by assuming that all investment assets are allocated to risk-free bonds (e.g., Treasury Inflation-Protected Securities [TIPS]). We made this simplifying assumption in order to focus attention on the role of longevity risk aversion in determining optimal consumption and spending rates during a retirement period of stochastic length.Indeed, the impact of financial risk aversion on optimal asset allocation has been the subject of many studies and is intuitively well understood. In contrast, the impact of longevity risk aversion on retirement spending rates has not received as much attention, nor are most practitioners even familiar with the concept. More than 75 million Baby Boomers are (still) hoping to retire one day—with their own stochastic remaining life spans—and will likely demand advice from their wealth managers on this very issue.Although neither our framework nor our mathematical solution is original—they can be traced back almost 80 years—we believe that the insights from a normative life-cycle model are worth emphasizing in the current environment, which has grown jaded by economic models and their prescriptions. Our pedagogical objective was to contrast the optimal (i.e., utility-maximizing) retirement spending policy with popular recommendations offered by the investment media and financial planners.Our working hypothesis was that counseling retirees to set initial spending from investable wealth at a constant inflation-adjusted rate (e.g., the widely popular 4 percent rule) is consistent with life-cycle consumption smoothing only under a very limited set of implausible preference parameters—that is, there is no universally optimal or safe retirement spending rate. Rather, the optimal forward-looking behavior in the face of personal longevity risk is to consume in proportion to survival probabilities—adjusted upward for pension income and downward for longevity risk aversion—as opposed to blindly withdrawing constant income for life. This framework also allows one to illustrate the (beneficial) impact of pension income annuities on the optimal plan.We believe that 21st century wealth managers who have grown accustomed to focusing their discussions with clients on the prism of risk and return should advocate dynamic spending policies in this manner. Thus, the intent of our study was not to dismiss or belittle widely used rules of thumb but rather to create a common language and help improve the dialogue between financial economists and the financial planning community. The stakes are simply too high to allow yet another naive rule of thumb to take hold in these complex and uncertain environments.

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