Efficient Post-retirement Asset Allocation

To examine post-retirement asset allocation, an extension to the classic Markowitz risk-return framework is suggested. Assuming that retirees make constant (real dollar) annual withdrawals from their portfolios, reward and risk measures are defined to be the mean and standard deviation of wealth remaining at end of life. Asset returns and time of death are both treated as random variables. Assuming constant lifetime asset allocation, the risk and reward measures can be evaluated analytically, and an efficient frontier can be determined. Life annuities can be used to extend the left-hand (low-risk) side of the efficient frontier. The desired level of wealth at end of life can be used to choose a desirable portfolio on the efficient frontier. The desirable portfolio strongly depends on the withdrawal rate. It is suggested (although not proven) that asset allocations strategies that vary with age do not add efficiency in this model, and asset allocation strategies that vary with wealth can add efficiency.