Annuitization and Asset Allocation with HARA Utlity
A new explanation for the well-known reluctance of retirees to buy life annuities is due to Milevsky and Young (2002, 2003). Specifically, the decision to buy longevity insurance is largely irreversible, so that the real option to delay annuitization generally has value. Milevsky and Young analyticaly identify and numerically estimate the RODA in a setting of constant relative risk aversion (CRRA). This paper extends the analysis of Milevsky and Young to the case of hyperbolic absolute risk aversion (HARA),the simplest representation of a consumption habit.The formula for the optimal timing of annuitization ias surprisingly simple, but yields only a myopic solution, that is, the precise date of annuitization cannot be ascertained in advance. The effect of increasing the subsistence consumption rate on the timing of annuity purchase is similar to the effect of increasing the curvature function of the utility function. As in the CRRA case studied by Milevsky and Young, delayed annuitization is associated with optimistic forward-looking estimates of the Sharpe ratio.
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