Optimal Asset Allocation and The Real Option to Delay Annuitization: It’s Not Now-or-Never

Abstract

Asset allocation and consumption towards the end of the life cycle is complicated by the uncertainty associated with the length of life. Although this risk can be hedged with life annuities, empirical evidence suggests that voluntary annuitization amongst the public is not very common, nor is it well understood. This paper develops a normative model of when, and if, one should purchase an immediate life annuity. This problem is particularly relevant given the increasing number of Defined Contribution pension plans in the U.S – for which participants must make this decision – and the corresponding trend away from Defined Benefit guarantees. Specifically, our main qualitative argument is that there is a real option – akin to the corporate finance usage of the word – embedded in the decision to annuitize. A life annuity can be viewed as a project with a positive net present value. However, quite distinct from a fixed-income bond or period certain annuity, once purchased, a life annuity can never be sold, reversed, or exchanged. Its purchase is final because of the severe moral hazard involved in trying to terminate a life-contingent claim. We use standard continuous-time technology to solve the optimal asset allocation and annuitization timing problem. We then define the value of the real option to defer annuitization (RODA) as the compensating utility loss from being unable to behave optimally. By using reasonable capital market and actuarial parameters, we estimate that the real option to defer annuitization is quite valuable until the mid-70s or mid-80s. Of course, the precise values depend on one’s gender, risk aversion, and subjective health assessment. Finally, we show that low-cost variable immediate annuities, which are currently not widely available, greatly reduce the option value to wait and create substantial welfare gains. This might explain the large number of TIAA-CREF participants who rightfully choose to annuitize their DC pension plan, as a result of the availability of both fixed and variable payments in the payout stage. JEL Classification: J26; G11

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