Optimal Consumption and Portfolio Choice for Retirees

Abstract:     
I solve the optimal consumption and portfolio choice problem of a retiree with recursive preferences and bequest motive. The retiree is endowed with both liquid assets and pre-annuitized wealth in Social Security and/or defined benefit pension plans. He chooses from an investment menu including an equity index, a risk-free asset, a private variable life annuity, and term life insurance with borrowing and short-sales constraints. Due to adverse selection, annuitization is irreversible, and the retiree's fraction of pre-annuitized wealth is an important endowment characteristic that determines his optimal consumption profile, equity-bond mix, and annuitization schedule. In the model the retiree can annuitize his liquid wealth anytime during his retirement life, and the option to defer annuitization can be valuable. Unlike fixed annuity, variable annuity allows the retiree to hedge longevity risk and earn an equity premium at the same time, and the gain is substantial for a retiree with relatively low risk aversion. Given the existing Social Security benefits, the irreversibility of future life annuity purchase incurs little utility loss. However, the utility loss due to the irreversibility of existing Social Security benefits can be big. I show that a transition from the current pay-as-you-go Social Security system to a personal investment-based system benefits retirees with high fraction of pre-annuitized wealth the most because the flexibility of choosing the optimal equity-bond mix for one's annuity portfolio reduces the cost of over-annuitization. Purchasing life insurance can also reduce the adverse effect of over-annuitization. However, it is effective only for impatient retirees with low Elasticity of Intergenerational Substitution.

Keywords: Portfolio choice, Life annuity, Social Security

JEL Classifications: G11, H55, J26, O16

Working Paper Series