Optimal Annuitization with Background Risk and Equity Exposure During Retirement

Abstract

We analyze annuity demand in a realistic life-cycle model in which we optimize over consumption and asset allocation. We incorporate background risk and incomplete annuity menus as possible drivers of deviations from full annuitization. Retirees face longevity ris k, capital market risk, inflation risk, and background risk. We model annuitization as a one-time decision at retirement. Contrary to what is often suggested in the literature, we find that in these settings full annuitizatio n remains close to optimal, irrespective of whether real or only nominal annuities are available. Under all circ umstances we find optimal annuitization levels above 95% of initial wealth. On the one hand annuitization is attractive due to the additional wealth created by the mortality credit, on the other hand annuities are irre versible and the annuity menu is incomplete. We show that the additional wealth effect dominates, optimally individuals annuitize almost their entire wealth at retirement to capture the mortality credit. Whenever liq uidity or equity exposure is desired, individuals save sizeable amounts out of their annuity income to smooth shocks due to background or inflation risk and/or to get equity exposure. We can identify this result, because we do not assume a priori that consumption equals annuity income in retirement and solve a dynamic programming problem for consumption and savings. Similarly, adding variable annuities to the menu does not increase welfare significantly, since individuals can save in order to get the desired equity exposure. Furthermore we find that for individuals who do not face (real) background risk, it is optimal to annuitiz e substantially less to receive the equity premium. Hence if both possible motives to annuitize less are considered jointly, they generally interact in such a way that full annuitization is optimal.