The Annuity Wager: Can Bonds Outperform a Life Annuity?

Abstract

This paper frames the decision to purchase a fixed immediate annuity as a wager that can be won or lost. The alternative bet is to hold a portfolio of long government bonds, drawing income and liquidating principal as necessary. There is some probability of ruin in either case: the bond portfolio may be exhausted while the bettor is still alive, or the bettor may die before the bond portfolio runs down. The paper applies a historical rather than mathematical lens to calculate the odds of each outcome. I examine 81 start dates from 1918 to 1998 inclusive, with an out-of-sample test from 1878 to 1917. The historical analysis finds that wager outcomes are contingent. Most notably, the annuity is the odds-on favorite when bond yields are very low. However, if the annuity provider cannot harvest a spread over the safe government bond yield and pass on part of that spread in the form of a higher annuity payout, then the analysis shows the bond portfolio to be the odds-on favorite over the stretch of history examined. Mortality credits alone are not enough to favor the annuity. In the middle case—given a yield spread but absent very low yields—the odds do not greatly favor either side of the bet. The historical account is further supported by analysis of the arithmetic of government bond returns and the mechanics of annuity payouts.

Keywords: life annuity, single premium immediate annuity, historical bond market returns, mortality credits, corporate bond premium, life expectancy, required minimum distributions

JEL Classification: G12, G22, N12