Risk and Return of the Tontine: A Brief Discussion

Abstract

This article analyzes the stochastic aspects of a tontine using a Gompertz distribution. In particular, the probabilistic and demographic risks of a tontine investment are examined. The expected value and variance of tontine payouts are calculated. Both parameters increase with age. The stochastic present value of a tontine payout is compared with the present value of a fixed annuity. It is shown that only at very high ages the tontine is more profitable than an annuity. Finally, the demographic risks associated with a tontine are discussed. Elasticities are used to calculate the impact of changes in modal age on the tontine payout. It is shown that the tontine payout is very sensitive to changes in modal age.