The Tontine Puzzle

Abstract

Retirement income tontines are financial arrangements where a pool of retirees shares idiosyncratic and systematic mortality risks. This paper analyzes stochastic dominance relations between tontines and annuities. In the presence of risk loadings and/or subjective probabilities underestimating the insurer’s pricing probabilities, we find the benefits of a properly designed tontine to dominate the benefits of a constant annuity in the almost first order stochastic dominance (AFSD) sense as defined by Leshno and Levy (2002). In particular, we show that this AFSD converges to first order stochastic dominance as the pool size in the tontine tends to infinity. These results imply that individuals prefer tontines with a sufficiently large pool size to annuities under utility preferences which are increasing and continuous in consumption. Such preferences include but are not limited to cumulative prospect theory and generalized expected utility preferences, which we use as examples to illustrate our theoretical findings. Our results present an interesting puzzle which we call “tontine puzzle”, raising the question why the development of the tontine market is still in its infancy in practice.

Keywords: Financial decision-making, retirement planning, risk sharing, almost stochastic dominance

JEL Classification: G22, H55, H23, I31, J32