Fair Tontine Annuity
67 Pages Posted: 3 Apr 2010
Date Written: March 26, 2010
An annuity is an arrangement in which an individual makes a one-time payment (the premium) to an insurer in exchange for a lifetime payment stream. Ideally, the expected present value of the payment stream matches the premium, making it a fair annuity. In practice, the payment stream is smaller than that, providing the insurer with a profit margin. This paper proposes a fair tontine annuity (FTA), an arrangement that provides a lifetime payment stream whose expected present value matches that of a fair annuity.
The FTA is based on a fair tontine. In a fair tontine, a group of members contribute to a pool, and each time a member dies, her contribution is divided among surviving members. The distribution to surviving members is made in unequal portions, according to a plan that provides each member with a fair bet, meaning a bet whose expected gain is zero. We show that, under broad conditions, such a plan exists and is readily constructed. Members may be of any age and gender and may contribute any desired amount. New members may join at any time, allowing the fair tontine to operate in perpetuity.
The FTA is formed by adding a few enhancements to the fair tontine. The result is something that closely resembles an annuity. The member makes a one-time contribution and receives payments on a fixed schedule (e.g., monthly) that last for his lifetime. The value of each payment is a random amount, with an expected value that is identical to the payment that would be made by a fair annuity. Thus, the FTA offers a higher expected payout than an insurer-provided annuity, since no profit is being extracted. Simulations show that the FTA outperforms a typical insurer-provided FTA not just on the average, but for virtually every member who lives more than just a few years, even with a pool as small as a few hundred members. Since the FTA imposes no risk on the provider, it can be offered by vendors other than insurers, such as mutual fund houses, retail brokers, etc.
Keywords: annuity, tontine, pension, retirement
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