Actuarial model for estimating the optimum rate of return of a joint-and-survivor annuity portfolio

Abstract

In actuarial science related to pension systems, it is widely assumed that the rate at which the reserves cover the payment of annuities (calculated for a given number of lives) is equal to the expected rate of return of the portfolios in which such reserves are invested. Given this assumption, pension fund managers may take greater risks to realize higher returns and subsequently reduce their pension liabilities. This study demonstrates that the discount rate used to calculate a two-life annuity and the expected return on the portfolio are not necessarily equal. A stochastic-based model is used to determine the proper discount rate for calculating the two-life annuity. The model includes fluctuations of both the interest rate and the payments made by the annuity. In general, this study contributes to the stability of pension systems by determining the appropriate discount rate when computing required actuarial reserves or the portfolio’s required rate of return given a reserve.