Oversaving in Long-Term Funds

Abstract

Endowment funds and similar institutions aim to generate a benefit stream of unlimited duration on the basis of an initially donated capital. Towards this purpose, responsible trustees need to design a spending policy as well as an investment policy. A combined spending and investment policy is said to be efficient if the total net present value of benefits that are paid according to the policy is equal to the initial capital, and inefficient if the total net present value is less than that. For several strategies, analytical expressions are given for the total net present value of benefits under the Black-Scholes assumptions. One of the strategies considered is the combination of a fixed-mix investment policy with a benefit policy that pays inflation-indexed benefits as long as ruin does not occur. This strategy is shown to be inefficient in many cases; the effective loss of capital can range from 5% to 15% under realistic parameter values. The inefficiency can be removed by adapting the investment policy and raising the benefits, without increasing the probability of ruin.