Optimal Spending Strategies for Sovereign Wealth Funds Using a Discrete-Time Life Cycle Model

Abstract

The paper analyses optimal spending of an endowment fund. The purpose is to find a spending rule which is optimal for the owners and which secures that the fund will last “forever”. This we do by finding closed form solutions of the optimal consumption to wealth ratio. We solve this problem using the life cycle model, where the agent can have preferences represented by expected utility or recursive utility. We apply our results to a sovereign wealth fund, and demonstrate that the optimal spending rate is significantly lower than the fund’s expected real rate of return, a rule which is in common use. Employing the latter as the spending rate, implies that the fund’s value deteriorates both in probability and in expectation, as time goes. For both kinds of long term convergence we find closed form threshold values. Spending below these values secures a sustainable fund.