Analytic Approximation for the Probability That a Portfolio Survives Forever

Abstract

The author investigates the interaction between the uncertainty of actual returns and the ability of a given asset allocation to allow a portfolio both to provide for current income needs and to generate enough real returns to meet future income needs (i.e., growth). The author derives a formula that measures the probability that the portfolio survives indefinitely, given annual disbursement assumptions. This formulation could be useful, for instance, in the definition of the investment and distribution parameters for charitable trusts.