The financial survival probability of living annuitants

Abstract

This study addresses the question of how long a given amount of capital will be able to fund a living annuitant if the following five parameters are known: expected retirement duration (i.e. years between date of retirement and date of death), return on investment, inflation, annual withdrawal amount and initial capital amount available. A model (the Pension Model) that graphically depicts the relationship between these parameters was developed. This model facilitates retirement planning by showing how retirement duration and withdrawal rates change the financial “Survival Probability” (SP), which is the probability of having enough capital to maintain a desired withdrawal rate for the expected retirement duration. The underlying model is based on long-term historical investment yields of equities, bonds and cash in South Africa using Monte Carlo simulation with Cholesky factorisation.