Modeling A Systematic Withdrawal Plan: A Stochastic Algorithm to Estimate Initial Fund Requirement

Abstract

A systematic withdrawal plan refers to monthly withdrawals from an appreciating fund, especially to provide retirement income. This study proposes a stochastic algorithm that outputs the initial amount required to sustain a systematic withdrawal plan for a target duration with a 90% safety margin, given an initial monthly withdrawal amount. The systematic withdrawal plan is based on the S&P 500. Initially, a deterministic function modeling a systematic withdrawal plan was created. This study showed that the monthly growth rate of the S&P 500 is normally distributed with a mean of 0.6933% per month and a standard deviation of 4.0266% per month. By randomly sampling monthly growth rate values from the distribution, stochastic simulations were run to identify the distribution of the fund’s longevity. The Kolmogorov–Smirnov test suggested that the simulated values of the fund’s longevity were log-normally distributed. Initially, the algorithm uses the deterministic function to find the 50% safety margin value for the initial fund requirement. Then, the algorithm uses stochastic simulations to find the log-normal longevity distribution. The 90 th percentile value of the log-normal longevity distribution is substituted into the deterministic function to calculate the 90% safety margin value for the initial fund requirement of a systematic withdrawal plan.