Withdrawal Success Estimation

TL;DR

This paper develops bounds on the probability of successfully completing scheduled withdrawals from a wealth process modeled by a Levy alpha-stable process, providing practical guidelines for initial investments.

Contribution

It introduces a novel lower bound for terminal wealth and applies it to withdrawal schedules, offering necessary conditions for successful withdrawals with high confidence.

Findings

Initial investment must be at least k times the withdrawal amount for k withdrawals with 95% confidence.

The bounds are specifically derived for wealth processes modeled by Levy alpha-stable distributions.

Practical guidelines are provided for retirement planning based on the initial investment and withdrawal schedule.

Abstract

Given a geometric Levy alpha-stable wealth process, a log-Levy alpha-stable lower bound is constructed for the terminal wealth of a regular investing schedule. Using a transformation, the lower bound is applied to a schedule of withdrawals occurring after an initial investment. As a result, an upper bound is described on the probability to complete a given schedule of withdrawals. For withdrawals of a constant amount at equidistant times, necessary conditions are given on the initial investment and parameters of the wealth process such that $k$ withdrawals can be made with 95% confidence. When the initial investment is in the S&P Composite Index and $2\leq k\leq 16$, then the initial investment must be at least $k$ times the amount of each withdrawal.