Graduation Year

2023

Date of Submission

12-2022

Document Type

Campus Only Senior Thesis

Degree Name

Bachelor of Arts

Department

Economics

Reader 1

Professor Benjamin Gillen, Ph.D.

Abstract

This paper reexamines William Bengen’s 4% rule through the lens of the financial independence, retire early (FIRE) movement using more recent equity and treasury data to run backtests and simulations. I explore Bengen’s original inflation-based withdrawal method and an alternative performance-based withdrawal method with a baseline portfolio to obtain withdrawal rates for a standard historical-average environment. Then, with a cyclical volatility cycle model of crash risk, I find optimal withdrawal rates for efficient portfolios of three risk profiles: conservative, neutral-risk, and aggressive. Backtests use 46-year historical returns while simulations use the most recent 10-year ones with a combination of random returns fluctuations and per-period crash risk random number generators. Comparison between portfolios is done with inflation-adjusted utility calculations. For each period, log base 10 of the withdrawal amount is calculated and multiplied by the product of all previous periods’ (1-inflation) to give each withdrawal’s utility. This process adjusts each withdrawal value by inflation. At the end, the sum of all these values is added to the log base 10 of the final balance, which is similarly adjusted for inflation, to give a total utility of the scenario. After running all backtests and simulations, I conclude that with uncertain returns and crash behavior, the optimal rate with Bengen’s inflation-based withdrawal style drops from the original 4.00% down to around 3.50%-3.75%. This is assuming an aggressive risk-profile portfolio. However, with a dynamic performance-based withdrawal style, the optimal withdrawal rate can be bumped up to 4.00% all while yielding a higher utility. For a FIRE retiree looking to maximize their long-term utility, an aggressive portfolio with performance-based withdrawals will be the optimal strategy.

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This thesis is restricted to the Claremont Colleges current faculty, students, and staff.

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