A 4% withdrawal rate for American retirement spending, derived from a discrete-time model of stochastic returns on assets and their sample moments
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915658475765760 |
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| author | Thomas, Drew M. |
| author_facet | Thomas, Drew M. |
| contents | What grounds the rule of thumb that a(n American) retiree can safely withdraw 4% of their initial retirement wealth in their first year of retirement, then increase that rate of consumption with inflation? I address that question with a discrete-time model of returns to a retirement portfolio consumed at a rate that grows by $s$ per period. The model's key parameter is $γ$, an $s$-adjusted rate of return to wealth, derived from the first 2-4 moments of the portfolio's probability distribution of returns; for a retirement lasting $t$ periods the model recommends a rate of consumption of $γ/ (1 - (1 - γ)^t)$. Estimation of $γ$ (and hence of the implied rate of spending in retirement) reveals that the 4% rule emerges from adjusting high expected rates of return down for: consumption growth, the variance in (and kurtosis of) returns to wealth, the longevity risk of a retiree potentially underestimating $t$, and the inclusion of bonds in retirement portfolios without leverage. The model supports leverage of retirement portfolios dominated by the S&P 500, with leverage ratios $> 1.6$ having been historically optimal under the model's approximations. Historical simulations of 30-year retirements suggest that the model proposes withdrawal rates having roughly even odds of success, that leverage greatly improves those odds for stocks-heavy portfolios, and that investing on margin could have allowed safe withdrawal rates $> 6$% per year. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_10273 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A 4% withdrawal rate for American retirement spending, derived from a discrete-time model of stochastic returns on assets and their sample moments Thomas, Drew M. Applications Portfolio Management Statistical Finance What grounds the rule of thumb that a(n American) retiree can safely withdraw 4% of their initial retirement wealth in their first year of retirement, then increase that rate of consumption with inflation? I address that question with a discrete-time model of returns to a retirement portfolio consumed at a rate that grows by $s$ per period. The model's key parameter is $γ$, an $s$-adjusted rate of return to wealth, derived from the first 2-4 moments of the portfolio's probability distribution of returns; for a retirement lasting $t$ periods the model recommends a rate of consumption of $γ/ (1 - (1 - γ)^t)$. Estimation of $γ$ (and hence of the implied rate of spending in retirement) reveals that the 4% rule emerges from adjusting high expected rates of return down for: consumption growth, the variance in (and kurtosis of) returns to wealth, the longevity risk of a retiree potentially underestimating $t$, and the inclusion of bonds in retirement portfolios without leverage. The model supports leverage of retirement portfolios dominated by the S&P 500, with leverage ratios $> 1.6$ having been historically optimal under the model's approximations. Historical simulations of 30-year retirements suggest that the model proposes withdrawal rates having roughly even odds of success, that leverage greatly improves those odds for stocks-heavy portfolios, and that investing on margin could have allowed safe withdrawal rates $> 6$% per year. |
| title | A 4% withdrawal rate for American retirement spending, derived from a discrete-time model of stochastic returns on assets and their sample moments |
| topic | Applications Portfolio Management Statistical Finance |
| url | https://arxiv.org/abs/2508.10273 |