Probabilistic Kelly Withdrawals Under Sharpe Ratio Uncertainty
Summary
The document considers how to draw regular income from a trading account while accounting for uncertainty in the estimated Sharpe ratio. It outlines three ways to represent that uncertainty: a distributional formula under a Gaussian return assumption, resampling observed returns with replacement, and parametric Monte Carlo simulation based on estimated distribution parameters. It then relates sustainable withdrawal rates to both the assumed Sharpe ratio and the selected confidence percentile.
Tables compare withdrawal estimates across Sharpe ratio assumptions and percentiles, including calculations with different risk-free rates. The examples illustrate that more optimistic performance estimates imply higher withdrawals, while conservative percentiles produce lower rates; at sufficiently low Sharpe ratios, some scenarios do not support a withdrawal while preserving starting capital. The author recommends avoiding highly optimistic assumptions and favors a median percentile as a practical reference. These are model-based illustrations rather than guarantees: results depend on the return distribution, the estimation method, the risk-free rate, and whether historical performance represents future trading.
Key ideas
- Sharpe ratio estimates have substantial sampling uncertainty, which should be reflected in withdrawal planning.
- Uncertainty can be modeled with a distributional formula, nonparametric bootstrap, or parametric simulation.
- Estimated sustainable withdrawals rise with assumed Sharpe ratio and with more optimistic confidence percentiles.
- The examples show that low Sharpe ratios may not support withdrawals while preserving starting capital.
- Withdrawal estimates depend on modeling assumptions and should not be treated as guaranteed income.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.