Adjusting Portfolio Weights for Sharpe Ratio Uncertainty

Summary

This document develops a portfolio weighting adjustment for uncertainty in estimated Sharpe ratios. It translates a difference in Sharpe ratios into a difference in expected returns, estimates uncertainty in that difference using the assets’ volatility, history length, and average correlation, and optimizes allocations at multiple points in the resulting distribution. Averaging those weights provides a bootstrap-style adjustment for an asset whose estimated performance differs from the portfolio average.

Examples show that the adjustment depends on both the size of the estimated Sharpe advantage and the evidence supporting it: with less history, a seemingly better asset may warrant much less weight, while high correlation reduces uncertainty in the return difference. The document also explores how the weights vary with history length, correlation, and the number of assets, then illustrates the adjustment in a futures system. Its assumptions include equal asset volatility and a common average correlation in the simplified model. The excerpts provide example calculations and portfolio weights, but little detail about out-of-sample validation or how well the assumptions fit real markets.

Key ideas

• Convert estimated Sharpe ratio differences into expected return differences before adjusting portfolio weights.
• Estimate uncertainty in the return difference using volatility, history length, and average correlation.
• Optimize weights across many plausible return estimates and average them to obtain a robust adjustment.
• Greater uncertainty can reduce the weight assigned to an asset with a higher estimated Sharpe ratio.
• The simplified analysis assumes equal volatilities and a shared average correlation across assets.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.