Risk-Adjusting Forecasts for Increased Portfolio Performance
Abstract
The Sharpe-ratio gap — the difference between the maximum attainable Sharpe ratio and the Sharpe ratio realized by an estimated portfolio — is the fundamental performance cost of estimation error in mean-variance investing. We decompose this gap into two additively separable components via a master inequality: a mean forecast error measured in risk-adjusted units (RAFE) and a precision-alignment error scaled by the investment opportunity set (C-RAFE). For each component we derive exact bias–variance identities, yielding closed-form expressions for classical estimators including the sample mean, linear shrinkage, James–Stein, and factor-model-based rules. We propagate these bias–variance profiles through portfolio-space mixing, nesting the two-fund rule of Kan and Zhou and the three-fund rule of Tu and Zhou as special cases. All portfolio rules map to a unified (x, y)-frontier in which the mean-side radius x and precision-side radius y jointly determine the expected Sharpe-ratio gap. Monte Carlo simulations confirm the theoretical bounds and reveal a dimensionality crossover: when the ratio of assets to observations exceeds a critical threshold, the estimation-free equally weighted portfolio dominates plug-in tangency.
Type
Publication
Working Paper (University of Liechtenstein)
Note
This is the next iteration of Lost in Translation? Risk-Adjusting RMSE for Economic Forecast Performance (Salcher, Stöckl & Hanke, Journal of Forecasting, 2026).
Where the published paper introduces risk-adjusted forecast-accuracy measures (RAFE, C-RAFE, T-RAFE) and documents their link to economic performance, the present paper derives the full bias–variance identity of the Sharpe-ratio gap and maps classical shrinkage and factor-model estimators onto a unified frontier of portfolio rules.