Risk-Adjusted Forecast Performance

Fri, 24 Apr 2026 00:00:00 +0000

Alpha Without Snake-Oil: Aligning Forecast Evaluation with Investor Objectives

Return forecasts are almost universally evaluated with statistical loss functions — RMSE, MAE, out-of-sample R² — inherited from the classical forecasting literature. Yet the investor’s objective is not statistical fit: it is economic performance, typically expressed through the Sharpe ratio of a mean-variance-optimized portfolio. This translation is far from innocuous. MSE-based criteria weight all forecast errors symmetrically and ignore the covariance structure through which errors actually enter the investor’s objective, so a model that looks excellent on standard accuracy metrics can still leave substantial economic value on the table.

This research program takes that disconnect as its central object of study. Rather than proposing yet another predictor, it asks: what is the right yardstick for evaluating forecasts whose end-use is portfolio construction, and how much of the observed “shortfall in attainable performance” can that yardstick actually explain?

Core contribution

The unifying construct is the Sharpe-ratio gap — the shortfall between the maximum attainable Sharpe ratio under perfect foresight and the Sharpe ratio realized by a portfolio built on estimated inputs. The program develops a risk-adjusted family of forecast-error measures — RAFE (Risk-Adjusted Forecast Error, mean side), C-RAFE (covariance/precision-alignment side), and T-RAFE (total) — that map directly to this gap. A master inequality decomposes the gap into two additively separable components, each admitting an exact bias–variance identity. The traditional RMSE emerges as a special case of this family under restrictive simplifying assumptions, making explicit which assumptions must be relaxed to recover economic relevance.

Key findings across the paper set

establishes the multivariate risk-adjusted error measure, shows that RMSE is a highly restrictive special case, and documents — in simulation and empirics — that RAFE and C-RAFE explain the Sharpe-ratio shortfall across a broad set of portfolio strategies where RMSE does not.
derives the full bias–variance identity of the Sharpe-ratio gap and maps classical shrinkage, James–Stein, and factor-model estimators onto a unified (x, y)-frontier, nesting the Kan–Zhou two-fund and Tu–Zhou three-fund rules as special cases.
shows that deliberately coarsening forecast inputs into ranks or groups improves Sharpe ratios relative to plug-in mean-variance — with gains increasing in the severity of estimation error, consistent with the bias–variance logic developed in the accompanying theory.
traces the microfoundations of parameter uncertainty to structural breaks in individual stocks, proposing break-age as a machine-learning-based proxy that is priced in the cross-section — grounding the abstract “estimation error” of the portfolio literature in an observable firm-level characteristic.

Ongoing work

Current extensions push the agenda in four directions: completing the Sharpe-gap bias–variance decomposition for a broader class of regularized and factor-based estimators; adapting risk-adjusted loss functions to regression and machine-learning training objectives; developing portfolio-aware model-selection criteria that replace OOS R² at the evaluation stage; and applying economically aligned objectives to AI-based asset allocation, where the mismatch between training loss and downstream Sharpe ratio is particularly acute.

Collaborators