Estimation-Robust Minimum-Variance Portfolio Allocation Under Factor-Loading Uncertainty

Abstract

We study sequential minimum-variance allocation when estimated market-factor loadings are uncertain. At each date, a horizon-one convex problem is solved using an ellipsoidal confidence region for the jointly estimated loading vector. The full loading covariance includes cross-asset residual dependence, and the uncertainty geometry is implemented either as a loading penalty or as an explicit worst-case exposure constraint. The principal walk-forward experiment uses the original nine U.S. sector exchange-traded funds from 2000 to 2024, yielding 6036 out-of-sample daily observations after a 252-day initial window. This fund-level opportunity set incorporates changes in underlying company constituents and therefore materially reduces the company-survivorship problem of a fixed stock panel, although the selected fund set remains subject to selection bias. An unrestricted past-only penalty selector over-regularizes: it chooses the largest normalized penalties on most dates and produces a negative long-short net return. We therefore report that frozen negative result and evaluate a separately frozen, economically guarded selector that caps the normalized penalty at 10. In long-short allocation, the guarded rule raises annualized net return from 1.13% under nominal beta targeting to 2.57%, lowers volatility from 10.72% to 8.39%, improves maximum drawdown from −38.67% to −24.42%, and reduces turnover and realized-beta dispersion. The paired Sharpe increase from 0.105 to 0.307 remains significant after false-discovery-rate correction. The result remains profitable across alternative estimation windows, transaction costs, and loading-covariance structures, and persists under a common monthly trading schedule. Its Sharpe is statistically indistinguishable from established uncertainty comparators, so universal dominance is not claimed. Long-only evidence favors zero or weak regularization. The results support economically bounded loading-uncertainty treatment in less-constrained portfolios, not unrestricted regularization or general robustness to distributional misspecification.