Estimation-Robust Minimum-Variance Portfolio Allocation Under Factor-Loading Uncertainty
- 1Independent Researcher
- 2Faculty of Engineering, Universidad de Talca, Curicó 3340000, Chile
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.
Related
- Sparsity Regularized and Robust Mean Variance Portfolio Selection Under Ellipsoidal Uncertainty
- Optimal Transport for Continuous-Time Mean-Variance Portfolio Selection
- Constrained Mean Variance Portfolio Selection under Reflected Factor Dynamics: Stochastic Riccati Equations, Neumann Problems,and a Deep Solver
- Dynamic mean-variance portfolio selection with no-shorting constraints and unknown investment opportunity sets
- Mean-Variance Portfolio Selection: Statistical Properties and Distributionally Robust Optimization
BibTeX
@article{carvalho2026estimationrobust,
title = {{Estimation-Robust Minimum-Variance Portfolio Allocation Under Factor-Loading Uncertainty}},
author = {Leonardo P. Carvalho and Jonathan M. Palma},
journal = {Mathematics},
year = {2026},
month = oct,
doi = {10.3390/math14203743},
url = {https://www.mdpi.com/2227-7390/14/20/3743},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Estimation-Robust Minimum-Variance Portfolio Allocation Under Factor-Loading Uncertainty
AU - Leonardo P. Carvalho
AU - Jonathan M. Palma
PY - 2026
DA - 2026/10/15
JO - Mathematics
DO - 10.3390/math14203743
UR - https://www.mdpi.com/2227-7390/14/20/3743
AB - 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.
SN - 2227-7390
ER -