Double Descent and Benign Overfitting in Portfolio Optimization

Details

Supervisors

Lassance, Nathan

Faculty

Louvain School of Management

Degree label

Master [120] : ingénieur de gestion, à finalité spécialisée

Abstract

enThis thesis examines to what extent the spectral structure of S&P 500 returns is compatible with the theoretical framework of benign overfitting, and what this implies for out-of-sample portfolio performance in a high-dimensional regime. Using monthly returns of 440 S&P 500 constituents over January 2000 to September 2025, we find that the spectral structure of returns is consistent with a tempered overfitting regime: over-parameterization is present but noise is not sufficiently diffuse to satisfy the isotropy conditions of Bartlett et al. (2020). Using the Moore-Penrose pseudoinverse, we document a double descent in out-of-sample variance around the interpolation threshold. We then show that Ridge regularization produces a double ascent in Sharpe ratio across complexity regimes. Adaptive calibration via hold-out cross-validation fails to achieve permanent ascent, while fixed strong shrinkage sustains stable risk-adjusted performance. Finally, we confirm the R² paradox empirically: predictive accuracy collapses in the over-parameterized regime while portfolio performance remains stable, illustrating that statistical accuracy and economic performance are distinct objectives.