The Virtue of Complexity: Benign Overfitting in Portfolio Construction

Details

Supervisors

Lassance, Nathan

Faculty

Louvain School of Management

Degree label

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

Abstract

enModern machine learning has shown that models complex enough to fit their training data perfectly can nonetheless generalize, a phenomenon known as benign overfitting. This stands in sharp contrast to the classical view in portfolio theory, where estimation error is expected to make optimized portfolios underperform the naive 1/𝑁 allocation. This thesis examines whether benign overfitting can also be observed in financial data and, if so, whether its statistical advantages translate into economically meaningful improvements in portfolio performance once factor exposures and transaction costs are taken into account. To answer this question, a two-part empirical study is conducted using Fama–French portfolios covering U.S., European, and emerging equity markets. The first part investigates the existence of double descent by sweeping a return regression through the interpolation threshold and testing the spectral conditions proposed by Bartlett et al. (2020). The second part evaluates whether these statistical properties improve portfolio construction by backtesting six portfolio strategies across rolling estimation windows. Performance is assessed through Sharpe ratios, five-factor attribution, transaction costs, and effective-rank diagnostics computed on the covariance matrices effectively inverted by each strategy. The results show that double descent is indeed present in financial data, and that introducing a very small amount of ridge regularization reduces the interpolation peak by two orders of magnitude. In highly over-parameterized settings, stabilized minimum-variance portfolios outperform the naive 1/𝑁 benchmark by roughly 30% in Sharpe ratio while remaining less risky, and this advantage survives a five-factor attribution, suggesting that it reflects genuine estimation alpha rather than systematic factor tilts. However, the premium is highly sensitive to implementation costs and disappears outside favourable market environments. The proposed diagnostics identify these environments before portfolio construction, while the refined Ridgelet 2 estimator is shown to fail on style-portfolio universes, exposing a limitation of the recent zero-variance portfolio framework of Chang et al. (2026). Overall, the findings suggest that the benefits of model complexity in portfolio allocation are neither universal nor accidental. They arise under specific and measurable conditions, namely short estimation windows, high-dimensional settings, covariance-based objectives, and sufficiently dispersed covariance spectra. Rather than a general principle, benign overfitting therefore provides a practical framework for identifying when additional model complexity is likely to improve real-world portfolio construction.