A comparison of statistical and machine learning approaches for shrinkage estimation in finance
Files
Bokungu_ 56362400_2026.pdf
UCLouvain restricted access - Adobe PDF
- 3.17 MB
Details
- Supervisors
- Faculty
- Degree label
- Abstract
- Covariance matrix estimation is a central challenge in portfolio optimisation. When the number of assets is large relative to available observations, the sample covariance becomes ill-conditioned or singular, leading to poor out-of-sample performance. Ledoit-Wolf (2004) shrinkage addresses this by combining the sample covariance with a structured target. This thesis investigates whether reinforcement learning (RL) can improve upon this analytical estimator and under which conditions. Three datasets of increasing concentration ratio are constructed: FF49, FF100, and FF300, an original construction combining three Fama-French 100-portfolio families. Three PPO agents are trained and compared against LW and OAS. A novel residual RL formulation, in which the agent learns a correction to the LW baseline, is proposed. Results reveal a non-monotone relationship between dimensionality and RL advantage: at moderate dimensionality, the residual agent is competitive with LW and achieves the best Sharpe ratio; at high concentration ratio, all RL agents fail while LW remains robust, reducing annual volatility from over 2,190% to 12%. Keywords: covariance matrix estimation, shrinkage, Ledoit-Wolf, reinforcement learning, portfolio optimisation, global minimum variance.