• Asset Pricing
• Factor estimation
• multifactor model
• PCA

The objective of this thesis is to assess the effectiveness of RP-PCA compared to PCA in estimating systematic risk factors. The first chapter provides a theoretical foundation for multifactor models, explaining their derivation and the key elements that any estimation method should capture. The second chapter revisits PCA, highlighting its limitations and the theoretical gap it leaves in risk factor estimation. By reconstructing the residual minimization equation used in PCA, it becomes clear that the method fails to account for mean returns, leading to an incomplete representation of systematic risk. RP-PCA addresses this shortfall by modifying the estimation framework to integrate both moments.
The third chapter shifts from theory to empirical analysis, comparing PCA and RP-PCA on both simulated and real market data. The goal is to assess whether RP-PCA’s theoretical advantages translate into superior performance in practice. The analysis considers both strong factors, which affect all assets (such as the market factor), and weak factors, which influence only specific subsets of assets, providing a comprehensive assessment of RP-PCA’s effectiveness.