Residual return extraction using Principal Component Equivalence method

Abstract

In this paper, we focus on the residual returns that are not explained by the common factors in financial asset returns. We propose a novel method to extract well-behaved residual returns based on principal component analysis (PCA). Traditional PCA requires determining the number of common factors, presenting a trade-off: increasing the number reduces common factors but also increases the potential for noise. Our proposed method randomly divides returns into two groups, extracts factors (PC) from one, and estimates eigenvalues from the other. Then, by creating a projection matrix that aims to transform eigenvalues to the same level, the proposed method can extract residual returns with better and more stable properties than PCA. Finally, we demonstrate that our method is capable of extracting residual returns with desirable properties through analysis based on both synthetic and real market data.