PCA and MLE-Based Statistical Factor Models for Asset Pricing

Asset pricing revolves around determining the theoretical value of an asset (stock) by evaluating a wide range of influence factors. High-dimensional data poses extraordinary challenges to asset pricing research as it results in a low signal-to-noise ratio environment that affects the computation of risk premia. Over the years data-driven solutions to the problems of empirical asset pricing have been found by developing a close bond with machine learning techniques. In practical applications, the use of dimensionality reduction techniques such as Statistical Factor Models exploit the concept of low dimensional spaces accounting for most of the variation in high dimensional data. This work explores the use of Statistical Factor Models based on conventional Principal Components Analysis and a novel Maximum Likelihood Estimation - computed numerically with the Expectation-Maximization algorithm using a centroid initialization method for smoother convergence. On comparing the implementations for 3 and 5 factors across various sample sizes, it was noted that that the proposed Maximum Likelihood Estimation based model outperforms the conventional Principal Components based factor model with a lower average mean deviation in L2 norm value for factor loadings.