STATISTICAL FACTOR MODELS IN U.S. EQUITY MARKETS USING PRINCIPLE COMPONENT ANALYSIS

Abstract

Most reasonable investment decisions take into consideration not only the expected return of the investment, but also the variance of the investment return. This is illustrated in the classic Markowitz Portfolio Optimization Problem, where we as the investor not only need to maximize a portfolio's expected return, but also attempt to minimize the portfolio's variance. Although higher expected returns normally come with higher risk, an investor can reduce the risk of a basket of equity investments by taking advantage of covariance of equities in the basket, meaning that we have a keen interest in estimating the covariance matrix of the equities in the market. However, given the large number of equities currently listed in the market, generating a complete covariance matrix with over three thousand rows and columns quickly becomes computationally exhausting. To alleviate this problem, we will reduce the dimensionality of the problem by modeling the returns using a set of statistical factors. In this thesis, we will use principal component analysis (PCA) to decompose the relationships between individual stocks for factor analysis and find that it is efficient in reducing the computational load of the optimization problem, but comes at the cost of increased portfolio variance, which is not desirable.