Regression Estimation for Portfolio Analysis

Abstract

The modern portfolio theory has played a significant role in finance since the seminal work of mean-variance analysis introduced by Harry Markowitz. The construction of mean-variance portfolio involves two stages, including estimating the unknown population mean and covariance matrix of asset returns, and solving the mean-variance optimization problem to obtain the optimal portfolio weights. However, due to estimation error, despite the popularity and simplicity of this process, the resulting optimal portfolio weights always show poor out-of-sample performance.

This study aims to identify a set of estimators for the mean and covariance matrix of asset returns that outperforms other competing estimators both analytically and empirically. First, I will propose the least squares estimators for the mean and covariance of asset returns. Next, I plan to analytically compare the proposed estimators against other competing methods in terms of their efficiency. Last, I will conduct a comprehensive empirical study to evaluate the out-of-sample performance of the portfolio constructed based on the proposed estimators.