Title: Portfolio Selection via Hybrid Graphical Least Square Estimation

Abstract: Regression analysis is often used in the portfolio optimization problem within the Markowitz mean-variance framework. The challenge exists when the number of assets v is larger than the sample size N. We consider a Graphical Least Squares method to deal with such problems. Unlike the regularization methods such as Ridge regression, LASSO and LARS, which always give biased estimates, the proposed method can give unbiased estimates for some parameters. The new approach assists in improving the portfolio performance by increasing the portfolio’s expected return and decreasing its risk, which consequently affects the Sharpe ratio. Another advantage of the proposed method is that it constructs a non-sparse (saturated) portfolio, which is more diversified in terms of stocks, and reduces the stock-specific risk.