Financial Models and Portfolio Optimizations in the U.S. Market

Abstract

Portfolio optimization is an essential task for investors to maximize the profit and minimize the risk in trading, which can be reflected in return and standard deviation respectively. This article selects ten well-known firms and S&P 500 index as the portfolio and calculates their basic descriptive data of annualized return, annualized standard deviation, and correlations. Next, this article applies Markowitz model and Single-index model to the portfolio optimizations, as well as setting five constraints for comparison. After using the above methods, this paper gives the results in tabular and graphic ways. It finds that optimizing with no restriction can generate the biggest permissible regions of the minimum-variance frontier; investors only long stocks under constraint 4 can guarantee a finite risk and a finite positive return, which has a robust performance. Moreover, Markowitz model is flexible in covariances, but the number of estimates could complicate the calculating process; Index model is simple to calculate in linear regression form, but it’s not highly sensitive to the covariance matrix. The purpose of this article is to prove the feasibility of optimization in future portfolio management and helps investors to construct the portfolios with the fundamental theory of financial models.