Study of Portfolio Performance Under Certain Restraint Comparison: Markowitz Model and Single Index Model on S&P 500

Abstract

The purpose of this study is to figure out what percentage of each stock should be in the optimal portfolio and minimal risk portfolio created by Markowitz Model and Sharpe's Single Index Model and to make a comparison of the portfolio model, as well as the return and risk differences between Markowitz Model and Single Index Model. The research is undertaken at the New York Stock Exchange on ten stocks which are from the S& P 500 index for the period May 2001 to May 2021, The data analysis technique is constrained optimization and regression analysis. The results show that the Single Index Model needs fewer estimators than Markowitz Model and simplifies the actual operation. But for some assets with the correlated residual return, the Markowitz model performs better than the Single Index Model. The optimal portfolio constructed with the Single Index Model has a higher return and risk than the optimal portfolio constructed with Markowitz Model. But for the minimal risk portfolio, the portfolio based on Markowitz Model performs better. And the portfolio including Stock Index has lower systemic risk.