Comparative Analysis of Portfolio Optimization Between Markowitz Model And Single Index Model

Abstract

The key factors which investors consider when investing are the risks and returns of the assets. Moreover, they may determine efficient investment portfolios using some financial models. The goal of this paper is to compare the various optimal portfolios constructed using the Markowitz Model and the Index Model and give possible explanations for the results. The data selected for this paper are stocks from ten companies, which are Adobe Inc., International Machines Corporation, SAP SE, Bank of America Corporation, Citigroup Inc., Wells Fargo & Company, The Travelers Companies, Southwest Airline Corporation, Alaska Air Group Inc., and Hawaiian Holdings Inc. The companies are selected from the technology sector, financial services sector, and the industrial sector of the economy in order to simulate real investment decisions. In specific, twenty years of total daily return data from the companies and the S&P 500 index are collected. The statistical analysis shows that the expected return of the optimal portfolio calculated by the Single Index Model is always higher than that of the Markowitz Model. The assumption, that all stocks are independent of each other, made by the Single Index Model may provide a partial explanation for the difference in the expected returns. Nonetheless, the specific effect of the difference is yet to be examined.