Comparison of Markowitz Model and Index Model in Capital Markets

Abstract

We are searching for an optimal portfolio that plays a significant role in portfolio management by maximizing the expected return subject to a constant risk or minimizing the risk for a constant expected return. In this work, we first calculate the basic statistical information of our risky instruments, the probability density functions, and the Q-Q plot to compare the daily and monthly data for ten stocks and one broad equity index. We conclude that the monthly returns data is much closer to a normal distribution. Second, when calculating the correlation coefficients, we find that the stocks of the same industry are often highly correlated. Third, through the plotting of the feasible portfolio regions using the Markowitz Model (MM) and the Index Model (IM) consisting of various portfolios under different constraints, calculating two essential points on the efficient frontier, and analyzing the CAL, we generalize that the contrast between the MM model and IM model have similar results whether there is weighted SPX. Compared with the IM model, the MM minimal variance portfolio and maximum Sharpe Ratio the olio the MM model is more desirable than the IM model. The introduction of the generic index SPX affects the results of both models to a certain extent. Finally, we use the Monte Carlo method to simulate that the generated points are all within the feasible region, which indicates that the sample results are reasonable. Our research not only further supplementary the empirical research of the MM model and IM model, but we provide investors with some investment suggestions for constructing portfolios.