Optimal Portfolio under Five Constraints in the Markowitz Model and the Index Model

Abstract

Investing in stocks is an inseparable part of modern life. Besides, choosing a good investment portfolio with high return and respectively low risk is the demand and desire of most modern investors. This paper tries to obtain an optimal investment portfolio to provide accurate and professional investment suggestions to the potential investors through the Markowitz Model and the Index Model under five different constraints. It has been considered several aspects to analyse the results: minimum variance portfolio, maximal Sharpe Ratio, etc. Some findings are given, including that the options of investment portfolio available under no constraint are larger compared to portfolios without permission of short-selling and investing SPX. Besides, the influence of the former is more significant than that of the latter; and then, the corresponding impact of different constraints ---is discussed through efficient frontiers. Additionally, comparing the Sharpe Ratio under two different models, it can be found that the Markowitz Model is a better option.