Study of Optimal Portfolio Performance on Markowitz and Index Model

Abstract

The choice of a portfolio optimization of shares has been for so long a subject of major interest in the field of investment and financial mathematics. This article aims to create a portfolio optimization which follows the objective of maximized return and minimized risk under given constraint among S&P 500 and the ten stocks, utilizing data collected from Yahoo! Data. The article ought to elucidate the Markowitz Model and Single Index Model in terms of generating a better result via comparing their distinct mechanisms in calculating their return percentage, standard deviation and Sharpe ratio, alongside with the corresponding efficiency frontier to compare their sharp ratio to determine a better model for each scenario. The result illustrates a better performance of the Markowitz Model in the aspect of producing a better portfolio optimization contrasting the Index Model in all the constraint except constraint three. Eventually backtesting was utilized to verify the feasibility.