Applying and analyzing the Model Portfolio Theory (MPT) by using Markowitz Model and index Model

Abstract

In this study, I apply the Markovitz Model(“MM”) and Index Model(“IM”). These Portfolio Optimization models estimate and optimize U.S. equity portfolios with some realistic additional constraints.

I was given a recent 20 years of historical daily total return data for ten stocks, which belong in groups to three different sectors (according to Yahoo! Finance), one (S&P 500) equity index (a total of eleven risky assets), and a proxy for risk-free rate (1-month Fed Funds rate). I aggregate the daily data to the monthly observations, and based on those monthly observations, I calculate all proper optimization inputs for the full Markowitz Model (“MM”) alongside the Index Model (“IM”). We use the optimization inputs (“IM”) and (“MM”) to explore some additional constraints.