The Research on the Differences Between the Markowitz Model and the Index Model under Different Constraints

Investment portfolio optimization has been a commonly discussed topic. This paper compared the differences between two established models regarding such topic, the Markowitz Model and the Index Model, by comparing the optimized portfolio outcomes formed by ten stocks, one equity index (the S&P 500 Index), and a proxy for the riskless asset (1-month Fed Funds Rate) under five different scenarios that each simulates a particular real-life circumstance, and concluded that while the Markowitz Model produced more optimistic results under situations with no constraints, with an arbitrary box constraint, and with a constraint of excluding the broad index, the Index Model outperformed the Markowitz Model under the constraints that simulate Regulation T and the U.S. mutual funds industry. This paper provided an analysis of the strengths and weaknesses of each model under different schemes by comparing the total returns, risks, and reward-to-volatility rate of each portfolio. It may also guide the investors who aim to optimize their portfolios to some extent.