Comparative Analysis of Portfolio Optimization under Various Constraints

The pursuit of optimal portfolio construction, whether through maximizing expected returns under a fixed level of risk or minimizing risk for a given expected return, constitutes a fundamental aspect of portfolio management. In this study, we analyzed essential statistical metrics for 22 risky assets including 1 index stock, checked about several assumptions, and applied portfolio optimization methods under different regulation requirements to compare the models between Markowitz Model (MM) and the Index Model (IM). We identified key points on the efficient frontier, the Capital Allocation Line (CAL), and feasible portfolios, and we came to the conclusion that MM model is more favorable compared to IM model in this case. By reviewing the different settings of each problem, a sensitivity analysis was also carried out to analyze the effect of regulation on the weights of our portfolio, risk and return, which is critical in practice for investors. This research not only contributes to the empirical literature on the MM and IM models but also offers practical investment recommendations for portfolio construction.