Markowitz Model and Index Model: A Comparative Study of Constructing Optimal Portfolios

In the field of investment, how to strike a balance between high returns and low risks has always been a challenge for investors. With the rise of modern portfolio theory (MPT) and index models, investors have more options for constructing optimal portfolios. This paper takes the US stock market as the research object, selects the S&P 500 index and six stocks representing different industries, uses the Markowitz model and the index model to optimize, and analyzes the optimal portfolio allocation, return, risk and Sharpe ratio of the two models under different constraints. It is found that the Markowitz model is more advantageous in risk diversification, while the index model relies more on the allocation of a single stock, especially the S&P 500 index. Both models perform similarly in terms of risk-adjusted returns, but the Markowitz model is slightly superior in terms of Sharpe ratio. In addition, there are differences in the portfolio allocation and risk-return characteristics of the two models under different constraints. The results of this study can help investors better understand the advantages and disadvantages of the two portfolio optimization models, and choose the appropriate model according to their own risk preferences and market environment to construct the optimal portfolio and achieve their investment objectives.