Author(s)

Zhiyue Chen, Leian Chen, Haoyang Jin, Qinyu Liu

Corresponding Author

Zhiyue Chen

ABSTRACT

With the existence of liquidity and volatility in stock and security markets, it is vital to establish efficient investment portfolios to control risks and yield profits. Thus, this project mainly employs the Markowitz model and Index model to implement portfolio analysis with respect to historical daily total return data for ten stocks from 2001 to 2021 and one equity index S&P500, to work out minimal risk frontier, minimal risk portfolio, maximal sharp ratio portfolio, efficient frontier, capital allocation line, and minimal return frontier of each model. Simultaneously to further analysis, the aforementioned problems using the Markowitz model and Index model are implemented and solved with five additional optimization constraints. Through empirical results with diverse constraints, we find out that the Markowitz model's returns are always higher than the Index's ones under five constraints in the minimum variance graph. Meanwhile, the index model can always achieve a higher sharp ratio than the Markowitz Model in the maximum sharp ratio. Thus, this project summarizes the regularity and differences of various kinds of diversification in both two models.

KEYWORDS

S&P500, Markowitz model, Capital allocation line, Risk portfolio