Comparative Study of Markowitz Mean-Variance Model and Harlow's Optimal LPM' Portfolio Model with MATLAB: Based on the Empirical Research of Precious Metal Investment in China

Risk management is the core issue of investment and assets management. Markowitz mean-variance model and Harlow's optimal LPM' portfolio model are both used for solving the optimal asset portfolio, so they are very useful. Because the two models have different ways to measure risk, the practical applications of the two models are quite different. This paper dose the comparative study of Markowitz mean-variance model and Harlow's optimal LPM' portfolio model based on an empirical research of Chinese precious metal investment market in order to reflect the characteristics of the two models. Firstly, this paper compares the theoretical and mathematical versions of two models to reflect two different ways of risk measure. Then, as it's hard to solve the optimal solutions of the two models, we use the standard functions provided by MATLAB and program a general purpose program through MATLAB M-files for solving the optimal portfolios. Finally, we use these two models to obtain the optimal precious metal portfolios and propose the precious metal investment advices, and summarize the characteristics of the two models based on the empirical research.