Research On Finding Optimal Portfolios Based on Markowitz Mean-Variance Model -- Constructing Efficient Frontier and Portfolio with Highest Sharpe Ratio Using 4 Assets in Chinese Market

Abstract

Markowitz mean-variance model is the foundation of modern investment science, and how to apply this model to construct optimal portfolios is always of interest. This paper uses the Markowitz mean-variance model and four typical assets in Chinese market to construct efficient frontier with highest expected return rate at each risk level and lowest risk at each expected return rate level, and the portfolios with the highest Sharpe ratio. There are three main results in this paper. Firstly, the efficient frontier has the U shape and V shape rotated   clockwise in the case of excluding and including risk-free asset respectively. Secondly, the theoretical efficient frontier obtained from mathematical formulas approximately coincide with those from the simulation experiments. Thirdly, the portfolio with the highest Sharpe ratio always occurs in the intersection point of the efficient frontier and its tangent line that passes through the risk-free asset. The results from this paper provide a convenient method of using mathematical formula for investor to construct optimal portfolios in real practice.