Optimal Portfolio Model Based on Value-at-Risk and Two-Fund Separation

Abstract

This paper uses value-at-risk to measure the risk of portfolios and develop an optimal portfolio model by minimizing the VaR subject to the constraint that the final wealth should meet the minimal acceptable limits. And we find that the optimal portfolio model based on VaR generates two-fund separation, so the portfolio can be replaced with two mutual funds, a risky asset and a risk-free asset. Finally we use the simplified model that only exists two assets to have empirical studies on how investors make his optimal portfolio choice between the two mutual funds in Shanghai stock market. The results show that as the acceptable return rises, the investor saves less, and the amount of wealth invested in stocks increases.