Mean-VaR Analysis and CAPM-A Theoretical Development

摘要

This paper analyzes the asset allocation decision-making process of a single investor in one-period horizon under the mean-VaR framework. We find that the decision-making process can be divided into two steps: Step one is to select the optimal risky portfolio and Step two is to determine the allocation ratio between the optimal risky portfolio and safe asset. In addition, we find that the optimal risky portfolio is independent from the investor's wealth and risk preference. Then, we apply the above conclusions in a capital market in which many investors have the same expectation, and we get the Two Fund Separation Theorem under the mean-VaR framework. Finally, we allow the investors' risk preference to change. If we use (Rf + VaR) to represent the investors' risk, the expected return in equilibrium for any investor is linearly correlated with his risk, which means we get the CAPM and capital market line under the mean-VaR framework.