均值-VaR分析与资本资产定价模型:一个理论拓展

在均值—VaR分析框架内首先从微观角度的单一投资期资产配置决策入手,发现投资者的资产配置决策分为两步:第一步确定最优风险资产组合,第二步确定无风险资产与最优风险资产组合之间的配置比率;并且最优风险资产组合同投资者的初始财富和风险偏好均无关。随后我们将上述微观模型应用到存在多个"一致预期"投资者的资本市场宏观模型当中去,在一系列假设条件下我们得到了均值—VaR框架下的两基金分立定理:各个投资者的最优投资组合都是由共同的最优风险资产组合和无风险资产组成,不同的只是二者之间的配置比率不同。最后我们允许投资者的风险下限可以变化,发现在用(Rf V浕R)代表风险的情况下,均衡情况下任何投资者的预期收益率都同其承担的风险水平存在着线性相关关系,这就得到了均值—VaR框架下的资本资产定价模型和资本市场线。

Mean-VaR Analysis and CAPM:A Theoretical Development

The paper analyzes the asset allocation decision-making process of a single investor in one-period horizon under the mean-VaR framework. We found 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 found 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-Funds Separation Theorem under the mean-VaR framework. Finally, we allow the investors' risk preference to change. If we use to represent the investors' risk, the expected return in equilibrium of any investor is linearly correlative with his risk, which means we get the CAPM and capital market line under the mean-VaR framework.