模型不确定性条件下的Robust投资组合有效前沿与CAPM

On the Robust Portfolio Frontier and CAPM under Model Uncertainty

本文提出了Robust投资组合有效前沿的概念,并研究了模型不确定性条件下的资本资产定价模型(CAPM)。研究发现,当市场上不存在无风险资产时,模型不确定性对风险资产投资比例的影响是非平等的,因此会导致投资组合的非分散化;而且此时的两基金分离定理以及零-βCAPM也不成立。但是当市场上存在无风险资产时,模型不确定性对风险资产投资比例的影响则是平等的,并且两基金分离定理仍然成立,因为任何Robust有效前沿组合都可以表示为市场组合与无风险资产的线性组合。而此时的CPAM仍然能够成立,只是在表达形式上增添了一个因子——不确定性因子;并且所有资产或资产组合的超额收益都可以分解为风险溢价与不确定性溢价两部分。

The paper takes model uncertainty into account in studying portfolio selection problems,and proposes a definition of robust portfolio frontier along the line of mean-variance analysis.We find that model uncertainty has unequal effects on portfolio weights of risky assets when risk-free asset is inaccessible,which leads to under-diversified portfolios.We also find that the two fund separation theorem no longer stands under robust portfolio frontier and the same is true for the zero-beta CAPM model.However,when there is a risk-free asset in the economy,we find that model uncertainty has equal effects on portfolio weights of risky assets,and that the two fund separation theorem still holds,as all robust frontier portfolios can be generated by the risk-free asset and the market portfolio.The CAPM model also can hold under equilibrium except for a change that there is an additional factor representing loading of model uncertainty,and the excess rate of return of any portfolio can be divided into risk premium and uncertainty premium.