The Heterogeneous Agent of CAPM based on Asset Chains
The key assumption of the classical Capital Asset Pricing Model(CAPM) is homogeneous belief,which means all investors hold the same expectation about the probability distribution for future returns of assets.Under this assumption,each efficient portfolio on the capital market line means a combination of risk-free asset and market portfolio of risky asset.The efficient portfolio contradicts with people's decisions on financial investments activities in the real world.For instance,besides the index-linked instrument products a large amount of differentiated financial products are provided for investors. The research proposes the assumption of heterogeneous beliefs based on the asset chains.While the asset formation changes on asset chains,the asset value evolves from book value of physical assets to intrinsic value of company,and then to market value of listed company.Investors hold heterogeneous beliefs because they have different opinions about the process of changing asset value on each node of asset chains. The research analyzes the difference of risk investment portfolios for heterogeneous investors by solving continuous time optimal investment and consumption models.The result shows that the two-fund separation theorem does not hold under heterogeneous belief.Investors hold different portfolios of risky assets instead of the unique market portfolio.Therefore the risk-free asset and unique market portfolios cannot construct efficient portfolios.Furthermore,the research finds that risk-free asset and three risky funds can help construct all efficient portfolios.These risky funds reflect three main systematic risks,including macroeconomic trend,market average rate of profit,and market liquidity.The construction of each risky fund is related to the probability distribution of assets return instead of the wealth and preference of investors.Therefore,the capital market line of classical CAPM can be transformed into a 4-dimension capital market hyperplane.Investors can select a portfolio among these three risky funds to hedge systematic risks according to their aversion to different systematic risks.The risk premium is equal to the summation of risk premium of each risky fund multiplying the corresponding beta instead of the risk premium of the unique market portfolio and beta. The data used in this research include trade and quote prices for a set of Shanghai A stocks traded from January 1999 to June 2008.By decomposing the assets return with the wavelet analysis,the research finds that asset returns have different sensitivities to different systematic risk factors.Therefore,investment portfolios based on multiple risky funds fit well with the requirement of investors with different opinions.The research finds that the model can differentiate the impact of asset returns between different systematic risks and help effectively explain investors' expectation about asset returns.