Zero-Beta CAPM with Heterogeneous Beliefs

Abstract

This paper extends the standard Black's zero-beta CAPM with homogeneous beliefs to the case with heterogeneous beliefs in terms of risk aversion coefficients, expected payoffs, and variance/covariance matrices of the payoffs of risky assets among heterogeneous agents within the mean-variance framework. Investors are bounded rational in the sense that they make their optimal decision based on their beliefs. By introducing and constructing a consensus belief of the market, we obtain equilibrium prices of risky assets and show that Black's zero-beta CAPM holds under the consensus belief. Various impacts of heterogeneity on the market equilibrium and agents' optimal portfolios are analyzed. In particular, we show that under market aggregation, the biased belief (from the market belief) of investors makes the optimal portfolio of the investor be mean-variance inefficient while the market portfolio is always on the efficient frontier. This demonstrates that, within this framework, bounded rational investors may never achieve their mean-variance efficiency under aggregation. At the same time, the efficiency of the whole market, measured by the efficiency of the market portfolio, can be achieved. The results also shed a light on the empirical finding that managed funds under-perform comparing to the market indices on average.