Existence of Equilibrium and Zero-Beta Pricing Formula in the Capital Asset Pricing Model with Heterogeneous Beliefs

Ning Sun

and

Zaifu Yang

We study a mean-variance capital asset pricing model (CAPM) in which investors have different probability beliefs about assets returns and different attitudes towards risk, all assets are risky, short-selling is allowed and satiation is possible. First, we prove that there exists a competitive equilibrium in the model under a rather general condition. This condition indicates a simple relationship among initial endowment vectors, risk aversion ratio functions, perceived mean vectors and covariance matrices of all investors. Secondly, we derive a zero-beta pricing formula for the model which generalizes the well known Black’s zero-beta pricing formula. In addition, we find in closed form an equilibrium price vector expressed in terms of perceived mean vectors, covariance matrices, and initial endowments of all investors.