Do heterogeneous beliefs diversify market risk?

It is believed that diversity is good for our society, but is it good for financial markets? In particular, does the diversity with respect to beliefs among investors reduce the market risk of risky assets? The current paper aims to answer this question. Within the standard mean-variance framework, we introduce heterogeneous beliefs not only in risk preferences and expected payoffs but also in variances/covariances. By aggregating heterogeneous beliefs into a market consensus belief, we obtain capital asset pricing model-like equilibrium price and return relationships under heterogeneous beliefs. We show that the market aggregate behaviour is in principle a weighted average of heterogeneous individual behaviours. The impact of heterogeneity on the market equilibrium price and risk premium is examined in general. In particular, we give a positive answer to the question in the title by considering some special structure in heterogeneous beliefs. In addition, we provide an explanation of Miller's long-standing hypothesis on the relation between a stock's risk and the divergence of opinions.