Divergence of opinion and valuation in a mean-variance framework

Purpose – The purpose of this paper is to examine the impact of heterogeneous expectations on the equilibrium value of a risky asset in a capital market populated by investors that choose mean-variance efficient portfolios. Design/methodology/approach – A single-period, discrete-time version of Williams' capital asset pricing model that incorporates heterogeneous beliefs regarding the mean vector of rates of return and homogeneous beliefs regarding the variance-covariance matrix of rates of return is developed. It is then employed to gauge the impact of both divergence of opinion and increases thereof on the equilibrium price of a risky asset. Findings – The value of a risky asset under heterogeneous beliefs differs from that under homogeneous beliefs as the former is biased towards the beliefs of wealthier and/or more risk tolerant investors. If the latter set of investors is optimistic (pessimistic), the value is higher (lower) than that which prevails in the absence of divergence of beliefs. Increasing divergence of opinion likewise affects the equilibrium price of a risky asset to accord more with the beliefs of wealthier and/or more risk tolerant investors. If the latter set of investors is optimistic (pessimistic), increasing dispersion of beliefs causes the value of a risky asset to rise (fall). Originality/value – A novel simplification and application of Williams' model of capital asset pricing is presented. The findings differ from conclusions derived in previous theoretical treatments of divergence of opinions in capital markets.