This paper provides a simple framework to study the effect of disagreement in a multi-asset market equilibrium by considering two agents who disagree about expected returns, variances, and correlation of returns of two risky assets. When agents' subjective beliefs are characterized by mean preserving spreads of a benchmark homogeneous belief, we show that the effect of the disagreement does not cancel out in general and the effect in a multi-asset market can be very different from a single asset market. In particular, the market risk premium can increase and the risk-free rate can decrease significantly even when the market is overoptimistic and overconfident.3 When the distributions of returns are normal, being pessimistic means perceiving a lower expected return than the one under the objective belief, and being doubtful means perceiving a larger standard deviation of returns than the one under the objective belief. 4 Meaning that more risk-tolerant agents perceive low expected returns (are more doubtful). , 2 = [ ] and ri,jk = Correli [rj, rk]. We use Bi: = (mi, Si) to denote the subjective belief of agent i. Disagreement in a Multi-Asset Market 8 The pessimism P measures the average pessimism across assets weighted by their weights in the market portfolio. However, since the amount of optimism/pessimism is the same for each asset, q1 = q2 = q, the average pessimism is simply given by -q.
Disagreement in a Multi-Asset Market