Liquidity and Valuation in an Uncertain Market with Multiple Risky Assets and Difference of Opinions

This paper explores the implication of asset correlation on illiquid risky assets arise from ambiguity in a market populated with traders who agree to disagree. An equilibrium model is proposed in a mean-variance framework. It focuses on how heterogeneity beliefs and ambiguity about a risky asset affects another through correlation; and in turn affects demand and market prices. After experiencing a common shock, traders become uncertain about future asset values respectively to their beliefs; asset prices deviate from equilibrium, forming bid and ask spreads. The findings seem to suggest (i) given enough ambiguity about expected payoffs, assets become illiquid in which trades cease to exist between bid and ask prices. The size of the spreads however depends on the correlation between risky assets. A spread reduction is generally observed in a more risky asset and an increase in a less risky asset with positive correlation. Thus, traders are more likely to trade an asset with greater expected payoff to reflect diminishing portfolio diversification advantage. (ii) Given trades are nonexistent for some level of ambiguity; there must be a condition that allows trades to exist. Threshold to trade depends on the level of common shock and the diversity of traders beliefs, but interestingly independent of correlation. Due to this disconnection between correlation and threshold to trade; in a market with many illiquid assets, a risky asset that is liquid cannot influence the liquidity of another related asset. Rather, liquidity is affected by the diversity of traders ’ beliefs and the size of common shock. Trading prices are thus derived. (iii) Contrary to general thinking, heterogeneity does not always decrease bid and ask spread, it depend on the level of initial equilibrium determined by market belief; in particular, the variance-covariance matrix depends on correlation. By relaxing independence between risky assets, the model captures the interdependence and in some cases lack thereof between bid and ask spreads, and thus prices. 1