Strategic Trading with Wealth Effects

We analyze asset prices and liquidity in an economy with large investors and many risky assets. The model allows for general investors' preferences and distributions of asset payoffs. We propose a constructive solution approach: solving for equilibrium reduces to solving nonlinear first-order ODE. We show that the equilibrium is unique under mild restrictions on payoffs and preferences. Liquidity risk is priced in equilibrium, leading to deviations from the consumption-CAPM. In stark contrast to a constant absolute risk aversion (CARA) benchmark, in a model with wealth effects, we obtain (1) illiquidity of risk-free assets (such as, e.g., Treasuries); (2) illiquidity contagion (a sell-off in one asset may have a price impact on assets with unrelated fundamentals) and asymmetry in cross-asset price impacts; (3) market liquidity may decrease in the number of traders and their wealth; and (4) in the presence of liquidity shortage, price impact may become negative giving rise to an illiquidity premium in asset prices; (5) safe assets are more illiquid because they have a larger price impact. In the presence of wealth heterogeneity, large traders trade more but also reduce their demands more. As a group, they account for a smaller fraction of orders compared to small investors. Fatter-tailed wealth distribution makes markets less liquid.