Liquidity risk and the dynamics of arbitrage capital

We develop a dynamic model of liquidity provision, in which hedgers can trade multiple risky assets with arbitrageurs. We compute the equilibrium in closed form when arbitrageurs’ utility over consumption is logarithmic or risk-neutral with a non-negativity constraint. Liquidity is increasing in arbitrageur wealth, while asset volatilities, correlations, and expected returns are hump-shaped. Liquidity is a priced risk factor: assets that suffer the most when liquidity decreases, e.g., those with volatile cashflows or in high supply by hedgers, offer the highest expected returns. When hedging needs are strong, arbitrageurs can choose to provide less liquidity even though liquidity provision is more profitable.