Optimal portfolio liquidation with cross-price impacts on trading

Abstract

Consider the portfolio liquidation problem in which a risk-neutral investor unwinds a large portfolio because of urgent liquidity issues. To measure market liquidity, both permanent and temporary cross-price impacts on trading are taken into consideration. First of all, we formulate this problem as a non-convex optimization problem with some constraints. Then we characterize the structural properties of the optimal liquidation strategies. We find that the investor prefers to sell more liquid assets which have lower permanent and temporary price impacts. In addition, we show that the investor likes to sell more of the assets that have a higher initial price. Finally, we develop a genetic algorithm to obtain the optimal solution for the above problem, and we also illustrate the efficiency of the algorithm. Policy implications of this paper are about how to liquidate a large portfolio in response to difficult economic conditions.