Optimal slice of a block trade

Abstract

In liquidation of a block trade, it is common to divide execution in order to minimize the total transaction cost, thereby balancing market impact costs and volatility effects. This paper formulates the execution scheduling as a static optimization problem assuming linear market impact and derives explicit solutions. It is shown that optimal execution duration and average cost are increasing functions of the initial portfolio size, which is consistent with trading practice and empirical studies. Our model provides explicit solutions for minimum liquidity-adjusted value-at-risk (L-VaR), which is particularly useful for risk management.