Optimal Liquidation

We consider the problem of portfolio liquidation with the aim of minimizing a combination of volatility risk and transaction costs arising from permanent and temporary market impact. For a simple linear cost model, we explicitly construct the efficient frontier in the space of time-dependent liquidation strategies, which have minimum expected cost for a given level of uncertainty. We consider the risk-reward tradeoff both from the point of view of classic mean-variance optimization, and from the standpoint of Value at Risk. This analysis leads to general insights into optimal portfolio trading, and to several applications including a definition of liquidity-adjusted value at risk.