Optimal Portfolio Liquidation with Distress Risk

Abstract

We analyze the problem of an investor who needs to unwind a portfolio in the face of recurring and uncertain liquidity needs, with a model that accounts for both permanent and temporary price impact of trading. We first show that a riskneutral investor who myopically deleverages his position to meet an immediate need or cash always prefers to sell more liquid assets. If the investor faces the possibility of a downstream shock, however, the solution differs in several important ways. If the ensuing shock is sufficiently large, the non-myopic investor unwinds positions more than immediately necessary and, all else being equal, prefers to retain more of the assets with low temporary price impact in order to hedge against the possible distress. More generally, optimal liquidation involves selling strictly more of the assets with a lower ratio of permanent to temporary impact, even if these assets are relatively illiquid. The results suggest that properly accounting for the possibility of future distress should play an important role in managing large portfolios.