On the Scholes Liquidation Problem

Abstract

How should an investor unwind a portfolio in the face of recurring and uncertain liquidity needs? We propose a model of portfolio liquidation in two periods to investigate this question, initially posed by Myron Scholes following the fall of Long Term Capital Management. We show that when the expectation of future liquidity needs is low, the optimal solution involves selling assets that have low permanent and temporary price impacts of trading. However, when there is a high probability of a large future liquidity need, the optimal solution involves retaining assets that have a small temporary impact of trading. In the face of potential future adversity, there is a high option-value to the temporary component of liquidity. The permanent component of liquidity does not share this feature, so that investors will prefer to sell assets with a low ratio of permanent to temporary price impact in the early stages of a crisis, and to hold on to assets with a high ratio of permanent to temporary price impact to protect themselves against an aggravation of the crisis.