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On the Scholes Liquidation Problem

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Author Info
David B. Brown
Bruce Ian Carlin
Miguel Sousa Lobo
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.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 15381.

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Date of creation: Sep 2009
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Handle: RePEc:nbr:nberwo:15381

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Find related papers by JEL classification:
G01 - Financial Economics - - General - - - Financial Crises
G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing

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  1. Bruce Ian Carlin & Miguel Sousa Lobo & S. Viswanathan, 2007. "Episodic Liquidity Crises: Cooperative and Predatory Trading," Journal of Finance, American Finance Association, vol. 62(5), pages 2235-2274, October. [Downloadable!] (restricted)
  2. Myron S. Scholes, 2000. "Crisis and Risk Management," American Economic Review, American Economic Association, vol. 90(2), pages 17-21, May. [Downloadable!] (restricted)
  3. Gur Huberman & Werner Stanzl, 2005. "Optimal Liquidity Trading," Review of Finance, Springer, vol. 9(2), pages 165-200, 06. [Downloadable!] (restricted)
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  4. Mark M. Carhart & Ron Kaniel & David K. Musto & Adam V. Reed, 2002. "Leaning for the Tape: Evidence of Gaming Behavior in Equity Mutual Funds," Journal of Finance, American Finance Association, vol. 57(2), pages 661-693, 04. [Downloadable!] (restricted)
  5. Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, vol. 1(1), pages 1-50, April. [Downloadable!] (restricted)
  6. Markus K. Brunnermeier, 2009. "Deciphering the Liquidity and Credit Crunch 2007-2008," Journal of Economic Perspectives, American Economic Association, vol. 23(1), pages 77-100, Winter.
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  7. Holthausen, Robert W. & Leftwich, Richard W. & Mayers, David, 1990. "Large-block transactions, the speed of response, and temporary and permanent stock-price effects," Journal of Financial Economics, Elsevier, vol. 26(1), pages 71-95, July. [Downloadable!] (restricted)
  8. Madhavan, Ananth & Cheng, Minder, 1997. "In Search of Liquidity: Block Trades in the Upstairs and Downstairs Markets," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 10(1), pages 175-203.
  9. Kraus, Alan & Stoll, Hans R, 1972. "Price Impacts of Block Trading on the New York Stock Exchange," Journal of Finance, American Finance Association, vol. 27(3), pages 569-88, June. [Downloadable!] (restricted)
  10. Tobias Adrian & Hyun Song Shin, 2008. "Financial intermediary leverage and value at risk," Staff Reports 338, Federal Reserve Bank of New York. [Downloadable!]
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