Dynamic Portfolio Selection in Arbitrage

This paper derives the optimal dynamic strategy for arbitrageurs with a finite horizon and non-myopic preferences facing a mean-reverting arbitrage opportunity (e.g. an equity pairs trade). We find that intertemporal hedging demands play an important role in determining how aggressively arbitrageurs trade against the mispricing and account for a large fraction of the total allocation to the arbitrage opportunity. While arbitrageurs typically bet against the mispricing, we analytically show that there is a critical level of mispricing beyond which further divergence precipitates a reduction in the allocation. When applied to Siamese twin shares our optimal strategy delivers a significant improvement in the realized Sharpe ratio and welfare relative to a simple threshold rule.

[1]  Burton G. Malkiel,et al.  THE VALUATION OF CLOSED-END INVESTMENT-COMPANY SHARES , 1977 .

[2]  Sanford J. Grossman,et al.  The Determinants of the Variability of Stock Market Prices , 1980 .

[3]  R. Shiller.  Stock Prices and Social Dynamics , 1984 .

[4]  C. Granger,et al.  Co-integration and error correction: representation, estimation and testing , 1987 .

[5]  A. Kyle,et al.  Smart Money, Noise Trading and Stock Price Behavior , 1988 .

[6]  Bradford Cornell,et al.  The Mispricing of U.S. Treasury Bonds: A Case Study , 1989 .

[7]  Eduardo S. Schwartz,et al.  Arbitrage in Stock Index Futures , 1990 .

[8]  L. Summers,et al.  Noise Trader Risk in Financial Markets , 1990, Journal of Political Economy.

[9]  Richard A. Ippolito.  Consumer Reaction to Measures of Poor Quality: Evidence from the Mutual Fund Industry , 1992, The Journal of Law and Economics.

[10]  A. Shleifer,et al.  The Limits of Arbitrage , 1995 .

[11]  Glenn Ellison,et al.  Risk Taking by Mutual Funds as a Response to Incentives , 1995, Journal of Political Economy.

[12]  Ts Kim,et al.  Dynamic Nonmyopic Portfolio Behavior , 1994 .

[13]  Luis M. Viceira,et al.  Consumption and Portfolio Decisions When Expected Returns are Time Varying , 1996 .

[14]  William N. Goetzmann,et al.  Pairs Trading: Performance of a Relative Value Arbitrage Rule , 1998 .

[15]  Peter Tufano,et al.  Costly Search and Mutual Fund Flows , 1998 .

[16]  N. Shephard,et al.  Likelihood INference for Discretely Observed Non-linear Diffusions , 2001 .

[17]  Kenneth A. Froot,et al.  How are Stock Prices Affected by the Location of Trade? , 1998 .

[18]  C. Alexander,et al.  Optimal hedging using cointegration , 1999, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[19]  Yangru Wu,et al.  Mean Reversion across National Stock Markets and Parametric Contrarian Investment Strategies , 2000 .

[20]  Erik Stafford,et al.  Limited Arbitrage in Equity Markets , 2000 .

[21]  Benjamin Croitoru,et al.  Equilibrium Mispricing in a Capital Market with Portfolio Constraints , 2000 .

[22]  Jun Liu,et al.  Losing Money on Arbitrage: Optimal Dynamic Portfolio Choice in Markets with Arbitrage Opportunities , 2000 .

[23]  D. Gasbarro,et al.  Evidence on the Mean‐Reverting Tendencies of Closed‐End Fund Discounts , 2003 .

[24]  Carol Alexander,et al.  The Cointegration Alpha: Enhanced Index Tracking and Long-Short Equity Market Neutral Strategies , 2002 .

[25]  Convergence Trading with Wealth Effects: An Amplification Mechanism in Financial Markets , 2002 .

[26]  R. Thaler,et al.  Anomalies: The Law of One Price in Financial Markets , 2003 .

[27]  Michael Boguslavsky,et al.  Arbitrage under Power , 2004 .

[28]  V. Agarwal,et al.  Flows, Performance, and Managerial Incentives in Hedge Funds , 2004 .