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Losing Money on Arbitrages: Optimal Dynamic Portfolio Choice in Markets with Arbitrage Opportunities

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  • Liu, Jun
  • Longstaff, Francis A
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    Abstract

    In theory, an investor can make infinite profits by taking unlimited positions in an arbitrage. In reality, however, investors must satisfy margin requirements which completely change the economics of arbitrage. We derive the optimal investment policy for a risk-averse investor in a market where there are arbitrage opportunities. We show that it is often optimal to underinvest in the arbitrage by taking a smaller position than margin constraints allow. In some cases, it is actually optimal for an investor to walk away from a pure arbitrage opportunity. Even when the optimal policy is followed, the arbitrage strategy may underperform the riskless asset or have an unimpressive Sharpe ratio. Furthermore, the arbitrage portfolio typically experiences losses at some point before the final convergence date. These results have important implications for the role of arbitrageurs in financial markets.

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    Bibliographic Info

    Paper provided by Anderson Graduate School of Management, UCLA in its series University of California at Los Angeles, Anderson Graduate School of Management with number qt48k8f97f.

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    Date of creation: 01 Jun 2000
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    Handle: RePEc:cdl:anderf:qt48k8f97f

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    1. Jean-Pierre Zigrand, 1999. "Arbitrage and Endogenous Market Integration," FMG Discussion Papers dp319, Financial Markets Group.
    2. Brennan, Michael J & Schwartz, Eduardo S, 1990. "Arbitrage in Stock Index Futures," The Journal of Business, University of Chicago Press, vol. 63(1), pages S7-31, January.
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    6. Willard, Gregory A & Dybvig, Philip H, 1999. "Empty Promises and Arbitrage," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 807-34.
    7. Andrei Shleifer & Robert W. Vishny, 1995. "The Limits of Arbitrage," NBER Working Papers 5167, National Bureau of Economic Research, Inc.
    8. Longstaff, Francis A, 1995. "Option Pricing and the Martingale Restriction," Review of Financial Studies, Society for Financial Studies, vol. 8(4), pages 1091-1124.
    9. De Long, J Bradford & Andrei Shleifer & Lawrence H. Summers & Robert J. Waldmann, 1990. "Noise Trader Risk in Financial Markets," Journal of Political Economy, University of Chicago Press, vol. 98(4), pages 703-38, August.
    10. Hindy, Ayman, 1995. "Viable prices in financial markets with solvency constraints," Journal of Mathematical Economics, Elsevier, vol. 24(2), pages 105-135.
    11. Carl Ackermann & Richard McEnally & David Ravenscraft, 1999. "The Performance of Hedge Funds: Risk, Return, and Incentives," Journal of Finance, American Finance Association, vol. 54(3), pages 833-874, 06.
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    13. Basak, Suleyman & Croitoru, Benjamin, 2000. "Equilibrium Mispricing in a Capital Market with Portfolio Constraints," Review of Financial Studies, Society for Financial Studies, vol. 13(3), pages 715-48.
    14. Dumas, Bernard, 1992. "Dynamic Equilibrium and the Real Exchange Rate in a Spatially Separated World," Review of Financial Studies, Society for Financial Studies, vol. 5(2), pages 153-80.
    15. Fung, William & Hsieh, David A, 1997. "Empirical Characteristics of Dynamic Trading Strategies: The Case of Hedge Funds," Review of Financial Studies, Society for Financial Studies, vol. 10(2), pages 275-302.
    16. Mark Grinblatt & Francis A. Longstaff, 2000. "Financial Innovation and the Role of Derivative Securities: An Empirical Analysis of the Treasury STRIPS Program," Journal of Finance, American Finance Association, vol. 55(3), pages 1415-1436, 06.
    17. Chen Zhiwu, 1995. "Financial Innovation and Arbitrage Pricing in Frictional Economies," Journal of Economic Theory, Elsevier, vol. 65(1), pages 117-135, February.
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    Cited by:
    1. John H. Cochrane, 2002. "Stocks as Money: Convenience Yield and the Tech-Stock Bubble," NBER Working Papers 8987, National Bureau of Economic Research, Inc.
    2. Liu, Jun & Longstaff, Francis A. & Mandell, Ravit E., 2000. "The Market Price of Credit Risk: An Empirical Analysis of Interest Rate Swap Spreads," University of California at Los Angeles, Anderson Graduate School of Management qt0zw4f9w6, Anderson Graduate School of Management, UCLA.
    3. Longstaff, Francis A., 2001. "The Flight-to-Liquidity Premium in U.S. Treasury Bond Prices," University of California at Los Angeles, Anderson Graduate School of Management qt7dc0t95b, Anderson Graduate School of Management, UCLA.
    4. Charles M. Jones & Owen A. Lamont, 2001. "Short Sale Constraints and Stock Returns," NBER Working Papers 8494, National Bureau of Economic Research, Inc.
    5. Vladislav Kargin, 2003. "Optimal Convergence Trading," Papers math/0302104, arXiv.org, revised Aug 2003.
    6. Francis A. Longstaff, 2004. "The Flight-to-Liquidity Premium in U.S. Treasury Bond Prices," The Journal of Business, University of Chicago Press, vol. 77(3), pages 511-526, July.
    7. Longstaff, Francis A & Santa-Clara, Pedro & Schwartz, Eduardo S, 2000. "The Relative Valuation of Caps and Swaptions: Theory and Empirical Evidence," University of California at Los Angeles, Anderson Graduate School of Management qt65f1914p, Anderson Graduate School of Management, UCLA.
    8. Xiong, Wei, 2001. "Convergence trading with wealth effects: an amplification mechanism in financial markets," Journal of Financial Economics, Elsevier, vol. 62(2), pages 247-292, November.

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