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Hedge-Fund Management With Liquidity Constraint

Author

Listed:
  • HUGO E. RAMIREZ

    (Faculty of Economics, Universidad del Rosario, Calle 12C No. 6-25 Bogotá, COL)

  • PETER DUCK

    (#x2020;School of Mathematics, The University of Manchester, Oxford road, Manchester, M13 9PL, UK)

  • PAUL V. JOHNSON

    (#x2020;School of Mathematics, The University of Manchester, Oxford road, Manchester, M13 9PL, UK)

  • SYDNEY HOWELL

    (#x2021;Business School, The University of Manchester, Oxford road, Manchester, M13 9PL, UK)

Abstract

We propose a model for a manager of a hedge fund with a liquidity constraint, where he is seeking to optimize his utility of wealth, with one and multiple period horizons. By using stochastic control techniques, we state the corresponding multi-dimensional Hamilton–Jacobi–Bellman partial differential equation and we use a robust numerical approximation to obtain its unique viscosity solution. We examine the effects of the liquidity constraint on managerial trading decisions and optimal allocation, finding that the manager behaves in a less risky manner. We also calculate the cost of being at sub-optimal positions as the difference in the certainty equivalent payoff for the manager. Moreover, we compare the values of a benchmark hedge fund with another one having a risky asset with a higher rate of return but less liquidity, finding that higher rate of return with a liquidity constraint does not always lead to greater return.

Suggested Citation

  • Hugo E. Ramirez & Peter Duck & Paul V. Johnson & Sydney Howell, 2019. "Hedge-Fund Management With Liquidity Constraint," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(06), pages 1-31, September.
    • Handle: RePEc:wsi:ijtafx:v:22:y:2019:i:06:n:s0219024919500262
    DOI: 10.1142/S0219024919500262
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    References listed on IDEAS

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