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Dynamic Programming Models and Algorithms for the Mutual Fund Cash Balance Problem

Listed author(s):
  • Juliana Nascimento


    (Department of Operations Research and Financial Engineering, Princeton University, Princeton, New Jersey 08540)

  • Warren Powell


    (Department of Operations Research and Financial Engineering, Princeton University, Princeton, New Jersey 08540)

Registered author(s):

    Fund managers have to decide the amount of a fund's assets that should be kept in cash, considering the trade-off between being able to meet shareholder redemptions and minimizing the opportunity cost from lost investment opportunities. In addition, they have to consider redemptions by individuals as well as institutional investors, the current performance of the stock market and interest rates, and the pattern of investments and redemptions that are correlated with market performance. We formulate the problem as a dynamic program, but this encounters the classic curse of dimensionality. To overcome this problem, we propose a provably convergent approximate dynamic programming algorithm. We also adapt the algorithm to an online environment, requiring no knowledge of the probability distributions for rates of return and interest rates. We use actual data for market performance and interest rates, and demonstrate the quality of the solution (compared to the optimal) for the top 10 mutual funds in each of nine fund categories. We show that our results closely match the optimal solution (in considerably less time), and outperform two static (newsvendor) models. The result is a simple policy that describes when money should be moved into and out of cash based on market performance.

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    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 56 (2010)
    Issue (Month): 5 (May)
    Pages: 801-815

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    Handle: RePEc:inm:ormnsc:v:56:y:2010:i:5:p:801-815
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    1. Russ Wermers, 2000. "Mutual Fund Performance: An Empirical Decomposition into Stock-Picking Talent, Style, Transactions Costs, and Expenses," Journal of Finance, American Finance Association, vol. 55(4), pages 1655-1703, August.
    2. Michael Faulkender & Rong Wang, 2006. "Corporate Financial Policy and the Value of Cash," Journal of Finance, American Finance Association, vol. 61(4), pages 1957-1990, August.
    3. Wright, Brian D & Williams, Jeffrey C, 1982. "The Economic Role of Commodity Storage," Economic Journal, Royal Economic Society, vol. 92(367), pages 596-614, September.
    4. Sethi, Suresh P., 1973. "A Note on Modeling Simple Dynamic Cash Balance Problems," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 8(04), pages 685-687, September.
    5. Brian D. Wright & Jeffrey C. Williams, 1984. "The Welfare Effects of the Introduction of Storage," The Quarterly Journal of Economics, Oxford University Press, vol. 99(1), pages 169-192.
    6. Bensoussan, Alain & Chutani, Anshuman & Sethi, Suresh, 2009. "Optimal Cash Management Under Uncertainty," MPRA Paper 19896, University Library of Munich, Germany.
    7. Heitor Almeida & Murillo Campello & Michael S. Weisbach, 2004. "The Cash Flow Sensitivity of Cash," Journal of Finance, American Finance Association, vol. 59(4), pages 1777-1804, August.
    8. Hinderer, K. & Waldmann, K. -H., 2001. "Cash management in a randomly varying environment," European Journal of Operational Research, Elsevier, vol. 130(3), pages 468-485, May.
    9. Srinivasan, Venkat & Kim, Yong H, 1986. "Deterministic cash flow management: State of the art and research directions," Omega, Elsevier, vol. 14(2), pages 145-166.
    10. Xuemin (Sterling) Yan, 2006. "The Determinants and Implications of Mutual Fund Cash Holdings: Theory and Evidence," Financial Management, Financial Management Association International, vol. 35(2), pages 67-91, June.
    11. George M. Constantinides, 2005. "Capital Market Equilibrium with Transaction Costs," World Scientific Book Chapters,in: Theory Of Valuation, chapter 7, pages 207-227 World Scientific Publishing Co. Pte. Ltd..
    12. Eppen, Gary D & Fama, Eugene F, 1969. "Cash Balance and Simple Dynamic Portfolio Problems with Proportional Costs," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 10(2), pages 119-133, June.
    13. Penttinen, Markku J., 1991. "Myopic and stationary solutions for stochastic cash balance problems," European Journal of Operational Research, Elsevier, vol. 52(2), pages 155-166, May.
    14. Jorjani, S & Lamar, BW, 1994. "Cash flow management network models with quantity discounting," Omega, Elsevier, vol. 22(2), pages 149-155, March.
    15. Gary D. Eppen & Eugene F. Fama, 1971. "Three Asset Cash Balance and Dynamic Portfolio Problems," Management Science, INFORMS, vol. 17(5), pages 311-319, January.
    16. Sethi, Suresh P. & Thompson, Gerald L., 1970. "Applications of Mathematical Control Theory to Finance: Modeling Simple Dynamic Cash Balance Problems," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 5(4-5), pages 381-394, December.
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