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

Author

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  • 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)

Abstract

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.

Suggested Citation

  • Juliana Nascimento & Warren Powell, 2010. "Dynamic Programming Models and Algorithms for the Mutual Fund Cash Balance Problem," Management Science, INFORMS, vol. 56(5), pages 801-815, May.
    • Handle: RePEc:inm:ormnsc:v:56:y:2010:i:5:p:801-815
    DOI: 10.1287/mnsc.1100.1143
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    References listed on IDEAS

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    2. Dötz, Niko & Weth, Mark, 2013. "Cash holdings of German open-end equity funds: Does ownership matter?," Discussion Papers 47/2013, Deutsche Bundesbank.
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    4. Fong, Tom Pak Wing & Sze, Angela Kin Wan & Ho, Edmund Ho Cheung, 2018. "Determinants of equity mutual fund flows – Evidence from the fund flow dynamics between Hong Kong and global markets," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 57(C), pages 231-247.
    5. Daniel R. Jiang & Warren B. Powell, 2015. "An Approximate Dynamic Programming Algorithm for Monotone Value Functions," Operations Research, INFORMS, vol. 63(6), pages 1489-1511, December.
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    8. Andrei Jirnyi & Vadym Lepetyuk, 2011. "A reinforcement learning approach to solving incomplete market models with aggregate uncertainty," Working Papers. Serie AD 2011-21, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    9. Kerstin Lamert & Benjamin R. Auer & Ralf Wunderlich, 2023. "Discretization of continuous-time arbitrage strategies in financial markets with fractional Brownian motion," Papers 2311.15635, arXiv.org.

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