IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v56y2010i5p801-815.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.1100.1143
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.1100.1143?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    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. 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 1655-1695, 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. Brian D. Wright & Jeffrey C. Williams, 1984. "The Welfare Effects of the Introduction of Storage," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 99(1), pages 169-192.
    5. Bensoussan, Alain & Chutani, Anshuman & Sethi, Suresh, 2009. "Optimal Cash Management Under Uncertainty," MPRA Paper 19896, University Library of Munich, Germany.
    6. 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.
    7. 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.
    8. 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.
    9. Juliana M. Nascimento & Warren B. Powell, 2009. "An Optimal Approximate Dynamic Programming Algorithm for the Lagged Asset Acquisition Problem," Mathematics of Operations Research, INFORMS, vol. 34(1), pages 210-237, February.
    10. George M. Constantinides, 2005. "Capital Market Equilibrium with Transaction Costs," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 7, pages 207-227, World Scientific Publishing Co. Pte. Ltd..
    11. Nir Halman & Diego Klabjan & Mohamed Mostagir & Jim Orlin & David Simchi-Levi, 2009. "A Fully Polynomial-Time Approximation Scheme for Single-Item Stochastic Inventory Control with Discrete Demand," Mathematics of Operations Research, INFORMS, vol. 34(3), pages 674-685, August.
    12. 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.
    13. Sethi, Suresh P., 1973. "A Note on Modeling Simple Dynamic Cash Balance Problems," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 8(4), pages 685-687, September.
    14. 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.
    15. 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.
    16. 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.
    17. Jorjani, S & Lamar, BW, 1994. "Cash flow management network models with quantity discounting," Omega, Elsevier, vol. 22(2), pages 149-155, March.
    18. 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.
    19. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ilya O. Ryzhov & Martijn R. K. Mes & Warren B. Powell & Gerald van den Berg, 2019. "Bayesian Exploration for Approximate Dynamic Programming," Operations Research, INFORMS, vol. 67(1), pages 198-214, January.
    2. Fong, Tom Pak Wing & Sze, Angela Kin Wan & Ho, Edmund Ho Cheung, 2022. "Do long-term institutional investors contribute to financial stability? – Evidence from equity investment in Hong Kong and international markets," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 77(C).
    3. Dötz, Niko & Weth, Mark, 2013. "Cash holdings of German open-end equity funds: Does ownership matter?," Discussion Papers 47/2013, Deutsche Bundesbank.
    4. 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).
    5. 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.
    6. Saif Benjaafar & Daniel Jiang & Xiang Li & Xiaobo Li, 2022. "Dynamic Inventory Repositioning in On-Demand Rental Networks," Management Science, INFORMS, vol. 68(11), pages 7861-7878, November.
    7. 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.
    8. 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.
    9. Sandun Perera & Winston Buckley & Hongwei Long, 2018. "Market-reaction-adjusted optimal central bank intervention policy in a forex market with jumps," Annals of Operations Research, Springer, vol. 262(1), pages 213-238, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Francisco Salas-Molina & Juan A. Rodríguez-Aguilar & Montserrat Guillen, 2023. "A multidimensional review of the cash management problem," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-35, December.
    2. 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.
    3. Cici, Gjergji & Dahm, Laura K. & Kempf, Alexander, 2014. "Trading efficiency of fund families: Impact on fund performance and investment behavior," CFR Working Papers 14-14, University of Cologne, Centre for Financial Research (CFR).
    4. Mikhail Simutin, 2014. "Cash Holdings and Mutual Fund Performance," Review of Finance, European Finance Association, vol. 18(4), pages 1425-1464.
    5. Andrew Ang & Dimitris Papanikolaou & Mark M. Westerfield, 2014. "Portfolio Choice with Illiquid Assets," Management Science, INFORMS, vol. 60(11), pages 2737-2761, November.
    6. Jon A. Fulkerson, 2013. "Is Timing Everything? The Value of Mutual Fund Manager Trades," Financial Management, Financial Management Association International, vol. 42(2), pages 243-261, June.
    7. Jonathan Witmer, 2017. "Strategic Complementarities and Money Market Fund Liquidity Management," Staff Working Papers 17-14, Bank of Canada.
    8. Francisco Salas-Molina & David Pla-Santamaria & Juan A. Rodriguez-Aguilar, 2018. "A multi-objective approach to the cash management problem," Annals of Operations Research, Springer, vol. 267(1), pages 515-529, August.
    9. Salas-Molina, Francisco & Martin, Francisco J. & Rodríguez-Aguilar, Juan A. & Serrà, Joan & Arcos, Josep Ll., 2017. "Empowering cash managers to achieve cost savings by improving predictive accuracy," International Journal of Forecasting, Elsevier, vol. 33(2), pages 403-415.
    10. Mark D. Walker & Qingqing Wu, 2019. "Equity issues when in distress," European Financial Management, European Financial Management Association, vol. 25(3), pages 489-519, June.
    11. Gormley, Fionnuala M. & Meade, Nigel, 2007. "The utility of cash flow forecasts in the management of corporate cash balances," European Journal of Operational Research, Elsevier, vol. 182(2), pages 923-935, October.
    12. Xiangbo Liu & Zijun Liu & Zhigang Qiu, 2015. "Investor Cash Flow and Mutual Fund Behavior," Manchester School, University of Manchester, vol. 83(1), pages 56-71, January.
    13. Goncalves-Pinto, Luis & Sotes-Paladino, Juan & Xu, Jing, 2018. "The invisible hand of internal markets in mutual fund families," Journal of Banking & Finance, Elsevier, vol. 89(C), pages 105-124.
    14. Dai, Min & Jin, Hanqing & Liu, Hong, 2011. "Illiquidity, position limits, and optimal investment for mutual funds," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1598-1630, July.
    15. Milan Szabo, 2022. "Meeting Investor Outflows in Czech Bond and Equity Funds: Horizontal or Vertical?," Working Papers 2022/6, Czech National Bank.
    16. Marcos Melo & Feruccio Bilich, 2013. "Expectancy balance model for cash flow," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 37(2), pages 240-252, April.
    17. Milan Szabo, 2022. "Meeting investor outflows in Czech bond and equity funds: horizontal or vertical?," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 49(4), pages 1123-1151, November.
    18. Korniotis, George & Bonaparte, Yosef & Kumar, Alok, 2020. "Income Risk and Stock Market Entry/Exit Decisions," CEPR Discussion Papers 15370, C.E.P.R. Discussion Papers.
    19. Van Son Lai & Duc Khuong Nguyen & William Sodjahin & Issouf Soumaré, 2018. "Discretionary Idiosyncratic Risk, Firm Cash Holdings and Investment," Working Papers 2018-008, Department of Research, Ipag Business School.
    20. Sherrill, D. Eli & Shirley, Sara E. & Stark, Jeffrey R., 2017. "Actively managed mutual funds holding passive investments: What do ETF positions tell us about mutual fund ability?," Journal of Banking & Finance, Elsevier, vol. 76(C), pages 48-64.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ormnsc:v:56:y:2010:i:5:p:801-815. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.