IDEAS home Printed from https://ideas.repec.org/a/inm/ordeca/v10y2013i3p189-199.html
   My bibliography  Save this article

Optimal Betting Under Parameter Uncertainty: Improving the Kelly Criterion

Author

Listed:
  • Rose D. Baker

    (Centre for Sports Business, Salford Business School, University of Salford, Salford M5 4WT, United Kingdom)

  • Ian G. McHale

    (Centre for Sports Business, Salford Business School, University of Salford, Salford M5 4WT, United Kingdom)

Abstract

The Kelly betting criterion ignores uncertainty in the probability of winning the bet and uses an estimated probability. In general, such replacement of population parameters by sample estimates gives poorer out-of-sample than in-sample performance. We show that to improve out-of-sample performance the size of the bet should be shrunk in the presence of this parameter uncertainty, and compare some estimates of the shrinkage factor. From a simulation study and from an analysis of some tennis betting data we show that the shrunken Kelly approaches developed here offer an improvement over the “raw” Kelly criterion. One approximate estimate of the shrinkage factor gives a “back of envelope” correction to the Kelly criterion that could easily be used by bettors. We also study bet shrinkage and swelling for general risk-averse utility functions and discuss the general implications of such results for decision theory.

Suggested Citation

  • Rose D. Baker & Ian G. McHale, 2013. "Optimal Betting Under Parameter Uncertainty: Improving the Kelly Criterion," Decision Analysis, INFORMS, vol. 10(3), pages 189-199, September.
    • Handle: RePEc:inm:ordeca:v:10:y:2013:i:3:p:189-199
    DOI: 10.1287/deca.2013.0271
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/deca.2013.0271
    Download Restriction: no
    File URL: https://libkey.io/10.1287/deca.2013.0271?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. Leonard Maclean & Edward Thorp & William Ziemba, 2010. "Long-term capital growth: the good and bad properties of the Kelly and fractional Kelly capital growth criteria," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 681-687.
    2. L. C. MacLean & W. T. Ziemba & G. Blazenko, 1992. "Growth Versus Security in Dynamic Investment Analysis," Management Science, INFORMS, vol. 38(11), pages 1562-1585, November.
    3. Matus Medo & Yury M. Pis'mak & Yi-Cheng Zhang, 2008. "Diversification and limited information in the Kelly game," Papers 0803.1364, arXiv.org, revised Jul 2008.
    4. Chris Whitrow, 2007. "Algorithms for optimal allocation of bets on many simultaneous events," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 56(5), pages 607-623, November.
    5. Johnnie E. V. Johnson & Owen Jones & Leilei Tang, 2006. "Exploring Decision Makers' Use of Price Information in a Speculative Market," Management Science, INFORMS, vol. 52(6), pages 897-908, June.
    6. Kan, Raymond & Zhou, Guofu, 2007. "Optimal Portfolio Choice with Parameter Uncertainty," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 42(3), pages 621-656, September.
    7. Kevin F. McCardle & Robert L. Winkler, 1992. "Repeated Gambles, Learning, and Risk Aversion," Management Science, INFORMS, vol. 38(6), pages 807-818, June.
    8. Joseph B. Kadane, 2011. "Partial-Kelly Strategies and Expected Utility: Small-Edge Asymptotics," Decision Analysis, INFORMS, vol. 8(1), pages 4-9, March.
    9. Boulier, Bryan L. & Stekler, H. O., 1999. "Are sports seedings good predictors?: an evaluation," International Journal of Forecasting, Elsevier, vol. 15(1), pages 83-91, February.
    10. Peter A. Griffin, 1984. "Different Measures of Win Rate for Optimal Proportional Betting," Management Science, INFORMS, vol. 30(12), pages 1540-1547, December.
    11. Leonard Maclean & William Ziemba & Yuming Li, 2005. "Time to wealth goals in capital accumulation," Quantitative Finance, Taylor & Francis Journals, vol. 5(4), pages 343-355.
    12. Grant, Andrew & Johnstone, David, 2010. "Finding profitable forecast combinations using probability scoring rules," International Journal of Forecasting, Elsevier, vol. 26(3), pages 498-510, July.
    13. MacLean, Leonard C. & Sanegre, Rafael & Zhao, Yonggan & Ziemba, William T., 2004. "Capital growth with security," Journal of Economic Dynamics and Control, Elsevier, vol. 28(5), pages 937-954, February.
    14. Medo, Matúš & Pis’mak, Yury M. & Zhang, Yi-Cheng, 2008. "Diversification and limited information in the Kelly game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(24), pages 6151-6158.
    15. Leonard MacLean & William Ziemba, 1999. "Growth versus security tradeoffs indynamic investment analysis," Annals of Operations Research, Springer, vol. 85(0), pages 193-225, January.
    16. David J. Johnstone & Victor Richmond R. Jose & Robert L. Winkler, 2011. "Tailored Scoring Rules for Probabilities," Decision Analysis, INFORMS, vol. 8(4), pages 256-268, 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. Barge-Gil, Andrés & García-Hiernaux, Alfredo, 2019. "Staking plans in sports betting under unknown true probabilities of the event," MPRA Paper 92196, University Library of Munich, Germany.
    2. Rakesh K. Sarin, 2013. "From the Editor —Optimal Betting, Reducing Unnecessary Mammography in Breast Cancer Diagnosis, Product Line Design, and Value of Information," Decision Analysis, INFORMS, vol. 10(3), pages 187-188, September.
    3. Michael R. Metel, 2018. "Kelly Betting on Horse Races with Uncertainty in Probability Estimates," Decision Analysis, INFORMS, vol. 15(1), pages 47-52, March.
    4. Andrés Barge-Gil & Alfredo Garcia-Hiernaux, 2020. "Staking in Sports Betting Under Unknown Probabilities: Practical Guide for Profitable Bettors," Journal of Sports Economics, , vol. 21(6), pages 593-609, August.
    5. Chu Dani & Wu Yifan & Swartz Tim B., 2018. "Modified Kelly criteria," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 14(1), pages 1-11, March.
    6. Hubáček, Ondřej & Šír, Gustav, 2023. "Beating the market with a bad predictive model," International Journal of Forecasting, Elsevier, vol. 39(2), pages 691-719.
    7. Andrew Grant & David Johnstone & Oh Kang Kwon, 2019. "A Probability Scoring Rule for Simultaneous Events," Decision Analysis, INFORMS, vol. 16(4), pages 301-313, December.
    8. Reza Yarbakhsh & Mahdieh Soleymani Baghshah & Hamidreza Karimaghaie, 2023. "Predicting risk/reward ratio in financial markets for asset management using machine learning," Papers 2311.09148, arXiv.org.

    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. D. J. Johnstone & S. Jones & V. R. R. Jose & M. Peat, 2013. "Measures of the economic value of probabilities of bankruptcy," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 176(3), pages 635-653, June.
    2. David J Johnstone, 2023. "Capital budgeting and Kelly betting," Australian Journal of Management, Australian School of Business, vol. 48(3), pages 625-651, August.
    3. G. Bottazzi & D. Giachini, 2019. "Far from the madding crowd: collective wisdom in prediction markets," Quantitative Finance, Taylor & Francis Journals, vol. 19(9), pages 1461-1471, September.
    4. Joseph B. Kadane, 2011. "Partial-Kelly Strategies and Expected Utility: Small-Edge Asymptotics," Decision Analysis, INFORMS, vol. 8(1), pages 4-9, March.
    5. David Johnstone & Stewart Jones & Oliver Jones & Steve Tulig, 2021. "Scoring Probability Forecasts by a User’s Bets Against a Market Consensus," Decision Analysis, INFORMS, vol. 18(3), pages 169-184, September.
    6. Matus Medo & Chi Ho Yeung & Yi-Cheng Zhang, 2008. "How to quantify the influence of correlations on investment diversification," Papers 0805.3397, arXiv.org, revised Feb 2009.
    7. Hubáček, Ondřej & Šír, Gustav, 2023. "Beating the market with a bad predictive model," International Journal of Forecasting, Elsevier, vol. 39(2), pages 691-719.
    8. David J. Johnstone, 2007. "The Parimutuel Kelly Probability Scoring Rule," Decision Analysis, INFORMS, vol. 4(2), pages 66-75, June.
    9. D. J. Johnstone, 2021. "Accounting information, disclosure, and expected utility: Do investors really abhor uncertainty?," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 48(1-2), pages 3-35, January.
    10. MacLean, Leonard C. & Zhao, Yonggan & Ziemba, William T., 2016. "Optimal capital growth with convex shortfall penalties," LSE Research Online Documents on Economics 65486, London School of Economics and Political Science, LSE Library.
    11. Scholz, Peter, 2012. "Size matters! How position sizing determines risk and return of technical timing strategies," CPQF Working Paper Series 31, Frankfurt School of Finance and Management, Centre for Practical Quantitative Finance (CPQF).
    12. Leonard C. MacLean & Yonggan Zhao & William T. Ziemba, 2016. "Optimal capital growth with convex shortfall penalties," Quantitative Finance, Taylor & Francis Journals, vol. 16(1), pages 101-117, January.
    13. Grant, Andrew & Johnstone, David, 2010. "Finding profitable forecast combinations using probability scoring rules," International Journal of Forecasting, Elsevier, vol. 26(3), pages 498-510, July.
    14. E. Babaei & I.V. Evstigneev & K.R. Schenk-Hoppé & M.V. Zhitlukhin, 2018. "Von Neumann-Gale Dynamics, Market Frictions, and Capital Growth," Economics Discussion Paper Series 1816, Economics, The University of Manchester.
    15. Luo Yong & Zhu Bo & Tang Yong, 2015. "Dynamic optimal capital growth of diversified investment," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(3), pages 577-588, March.
    16. Ziemba, William, 2016. "A response to Professor Paul A. Samuelson's objections to Kelly capital growth investing," LSE Research Online Documents on Economics 119002, London School of Economics and Political Science, LSE Library.
    17. Medo, Matús & Yeung, Chi Ho & Zhang, Yi-Cheng, 2009. "How to quantify the influence of correlations on investment diversification," International Review of Financial Analysis, Elsevier, vol. 18(1-2), pages 34-39, March.
    18. MacLean, Leonard C. & Zhao, Yonggan & Ziemba, William T., 2014. "Optimal capital growth with convex shortfall penalties," LSE Research Online Documents on Economics 59292, London School of Economics and Political Science, LSE Library.
    19. Whelan, Karl, 2023. "Fortune's Formula or the Road to Ruin? The Generalized Kelly Criterion With Multiple Outcomes," MPRA Paper 116927, University Library of Munich, Germany.
    20. Andrew Grant & David Johnstone & Oh Kang Kwon, 2008. "Optimal Betting Strategies for Simultaneous Games," Decision Analysis, INFORMS, vol. 5(1), pages 10-18, March.

    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:ordeca:v:10:y:2013:i:3:p:189-199. 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.