IDEAS home Printed from https://ideas.repec.org/p/zbw/irtgdp/2019004.html
   My bibliography  Save this paper

Constrained Kelly portfolios under alpha-stable laws

Author

Listed:
  • Wesselhöfft, Niels
  • Härdle, Wolfgang Karl

Abstract

This paper provides a detailed framework for modeling portfolios, achieving the highest growth rate under subjective risk constraints such as Value at Risk (VaR) in the presence of stable laws. Although the maximization of the expected logarithm of wealth induces outperforming any other significantly different strategy, the Kelly Criterion implies larger bets than a risk-averse investor would accept. Restricting the Kelly optimization by spectral risk measures, the authors provide a generalized mapping for different measures of growth and security. Analyzing over 30 years of S&P 500 returns for different sampling frequencies, the authors find evidence for leptokurtic behavior for all respective sampling frequencies. Given that lower sampling frequencies imply a smaller number of data points, this paper argues in favor of α-stable laws and its scaling behavior to model financial market returns for a given horizon in an i.i.d. world. Instead of simulating from the class of elliptically stable distributions, a nonparametric scaling approximation, based on the data-set itself, is proposed. Our paper also uncovers that including long put options into the portfolio optimization, improves the growth criterion for a given security level, leading to a new Kelly portfolio providing the highest geometric mean.

Suggested Citation

  • Wesselhöfft, Niels & Härdle, Wolfgang Karl, 2019. "Constrained Kelly portfolios under alpha-stable laws," IRTG 1792 Discussion Papers 2019-004, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    • Handle: RePEc:zbw:irtgdp:2019004
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/230780/1/irtg1792dp2019-004.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. McFarland, James W & Pettit, R Richardson & Sung, Sam K, 1982. "The Distribution of Foreign Exchange Price Changes: Trading Day Effects and Risk Measurement," Journal of Finance, American Finance Association, vol. 37(3), pages 693-715, June.
    3. Phillip Kearns & Adrian Pagan, 1997. "Estimating The Density Tail Index For Financial Time Series," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 171-175, May.
    4. Acerbi, Carlo, 2002. "Spectral measures of risk: A coherent representation of subjective risk aversion," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1505-1518, July.
    5. Basak, Suleyman & Shapiro, Alexander, 2001. "Value-at-Risk-Based Risk Management: Optimal Policies and Asset Prices," Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 371-405.
    6. Westerfield, Randolph, 1977. "The Distribution of Common Stock Price Changes: An Application of Transactions Time and Subordinated Stochastic Models," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(5), pages 743-765, December.
    7. Donald B. Hausch & William T. Ziemba, 1985. "Transactions Costs, Extent of Inefficiencies, Entries and Multiple Wagers in a Racetrack Betting Model," Management Science, INFORMS, vol. 31(4), pages 381-394, April.
    8. J. Tobin, 1958. "Liquidity Preference as Behavior Towards Risk," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 25(2), pages 65-86.
    9. Benoit Mandelbrot, 1963. "New Methods in Statistical Economics," Journal of Political Economy, University of Chicago Press, vol. 71, pages 421-421.
    10. Pavel Cizek & Wolfgang Karl Härdle & Rafal Weron, 2011. "Statistical Tools for Finance and Insurance (2nd edition)," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook1101.
    11. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    12. Hansen, Bruce E., 2015. "Shrinkage Efficiency Bounds," Econometric Theory, Cambridge University Press, vol. 31(4), pages 860-879, August.
    13. Gençay, Ramazan & Dacorogna, Michel & Muller, Ulrich A. & Pictet, Olivier & Olsen, Richard, 2001. "An Introduction to High-Frequency Finance," Elsevier Monographs, Elsevier, edition 1, number 9780122796715.
    14. Roll, Richard, 1973. "Evidence on the "Growth-Optimum" Model," Journal of Finance, American Finance Association, vol. 28(3), pages 551-566, June.
    Full references (including those not matched with items on IDEAS)

    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. Niels Wesselhöfft & Wolfgang K. Härdle, 2020. "Risk-Constrained Kelly Portfolios Under Alpha-Stable Laws," Computational Economics, Springer;Society for Computational Economics, vol. 55(3), pages 801-826, March.
    2. Sonntag, Dominik, 2018. "Die Theorie der fairen geometrischen Rendite [The Theory of Fair Geometric Returns]," MPRA Paper 87082, University Library of Munich, Germany.
    3. Wesselhöfft, Niels & Härdle, Wolfgang Karl, 2019. "Estimating low sampling frequency risk measure by high-frequency data," IRTG 1792 Discussion Papers 2019-003, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    4. Detlef Seese & Christof Weinhardt & Frank Schlottmann (ed.), 2008. "Handbook on Information Technology in Finance," International Handbooks on Information Systems, Springer, number 978-3-540-49487-4, November.
    5. Selçuk, Faruk & Gençay, Ramazan, 2006. "Intraday dynamics of stock market returns and volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 375-387.
    6. Adil Rengim Cetingoz & Jean-David Fermanian & Olivier Gu'eant, 2022. "Risk Budgeting Portfolios: Existence and Computation," Papers 2211.07212, arXiv.org, revised Sep 2023.
    7. Rubing Liang & Binbin Qin & Qiang Xia, 2024. "Bayesian Inference for Mixed Gaussian GARCH-Type Model by Hamiltonian Monte Carlo Algorithm," Computational Economics, Springer;Society for Computational Economics, vol. 63(1), pages 193-220, January.
    8. Luciano de Castro & Antonio F. Galvao & Gabriel Montes-Rojas & Jose Olmo, 2022. "Portfolio selection in quantile decision models," Annals of Finance, Springer, vol. 18(2), pages 133-181, June.
    9. Rockafellar, R. Tyrrell & Uryasev, Stan & Zabarankin, Michael, 2006. "Master funds in portfolio analysis with general deviation measures," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 743-778, February.
    10. Dipankar Mondal & N. Selvaraju, 2022. "Convexity, two-fund separation and asset ranking in a mean-LPM portfolio selection framework," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(1), pages 225-248, March.
    11. Anders Johansson, 2009. "An analysis of dynamic risk in the Greater China equity markets," Journal of Chinese Economic and Business Studies, Taylor & Francis Journals, vol. 7(3), pages 299-320.
    12. Chia-Lin Chang & Jukka Ilomäki & Hannu Laurila & Michael McAleer, 2018. "Long Run Returns Predictability and Volatility with Moving Averages," Risks, MDPI, vol. 6(4), pages 1-18, September.
    13. Hany Shawky & Ronald Forbes & Alan Frankle, 1983. "Liquidity Services and Capital Market Equilibrium: The Case for Money Market Mutual Funds," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 6(2), pages 141-152, June.
    14. Giovanni Bonaccolto & Massimiliano Caporin & Sandra Paterlini, 2018. "Asset allocation strategies based on penalized quantile regression," Computational Management Science, Springer, vol. 15(1), pages 1-32, January.
    15. Rostagno, Luciano Martin, 2005. "Empirical tests of parametric and non-parametric Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) measures for the Brazilian stock market index," ISU General Staff Papers 2005010108000021878, Iowa State University, Department of Economics.
    16. Dimitrios G. Konstantinides & Georgios C. Zachos, 2019. "Exhibiting Abnormal Returns Under a Risk Averse Strategy," Methodology and Computing in Applied Probability, Springer, vol. 21(2), pages 551-566, June.
    17. Bao, Te & Diks, Cees & Li, Hao, 2018. "A generalized CAPM model with asymmetric power distributed errors with an application to portfolio construction," Economic Modelling, Elsevier, vol. 68(C), pages 611-621.
    18. Leitner Johannes, 2005. "Optimal portfolios with expected loss constraints and shortfall risk optimal martingale measures," Statistics & Risk Modeling, De Gruyter, vol. 23(1/2005), pages 49-66, January.
    19. Zubanov, Nick & Cadsby, Bram & Song, Fei, 2017. "The," IZA Discussion Papers 10542, Institute of Labor Economics (IZA).
    20. Paulo Coutinho & Benjamin Miranda Tabak, 2003. "Decentralized Portfolio Management," Brazilian Review of Finance, Brazilian Society of Finance, vol. 1(2), pages 243-270.

    More about this item

    Keywords

    growth-optimal; Kelly criterion; protective put; portfolio optimization; stable distribution; Value at Risk;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

    Statistics

    Access and download statistics

    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:zbw:irtgdp:2019004. 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: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/wfhubde.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.