IDEAS home Printed from https://ideas.repec.org/a/spr/comgts/v18y2021i3d10.1007_s10287-021-00395-8.html
   My bibliography  Save this article

Quantile-based optimal portfolio selection

Author

Listed:
  • Taras Bodnar

    (Stockholm University)

  • Mathias Lindholm

    (Stockholm University)

  • Erik Thorsén

    (Stockholm University)

  • Joanna Tyrcha

    (Stockholm University)

Abstract

In this paper the concept of quantile-based optimal portfolio selection is introduced and a specific portfolio connected to it, the conditional value-of-return (CVoR) portfolio, is proposed. The CVoR is defined as the mean excess return or the conditional value-at-risk (CVaR) of the return distribution. The portfolio selection consists solely of quantile-based risk and return measures. Financial institutions that work in the context of Basel 4 use CVaR as a risk measure. In this regulatory framework sufficient and necessary conditions for optimality of the CVoR portfolio are provided under a general distributional assumption. Moreover, it is shown that the CVoR portfolio is mean-variance efficient when the returns are assumed to follow an elliptically contoured distribution. Under this assumption the closed-form expression for the weights and characteristics of the CVoR portfolio are obtained. Finally, the introduced methods are illustrated in an empirical study based on monthly data of returns on stocks included in the S&P index. It is shown that the new portfolio selection strategy outperforms several alternatives in terms of the final investor wealth.

Suggested Citation

  • Taras Bodnar & Mathias Lindholm & Erik Thorsén & Joanna Tyrcha, 2021. "Quantile-based optimal portfolio selection," Computational Management Science, Springer, vol. 18(3), pages 299-324, July.
    • Handle: RePEc:spr:comgts:v:18:y:2021:i:3:d:10.1007_s10287-021-00395-8
    DOI: 10.1007/s10287-021-00395-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10287-021-00395-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10287-021-00395-8?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Gordon J. Alexander & Alexandre M. Baptista, 2004. "A Comparison of VaR and CVaR Constraints on Portfolio Selection with the Mean-Variance Model," Management Science, INFORMS, vol. 50(9), pages 1261-1273, September.
    2. Taras Bodnar & Solomiia Dmytriv & Nestor Parolya & Wolfgang Schmid, 2017. "Tests for the weights of the global minimum variance portfolio in a high-dimensional setting," Papers 1710.09587, arXiv.org, revised Jul 2019.
    3. 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.
    4. Louis K.C. Chan & Jason Karceski & Josef Lakonishok, 1999. "On Portfolio Optimization: Forecasting Covariances and Choosing the Risk Model," NBER Working Papers 7039, National Bureau of Economic Research, Inc.
    5. Bodnar, Taras & Mazur, Stepan & Okhrin, Yarema, 2017. "Bayesian estimation of the global minimum variance portfolio," European Journal of Operational Research, Elsevier, vol. 256(1), pages 292-307.
    6. Alexander, Gordon J. & Baptista, Alexandre M., 2002. "Economic implications of using a mean-VaR model for portfolio selection: A comparison with mean-variance analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 26(7-8), pages 1159-1193, July.
    7. Eling, Martin, 2014. "Fitting asset returns to skewed distributions: Are the skew-normal and skew-student good models?," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 45-56.
    8. B. Fastrich & S. Paterlini & P. Winker, 2015. "Constructing optimal sparse portfolios using regularization methods," Computational Management Science, Springer, vol. 12(3), pages 417-434, July.
    9. Golosnoy, Vasyl & Gribisch, Bastian & Seifert, Miriam Isabel, 2019. "Exponential smoothing of realized portfolio weights," Journal of Empirical Finance, Elsevier, vol. 53(C), pages 222-237.
    10. David Bauder & Taras Bodnar & Nestor Parolya & Wolfgang Schmid, 2021. "Bayesian mean–variance analysis: optimal portfolio selection under parameter uncertainty," Quantitative Finance, Taylor & Francis Journals, vol. 21(2), pages 221-242, February.
    11. Taras Bodnar & Wolfgang Schmid, 2009. "Econometrical analysis of the sample efficient frontier," The European Journal of Finance, Taylor & Francis Journals, vol. 15(3), pages 317-335.
    12. Mahmoud Hamada & Emiliano A. Valdez, 2008. "CAPM and Option Pricing With Elliptically Contoured Distributions," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(2), pages 387-409, June.
    13. 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.
    14. Wolfgang Schmid & Taras Zabolotskyy, 2008. "On the existence of unbiased estimators for the portfolio weights obtained by maximizing the Sharpe ratio," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 92(1), pages 29-34, February.
    15. Merton, Robert C., 1972. "An Analytic Derivation of the Efficient Portfolio Frontier," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 7(4), pages 1851-1872, September.
    16. Owen, Joel & Rabinovitch, Ramon, 1983. "On the Class of Elliptical Distributions and Their Applications to the Theory of Portfolio Choice," Journal of Finance, American Finance Association, vol. 38(3), pages 745-752, June.
    17. Merton, Robert C., 1980. "On estimating the expected return on the market : An exploratory investigation," Journal of Financial Economics, Elsevier, vol. 8(4), pages 323-361, December.
    18. Ban Kawas & Aurelie Thiele, 2017. "Log-robust portfolio management with parameter ambiguity," Computational Management Science, Springer, vol. 14(2), pages 229-256, April.
    19. Adam, Alexandre & Houkari, Mohamed & Laurent, Jean-Paul, 2008. "Spectral risk measures and portfolio selection," Journal of Banking & Finance, Elsevier, vol. 32(9), pages 1870-1882, September.
    20. Begoña Font, 2016. "Bootstrap estimation of the efficient frontier," Computational Management Science, Springer, vol. 13(4), pages 541-570, October.
    21. Huang, Dashan & Zhu, Shushang & Fabozzi, Frank J. & Fukushima, Masao, 2010. "Portfolio selection under distributional uncertainty: A relative robust CVaR approach," European Journal of Operational Research, Elsevier, vol. 203(1), pages 185-194, May.
    22. C. Adcock, 2010. "Asset pricing and portfolio selection based on the multivariate extended skew-Student-t distribution," Annals of Operations Research, Springer, vol. 176(1), pages 221-234, April.
    23. Jiang, Chun-Fu & Peng, Hong-Yi & Yang, Yu-Kuan, 2016. "Tail variance of portfolio under generalized Laplace distribution," Applied Mathematics and Computation, Elsevier, vol. 282(C), pages 187-203.
    24. Best, Michael J & Grauer, Robert R, 1991. "On the Sensitivity of Mean-Variance-Efficient Portfolios to Changes in Asset Means: Some Analytical and Computational Results," The Review of Financial Studies, Society for Financial Studies, vol. 4(2), pages 315-342.
    25. Alexandre Adam & Mohamed Houkari & Jean-Paul Laurent, 2008. "Spectral risk measures and portfolio selection," Post-Print hal-03676385, HAL.
    26. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    27. Boukouvala, Fani & Misener, Ruth & Floudas, Christodoulos A., 2016. "Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO," European Journal of Operational Research, Elsevier, vol. 252(3), pages 701-727.
    28. Chan, Louis K C & Karceski, Jason & Lakonishok, Josef, 1999. "On Portfolio Optimization: Forecasting Covariances and Choosing the Risk Model," The Review of Financial Studies, Society for Financial Studies, vol. 12(5), pages 937-974.
    29. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
    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. Vidal-Llana, Xenxo & Guillén, Montserrat, 2022. "Cross-sectional quantile regression for estimating conditional VaR of returns during periods of high volatility," The North American Journal of Economics and Finance, Elsevier, vol. 63(C).
    2. Francesca Mariani & Gloria Polinesi & Maria Cristina Recchioni, 2022. "A tail-revisited Markowitz mean-variance approach and a portfolio network centrality," Computational Management Science, Springer, vol. 19(3), pages 425-455, July.
    3. Taras Bodnar & Dmytro Ivasiuk & Nestor Parolya & Wolfgang Schmid, 2023. "Multi-period power utility optimization under stock return predictability," Computational Management Science, Springer, vol. 20(1), pages 1-27, December.

    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. Taras Bodnar & Mathias Lindholm & Vilhelm Niklasson & Erik Thors'en, 2020. "Bayesian Quantile-Based Portfolio Selection," Papers 2012.01819, arXiv.org.
    2. Bodnar, Taras & Lindholm, Mathias & Niklasson, Vilhelm & Thorsén, Erik, 2022. "Bayesian portfolio selection using VaR and CVaR," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    3. Taras Bodnar & Yarema Okhrin & Valdemar Vitlinskyy & Taras Zabolotskyy, 2018. "Determination and estimation of risk aversion coefficients," Computational Management Science, Springer, vol. 15(2), pages 297-317, June.
    4. Brandtner, Mario, 2013. "Conditional Value-at-Risk, spectral risk measures and (non-)diversification in portfolio selection problems – A comparison with mean–variance analysis," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 5526-5537.
    5. Penaranda, Francisco, 2007. "Portfolio choice beyond the traditional approach," LSE Research Online Documents on Economics 24481, London School of Economics and Political Science, LSE Library.
    6. Bodnar, Taras & Parolya, Nestor & Thorsén, Erik, 2023. "Is the empirical out-of-sample variance an informative risk measure for the high-dimensional portfolios?," Finance Research Letters, Elsevier, vol. 54(C).
    7. Ruili Sun & Tiefeng Ma & Shuangzhe Liu & Milind Sathye, 2019. "Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review," JRFM, MDPI, vol. 12(1), pages 1-34, March.
    8. Mario Brandtner, 2016. "Spektrale Risikomaße: Konzeption, betriebswirtschaftliche Anwendungen und Fallstricke," Management Review Quarterly, Springer, vol. 66(2), pages 75-115, April.
    9. Gordon J. Alexander & Alexandre M. Baptista & Shu Yan, 2009. "Reducing estimation risk in optimal portfolio selection when short sales are allowed," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 30(5), pages 281-305.
    10. Omid Momen & Akbar Esfahanipour & Abbas Seifi, 2020. "A robust behavioral portfolio selection: model with investor attitudes and biases," Operational Research, Springer, vol. 20(1), pages 427-446, March.
    11. Alexander, Gordon J. & Baptista, Alexandre M., 2008. "Active portfolio management with benchmarking: Adding a value-at-risk constraint," Journal of Economic Dynamics and Control, Elsevier, vol. 32(3), pages 779-820, March.
    12. Bodnar Taras & Schmid Wolfgang & Zabolotskyy Tara, 2012. "Minimum VaR and minimum CVaR optimal portfolios: Estimators, confidence regions, and tests," Statistics & Risk Modeling, De Gruyter, vol. 29(4), pages 281-314, November.
    13. Taras Bodnar & Taras Zabolotskyy, 2017. "How risky is the optimal portfolio which maximizes the Sharpe ratio?," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(1), pages 1-28, January.
    14. Muhinyuza, Stanislas & Bodnar, Taras & Lindholm, Mathias, 2020. "A test on the location of the tangency portfolio on the set of feasible portfolios," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    15. Brandtner, Mario & Kürsten, Wolfgang & Rischau, Robert, 2018. "Entropic risk measures and their comparative statics in portfolio selection: Coherence vs. convexity," European Journal of Operational Research, Elsevier, vol. 264(2), pages 707-716.
    16. Taras Bodnar & Wolfgang Schmid & Taras Zabolotskyy, 2013. "Asymptotic behavior of the estimated weights and of the estimated performance measures of the minimum VaR and the minimum CVaR optimal portfolios for dependent data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(8), pages 1105-1134, November.
    17. Brandtner, Mario, 2018. "Expected Shortfall, spectral risk measures, and the aggravating effect of background risk, or: risk vulnerability and the problem of subadditivity," Journal of Banking & Finance, Elsevier, vol. 89(C), pages 138-149.
    18. David Bauder & Taras Bodnar & Nestor Parolya & Wolfgang Schmid, 2021. "Bayesian mean–variance analysis: optimal portfolio selection under parameter uncertainty," Quantitative Finance, Taylor & Francis Journals, vol. 21(2), pages 221-242, February.
    19. Jing Li & Mingxin Xu, 2013. "Optimal Dynamic Portfolio with Mean-CVaR Criterion," Risks, MDPI, vol. 1(3), pages 1-29, November.
    20. Sungchul Hong & Jong-June Jeon, 2023. "Uniform Pessimistic Risk and Optimal Portfolio," Papers 2303.07158, arXiv.org.

    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:spr:comgts:v:18:y:2021:i:3:d:10.1007_s10287-021-00395-8. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.