IDEAS home Printed from https://ideas.repec.org/a/spr/rvmgts/v18y2024i7d10.1007_s11846-023-00715-z.html
   My bibliography  Save this article

Robust mean-to-CVaR optimization under ambiguity in distributions means and covariance

Author

Listed:
  • Somayyeh Lotfi

    (University of Cyprus)

  • Stavros A. Zenios

    (Durham University
    University of Cyprus
    Cyprus Academy of Sciences, Letters, and Arts
    Bruegel)

Abstract

We develop a robust mean-to-CVaR portfolio optimization model under interval ambiguity in returns means and covariance. The robust model satisfies second-order stochastic dominance consistency and is formulated as a semi-definite cone program. We use two controlled experiments to document the sensitivity of the optimal allocations to the ambiguity when asset correlation varies, and to the ambiguity intervals. We find that means ambiguity has a higher impact than covariance ambiguity. We apply the model to US equities data to corroborate works showing that ambiguity in mean returns induces a home bias; it can explain the puzzle in a two-country setting but not with three countries. We further establish that covariance ambiguity also induces bias, but with lower impact that can not explain the puzzle. Our results suggest what is needed for the ambiguity channel to provide a full explanation of the puzzle. The findings are robust to alternative model specifications and outliers.

Suggested Citation

  • Somayyeh Lotfi & Stavros A. Zenios, 2024. "Robust mean-to-CVaR optimization under ambiguity in distributions means and covariance," Review of Managerial Science, Springer, vol. 18(7), pages 2115-2140, July.
  • Handle: RePEc:spr:rvmgts:v:18:y:2024:i:7:d:10.1007_s11846-023-00715-z
    DOI: 10.1007/s11846-023-00715-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11846-023-00715-z
    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/s11846-023-00715-z?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. A. Paç & Mustafa Pınar, 2014. "Robust portfolio choice with CVaR and VaR under distribution and mean return ambiguity," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 875-891, October.
    2. 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.
    3. Gala, Vito D. & Pagliardi, Giovanni & Zenios, Stavros A., 2023. "Global political risk and international stock returns," Journal of Empirical Finance, Elsevier, vol. 72(C), pages 78-102.
    4. Ravi Jagannathan & Tongshu Ma, 2003. "Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps," Journal of Finance, American Finance Association, vol. 58(4), pages 1651-1683, August.
    5. H. Henry Cao & Tan Wang & Harold H. Zhang, 2005. "Model Uncertainty, Limited Market Participation, and Asset Prices," The Review of Financial Studies, Society for Financial Studies, vol. 18(4), pages 1219-1251.
    6. R.H. Tütüncü & M. Koenig, 2004. "Robust Asset Allocation," Annals of Operations Research, Springer, vol. 132(1), pages 157-187, November.
    7. 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.
    8. Phelim Boyle & Lorenzo Garlappi & Raman Uppal & Tan Wang, 2012. "Keynes Meets Markowitz: The Trade-Off Between Familiarity and Diversification," Management Science, INFORMS, vol. 58(2), pages 253-272, February.
    9. Raman Uppal & Tan Wang, 2003. "Model Misspecification and Underdiversification," Journal of Finance, American Finance Association, vol. 58(6), pages 2465-2486, December.
    10. David Easley & Maureen O'Hara, 2009. "Ambiguity and Nonparticipation: The Role of Regulation," The Review of Financial Studies, Society for Financial Studies, vol. 22(5), pages 1817-1843, May.
    11. Stoyan Stoyanov & Svetlozar Rachev & Frank Fabozzi, 2013. "Sensitivity of portfolio VaR and CVaR to portfolio return characteristics," Annals of Operations Research, Springer, vol. 205(1), pages 169-187, May.
    12. Peijnenburg, Kim, 2018. "Life-Cycle Asset Allocation with Ambiguity Aversion and Learning," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 53(5), pages 1963-1994, October.
    13. L. Jeff Hong & Guangwu Liu, 2009. "Simulating Sensitivities of Conditional Value at Risk," Management Science, INFORMS, vol. 55(2), pages 281-293, February.
    14. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    15. Michal Kaut & Hercules Vladimirou & Stein W. Wallace & Stavros A. Zenios, 2007. "Stability analysis of portfolio management with conditional value-at-risk," Quantitative Finance, Taylor & Francis Journals, vol. 7(4), pages 397-409.
    16. Epstein, Larry G. & Miao, Jianjun, 2003. "A two-person dynamic equilibrium under ambiguity," Journal of Economic Dynamics and Control, Elsevier, vol. 27(7), pages 1253-1288, May.
    17. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
    18. Farinelli, Simone & Ferreira, Manuel & Rossello, Damiano & Thoeny, Markus & Tibiletti, Luisa, 2008. "Beyond Sharpe ratio: Optimal asset allocation using different performance ratios," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2057-2063, October.
    19. Dow, James & Werlang, Sergio Ribeiro da Costa, 1992. "Uncertainty Aversion, Risk Aversion, and the Optimal Choice of Portfolio," Econometrica, Econometric Society, vol. 60(1), pages 197-204, January.
    20. Efstathios Paparoditis & Dimitris N. Politis, 2003. "Residual-Based Block Bootstrap for Unit Root Testing," Econometrica, Econometric Society, vol. 71(3), pages 813-855, May.
    21. Laurent El Ghaoui & Maksim Oks & Francois Oustry, 2003. "Worst-Case Value-At-Risk and Robust Portfolio Optimization: A Conic Programming Approach," Operations Research, INFORMS, vol. 51(4), pages 543-556, August.
    22. Sebastián Ceria & Robert A Stubbs, 2006. "Incorporating estimation errors into portfolio selection: Robust portfolio construction," Journal of Asset Management, Palgrave Macmillan, vol. 7(2), pages 109-127, July.
    23. Epstein, Larry G & Wang, Tan, 1994. "Intertemporal Asset Pricing Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 62(2), pages 283-322, March.
    24. Lotfi, Somayyeh & Zenios, Stavros A., 2018. "Robust VaR and CVaR optimization under joint ambiguity in distributions, means, and covariances," European Journal of Operational Research, Elsevier, vol. 269(2), pages 556-576.
    25. Kai Ye & Panos Parpas & Berç Rustem, 2012. "Robust portfolio optimization: a conic programming approach," Computational Optimization and Applications, Springer, vol. 52(2), pages 463-481, June.
    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. Shushang Zhu & Masao Fukushima, 2009. "Worst-Case Conditional Value-at-Risk with Application to Robust Portfolio Management," Operations Research, INFORMS, vol. 57(5), pages 1155-1168, October.
    28. 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.
    29. repec:bla:jfinan:v:58:y:2003:i:4:p:1651-1684 is not listed on IDEAS
    30. Michael J. Best & Robert R. Grauer, 1991. "Sensitivity Analysis for Mean-Variance Portfolio Problems," Management Science, INFORMS, vol. 37(8), pages 980-989, August.
    31. 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.
    32. John M. Mulvey & Robert J. Vanderbei & Stavros A. Zenios, 1995. "Robust Optimization of Large-Scale Systems," Operations Research, INFORMS, vol. 43(2), pages 264-281, April.
    33. D. Goldfarb & G. Iyengar, 2003. "Robust Portfolio Selection Problems," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 1-38, February.
    34. 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.
    35. Chiaki Hara & Toshiki Honda, 2022. "Implied Ambiguity: Mean-Variance Inefficiency and Pricing Errors," Management Science, INFORMS, vol. 68(6), pages 4246-4260, 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. Lotfi, Somayyeh & Zenios, Stavros A., 2018. "Robust VaR and CVaR optimization under joint ambiguity in distributions, means, and covariances," European Journal of Operational Research, Elsevier, vol. 269(2), pages 556-576.
    2. Kellerer, Belinda, 2019. "Portfolio Optimization and Ambiguity Aversion," Junior Management Science (JUMS), Junior Management Science e. V., vol. 4(3), pages 305-338.
    3. Jiang, Julia & Liu, Jun & Tian, Weidong & Zeng, Xudong, 2022. "Portfolio concentration, portfolio inertia, and ambiguous correlation," Journal of Economic Theory, Elsevier, vol. 203(C).
    4. Maillet, Bertrand & Tokpavi, Sessi & Vaucher, Benoit, 2015. "Global minimum variance portfolio optimisation under some model risk: A robust regression-based approach," European Journal of Operational Research, Elsevier, vol. 244(1), pages 289-299.
    5. Maria Scutellà & Raffaella Recchia, 2013. "Robust portfolio asset allocation and risk measures," Annals of Operations Research, Springer, vol. 204(1), pages 145-169, April.
    6. Lorenzo Garlappi & Raman Uppal & Tan Wang, 2007. "Portfolio Selection with Parameter and Model Uncertainty: A Multi-Prior Approach," The Review of Financial Studies, Society for Financial Studies, vol. 20(1), pages 41-81, January.
    7. Phelim Boyle & Lorenzo Garlappi & Raman Uppal & Tan Wang, 2012. "Keynes Meets Markowitz: The Trade-Off Between Familiarity and Diversification," Management Science, INFORMS, vol. 58(2), pages 253-272, February.
    8. repec:esx:essedp:770 is not listed on IDEAS
    9. Lotfi, Somayyeh & Zeniosn, Stravros A., 2016. "Equivalence of Robust VaR and CVaR Optimization," Working Papers 16-03, University of Pennsylvania, Wharton School, Weiss Center.
    10. Agarwal, Vikas & Arisoy, Y. Eser & Naik, Narayan Y., 2017. "Volatility of aggregate volatility and hedge fund returns," Journal of Financial Economics, Elsevier, vol. 125(3), pages 491-510.
    11. Massimo Guidolin & Francesca Rinaldi, 2013. "Ambiguity in asset pricing and portfolio choice: a review of the literature," Theory and Decision, Springer, vol. 74(2), pages 183-217, February.
    12. Kanin Anantanasuwong & Roy Kouwenberg & Olivia S. Mitchell & Kim Peijnenburg, 2024. "Ambiguity attitudes for real-world sources: field evidence from a large sample of investors," Experimental Economics, Springer;Economic Science Association, vol. 27(3), pages 548-581, July.
    13. Jang Ho Kim & Woo Chang Kim & Frank J. Fabozzi, 2014. "Recent Developments in Robust Portfolios with a Worst-Case Approach," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 103-121, April.
    14. Alireza Ghahtarani & Ahmed Saif & Alireza Ghasemi, 2022. "Robust portfolio selection problems: a comprehensive review," Operational Research, Springer, vol. 22(4), pages 3203-3264, September.
    15. Philipp K. Illeditsch & Jayant V. Ganguli & Scott Condie, 2021. "Information Inertia," Journal of Finance, American Finance Association, vol. 76(1), pages 443-479, February.
    16. Dimmock, Stephen G. & Kouwenberg, Roy & Mitchell, Olivia S. & Peijnenburg, Kim, 2016. "Ambiguity aversion and household portfolio choice puzzles: Empirical evidence," Journal of Financial Economics, Elsevier, vol. 119(3), pages 559-577.
    17. Alireza Ghahtarani & Ahmed Saif & Alireza Ghasemi, 2021. "Robust Portfolio Selection Problems: A Comprehensive Review," Papers 2103.13806, arXiv.org, revised Jan 2022.
    18. Sujoy Mukerji & Han N. Ozsoylev & Jean‐Marc Tallon, 2023. "Trading Ambiguity: A Tale Of Two Heterogeneities," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 64(3), pages 1127-1164, August.
    19. Hui Chen & Nengjiu Ju & Jianjun Miao, 2014. "Dynamic Asset Allocation with Ambiguous Return Predictability," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 17(4), pages 799-823, October.
    20. Meyer, Steffen & Uhr, Charline, 2024. "Ambiguity and private investors’ behavior after forced fund liquidations," Journal of Financial Economics, Elsevier, vol. 156(C).
    21. Kolm, Petter N. & Tütüncü, Reha & Fabozzi, Frank J., 2014. "60 Years of portfolio optimization: Practical challenges and current trends," European Journal of Operational Research, Elsevier, vol. 234(2), pages 356-371.

    More about this item

    Keywords

    Ambiguity; Conditional Value-at-Risk; International portfolios; Equity home bias puzzle;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

    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:spr:rvmgts:v:18:y:2024:i:7:d:10.1007_s11846-023-00715-z. 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.