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Portfolio diversification and model uncertainty: a robust dynamic mean-variance approach

Author

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  • Huyên Pham

    (LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - UPD7 - Université Paris Diderot - Paris 7 - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique, ENSAE - Ecole Nationale de la Statistique et de l'Analyse Economique - Ecole Nationale de la Statistique et de l'Analyse Economique)

  • Xiaoli Wei

    (LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - UPD7 - Université Paris Diderot - Paris 7 - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique)

  • Chao Zhou

    (NUS - National University of Singapore)

Abstract
This paper focuses on a dynamic multi-asset mean-variance portfolio selection problem under model uncertainty. We develop a continuous time framework for taking into account ambiguity aversion about both expected return rates and correlation matrix of the assets, and for studying the join effects on portfolio diversification. The dynamic setting allows us to consider time varying ambiguity sets, which include the cases where the drift and correlation are estimated on a rolling window of historical data or when the investor takes into account learning on the ambiguity. In this context, we prove a general separation principle for the associated robust control problem, which allows us to reduce the determination of the optimal dynamic strategy to the parametric computation of the minimal risk premium function. Our results provide a justification for under-diversification, as documented in empirical studies and in the static models [16], [34]. Furthermore, we explicitly quantify the degree of under-diversification in terms of correlation bounds and Sharpe ratios proximities, and emphasize the different features induced by drift and correlation ambiguity. In particular, we show that an investor with a poor confidence in the expected return estimation does not hold any risky asset, and on the other hand, trades only one risky asset when the level of ambiguity on correlation matrix is large. We also provide a complete picture of the diversification for the optimal robust portfolio in the three-asset case JEL Classification: G11, C61 MSC Classification: 91G10, 91G80, 60H30

Suggested Citation

  • Huyên Pham & Xiaoli Wei & Chao Zhou, 2021. "Portfolio diversification and model uncertainty: a robust dynamic mean-variance approach," Working Papers hal-01867133, HAL.
  • Handle: RePEc:hal:wpaper:hal-01867133
    DOI: 10.1111/mafi.12320
    Note: View the original document on HAL open archive server: https://hal.science/hal-01867133v3
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    References listed on IDEAS

    as
    1. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
    2. 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.
    3. Laurent E. Calvet & John Y. Campbell & Paolo Sodini, 2007. "Down or Out: Assessing the Welfare Costs of Household Investment Mistakes," Journal of Political Economy, University of Chicago Press, vol. 115(5), pages 707-747, October.
    4. 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.
    5. Raman Uppal & Tan Wang, 2003. "Model Misspecification and Underdiversification," Journal of Finance, American Finance Association, vol. 58(6), pages 2465-2486, December.
    6. Amine Ismail & Huy^en Pham, 2016. "Robust Markowitz mean-variance portfolio selection under ambiguous covariance matrix ," Papers 1610.06805, arXiv.org, revised Mar 2017.
    7. Guidolin, Massimo & Liu, Hening, 2016. "Ambiguity Aversion and Underdiversification," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 51(4), pages 1297-1323, August.
    8. Qian Lin & Frank Riedel, 2014. "Optimal consumption and portfolio choice with ambiguity," Papers 1401.1639, arXiv.org.
    9. Duan Li & Wan‐Lung Ng, 2000. "Optimal Dynamic Portfolio Selection: Multiperiod Mean‐Variance Formulation," Mathematical Finance, Wiley Blackwell, vol. 10(3), pages 387-406, July.
    10. French, Kenneth R & Poterba, James M, 1991. "Investor Diversification and International Equity Markets," American Economic Review, American Economic Association, vol. 81(2), pages 222-226, May.
    11. repec:bla:jfinan:v:58:y:2003:i:4:p:1651-1684 is not listed on IDEAS
    12. Cooper, Ian & Kaplanis, Evi, 1994. "Home Bias in Equity Portfolios, Inflation Hedging, and International Capital Market Equilibrium," The Review of Financial Studies, Society for Financial Studies, vol. 7(1), pages 45-60.
    13. Anis Matoussi & Dylan Possamaï & Chao Zhou, 2015. "Robust Utility Maximization In Nondominated Models With 2bsde: The Uncertain Volatility Model," Mathematical Finance, Wiley Blackwell, vol. 25(2), pages 258-287, April.
    14. Revaz Tevzadze & Teimuraz Toronjadze & Tamaz Uzunashvili, 2013. "Robust utility maximization for a diffusion market model with misspecified coefficients," Finance and Stochastics, Springer, vol. 17(3), pages 535-563, July.
    15. Huberman, Gur, 2001. "Familiarity Breeds Investment," The Review of Financial Studies, Society for Financial Studies, vol. 14(3), pages 659-680.
    16. Alexander Schied, 2007. "Optimal investments for risk- and ambiguity-averse preferences: a duality approach," Finance and Stochastics, Springer, vol. 11(1), pages 107-129, January.
    17. Dirk Becherer & Klebert Kentia, 2017. "Good Deal Hedging and Valuation under Combined Uncertainty about Drift and Volatility," Papers 1704.02505, arXiv.org.
    18. Paul Glasserman & Xingbo Xu, 2013. "Robust Portfolio Control with Stochastic Factor Dynamics," Operations Research, INFORMS, vol. 61(4), pages 874-893, August.
    19. Todd Mitton & Keith Vorkink, 2007. "Equilibrium Underdiversification and the Preference for Skewness," The Review of Financial Studies, Society for Financial Studies, vol. 20(4), pages 1255-1288.
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    Cited by:

    1. Lin, Qian & Luo, Yulei & Sun, Xianming, 2022. "Robust investment strategies with two risky assets," Journal of Economic Dynamics and Control, Elsevier, vol. 134(C).

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    More about this item

    Keywords

    Continuous-time Markowitz problem; model uncertainty; ambiguous drift and correlation; separation principle; portfolio diversification; time varying ambiguity sets; portfolio diversication; G11; C61 MSC Classification: 91G10; 91G80; 60H30 Continuous-time Markowitz problem;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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