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Optimal Portfolio Diversification Using the Maximum Entropy Principle


  • Anil Bera
  • Sung Park


Markowitz's mean-variance (MV) efficient portfolio selection is one of the most widely used approaches in solving portfolio diversification problem. However, contrary to the notion of diversification, MV approach often leads to portfolios highly concentrated on a few assets. Also, this method leads to poor out-of-sample performances. Entropy is a well-known measure of diversity and also has a shrinkage interpretation. In this article, we propose to use cross- entropy measure as the objective function with side conditions coming from the mean and variance-covariance matrix of the resampled asset returns. This automatically captures the degree of imprecision of input estimates. Our approach can be viewed as a shrinkage estimation of portfolio weights (probabilities) which are shrunk towards the predetermined portfolio, for example, equally weighted portfolio or minimum variance portfolio. Our procedure is illustrated with an application to the international equity indexes.

Suggested Citation

  • Anil Bera & Sung Park, 2008. "Optimal Portfolio Diversification Using the Maximum Entropy Principle," Econometric Reviews, Taylor & Francis Journals, vol. 27(4-6), pages 484-512.
  • Handle: RePEc:taf:emetrv:v:27:y:2008:i:4-6:p:484-512 DOI: 10.1080/07474930801960394

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    References listed on IDEAS

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    Cited by:

    1. David E. Allen & Michael McAleer & Robert Powell & Abhay K. Singh, 2013. "A Non-Parametric and Entropy Based Analysis of the Relationship between the VIX and S&P 500," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 6(1), pages 1-25, October.
    2. Billio, Monica & Casarin, Roberto & Costola, Michele & Pasqualini, Andrea, 2016. "An entropy-based early warning indicator for systemic risk," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 45(C), pages 42-59.
    3. Yunker, James A. & Melkumian, Alla A., 2010. "The effect of capital wealth on optimal diversification: Evidence from the Survey of Consumer Finances," The Quarterly Review of Economics and Finance, Elsevier, vol. 50(1), pages 90-98, February.
    4. repec:dau:papers:123456789/4688 is not listed on IDEAS
    5. David E Allen & Michael McAleer & Abhay K Singh, 2017. "An entropy-based analysis of the relationship between the DOW JONES Index and the TRNA Sentiment series," Applied Economics, Taylor & Francis Journals, vol. 49(7), pages 677-692, February.
    6. Thorsten Poddig & Albina Unger, 2012. "On the robustness of risk-based asset allocations," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 26(3), pages 369-401, September.
    7. Yue, Wei & Wang, Yuping, 2017. "A new fuzzy multi-objective higher order moment portfolio selection model for diversified portfolios," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 124-140.
    8. repec:pal:assmgt:v:17:y:2016:i:4:d:10.1057_jam.2016.10 is not listed on IDEAS
    9. repec:eee:eneeco:v:64:y:2017:i:c:p:286-297 is not listed on IDEAS
    10. repec:eee:tefoso:v:127:y:2018:i:c:p:8-22 is not listed on IDEAS
    11. repec:spr:opsear:v:54:y:2017:i:3:d:10.1007_s12597-016-0289-y is not listed on IDEAS
    12. Frahm, Gabriel & Wiechers, Christof, 2011. "On the diversification of portfolios of risky assets," Discussion Papers in Econometrics and Statistics 2/11, University of Cologne, Institute of Econometrics and Statistics.
    13. Silva, Thuener & Pinheiro, Plácido Rogério & Poggi, Marcus, 2017. "A more human-like portfolio optimization approach," European Journal of Operational Research, Elsevier, vol. 256(1), pages 252-260.
    14. Máté, Gabriell & Néda, Zoltán, 2016. "The advantage of inhomogeneity — Lessons from a noise driven linearized dynamical system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 445(C), pages 310-317.
    15. repec:agr:journl:v:4(613):y:2017:i:4(613):p:33-42 is not listed on IDEAS


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