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Measuring Portfolio Diversification

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  • Ulrich Kirchner
  • Caroline Zunckel

Abstract

In the market place, diversification reduces risk and provides protection against extreme events by ensuring that one is not overly exposed to individual occurrences. We argue that diversification is best measured by characteristics of the combined portfolio of assets and introduce a measure based on the information entropy of the probability distribution for the final portfolio asset value. For Gaussian assets the measure is a logarithmic function of the variance and combining independent Gaussian assets of equal variance adds an amount to the diversification. The advantages of this measure include that it naturally extends to any type of distribution and that it takes all moments into account. Furthermore, it can be used in cases of undefined weights (zero-cost assets) or moments. We present examples which apply this measure to derivative overlays.

Suggested Citation

  • Ulrich Kirchner & Caroline Zunckel, 2011. "Measuring Portfolio Diversification," Papers 1102.4722, arXiv.org.
    • Handle: RePEc:arx:papers:1102.4722
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    Cited by:

    1. Xiaomeng Lu & Jiaojiao Guo & Hailing Zhou, 2021. "Digital financial inclusion development, investment diversification, and household extreme portfolio risk," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 61(5), pages 6225-6261, December.
    2. Gilles Boevi Koumou, 2020. "Diversification and portfolio theory: a review," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 34(3), pages 267-312, September.
    3. Adeola Oyenubi, 2019. "Diversification Measures and the Optimal Number of Stocks in a Portfolio: An Information Theoretic Explanation," Computational Economics, Springer;Society for Computational Economics, vol. 54(4), pages 1443-1471, December.
    4. Mihaly Ormos & David Zibriczky, 2015. "Entropy-Based Financial Asset Pricing," Papers 1501.01155, arXiv.org.
    5. Mihály Ormos & Dávid Zibriczky, 2014. "Entropy-Based Financial Asset Pricing," PLOS ONE, Public Library of Science, vol. 9(12), pages 1-21, December.
    6. Schneider, Andreas, 2020. "Credit cooperatives: Market structure, competition, and conduct. Exploring the case of Paraguay," MPRA Paper 102309, University Library of Munich, Germany.
    7. Shuo Sun & Molei Qin & Xinrun Wang & Bo An, 2023. "PRUDEX-Compass: Towards Systematic Evaluation of Reinforcement Learning in Financial Markets," Papers 2302.00586, arXiv.org, revised Mar 2023.
    8. Grilli, Luca & Santoro, Domenico, 2020. "Boltzmann Entropy in Cryptocurrencies: A Statistical Ensemble Based Approach," MPRA Paper 99591, University Library of Munich, Germany.

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