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Multi-dimensional portfolio risk and its diversification: A note

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  • Kim, Woohwan
  • Kim, Young Min
  • Kim, Tae-Hwan
  • Bang, Seungbeom

Abstract

We propose that the “risk” of a portfolio has three components: variance, skewness, and kurtosis. Whereas most previous papers have focused on how variance is diversified, we use both analysis and simulations to investigate how skewness and kurtosis are diversified when the number of stocks in a well-diversified portfolio is increased. We find that, first, when a portfolio is skewed and fat-tailed, its variance, skewness, and kurtosis are simultaneously reduced as the number of risky assets in the portfolio increases. When the risky assets in a portfolio are moderately correlated, the three components tend to decrease and eventually converge to nonzero values, which define the portfolio's true multidimensional systematic risk and hence allow diversification of its multidimensional nonsystematic risk. Second, the skewness risk of a portfolio tends to decrease more slowly than variance and kurtosis risk, indicating that, among the three, skewness is the hardest to diversify.

Suggested Citation

  • Kim, Woohwan & Kim, Young Min & Kim, Tae-Hwan & Bang, Seungbeom, 2018. "Multi-dimensional portfolio risk and its diversification: A note," Global Finance Journal, Elsevier, vol. 35(C), pages 147-156.
    • Handle: RePEc:eee:glofin:v:35:y:2018:i:c:p:147-156
    DOI: 10.1016/j.gfj.2017.10.001
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    References listed on IDEAS

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    1. John Y. Campbell & Martin Lettau & Burton G. Malkiel & Yexiao Xu, 2001. "Have Individual Stocks Become More Volatile? An Empirical Exploration of Idiosyncratic Risk," Journal of Finance, American Finance Association, vol. 56(1), pages 1-43, February.
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    Cited by:

    1. Azra Zaimovic & Adna Omanovic & Almira Arnaut-Berilo, 2021. "How Many Stocks Are Sufficient for Equity Portfolio Diversification? A Review of the Literature," JRFM, MDPI, vol. 14(11), pages 1-30, November.

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    More about this item

    Keywords

    Diversification; Skewness; Kurtosis; Systematic risk; Multidimensional risk;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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