Multi-dimensional portfolio risk and its diversification: A note

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

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)147-156
Number of pages10
JournalGlobal Finance Journal
Publication statusPublished - 2018

Bibliographical note

Funding Information:
Funding: Tae-Hwan Kim is grateful for financial support from the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea ( NRF-2017S1A5A2A01025435 ).

Publisher Copyright:
© 2017 Elsevier Inc.

All Science Journal Classification (ASJC) codes

  • Finance
  • Economics and Econometrics


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