### 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.

Original language | English |
---|---|

Pages (from-to) | 147-156 |

Number of pages | 10 |

Journal | Global Finance Journal |

Volume | 35 |

DOIs | |

Publication status | Published - 2018 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Finance
- Economics and Econometrics

### Cite this

*Global Finance Journal*,

*35*, 147-156. https://doi.org/10.1016/j.gfj.2017.10.001

}

*Global Finance Journal*, vol. 35, pp. 147-156. https://doi.org/10.1016/j.gfj.2017.10.001

**Multi-dimensional portfolio risk and its diversification : A note.** / Kim, Woohwan; Kim, Young Min; Kim, Tae-Hwan; Bang, Seungbeom.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Multi-dimensional portfolio risk and its diversification

T2 - A note

AU - Kim, Woohwan

AU - Kim, Young Min

AU - Kim, Tae-Hwan

AU - Bang, Seungbeom

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85031397669&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85031397669&partnerID=8YFLogxK

U2 - 10.1016/j.gfj.2017.10.001

DO - 10.1016/j.gfj.2017.10.001

M3 - Article

AN - SCOPUS:85031397669

VL - 35

SP - 147

EP - 156

JO - Global Finance Journal

JF - Global Finance Journal

SN - 1044-0283

ER -