Multi-dimensional portfolio risk and its diversification: A note

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

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)147-156
Number of pages10
JournalGlobal Finance Journal
Volume35
DOIs
Publication statusPublished - 2018 Jan 1

Fingerprint

Diversification
Portfolio risk
Skewness
Kurtosis
Assets
Simulation
Systematic risk
Variance components

All Science Journal Classification (ASJC) codes

  • Finance
  • Economics and Econometrics

Cite this

Kim, Woohwan ; Kim, Young Min ; Kim, Tae-Hwan ; Bang, Seungbeom. / Multi-dimensional portfolio risk and its diversification : A note. In: Global Finance Journal. 2018 ; Vol. 35. pp. 147-156.
@article{c68064d04001452299ece17cac0d41ce,
title = "Multi-dimensional portfolio risk and its diversification: A note",
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.",
author = "Woohwan Kim and Kim, {Young Min} and Tae-Hwan Kim and Seungbeom Bang",
year = "2018",
month = "1",
day = "1",
doi = "10.1016/j.gfj.2017.10.001",
language = "English",
volume = "35",
pages = "147--156",
journal = "Global Finance Journal",
issn = "1044-0283",
publisher = "Elsevier",

}

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

In: Global Finance Journal, Vol. 35, 01.01.2018, p. 147-156.

Research output: Contribution to journalArticle

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 -