IDEAS home Printed from https://ideas.repec.org/a/eee/glofin/v35y2018icp147-156.html
   My bibliography  Save this article

Multi-dimensional portfolio risk and its diversification: A note

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S1044028317302314
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.gfj.2017.10.001?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    2. Harvey, Campbell R. & Siddique, Akhtar, 1999. "Autoregressive Conditional Skewness," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(4), pages 465-487, December.
    3. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    4. Ang, Andrew & Chen, Joseph, 2002. "Asymmetric correlations of equity portfolios," Journal of Financial Economics, Elsevier, vol. 63(3), pages 443-494, March.
    5. Colm Kearney & Valerio Potì, 2008. "Have European Stocks become More Volatile? An Empirical Investigation of Idiosyncratic and Market Risk in the Euro Area," European Financial Management, European Financial Management Association, vol. 14(3), pages 419-444, June.
    6. Rui Albuquerque, 2012. "Skewness in Stock Returns: Reconciling the Evidence on Firm Versus Aggregate Returns," The Review of Financial Studies, Society for Financial Studies, vol. 25(5), pages 1630-1673.
    7. Robert F. Dittmar, 2002. "Nonlinear Pricing Kernels, Kurtosis Preference, and Evidence from the Cross Section of Equity Returns," Journal of Finance, American Finance Association, vol. 57(1), pages 369-403, February.
    8. Giovanni Barone Adesi & Patrick Gagliardini & Giovanni Urga, 2004. "Testing Asset Pricing Models With Coskewness," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 474-485, October.
    9. François Longin & Bruno Solnik, 2001. "Extreme Correlation of International Equity Markets," Journal of Finance, American Finance Association, vol. 56(2), pages 649-676, April.
    10. Potì, Valerio & Wang, DengLi, 2010. "The coskewness puzzle," Journal of Banking & Finance, Elsevier, vol. 34(8), pages 1827-1838, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Woohwan Kim & Young Min Kim & Tae-Hwan Kim & Seungbeom Bang, 2015. "Multi-dimensional Risk and its Diversification," Working papers 2015rwp-81, Yonsei University, Yonsei Economics Research Institute.
    2. Chung, Y. Peter & Hong, Hyun A. & Kim, S. Thomas, 2019. "What causes the asymmetric correlation in stock returns?," Journal of Empirical Finance, Elsevier, vol. 54(C), pages 190-212.
    3. Chollete, Lorán & de la Peña, Victor & Lu, Ching-Chih, 2011. "International diversification: A copula approach," Journal of Banking & Finance, Elsevier, vol. 35(2), pages 403-417, February.
    4. Chollete, Loran & Ning, Cathy, 2010. "Asymmetric Dependence in US Financial Risk Factors?," UiS Working Papers in Economics and Finance 2011/2, University of Stavanger.
    5. Huang, Wei & Liu, Qianqiu & Ghon Rhee, S. & Wu, Feng, 2012. "Extreme downside risk and expected stock returns," Journal of Banking & Finance, Elsevier, vol. 36(5), pages 1492-1502.
    6. Boubaker, Heni & Sghaier, Nadia, 2013. "Portfolio optimization in the presence of dependent financial returns with long memory: A copula based approach," Journal of Banking & Finance, Elsevier, vol. 37(2), pages 361-377.
    7. Elyasiani, Elyas & Mansur, Iqbal, 2017. "Hedge fund return, volatility asymmetry, and systemic effects: A higher-moment factor-EGARCH model," Journal of Financial Stability, Elsevier, vol. 28(C), pages 49-65.
    8. Chollete, Lorán & de la Peña, Victor & Lu, Ching-Chih, 2012. "International diversification: An extreme value approach," Journal of Banking & Finance, Elsevier, vol. 36(3), pages 871-885.
    9. Lee, Kuan-Hui & Yang, Cheol-Won, 2022. "The world price of tail risk," Pacific-Basin Finance Journal, Elsevier, vol. 71(C).
    10. Chang, Bo Young & Christoffersen, Peter & Jacobs, Kris, 2013. "Market skewness risk and the cross section of stock returns," Journal of Financial Economics, Elsevier, vol. 107(1), pages 46-68.
    11. Bernardi, Mauro & Catania, Leopoldo, 2018. "Portfolio optimisation under flexible dynamic dependence modelling," Journal of Empirical Finance, Elsevier, vol. 48(C), pages 1-18.
    12. Charles Ka Yui Leung & Patrick Wai Yin Cheung & Edward Chi Ho Tang, 2013. "Financial Crisis and the Co-movements of Housing Sub-markets: Do relationships change after a crisis?," International Real Estate Review, Global Social Science Institute, vol. 16(1), pages 68-118.
    13. Yousaf, Imran & Pham, Linh & Goodell, John W., 2023. "The connectedness between meme tokens, meme stocks, and other asset classes: Evidence from a quantile connectedness approach," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 82(C).
    14. Massimo Guidolin & Giovanna Nicodano, 2009. "Small caps in international equity portfolios: the effects of variance risk," Annals of Finance, Springer, vol. 5(1), pages 15-48, January.
    15. Rakesh Gupta & Junhao Yang & Thadavillil Jithendranathan, 2017. "Diversification into Emerging Markets – An Australian and the US Perspective Using a Time-varying Approach," Australian Economic Papers, Wiley Blackwell, vol. 56(2), pages 134-162, June.
    16. Shynkevich, Andrei, 2013. "Time-series momentum as an intra- and inter-industry effect: Implications for market efficiency," Journal of Economics and Business, Elsevier, vol. 69(C), pages 64-85.
    17. Ayadi, Mohamed A. & Cao, Xu & Lazrak, Skander & Wang, Yan, 2019. "Do idiosyncratic skewness and kurtosis really matter?," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).
    18. Cerrato, Mario & Crosby, John & Kim, Minjoo & Zhao, Yang, 2015. "US Monetary and Fiscal Policies - Conflict or Cooperation?," SIRE Discussion Papers 2015-78, Scottish Institute for Research in Economics (SIRE).
    19. Riza Demirer & Donald Lien, 2004. "Firm-level return dispersion and correlation asymmetry: challenges for portfolio diversification," Applied Financial Economics, Taylor & Francis Journals, vol. 14(6), pages 447-456.
    20. Alexander, Gordon J. & Baptista, Alexandre M., 2009. "Stress testing by financial intermediaries: Implications for portfolio selection and asset pricing," Journal of Financial Intermediation, Elsevier, vol. 18(1), pages 65-92, January.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:glofin:v:35:y:2018:i:c:p:147-156. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/620162 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.