IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i11p1990-d441520.html
   My bibliography  Save this article

GO-GJRSK Model with Application to Higher Order Risk-Based Portfolio

Author

Listed:
  • Kei Nakagawa

    (NOMURA Asset Management Co. Ltd., 2-2-1, Toyosu, Koto-ku, Tokyo 135-0061, Japan)

  • Yusuke Uchiyama

    (MAZIN Inc., 3-29-14 Nishi-Asakusa, Tito city, Tokyo 111-0035, Japan)

Abstract

There are three distinguishing features in the financial time series, such as stock prices, are as follows: (1) Non-normality, (2) serial correlation, and (3) leverage effect. All three points need to be taken into account to model the financial time series. However, multivariate financial time series modeling involves a large number of stocks, with many parameters to be estimated. Therefore, there are few examples of multivariate financial time series modeling that explicitly deal with higher-order moments. Furthermore, there is no multivariate financial time series model that takes all three characteristics above into account. In this study, we propose the generalized orthogonal (GO)-Glosten, Jagannathan, and Runkle GARCH (GJR) model which extends the GO-generalized autoregressive conditional heteroscedasticity (GARCH) model and incorporates the three features of the financial time series. We confirm the effectiveness of the proposed model by comparing the performance of risk-based portfolios with higher-order moments. The results show that the performance with our proposed model is superior to that with baseline methods, and indicate that estimation methods are important in risk-based portfolios with higher moments.

Suggested Citation

  • Kei Nakagawa & Yusuke Uchiyama, 2020. "GO-GJRSK Model with Application to Higher Order Risk-Based Portfolio," Mathematics, MDPI, vol. 8(11), pages 1-12, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:1990-:d:441520
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/11/1990/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/11/1990/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Weide, R. van der, 2002. "Generalized Orthogonal GARCH. A Multivariate GARCH model," CeNDEF Working Papers 02-02, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    2. Victor DeMiguel & Lorenzo Garlappi & Raman Uppal, 2009. "Optimal Versus Naive Diversification: How Inefficient is the 1-N Portfolio Strategy?," The Review of Financial Studies, Society for Financial Studies, vol. 22(5), pages 1915-1953, May.
    3. Eric Jondeau & Michael Rockinger, 2006. "Optimal Portfolio Allocation under Higher Moments," European Financial Management, European Financial Management Association, vol. 12(1), pages 29-55, January.
    4. Brian Boyer & Todd Mitton & Keith Vorkink, 2010. "Expected Idiosyncratic Skewness," The Review of Financial Studies, Society for Financial Studies, vol. 23(1), pages 169-202, January.
    5. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    6. Kei Nakagawa & Mitsuyoshi Imamura & Kenichi Yoshida, 2018. "Risk-Based Portfolios with Large Dynamic Covariance Matrices," IJFS, MDPI, vol. 6(2), pages 1-14, May.
    7. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    8. Fama, Eugene F. & French, Kenneth R., 2015. "A five-factor asset pricing model," Journal of Financial Economics, Elsevier, vol. 116(1), pages 1-22.
    9. Vijay K. Chopra & William T. Ziemba, 2013. "The Effect of Errors in Means, Variances, and Covariances on Optimal Portfolio Choice," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 21, pages 365-373, World Scientific Publishing Co. Pte. Ltd..
    10. Robert F. Engle & Olivier Ledoit & Michael Wolf, 2019. "Large Dynamic Covariance Matrices," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(2), pages 363-375, April.
    11. Jegadeesh, Narasimhan & Titman, Sheridan, 1993. "Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency," Journal of Finance, American Finance Association, vol. 48(1), pages 65-91, March.
    12. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    13. repec:dau:papers:123456789/4688 is not listed on IDEAS
    14. Jegadeesh, Narasimhan, 1990. "Evidence of Predictable Behavior of Security Returns," Journal of Finance, American Finance Association, vol. 45(3), pages 881-898, July.
    15. Yusuke Uchiyama & Kei Nakagawa, 2020. "TPLVM: Portfolio Construction by Student's $t$-process Latent Variable Model," Papers 2002.06243, arXiv.org.
    16. Rajbir-Singh Nirwan & Nils Bertschinger, 2018. "Applications of Gaussian Process Latent Variable Models in Finance," Papers 1806.03294, arXiv.org, revised Apr 2019.
    17. Lionel Martellini & Volker Ziemann, 2010. "Improved Estimates of Higher-Order Comoments and Implications for Portfolio Selection," The Review of Financial Studies, Society for Financial Studies, vol. 23(4), pages 1467-1502, April.
    18. Chan, Joshua C.C. & Grant, Angelia L., 2016. "Modeling energy price dynamics: GARCH versus stochastic volatility," Energy Economics, Elsevier, vol. 54(C), pages 182-189.
    19. Leon, Angel & Rubio, Gonzalo & Serna, Gregorio, 2005. "Autoregresive conditional volatility, skewness and kurtosis," The Quarterly Review of Economics and Finance, Elsevier, vol. 45(4-5), pages 599-618, September.
    20. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-350, July.
    21. Roy van der Weide, 2002. "GO-GARCH: a multivariate generalized orthogonal GARCH model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 549-564.
    22. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
    23. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    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. Yusuke Uchiyama & Kei Nakagawa, 2022. "Schr\"{o}dinger Risk Diversification Portfolio," Papers 2202.09939, arXiv.org.

    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. Ruili Sun & Tiefeng Ma & Shuangzhe Liu & Milind Sathye, 2019. "Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review," JRFM, MDPI, vol. 12(1), pages 1-34, March.
    2. Kwangmin Jung & Donggyu Kim & Seunghyeon Yu, 2021. "Next Generation Models for Portfolio Risk Management: An Approach Using Financial Big Data," Papers 2102.12783, arXiv.org, revised Feb 2022.
    3. Santos, André A.P. & Moura, Guilherme V., 2014. "Dynamic factor multivariate GARCH model," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 606-617.
    4. Vincenzo Candila, 2013. "A Comparison of the Forecasting Performances of Multivariate Volatility Models," Working Papers 3_228, Dipartimento di Scienze Economiche e Statistiche, Università degli Studi di Salerno.
    5. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, Department of Economics and Business Economics, Aarhus University.
    6. Sebastien Valeyre & Sofiane Aboura & Denis Grebenkov, 2019. "The Reactive Beta Model," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 42(1), pages 71-113, March.
    7. M. Raddant & T. Di Matteo, 2023. "A look at financial dependencies by means of econophysics and financial economics," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 18(4), pages 701-734, October.
    8. Wang, Yudong & Liu, Li & Ma, Feng & Wu, Chongfeng, 2016. "What the investors need to know about forecasting oil futures return volatility," Energy Economics, Elsevier, vol. 57(C), pages 128-139.
    9. De Nard, Gianluca & Engle, Robert F. & Ledoit, Olivier & Wolf, Michael, 2022. "Large dynamic covariance matrices: Enhancements based on intraday data," Journal of Banking & Finance, Elsevier, vol. 138(C).
    10. Zexuan Yin & Paolo Barucca, 2022. "Variational Heteroscedastic Volatility Model," Papers 2204.05806, arXiv.org.
    11. Rayadurgam, Vikram Chandramouli & Mangalagiri, Jayasree, 2023. "Does inclusion of GARCH variance in deep learning models improve financial contagion prediction?," Finance Research Letters, Elsevier, vol. 54(C).
    12. João Caldeira & Guilherme Moura & André A.P. Santos, 2012. "Portfolio optimization using a parsimonious multivariate GARCH model: application to the Brazilian stock market," Economics Bulletin, AccessEcon, vol. 32(3), pages 1848-1857.
    13. Jarjour, Riad & Chan, Kung-Sik, 2020. "Dynamic conditional angular correlation," Journal of Econometrics, Elsevier, vol. 216(1), pages 137-150.
    14. Zexuan Yin & Paolo Barucca, 2022. "Neural Generalised AutoRegressive Conditional Heteroskedasticity," Papers 2202.11285, arXiv.org.
    15. Cheng Yu & Dong Li & Feiyu Jiang & Ke Zhu, 2023. "Matrix GARCH Model: Inference and Application," Papers 2306.05169, arXiv.org.
    16. Rahman, Md Lutfur & Troster, Victor & Uddin, Gazi Salah & Yahya, Muhammad, 2022. "Systemic risk contribution of banks and non-bank financial institutions across frequencies: The Australian experience," International Review of Financial Analysis, Elsevier, vol. 79(C).
    17. Chabi-Yo, Fousseni & Huggenberger, Markus & Weigert, Florian, 2022. "Multivariate crash risk," Journal of Financial Economics, Elsevier, vol. 145(1), pages 129-153.
    18. Le, Trung H., 2021. "International portfolio allocation: The role of conditional higher moments," International Review of Economics & Finance, Elsevier, vol. 74(C), pages 33-57.
    19. Keunbae Ahn, 2021. "Predictable Fluctuations in the Cross-Section and Time-Series of Asset Prices," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2021.
    20. Kwangmin Jung & Donggyu Kim & Seunghyeon Yu, 2022. "Next generation models for portfolio risk management: An approach using financial big data," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 89(3), pages 765-787, September.

    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:gam:jmathe:v:8:y:2020:i:11:p:1990-:d:441520. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.