IDEAS home Printed from https://ideas.repec.org/p/aah/create/2021-05.html
   My bibliography  Save this paper

Asset Pricing Using Block-Cholesky GARCH and Time-Varying Betas

Author

Listed:
  • Stefano Grassi

    (University of Rome 'Tor Vergata', Department of Economics and Finance, Facoltà di Economia, and CREATES)

  • Francesco Violante

    (CREST, GENES, ENSAE Paris, Institut Polytechnique de Paris, and CREATES)

Abstract

Starting from the Cholesky-GARCH model, recently proposed by Darolles, Francq, and Laurent (2018), the paper introduces the Block-Cholesky GARCH (BC-GARCH). This new model adapts in a natural way to the asset pricing framework. After deriving conditions for stationarity, uniform invertibility and beta tracking, we investigate the finite sample properties of a variety of maximum likelihood estimators suited for the BC-GARCH by means of an extensive Monte Carlo experiment. We illustrate the usefulness of the BC-GARCH in two empirical applications. The first tests for the presence of beta spillovers in a bivariate system in the context of the Fama and French (1993) three factor framework. The second empirical application consists of a large scale exercise exploring the cross-sectional variation of expected returns for 40 industry portfolios.

Suggested Citation

  • Stefano Grassi & Francesco Violante, 2021. "Asset Pricing Using Block-Cholesky GARCH and Time-Varying Betas," CREATES Research Papers 2021-05, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2021-05
    as

    Download full text from publisher

    File URL: https://repec.econ.au.dk/repec/creates/rp/21/rp21_05.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    2. Fama, Eugene F & French, Kenneth R, 1992. "The Cross-Section of Expected Stock Returns," Journal of Finance, American Finance Association, vol. 47(2), pages 427-465, June.
    3. Darolles, Serge & Francq, Christian & Laurent, Sébastien, 2018. "Asymptotics of Cholesky GARCH models and time-varying conditional betas," Journal of Econometrics, Elsevier, vol. 204(2), pages 223-247.
    4. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
    5. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(1), pages 122-150, February.
    6. Rasmus S. Pedersen & Anders Rahbek, 2014. "Multivariate variance targeting in the BEKK–GARCH model," Econometrics Journal, Royal Economic Society, vol. 17(1), pages 24-55, February.
    7. John Lintner, 1965. "Security Prices, Risk, And Maximal Gains From Diversification," Journal of Finance, American Finance Association, vol. 20(4), pages 587-615, December.
    8. Fama, Eugene F & MacBeth, James D, 1973. "Risk, Return, and Equilibrium: Empirical Tests," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 607-636, May-June.
    9. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
    10. Raymond Kan & Chu Zhang, 1999. "Two‐Pass Tests of Asset Pricing Models with Useless Factors," Journal of Finance, American Finance Association, vol. 54(1), pages 203-235, February.
    11. Hafner, Christian M. & Preminger, Arie, 2009. "On asymptotic theory for multivariate GARCH models," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2044-2054, October.
    12. Gian Piero Aielli, 2013. "Dynamic Conditional Correlation: On Properties and Estimation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(3), pages 282-299, July.
    13. 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.
    14. Peter Reinhard Hansen & Asger Lunde & Valeri Voev, 2014. "Realized Beta Garch: A Multivariate Garch Model With Realized Measures Of Volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(5), pages 774-799, August.
    15. Connor, Gregory, 1984. "A unified beta pricing theory," Journal of Economic Theory, Elsevier, vol. 34(1), pages 13-31, October.
    16. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    17. Kleibergen, Frank, 2009. "Tests of risk premia in linear factor models," Journal of Econometrics, Elsevier, vol. 149(2), pages 149-173, April.
    18. González, Mariano & Nave, Juan & Rubio, Gonzalo, 2012. "The Cross Section of Expected Returns with MIDAS Betas," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 47(1), pages 115-135, February.
    19. Fermanian, Jean-David & Malongo, Hassan, 2017. "On The Stationarity Of Dynamic Conditional Correlation Models," Econometric Theory, Cambridge University Press, vol. 33(3), pages 636-663, June.
    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. Boussama, Farid & Fuchs, Florian & Stelzer, Robert, 2011. "Stationarity and geometric ergodicity of BEKK multivariate GARCH models," Stochastic Processes and their Applications, Elsevier, vol. 121(10), pages 2331-2360, October.
    22. Francq, Christian & Zakoïan, Jean-Michel, 2012. "Qml Estimation Of A Class Of Multivariate Asymmetric Garch Models," Econometric Theory, Cambridge University Press, vol. 28(1), pages 179-206, February.
    Full references (including those not matched with items on IDEAS)

    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. Marco Barassi & Lajos Horváth & Yuqian Zhao, 2020. "Change‐Point Detection in the Conditional Correlation Structure of Multivariate Volatility Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(2), pages 340-349, April.
    2. de Almeida, Daniel & Hotta, Luiz K. & Ruiz, Esther, 2018. "MGARCH models: Trade-off between feasibility and flexibility," International Journal of Forecasting, Elsevier, vol. 34(1), pages 45-63.
    3. Asgharian, Hossein & Christiansen, Charlotte & Hou, Ai Jun & Wang, Weining, 2021. "Long- and short-run components of factor betas: Implications for stock pricing," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 74(C).
    4. Cheng Yu & Dong Li & Feiyu Jiang & Ke Zhu, 2023. "Matrix GARCH Model: Inference and Application," Papers 2306.05169, arXiv.org.
    5. 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.
    6. Boubacar Maïnassara, Y. & Kadmiri, O. & Saussereau, B., 2022. "Estimation of multivariate asymmetric power GARCH models," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    7. Hossein Asgharian & Charlotte Christiansen & Ai Jun Hou & Weining Wang, 2017. "Long- and Short-Run Components of Factor Betas: Implications for Equity Pricing," CREATES Research Papers 2017-34, Department of Economics and Business Economics, Aarhus University.
    8. Figlioli, Bruno & Lima, Fabiano Guasti, 2019. "Stock pricing in Latin America: The synchronicity effect," Emerging Markets Review, Elsevier, vol. 39(C), pages 1-17.
    9. Gregory Connor & Lisa R. Goldberg & Robert A. Korajczyk, 2010. "Portfolio Risk Analysis," Economics Books, Princeton University Press, edition 1, number 9224.
    10. Amit Goyal, 2012. "Empirical cross-sectional asset pricing: a survey," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 26(1), pages 3-38, March.
    11. Bollerslev, Tim & Patton, Andrew J. & Quaedvlieg, Rogier, 2020. "Multivariate leverage effects and realized semicovariance GARCH models," Journal of Econometrics, Elsevier, vol. 217(2), pages 411-430.
    12. Zhong, Angel, 2018. "Idiosyncratic volatility in the Australian equity market," Pacific-Basin Finance Journal, Elsevier, vol. 50(C), pages 105-125.
    13. Bradrania, Reza & Veron, Jose Francisco, 2023. "The beta anomaly in the Australian stock market and the lottery demand," Pacific-Basin Finance Journal, Elsevier, vol. 77(C).
    14. Noureldin, Diaa & Shephard, Neil & Sheppard, Kevin, 2014. "Multivariate rotated ARCH models," Journal of Econometrics, Elsevier, vol. 179(1), pages 16-30.
    15. Francq, Christian & Zakoian, Jean-Michel, 2014. "Estimating multivariate GARCH and stochastic correlation models equation by equation," MPRA Paper 54250, University Library of Munich, Germany.
    16. Joachim Freyberger & Andreas Neuhierl & Michael Weber, 2020. "Dissecting Characteristics Nonparametrically," The Review of Financial Studies, Society for Financial Studies, vol. 33(5), pages 2326-2377.
    17. Darolles, Serge & Francq, Christian & Laurent, Sébastien, 2018. "Asymptotics of Cholesky GARCH models and time-varying conditional betas," Journal of Econometrics, Elsevier, vol. 204(2), pages 223-247.
    18. Da, Zhi & Guo, Re-Jin & Jagannathan, Ravi, 2012. "CAPM for estimating the cost of equity capital: Interpreting the empirical evidence," Journal of Financial Economics, Elsevier, vol. 103(1), pages 204-220.
    19. Liu, Jinjing, 2023. "A novel downside beta and expected stock returns," International Review of Financial Analysis, Elsevier, vol. 85(C).
    20. Anatolyev, Stanislav & Mikusheva, Anna, 2022. "Factor models with many assets: Strong factors, weak factors, and the two-pass procedure," Journal of Econometrics, Elsevier, vol. 229(1), pages 103-126.

    More about this item

    Keywords

    Cholesky decomposition; Multivariate GARCH; Asset Pricing; Time Varying Beta; Two Pass Regression;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:aah:create:2021-05. 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: the person in charge (email available below). General contact details of provider: http://www.econ.au.dk/afn/ .

    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.