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Nonparametric Dynamic Conditional Beta

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  • John M Maheu
  • Azam Shamsi Zamenjani

Abstract

This article derives a dynamic beta representation using a Bayesian semiparametric multivariate generalized autoregressive conditional heteroskedasticity (GARCH) model. The conditional joint distribution of excess stock returns and market excess returns is modeled as a countably infinite mixture of normals. This allows for deviations from the elliptic family of distributions. Empirically, we find the time-varying beta of a stock nonlinearly depends on the expected value of excess market returns. The nonlinear dependence is robust to different GARCH specifications as well as more factors in the model. In highly volatile markets, beta is almost constant, while in stable markets, the beta coefficient can depend asymmetrically on the expected market excess return. We extend the model to several factors and find empirical support for a three-factor model with nonlinear factor sensitives.

Suggested Citation

  • John M Maheu & Azam Shamsi Zamenjani, 2021. "Nonparametric Dynamic Conditional Beta," Journal of Financial Econometrics, Oxford University Press, vol. 19(4), pages 583-613.
    • Handle: RePEc:oup:jfinec:v:19:y:2021:i:4:p:583-613.
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbz024
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    References listed on IDEAS

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    1. Jensen, Mark J. & Maheu, John M., 2013. "Bayesian semiparametric multivariate GARCH modeling," Journal of Econometrics, Elsevier, vol. 176(1), pages 3-17.
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    3. Bauwens, Luc & Lubrano, Michel & Richard, Jean-Francois, 2000. "Bayesian Inference in Dynamic Econometric Models," OUP Catalogue, Oxford University Press, number 9780198773139.
    4. Engle, Robert F & Ng, Victor K, 1993. "Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, vol. 48(5), pages 1749-1778, December.
    5. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-131, February.
    6. 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.
    7. 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.
    8. Choudhry, Taufiq, 2002. "The Stochastic Structure of the Time-Varying Beta: Evidence from UK Companies," Manchester School, University of Manchester, vol. 70(6), pages 768-791, December.
    9. McCurdy, Thomas H & Morgan, Ieuan, 1992. "Evidence of Risk Premiums in Foreign Currency Futures Markets," Review of Financial Studies, Society for Financial Studies, vol. 5(1), pages 65-83.
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    Cited by:

    1. 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.
    2. Li, Chenxing, 2022. "A multivariate GARCH model with an infinite hidden Markov mixture," MPRA Paper 112792, University Library of Munich, Germany.

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    More about this item

    Keywords

    nonparametric; Dirichlet process mixture; GARCH; beta;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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