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Bayesian Analysis of Linear Factor Models with Latent Factors, Multivariate Stochastic Volatility, and APT Pricing Restrictions

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  • Nardari, Federico
  • Scruggs, John T.

Abstract

We analyze a new class of linear factor models in which the factors are latent and the covariance matrix of excess returns follows a multivariate stochastic volatility process. We evaluate cross-sectional restrictions suggested by the arbitrage pricing theory (APT), compare competing stochastic volatility specifications for the covariance matrix, and test for the number of factors. We also examine whether return predictability can be attributed to time-varying factor risk premia. Analysis of these models is feasible due to recent advances in Bayesian Markov chain Monte Carlo (MCMC) methods. We find that three latent factors with multivariate stochastic volatility best explain excess returns for a sample of 10 size decile portfolios. The data strongly favor models constrained by APT pricing restrictions over otherwise identical unconstrained models.

Suggested Citation

  • Nardari, Federico & Scruggs, John T., 2007. "Bayesian Analysis of Linear Factor Models with Latent Factors, Multivariate Stochastic Volatility, and APT Pricing Restrictions," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 42(4), pages 857-891, December.
    • Handle: RePEc:cup:jfinqa:v:42:y:2007:i:04:p:857-891_00
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    Cited by:

    1. Daniele Bianchi & Massimo Guidolin & Francesco Ravazzolo, 2018. "Dissecting the 2007–2009 Real Estate Market Bust: Systematic Pricing Correction or Just a Housing Fad?," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 16(1), pages 34-62.
    2. Daniele Bianchi & Kenichiro McAlinn, 2018. "Large-Scale Dynamic Predictive Regressions," Papers 1803.06738, arXiv.org.
    3. Daniele Bianchi & Massimo Guidolin & Francesco Ravazzolo, 2017. "Macroeconomic Factors Strike Back: A Bayesian Change-Point Model of Time-Varying Risk Exposures and Premia in the U.S. Cross-Section," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 110-129, January.
    4. Chan, Joshua C.C. & Grant, Angelia L., 2016. "Fast computation of the deviance information criterion for latent variable models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 847-859.
    5. Hsieh, Ping-Hung & Yang, J. Jimmy, 2009. "A censored stochastic volatility approach to the estimation of price limit moves," Journal of Empirical Finance, Elsevier, vol. 16(2), pages 337-351, March.
    6. Henkel, Sam James & Martin, J. Spencer & Nardari, Federico, 2011. "Time-varying short-horizon predictability," Journal of Financial Economics, Elsevier, vol. 99(3), pages 560-580, March.
    7. Malefaki, Valia, 2015. "On Flexible Linear Factor Stochastic Volatility Models," MPRA Paper 62216, University Library of Munich, Germany.
    8. Tsunehiro Ishihara & Yasuhiro Omori, 2017. "Portfolio optimization using dynamic factor and stochastic volatility: evidence on Fat-tailed errors and leverage," The Japanese Economic Review, Japanese Economic Association, vol. 68(1), pages 63-94, March.
    9. Mike K. P. So & C. Y. Choi, 2009. "A threshold factor multivariate stochastic volatility model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 28(8), pages 712-735.
    10. Weber, Enzo, 2013. "Decomposing U.S. Stock Market Comovement into spillovers and common factors," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 106-118.
    11. Humberto Valencia Herrera, 2011. "Value at Risk and Return from the Use of Bayesian Methods for Stress Testing in a World Asset Allocation and the 2008-2009 Crisis," Revista de Administración, Finanzas y Economía (Journal of Management, Finance and Economics), Tecnológico de Monterrey, Campus Ciudad de México, vol. 5(1), pages 33-49.
    12. Ahmed, Shamim & Bu, Ziwen & Symeonidis, Lazaros & Tsvetanov, Daniel, 2023. "Which factor model? A systematic return covariation perspective," Journal of International Money and Finance, Elsevier, vol. 136(C).
    13. Tsunehiro Ishihara & Yasuhiro Omori, 2017. "Portfolio optimization using dynamic factor and stochastic volatility: evidence on Fat-tailed errors and leverage," The Japanese Economic Review, Springer, vol. 68(1), pages 63-94, March.
    14. Daniele Bianchi & Massimo Guidolin & Francesco Ravazzolo, 2018. "Dissecting the 2007–2009 Real Estate Market Bust: Systematic Pricing Correction or Just a Housing Fad?," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 16(1), pages 34-62.
    15. Doron Avramov & Guofu Zhou, 2010. "Bayesian Portfolio Analysis," Annual Review of Financial Economics, Annual Reviews, vol. 2(1), pages 25-47, December.
    16. Lopes, Hedibert F. & McCulloch, Robert E. & Tsay, Ruey S., 2022. "Parsimony inducing priors for large scale state–space models," Journal of Econometrics, Elsevier, vol. 230(1), pages 39-61.
    17. Giorgio Calzolari & Roxana Halbleib & Christian Mucher, 2023. "Sequential Estimation of Multivariate Factor Stochastic Volatility Models," Papers 2302.07052, arXiv.org.
    18. Ouysse, Rachida & Kohn, Robert, 2010. "Bayesian variable selection and model averaging in the arbitrage pricing theory model," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3249-3268, December.
    19. Gregor Kastner & Sylvia Fruhwirth-Schnatter & Hedibert Freitas Lopes, 2016. "Efficient Bayesian Inference for Multivariate Factor Stochastic Volatility Models," Papers 1602.08154, arXiv.org, revised Jul 2017.

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