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

Published online by Cambridge University Press:  06 April 2009

Federico Nardari  and
John T. Scruggs
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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.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 42 , Issue 4 , December 2007 , pp. 857 - 891
Copyright
Copyright © School of Business Administration, University of Washington 2007

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References

Aguilar, O., and West, M.. “Bayesian Dynamic Factor Models and Portfolio Allocation.” Journal of Business and Economic Statistics, 18 (2000), 338–357.CrossRefGoogle Scholar
Avramov, D. “Stock Return Predictability and Model Uncertainty.” Journal of Financial Economics, 64 (2002), 423–458.CrossRefGoogle Scholar
Avramov, D. “Stock Return Predictability and Asset Pricing Models.” Review of Financial Studies, 17 (2004), 699–738.CrossRefGoogle Scholar
Avramov, D., and Chao, J. C.. “An Exact Bayes Test of Asset Pricing Models with Application to International Markets.” Journal of Business, 79 (2006), 293–323.CrossRefGoogle Scholar
Banz, R. W. “The Relationship between Return and Market Value of Common Stocks.” Journal of Financial Economics, 9 (1981), 3–18.CrossRefGoogle Scholar
Berger, J., and Pericchi, L. R.. “The Intrinsic Bayes Factor for Model Selection and Prediction.” Journal of the American Statistical Association, 91 (1996), 109–122.CrossRefGoogle Scholar
Bossaerts, P., and Green, R. C.. “A General Equilibrium Model of Changing Risk Premia: Theory and Tests.” Review of Financial Studies, 2 (1989), 467–493.CrossRefGoogle Scholar
Brown, S. J., and Otsuki, T.. “Risk Premia in Pacific-Basin Capital Markets.” Pacific-Basin Finance Journal, 1 (1993), 235–261.CrossRefGoogle Scholar
Brown, S. J., and Weinstein, M. I.. “A New Approach to Asset PricingModels: The Bilinear Paradigm.” Journal of Finance, 38 (1983), 711–743.CrossRefGoogle Scholar
Burmeister, E., and McElroy, M. B.. “Joint Estimation of Factor Sensitivities and Risk Premia for the Arbitrage Pricing Theory.” Journal of Finance, 43 (1988), 721–733.CrossRefGoogle Scholar
Campbell, J. Y. “Stock Returns and the Term Structure.” Journal of Financial Economics, 18 (1987), 373–399.CrossRefGoogle Scholar
Chib, S. “Marginal Likelihood From the Gibbs Output.” Journal of the American Statistical Association, 90 (1995), 1313–1321.CrossRefGoogle Scholar
Chib, S., and Greenberg, E.. “Understanding the Metropolis-Hastings Algorithm.” American Statistician, 49 (1995), 327–335.CrossRefGoogle Scholar
Chib, S., and Jeliazkov, I.. “Marginal Likelihood from the Metropolis-Hastings Output.” Journal of the American Statistical Association, 96 (2001), 270–281.CrossRefGoogle Scholar
Chib, S.; Nardari, F.; and Shephard, N.. “Markov Chain Monte Carlo Methods for Stochastic Volatility Models.” Journal of Econometrics, 108 (2002), 281–316.CrossRefGoogle Scholar
Chib, S.; Nardari, F.; and Shephard, N.. “Analysis of High Dimensional Multivariate Stochastic Volatility Models.” Journal of Econometrics, 134 (2006), 341–371.CrossRefGoogle Scholar
Connolly, R. A. “A Posterior Odds Analysis of the Weekend Effect.” Journal of Econometrics, 49 (1991), 51–104.CrossRefGoogle Scholar
Connor, G. “A Unified Beta Pricing Theory.” Journal of Economic Theory, 34 (1984), 13–31.CrossRefGoogle Scholar
Connor, G., and Korajczyk, R. A.. “Performance Measurement with the Arbitrage Pricing Theory: A New Framework for Analysis.” Journal of Financial Economics, 15 (1986), 373–394.CrossRefGoogle Scholar
Connor, G., and Korajczyk, R. A.. “Risk and Return in an Equilibrium APT: Application of a New Test Methodology.” Journal of Financial Economics, 21 (1988), 255–289.CrossRefGoogle Scholar
Connor, G., and Korajczyk, R. A.. “An Intertemporal Equilibrium Beta Pricing Model.” Review of Financial Studies, 2 (1989), 373–392.CrossRefGoogle Scholar
Connor, G., and Korajczyk, R. A.. “The Arbitrage Pricing Theory and Multifactor Models of Asset Returns.” In Finance, Jarrow, R. A., Maksimovic, V., Ziemba, W. T., eds., Vol. 9, Handbooks in Operations Research and Management Science. Amsterdam: North-Holland (1995).Google Scholar
Doucet, A.; de Freitas, N.; and Gordon, N.. Sequential Monte Carlo Methods in Practice. NewYork: Springer-Verlag (2001).CrossRefGoogle Scholar
Engle, R. F.; Ng, V. K.; and Rothschild, M.. “Asset Pricing with a Factor-ARCH Covariance Structure: Empirical Estimates for Treasury Bills.” Journal of Econometrics, 45 (1990), 213–237.CrossRefGoogle Scholar
Evans, M. D. D. “Expected Returns, Time-Varying Risk, and Risk Premia.” Journal of Finance, 49 (1994), 655–679.Google Scholar
Fama, E. F., and French, K. R.. “Dividend Yields and Expected Stock Returns.” Journal of Financial Economics, 22 (1988), 3–25.CrossRefGoogle Scholar
Fama, E. F., and French, K. R.. “Business Conditions and Expected Returns on Stocks and Bonds.” Journal of Financial Economics, 25 (1989), 23–49.CrossRefGoogle Scholar
Fama, E. F., and Schwert, G. W.. “Asset Returns and Inflation.” Journal of Financial Economics, 5 (1977), 115–146.CrossRefGoogle Scholar
Ferson, W. E. “Changes in Expected Security Returns, Risk, and the Level of Interest Rates.” Journal of Finance, 44 (1989), 1191–1217.CrossRefGoogle Scholar
Ferson, W. E., and Harvey, C. R.. “The Variation of Economic Risk Premiums.” Journal of Political Economy, 99 (1991), 385–415.CrossRefGoogle Scholar
Ferson, W. E., and Korajczyk, R. A.. “Do Arbitrage Pricing Models Explain the Predictability of Stock Returns?” Journal of Business, 68 (1995), 309–349.CrossRefGoogle Scholar
Geweke, J., and Zhou, G.. “Measuring the Pricing Error of the Arbitrage Pricing Theory.” Review of Financial Studies, 9 (1996), 557–587.CrossRefGoogle Scholar
Ghysels, E. “On Stable Factor Structures in the Pricing of Risk: Do Time-Varying Betas Help or Hurt?” Journal of Finance, 53 (1998), 549–573.CrossRefGoogle Scholar
Ghysels, E.; Harvey, A. C.; and Renault, E.. “Stochastic Volatility.” In Handbook of Statistics, Maddala, G. S., Rao, C. R., eds., Vol. 14. Amsterdam: North-Holland (1996).Google Scholar
Gibbons, M. R., and Ferson, W. E.. “Testing Asset Pricing Models with Changing Expectations and an Unobservable Market Portfolio.” Journal of Financial Economics, 14 (1985), 217–236.CrossRefGoogle Scholar
Gibbons, M. R.; Ross, S. A.; and Shanken, J.. “A Test of the Efficiency of a Given Portfolio.” Econometrica, 57 (1989), 1121–1152.CrossRefGoogle Scholar
Harvey, C. R. “Time-Varying Conditional Covariances in Tests of Asset Pricing Models.” Journal of Financial Economics, 24 (1989), 289–317.CrossRefGoogle Scholar
Harvey, C. R., and Zhou, G.. “Bayesian Inference in Asset Pricing Tests.” Journal of Financial Economics, 26 (1990), 221–254.CrossRefGoogle Scholar
Jacquier, E.; Polson, N. G.; and Rossi, P. E.. “Bayesian Analysis of Stochastic Volatility Models (with discussion).” Journal of the American Statistical Association, 12 (1994), 371–417.Google Scholar
Jones, C. S. “Extracting Factors from Heteroskedastic Asset Returns.” Journal of Financial Economics, 62 (2001), 293–325.CrossRefGoogle Scholar
Kass, R. E., and Raftery, A. E.. “Bayes Factors.” Journal of the American Statistical Association, 90 (1995), 773–795.CrossRefGoogle Scholar
Keim, D. B. “Size-Related Anomalies and Stock Return Seasonality: Further Empirical Evidence.” Journal of Financial Economics, 12 (1983), 13–32.CrossRefGoogle Scholar
Kim, S.; Shephard, N.; and Chib, S.. “Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models.” Review of Economic Studies, 65 (1998), 361–393.CrossRefGoogle Scholar
King, M.; Sentana, E.; and Wadhwani, S.. “Volatility and Links between National Stock Markets.” Econometrica, 62 (1994), 901–933.CrossRefGoogle Scholar
Kirby, C. “The Restrictions on Predictability Implied by Rational Asset Pricing Models.” Review of Financial Studies, 11 (1998), 343–382.CrossRefGoogle Scholar
Klein, R.W., and Brown, S. J.. “Model Selection When There is ‘Minimal’ Prior Information.” Econometrica, 52 (1984), 1291–1312.CrossRefGoogle Scholar
Lehmann, B. N., and Modest, D. M.. “The Empirical Foundations of the Arbitrage Pricing Theory.” Journal of Financial Economics, 21 (1988), 213–254.CrossRefGoogle Scholar
McCulloch, R., and Rossi, P. E.. “A Bayesian Approach to Testing the Arbitrage Pricing Theory.” Journal of Econometrics, 49 (1991), 141–168.CrossRefGoogle Scholar
McElroy, M. B., and Burmeister, E.. “Arbitrage Pricing Theory as a Restricted Nonlinear Multivariate Regression Model: ITNLSUR Estimates.” Journal of Business and Economic Statistics, 6 (1988), 29–42.Google Scholar
Moskowitz, T. J. “An Analysis of Covariance Risk and Pricing Anomalies.” Review of Financial Studies, 16 (2003), 417–457.CrossRefGoogle Scholar
Ng, V. K.; Engle, R. F.; and Rothschild, M.. “A Multi-Dynamic-Factor Model for Stock Returns.” Journal of Econometrics, 52 (1992), 245–266.CrossRefGoogle Scholar
O'Hagan, A.Bayesian Inference, Kendall's Advanced Theory of Statistics: Vol. 2B. London: Edward Arnold (1994).Google Scholar
Pitt, M. K., and Shephard, N.. “Filtering via Simulation: Auxiliary Particle Filters.” Journal of the American Statistical Association, 94 (1999), 590–599.CrossRefGoogle Scholar
Reinganum, M. R. “Misspecification of Capital Asset Pricing: Empirical Anomalies Based on Earnings Yields and Market Values.” Journal of Financial Economics, 9 (1981), 19–46.CrossRefGoogle Scholar
Roll, R., and Ross, S. A.. “An Empirical Investigation of the Arbitrage Pricing Theory.” Journal of Finance, 35 (1980), 1073–1103.CrossRefGoogle Scholar
Ross, S. A. “The Arbitrage Pricing Theory of Capital Asset Pricing.” Journal of Economic Theory, 13 (1976), 341–360.CrossRefGoogle Scholar
Ross, S. A. “Return, Risk and Arbitrage.” In Risk and Return in Finance, Friend, I., Bicksler, J. L., eds. Cambridge, MA: Ballinger (1977).Google Scholar
Schwert, G. W. “Anomalies and Market Efficiency.” NBER Working Paper 9277 (2002).CrossRefGoogle Scholar
Shanken, J. “A Bayesian Approach to Testing Portfolio Efficiency.” Journal of Financial Economics, 19 (1987), 195–215.CrossRefGoogle Scholar
Shanken, J. “Intertemporal Asset Pricing: An Empirical Investigation.” Journal of Econometrics, 45 (1990), 99–120.CrossRefGoogle Scholar
Sharpe, W. F. “A Simplified Model For Portfolio Analysis.” Management Science, 99 (1963), 277–293.CrossRefGoogle Scholar
Shiller, R. J. “Stock Prices and Social Dynamics.” Brookings Papers on Economic Activity, 2 (1984), 457–498.CrossRefGoogle Scholar
Taylor, S. J. “Modeling Stochastic Volatility: A Review and Comparative Study.” Mathematical Finance, 4 (1994), 183–204.CrossRefGoogle Scholar
Zellner, A.An Introduction to Bayesian Inference in Econometrics. New York: J. Wiley and Sons, Inc. (1971).Google Scholar
Zhou, G. “Analytical GMM Tests: Asset Pricing with Time-Varying Risk Premiums.” Review of Financial Studies, 7 (1994), 687–709.CrossRefGoogle Scholar