Bayesian Variable Selection of Risk Factors in the APT Model
In this paper we use a probabilistic approach to risk factor selection in the arbitrage pricing theory model. The methodology uses a bayesian framework to simultaneously select the pervasive risk factors and estimate the model. This will enable correct inference and testing of the implications of the APT model. Furthermore, we are able to make inference on any function of the parameters, in particular the pricing errors. We can also carry out tests of efficiency of the APT using the posterior odds ratio and bayesian confidence intervals. We investigate the macroeconomic risk factors of Chen, Roll, and Ross (1986) and the firm characteristic factors of Fama and French (1992,1993). Using monthly portfolio returns grouped by size and book to market, we find that the economic variables have zero risk premia although some appear to have non zero posterior probability. The "Market" factor is not priced. An APT model with factors mimicking size (SMB), book to market equity (HML), value-weighted portfolio and Standard and Poor, is supported by a conditionally independent prior and offers a significant decrease in the pricing error over a two-factor APT with SMB and HML. The posterior probability and cumulative distributions functions of the average risk premia and the pricing errors are compared to the normal distribution. The results show that under certain conditions the distortions are very small.
|Date of creation:||Oct 2007|
|Date of revision:|
|Contact details of provider:|| Postal: |
Fax: +61)-2- 9313- 6337
Web page: http://www.economics.unsw.edu.au/
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Geweke, John & Zhou, Guofu, 1996.
"Measuring the Pricing Error of the Arbitrage Pricing Theory,"
Review of Financial Studies,
Society for Financial Studies, vol. 9(2), pages 557-87.
- John Geweke & Guofu Zhou, 1996. "Measuring the Pricing Error of the Arbitrage Pricing Theory," CEMA Working Papers 276, China Economics and Management Academy, Central University of Finance and Economics.
- John Geweke & Guofu Zhou, 1995. "Measuring the pricing error of the arbitrage pricing theory," Staff Report 189, Federal Reserve Bank of Minneapolis.
- Chen, Nai-Fu & Roll, Richard & Ross, Stephen A, 1986. "Economic Forces and the Stock Market," The Journal of Business, University of Chicago Press, vol. 59(3), pages 383-403, July.
- Ferson, Wayne E & Harvey, Campbell R, 1991. "The Variation of Economic Risk Premiums," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 385-415, April.
- Liang, Feng & Paulo, Rui & Molina, German & Clyde, Merlise A. & Berger, Jim O., 2008. "Mixtures of g Priors for Bayesian Variable Selection," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 410-423, March.
- Smith, Michael & Kohn, Robert, 1996.
"Nonparametric regression using Bayesian variable selection,"
Journal of Econometrics,
Elsevier, vol. 75(2), pages 317-343, December.
- Smith, M. & Kohn, R., . "Nonparametric Regression using Bayesian Variable Selection," Statistics Working Paper _009, Australian Graduate School of Management.
- Burmeister, Edwin & McElroy, Marjorie B, 1988. " Joint Estimation of Factor Sensitivities and Risk Premia for the Arbitrage Pricing Theory," Journal of Finance, American Finance Association, vol. 43(3), pages 721-33, July.
- 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.
- Ouysse, Rachida, 2006. "Consistent variable selection in large panels when factors are observable," Journal of Multivariate Analysis, Elsevier, vol. 97(4), pages 946-984, April.
- Smith M. & Kohn R., 2002. "Parsimonious Covariance Matrix Estimation for Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1141-1153, December.
When requesting a correction, please mention this item's handle: RePEc:swe:wpaper:2007-32. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Gabriele Gratton)
If references are entirely missing, you can add them using this form.