IDEAS home Printed from https://ideas.repec.org/p/fip/fedmsr/189.html
   My bibliography  Save this paper

Measuring the pricing error of the arbitrage pricing theory

Author

Listed:
  • John F. Geweke
  • Guofu Zhou

Abstract

This paper provides an exact Bayesian framework for analyzing the arbitrage pricing theory (APT). Based on the Gibbs sampler, we show how to obtain the exact posterior distributions for functions of interest in the factor model. In particular, we propose a measure of the APT pricing deviations and obtain its exact posterior distribution. Using monthly portfolio returns grouped by industry and market capitalization, we find that there is little improvement in reducing the pricing errors by including more factors beyond the first one.

Suggested Citation

  • John F. Geweke & Guofu Zhou, 1995. "Measuring the pricing error of the arbitrage pricing theory," Staff Report 189, Federal Reserve Bank of Minneapolis.
  • Handle: RePEc:fip:fedmsr:189
    as

    Download full text from publisher

    File URL: http://www.minneapolisfed.org/research/common/pub_detail.cfm?pb_autonum_id=470
    Download Restriction: no

    File URL: http://minneapolisfed.org/research/sr/sr189.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-1339, November.
    2. Shanken, Jay, 1992. "The Current State of the Arbitrage Pricing Theory," Journal of Finance, American Finance Association, vol. 47(4), pages 1569-1574, September.
    3. Roll, Richard & Ross, Stephen A, 1980. "An Empirical Investigation of the Arbitrage Pricing Theory," Journal of Finance, American Finance Association, vol. 35(5), pages 1073-1103, December.
    4. Harvey, Campbell R. & Zhou, Guofu, 1990. "Bayesian inference in asset pricing tests," Journal of Financial Economics, Elsevier, vol. 26(2), pages 221-254, August.
    5. Stephen A. Ross, 2013. "The Arbitrage Theory of Capital Asset Pricing," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 1, pages 11-30, World Scientific Publishing Co. Pte. Ltd..
    6. Connor, Gregory & Korajczyk, Robert A., 1986. "Performance measurement with the arbitrage pricing theory : A new framework for analysis," Journal of Financial Economics, Elsevier, vol. 15(3), pages 373-394, March.
    7. John F. Geweke, 1991. "Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments," Staff Report 148, Federal Reserve Bank of Minneapolis.
    8. Shanken, Jay, 1987. "Multivariate proxies and asset pricing relations : Living with the Roll critique," Journal of Financial Economics, Elsevier, vol. 18(1), pages 91-110, March.
    9. Shanken, Jay, 1982. "The Arbitrage Pricing Theory: Is It Testable?," Journal of Finance, American Finance Association, vol. 37(5), pages 1129-1140, December.
    10. Chamberlain, Gary & Rothschild, Michael, 1983. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Econometrica, Econometric Society, vol. 51(5), pages 1281-1304, September.
    11. Connor, Gregory, 1984. "A unified beta pricing theory," Journal of Economic Theory, Elsevier, vol. 34(1), pages 13-31, October.
    12. McCulloch, Robert & Rossi, Peter E., 1991. "A bayesian approach to testing the arbitrage pricing theory," Journal of Econometrics, Elsevier, vol. 49(1-2), pages 141-168.
    13. Gibbons, Michael R & Ross, Stephen A & Shanken, Jay, 1989. "A Test of the Efficiency of a Given Portfolio," Econometrica, Econometric Society, vol. 57(5), pages 1121-1152, September.
    14. Chen, Nai-fu, 1983. "Some Empirical Tests of the Theory of Arbitrage Pricing," Journal of Finance, American Finance Association, vol. 38(5), pages 1393-1414, December.
    15. Connor, Gregory & Korajczyk, Robert A., 1988. "Risk and return in an equilibrium APT : Application of a new test methodology," Journal of Financial Economics, Elsevier, vol. 21(2), pages 255-289, September.
    16. Dybvig, Philip H., 1983. "An explicit bound on individual assets' deviations from APT pricing in a finite economy," Journal of Financial Economics, Elsevier, vol. 12(4), pages 483-496, December.
    17. Shanken, Jay, 1987. "A Bayesian approach to testing portfolio efficiency," Journal of Financial Economics, Elsevier, vol. 19(2), pages 195-215, December.
    18. Connor, Gregory & Korajczyk, Robert A, 1993. "A Test for the Number of Factors in an Approximate Factor Model," Journal of Finance, American Finance Association, vol. 48(4), pages 1263-1291, September.
    19. Kloek, Tuen & van Dijk, Herman K, 1978. "Bayesian Estimates of Equation System Parameters: An Application of Integration by Monte Carlo," Econometrica, Econometric Society, vol. 46(1), pages 1-19, January.
    20. McCulloch, Robert & Rossi, Peter E., 1990. "Posterior, predictive, and utility-based approaches to testing the arbitrage pricing theory," Journal of Financial Economics, Elsevier, vol. 28(1-2), pages 7-38.
    21. 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.
    22. Lehmann, Bruce N. & Modest, David M., 1988. "The empirical foundations of the arbitrage pricing theory," Journal of Financial Economics, Elsevier, vol. 21(2), pages 213-254, September.
    23. Brown, Stephen J, 1989. " The Number of Factors in Security Returns," Journal of Finance, American Finance Association, vol. 44(5), pages 1247-1262, December.
    24. Grinblatt, Mark & Titman, Sheridan, 1983. "Factor pricing in a finite economy," Journal of Financial Economics, Elsevier, vol. 12(4), pages 497-507, December.
    25. 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.
    26. Gibbons, Michael R., 1982. "Multivariate tests of financial models : A new approach," Journal of Financial Economics, Elsevier, vol. 10(1), pages 3-27, March.
    27. Black, Fischer, 1972. "Capital Market Equilibrium with Restricted Borrowing," The Journal of Business, University of Chicago Press, vol. 45(3), pages 444-455, July.
    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. Michailidis, G., 2009. "Multivariate methods in examining macroeconomic variables effect on Greek stock market returns, 1997-2004," Applied Econometrics and International Development, Euro-American Association of Economic Development, vol. 9(1).
    2. 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.
    3. Nawalkha, Sanjay K., 1997. "A multibeta representation theorem for linear asset pricing theories," Journal of Financial Economics, Elsevier, vol. 46(3), pages 357-381, December.
    4. 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.
    5. Shanken, Jay & Weinstein, Mark I., 2006. "Economic forces and the stock market revisited," Journal of Empirical Finance, Elsevier, vol. 13(2), pages 129-144, March.
    6. Attiya Y. Javed, 2000. "Alternative Capital Asset Pricing Models: A Review of Theory and Evidence," PIDE-Working Papers 2000:179, Pakistan Institute of Development Economics.
    7. Erdinc Altay, 2003. "The Effect of Macroeconomic Factors on Asset Returns: A Comparative Analysis of the German and the Turkish Stock Markets in an APT Framework," Finance 0307006, University Library of Munich, Germany.
    8. Jones, Christopher S., 2001. "Extracting factors from heteroskedastic asset returns," Journal of Financial Economics, Elsevier, vol. 62(2), pages 293-325, November.
    9. Chadwick, Meltem, 2010. "Performance of Bayesian Latent Factor Models in Measuring Pricing Errors," MPRA Paper 79060, University Library of Munich, Germany.
    10. Zura Kakushadze, 2015. "Heterotic Risk Models," Papers 1508.04883, arXiv.org, revised Jan 2016.
    11. Chu Zhang, 2009. "Testing the APT with the Maximum Sharpe Ratio of Extracted Factors," Management Science, INFORMS, vol. 55(7), pages 1255-1266, July.
    12. Zura Kakushadze & Willie Yu, 2016. "Statistical Risk Models," Papers 1602.08070, arXiv.org, revised Jan 2017.
    13. Enrique Sentana, 1993. "The econometrics of the stock market II: asset pricing," Investigaciones Economicas, FundaciĆ³n SEPI, vol. 17(3), pages 421-444, September.
    14. Zura Kakushadze & Willie Yu, 2016. "Multifactor Risk Models and Heterotic CAPM," Papers 1602.04902, arXiv.org, revised Mar 2016.
    15. Michael Rothschild, 1985. "Asset Pricing Theories," NBER Technical Working Papers 0044, National Bureau of Economic Research, Inc.
    16. Robert W. Faff, 1993. "A Multivariate Test of an Equilibrium APT with Time Varying Risk Premia in the Australian Equity Market," Australian Journal of Management, Australian School of Business, vol. 17(2), pages 233-258, December.
    17. Seung C. Ahn & Alex R. Horenstein, 2017. "Asset Pricing and Excess Returns over the Market Return," Working Papers 2017-12, University of Miami, Department of Economics.
    18. Kandel, Shmuel & McCulloch, Robert & Stambaugh, Robert F, 1995. "Bayesian Inference and Portfolio Efficiency," Review of Financial Studies, Society for Financial Studies, vol. 8(1), pages 1-53.
    19. Stefano Giglio & Dacheng Xiu, 2017. "Inference on Risk Premia in the Presence of Omitted Factors," NBER Working Papers 23527, National Bureau of Economic Research, Inc.
    20. Christophe Morel, 2001. "Stock selection using a multi-factor model - empirical evidence from the French stock market," The European Journal of Finance, Taylor & Francis Journals, vol. 7(4), pages 312-334.

    More about this item

    Keywords

    Arbitrage; Prices;

    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:fip:fedmsr:189. 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: . General contact details of provider: https://edirc.repec.org/data/cfrbmus.html .

    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: Jannelle Ruswick The email address of this maintainer does not seem to be valid anymore. Please ask Jannelle Ruswick to update the entry or send us the correct address (email available below). General contact details of provider: https://edirc.repec.org/data/cfrbmus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.