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Measuring the Pricing Error of the Arbitrage Pricing Theory

  • John Geweke

    (University of Minnesota
    Federal Reserve Bank of Minneapolis)

  • Guofu Zhou

    (Washington University)

This article 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.

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Paper provided by China Economics and Management Academy, Central University of Finance and Economics in its series CEMA Working Papers with number 276.

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Length: 31 pages
Date of creation: 1996
Date of revision:
Publication status: Published in the Review of Financial Studies, Summer 1996, Vol. 9, No. 2, pp. 557-587
Handle: RePEc:cuf:wpaper:276
Contact details of provider: Web page: http://cema.cufe.edu.cn/

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  1. 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.
  2. Grinblatt, Mark & Titman, Sheridan, 1983. "Factor pricing in a finite economy," Journal of Financial Economics, Elsevier, vol. 12(4), pages 497-507, December.
  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. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. Shanken, Jay, 1987. "A Bayesian approach to testing portfolio efficiency," Journal of Financial Economics, Elsevier, vol. 19(2), pages 195-215, December.
  10. Shanken, Jay, 1982. " The Arbitrage Pricing Theory: Is It Testable?," Journal of Finance, American Finance Association, vol. 37(5), pages 1129-40, December.
  11. Shanken, Jay, 1992. " The Current State of the Arbitrage Pricing Theory," Journal of Finance, American Finance Association, vol. 47(4), pages 1569-74, September.
  12. Gibbons, Michael R., 1982. "Multivariate tests of financial models : A new approach," Journal of Financial Economics, Elsevier, vol. 10(1), pages 3-27, March.
  13. 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 1263-91, September.
  14. 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.
  15. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November.
  16. Connor, Gregory, 1984. "A unified beta pricing theory," Journal of Economic Theory, Elsevier, vol. 34(1), pages 13-31, October.
  17. Harvey, Campbell R. & Zhou, Guofu, 1990. "Bayesian inference in asset pricing tests," Journal of Financial Economics, Elsevier, vol. 26(2), pages 221-254, August.
  18. 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 1121-52, September.
  19. 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.
  20. Chamberlain, Gary & Rothschild, Michael, 1983. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Econometrica, Econometric Society, vol. 51(5), pages 1281-304, September.
  21. 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.
  22. Brown, Stephen J, 1989. " The Number of Factors in Security Returns," Journal of Finance, American Finance Association, vol. 44(5), pages 1247-62, December.
  23. John Geweke, 1991. "Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments," Staff Report 148, Federal Reserve Bank of Minneapolis.
  24. 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.
  25. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
  26. Black, Fischer, 1972. "Capital Market Equilibrium with Restricted Borrowing," The Journal of Business, University of Chicago Press, vol. 45(3), pages 444-55, July.
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