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Measuring the pricing error of the arbitrage pricing theory

  • John Geweke
  • Guofu Zhou

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.

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Paper provided by Federal Reserve Bank of Minneapolis in its series Staff Report with number 189.

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Date of creation: 1995
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Handle: RePEc:fip:fedmsr:189
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  1. 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.
  2. Shanken, Jay, 1987. "A Bayesian approach to testing portfolio efficiency," Journal of Financial Economics, Elsevier, vol. 19(2), pages 195-215, December.
  3. 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.
  4. Connor, Gregory, 1984. "A unified beta pricing theory," Journal of Economic Theory, Elsevier, vol. 34(1), pages 13-31, October.
  5. 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.
  6. John Geweke, 1991. "Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments," Staff Report 148, Federal Reserve Bank of Minneapolis.
  7. 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.
  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. Brown, Stephen J, 1989. " The Number of Factors in Security Returns," Journal of Finance, American Finance Association, vol. 44(5), pages 1247-62, December.
  10. 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.
  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. 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.
  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 1121-52, September.
  14. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
  15. 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.
  16. Grinblatt, Mark & Titman, Sheridan, 1983. "Factor pricing in a finite economy," Journal of Financial Economics, Elsevier, vol. 12(4), pages 497-507, December.
  17. 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.
  18. Shanken, Jay, 1982. " The Arbitrage Pricing Theory: Is It Testable?," Journal of Finance, American Finance Association, vol. 37(5), pages 1129-40, December.
  19. 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.
  20. 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.
  21. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November.
  22. 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.
  23. 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.
  24. Harvey, Campbell R. & Zhou, Guofu, 1990. "Bayesian inference in asset pricing tests," Journal of Financial Economics, Elsevier, vol. 26(2), pages 221-254, August.
  25. Gibbons, Michael R., 1982. "Multivariate tests of financial models : A new approach," Journal of Financial Economics, Elsevier, vol. 10(1), pages 3-27, March.
  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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