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Measuring the pricing error of the arbitrage pricing theory

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Author Info
John Geweke
Guofo Zhou

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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.

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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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Related research
Keywords: Arbitrage ; Prices;

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References listed on IDEAS
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.:
  1. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November. [Downloadable!] (restricted)
  2. 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. [Downloadable!] (restricted)
  3. Shanken, Jay, 1992. " The Current State of the Arbitrage Pricing Theory," Journal of Finance, American Finance Association, vol. 47(4), pages 1569-74, September. [Downloadable!] (restricted)
  4. Grinblatt, Mark & Titman, Sheridan, 1983. "Factor pricing in a finite economy," Journal of Financial Economics, Elsevier, vol. 12(4), pages 497-507, December. [Downloadable!] (restricted)
  5. Harvey, Campbell R. & Zhou, Guofu, 1990. "Bayesian inference in asset pricing tests," Journal of Financial Economics, Elsevier, vol. 26(2), pages 221-254, August. [Downloadable!] (restricted)
  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. [Downloadable!]
  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. [Downloadable!] (restricted)
  8. 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. [Downloadable!] (restricted)
  9. 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. [Downloadable!] (restricted)
  10. Shanken, Jay, 1987. "A Bayesian approach to testing portfolio efficiency," Journal of Financial Economics, Elsevier, vol. 19(2), pages 195-215, December. [Downloadable!] (restricted)
  11. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December. [Downloadable!] (restricted)
  12. Shanken, Jay, 1982. " The Arbitrage Pricing Theory: Is It Testable?," Journal of Finance, American Finance Association, vol. 37(5), pages 1129-40, December. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
  14. 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. [Downloadable!] (restricted)
    Other versions:
  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. [Downloadable!] (restricted)
  16. 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. [Downloadable!] (restricted)
  17. 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. [Downloadable!] (restricted)
  18. 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. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
  20. Brown, Stephen J, 1989. " The Number of Factors in Security Returns," Journal of Finance, American Finance Association, vol. 44(5), pages 1247-62, December. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
  22. Black, Fischer, 1972. "Capital Market Equilibrium with Restricted Borrowing," Journal of Business, University of Chicago Press, vol. 45(3), pages 444-55, July. [Downloadable!] (restricted)
  23. 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. [Downloadable!] (restricted)
Full references

Cited by:
(explanations, 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.)

  1. Éric Jacquier & Nicholas G. Polson & Peter E. Rossi, 1999. "Stochastic Volatility: Univariate and Multivariate Extensions," CIRANO Working Papers 99s-26, CIRANO. [Downloadable!]
    Other versions:
  2. Charles S. Bos & Ronald J. Mahieu & Herman K. van Dijk, 2001. "Daily Exchange Rate Behaviour and Hedging of Currency Risk," Tinbergen Institute Discussion Papers 01-017/4, Tinbergen Institute. [Downloadable!]
    Other versions:
  3. Gabriele Fiorentini & Enrique Sentana & Neil Shephard, 2004. "Likelihood-based estimation of latent generalised ARCH structures," OFRC Working Papers Series 2004fe02, Oxford Financial Research Centre. [Downloadable!]
    Other versions:
  4. Roberto Tatiwa Ferreira & Luiz Ivan de Melo Castelar, 2005. "Forecasting Quarterly Brazilian Gdp Growth Rate With Linear And Nonlinear Diffusion Index Models," Anais do XXXIII Encontro Nacional de Economia [Proceedings of the 33th Brazilian Economics Meeting] 029, ANPEC - Associação Nacional dos Centros de Pósgraduação em Economia [Brazilian Association of Graduate Programs in Economics]. [Downloadable!]
  5. Mohamed Saidane & Christian Lavergne, 2007. "A structured variational learning approach for switching latent factor models," AStA Advances in Statistical Analysis, Springer, vol. 91(3), pages 245-268, October. [Downloadable!] (restricted)
  6. Wolfgang Reichmuth & Samad Sarferaz, 2008. "Bayesian Demographic Modeling and Forecasting: An Application to U.S. Mortality," SFB 649 Discussion Papers SFB649DP2008-052, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  7. Robert Kohn & Rachida Ouysse, 2007. "Bayesian Variable Selection of Risk Factors in the APT Model," Discussion Papers 2007-32, School of Economics, The University of New South Wales. [Downloadable!]
  8. Bork, Lasse, 2009. "Estimating US Monetary Policy Shocks Using a Factor-Augmented Vector Autoregression: An EM Algorithm Approach," Finance Research Group Working Papers F-2009-03, University of Aarhus, Aarhus School of Business, Department of Business Studies. [Downloadable!]
  9. Lasse Bork, 2009. "Estimating US Monetary Policy Shocks Using a Factor-Augmented Vector Autoregression: An EM Algorithm Approach," CREATES Research Papers 2009-11, School of Economics and Management, University of Aarhus. [Downloadable!]
  10. Necati Tekatli, 2007. "Generalized Factor Models: A Bayesian Approach," UFAE and IAE Working Papers 730.08, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC). [Downloadable!]
  11. James H. Stock & Mark W. Watson, 1998. "Diffusion Indexes," NBER Working Papers 6702, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  12. Borus Jungbacker & Siem Jan Koopman, 2008. "Likelihood-based Analysis for Dynamic Factor Models," Tinbergen Institute Discussion Papers 08-007/4, Tinbergen Institute. [Downloadable!]
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