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The existence theorem of approximate multibeta representation for multifactor pricing models with unobservable omitted variables: A technical note

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  • Jeng, Jau-Lian

Abstract

This paper extends the approximate multibeta representation of Reisman [Reisman, H. (1988), A general approach to the APT, Econometrica, 56, 473-476, Reisman, H. (1992), Reference variables, factor structure, and the approximate multibeta representation, Journal of Finance, 47(4), 1303-1314] with insufficient information. An existence theorem is presented that if the projection error (when regressing the excess returns on a presumed information set of reference variables with linearity) follows the dependence conditions of a mixing random field, there exists an approximate multibeta representation for the risk premium. This result holds even though the linearity is an incorrect specification and/or that the included variables are not sufficiently informative for the model. In particular, the theorem includes omitted (dynamic) factor(s) which may cause unknown inter-temporal or cross-sectional memory in projection errors. An alternative model selection approach is suggested for the specification of risk premium in empirical finance.

Suggested Citation

  • Jeng, Jau-Lian, 2008. "The existence theorem of approximate multibeta representation for multifactor pricing models with unobservable omitted variables: A technical note," Global Finance Journal, Elsevier, vol. 19(1), pages 11-18.
  • Handle: RePEc:eee:glofin:v:19:y:2008:i:1:p:11-18
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    References listed on IDEAS

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    1. Shanken, Jay, 1992. " The Current State of the Arbitrage Pricing Theory," Journal of Finance, American Finance Association, vol. 47(4), pages 1569-1574, September.
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    4. Reisman, Haim, 1992. " Reference Variables, Factor Structure, and the Approximate Multibeta Representation," Journal of Finance, American Finance Association, vol. 47(4), pages 1303-1314, September.
    5. 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.
    6. Gibbons, Michael R. & Ferson, Wayne, 1985. "Testing asset pricing models with changing expectations and an unobservable market portfolio," Journal of Financial Economics, Elsevier, vol. 14(2), pages 217-236, June.
    7. John Lintner, 1965. "Security Prices, Risk, And Maximal Gains From Diversification," Journal of Finance, American Finance Association, vol. 20(4), pages 587-615, 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.
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    10. 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.
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