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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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