Underspecification of the Empirical Return-Factor Model and a Factor Analytic Augmentation as a Solution to Factor Omission

32 Pages Posted: 28 May 2019

See all articles by Jan Szczygielski

Jan Szczygielski

University of Pretoria

Leon Brummer

affiliation not provided to SSRN

Hendrik Wolmarans

affiliation not provided to SSRN

Date Written: April 30, 2019

Abstract

Factor omission in time-series models that relate asset returns to pre-specified factor sets is a common problem. A proposed solution to underspecification is the use of a residual market factor which is assumed to be a catch-all proxy for omitted factors. This study shows that a specification that incorporates a set of carefully selected macroeconomic factors will be underspecified and that underspecification has extensive consequences for model estimation and interpretation. Moreover, the inclusion of residual market factors will alleviate but not eliminate the consequences of underspecification. To ensure that an approximation of the diagonality assumption holds, a factor analytic augmentation should be included. Although the early use of factor analytically derived factor scores in factor models has been criticized, augmenting a model comprising pre-specified factors with statistical factors derived from the residuals results in an accurately specified model.

Keywords: linear factor model, underspecification, Arbitrage Pricing Theory, asset pricing

JEL Classification: C01, C22, C58, G12

Suggested Citation

Szczygielski, Jan and Brummer, Lean and Wolmarans, Hendrik, Underspecification of the Empirical Return-Factor Model and a Factor Analytic Augmentation as a Solution to Factor Omission (April 30, 2019). Available at SSRN: https://ssrn.com/abstract=3380244 or http://dx.doi.org/10.2139/ssrn.3380244

Jan Szczygielski (Contact Author)

University of Pretoria ( email )

Physical Address Economic and Management Sciences
Pretoria, Gauteng 0002
South Africa

Lean Brummer

affiliation not provided to SSRN

Hendrik Wolmarans

affiliation not provided to SSRN

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