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Unconditional Tests of Linear Asset Pricing Models with Time‐Varying Betas
Author(s) -
Zhou Ji,
Paseka Alex
Publication year - 2017
Publication title -
financial review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.621
H-Index - 47
eISSN - 1540-6288
pISSN - 0732-8516
DOI - 10.1111/fire.12129
Subject(s) - econometrics , capital asset pricing model , constraint (computer aided design) , economics , risk premium , factor analysis , stochastic discount factor , mathematics , covariance , affine transformation , statistics , geometry , pure mathematics
In conditional affine factor models, estimated risk prices should satisfy certain unconditional constraints. Specifically, a cross‐sectional estimate of the unconditional slope associated with a risk factor should equal the average price of risk of the factor. The estimated slope associated with the product of a risk factor and an instrument should be equal to the covariance of the factor risk premium with the instrument. We show that the constraints only apply to the conditional models with time‐varying betas. We identify an unconditional constraint on unconditional betas for time‐varying beta models and incorporate it into model tests. We show that imposing this unconditional constraint changes estimates of unconditional betas and risk prices significantly.