Linear Approximations and Conditional Asset Pricing Models

Michael W. Brandt, Duke University.

David A. Chapman, Boston College.


If a nonlinear risk premium in a conditional asset pricing model is approximated with a linear function, as is commonly done in empirical research, the fitted model is misspecified. We use a generic reduced-form model economy with modest risk premium nonlinearity to examine the size of the resulting misspecification-induced pricing errors. Pricing errors from modest nonlinearity can be large, and a version of a test for nonlinearity based on risk premiums rather than pricing errors has reasonable power properties after properly controlling for the size of the test. We conclude by examining the importance of modest nonlinearity in the recent structural general equilibrium model of Papanikolaou (2011).

A copy of the current version of the paper can be downloaded here.

The Matlab code used to produce the results in the paper can be downloaded (in a compressed file) here.