Conditional nonlinear asset pricing kernels and the size and book-to-market effects

We develop and test asset pricing model formulations that are simultaneously conditional and nonlinear. Formulations based upon five popular asset pricing models are tested against the widely studied Fama and French (1993) twenty-five size and book-to-market sorted portfolios. Test results indicate that the conditional nonlinear specification of the Fama and French (1993) three state variable model (FF3) is the only specification not rejected by the data and thus capable of pricing the “size” and “book-to-market” effects simultaneously. The pricing performance of the FF3 conditional nonlinear pricing kernel is confirmed by robustness tests on out-of-sample data as well as tests with alternative instrumental and conditioning variables. While Bansal and Viswanathan (1993) and Chapman (1997) find unconditional nonlinear pricing kernels sufficient to capture the size effect alone, our results indicate that similar unconditional nonlinear pricing kernels considered here do not price the size and book-to-market effects simultaneously. However, nested model tests indicate that, in isolation, both conditioning information and nonlinearity significantly improve the pricing kernel performance for all five asset pricing models. The success of the conditional nonlinear FF3 model also suggests that the combination of conditioning and nonlinearity is critical to pricing kernel design. Implications for both academic researchers and practitioners are considered.