Does the Nonlinear APT Outperform the Conditional CAPM?

The conditional CAPM and the nonlinear APT are two important extensions of the Sharpe-Lintner constant beta CAPM. Bansal, Hsieh, and Viswanathan (1993), and Ghysels (1998) suggest that the nonlinear APT is empirically more successful than the conditional CAPM. Using a flexible nonparametric version of the conditional CAPM, we get the opposite result: the conditional CAPM does a substantially better job than the nonlinear APT in explaining the cross-section of time-varying expected returns on stocks. Moreover, we find simulation evidence that the econometric tools commonly recommended for nonlinear APT models are inadequate to detect misspecified models in finite samples. The Capital Asset Pricing Model (CAPM) of Sharpe (1964) and Lintner (1965) has been a focal point in the field of empirical asset pricing for more than thirty years now. Although the static version of the CAPM managed to withstand intense econometric investigation for decades, recent tests indicate that this static single-beta model is not quite enough for explaining expected returns on stocks.1 Financial economists are therefore searching for an empirically successful extension of the CAPM. Two classes of models, conditional linear factor models and nonlinear APT models, have received particular attention in the literature. Conditional asset pricing models are motivated by a couple of appealing developments. On one hand, recent research has documented mounting evidence of time-varying betas and time-varying risk premia. On the other hand, as Dybvig and Ross (1985) and Hansen and Richard (1987) show, the conditional version of the CAPM can hold perfectly even when the static version has serious pricing errors. In general, conditional models (with single factor or multiple factors) that allow for time-varying betas and risk premia can perform substantially better than unconditional models. Thus to explain the cross-section of asset returns, it is natural to consider time-varying beta models. In fact, numerous researchers such as Gibbons and Ferson (1985), Ferson, Kandel, and Stambaugh (1987), Bollerslev, Engle, and Wooldridge (1988), Harvey (1989), Shanken (1990), Carhart, Krail, Steven, and Welch (1995), Cochrane (1996), He, Kan, Ng, and Zhang (1996), Jagannathan and Wang (1996), Ferson and Siegel (1998), and Ferson and Harvey (1999) have studied various forms of conditional linear factor models. A different approach to extending the static CAPM is to consider unconditional nonlinear pricing models. A hypothesis of particular interest is that nonlinearity of the pricing kernel in the market return is important in asset valuation. Following Rubinstein (1973), for example, Kraus and Litzenberger (1976, 1983) derived a three-moment asset pricing model by assuming that investors have a preference for positive return skewness in their portfolios. In contrast to the CAPM which has a linear pricing kernel, the pricing kernel of this model 1For example, see Chan, Hamao, and Lakonishok (1991), and Fama and French (1992, 1993, 1996).