What is the Consumption-CAPM Missing? An Information-Theoretic Framework for the Analysis of Asset Pricing Models

We study a broad class of asset pricing models in which the stochastic discount factor (SDF) can be factorized into an observable component (e.g., a parametric function of consumption) and a potentially unobservable one (e.g., habit level or the return on total wealth). Exploiting this decomposition we derive new entropy bounds that restrict the admissible regions for the SDF and its components. Without using this decomposition, we show that, to a second order approximation, entropy bounds are equivalent to the canonical Hansen-Jagannathan bounds. However, bounds based on our decomposition have higher information content, are generally tighter, and naturally exploit the restriction that the SDF is a positive random variable. In addition, our information-theoretic framework enables us to extract a non-parametric estimate of the unobservable component of the SDF. Empirically we find that this component, in addition to following a clear business cycle pattern, has significant correlation with financial market crashes unrelated to economy-wide contractions. We apply our methodology to the leading consumption-based asset pricing models, gaining new insights about their empirical performance and finding empirical support for the Long Run Risk framework