The Term Structures of Co-entropy in International Financial Markets

We propose a new entropy-based correlation measure (co-entropy) to evaluate the performance of international asset pricing models. Co-entropy summarizes in a single number the extent of co-dependence between two variables beyond normality. We document that the co-entropy of international stochastic discount factors (SDFs) can be decomposed into a series of entropy-based correlations of permanent and transitory components of the SDFs. We derive bounds and restrictions on co-entropies of these components, which we then use to analyze the composition of co-dependence of international SDFs. A large cross-section of countries is employed to provide empirical evidence on the entropy-based correlations at various horizons. We find that the co-entropy of the transitory components is always sizably smaller than the co-entropy of the permanent components, with the latter usually being very close to one. Furthermore, the entropy based correlation of transitory components of SDFs increases with the investment horizon, which features an upward sloping term structure of co-entropies. We confront several state-of-the-art international finance models with these empirical regularities, and find that existing models cannot account for the composition of codependence at all horizons.