Short-Term Momentum and LongTerm Reversal of Returns under Limited Enforceability and Belief Heterogeneity

We evaluate the ability of the Lucas [25] tree and the Alvarez-Jermann [3] models, both with homogeneous as well as heterogeneous beliefs, to generate a time series of excess returns that displays both short-term momentum and long-term reversal, i.e., positive autocorrelation in the short-run and negative autocorrelation in the long-run. Our analysis is based on a methodological contribution that consists in (i) a recursive characterisation of the set of constrained Pareto optimal allocations in economies with limited enforceability and belief heterogeneity and (ii) an alternative decentralisation of these allocations as competitive equilibria with endogenous borrowing constraints. We calibrate the model to U.S. data as in Alvarez and Jermann [4]. We find that only the Alvarez-Jermann model with heterogeneous beliefs delivers autocorrelations that not only have the correct sign but are also of magnitude similar to the US data.