What Do We Really Know About the Cross-Sectional Relation Between Past and Expected Returns?

Multihorizon temporal relationships between stock returns are complex due to confounding sources of return premia, microstructure effects, and changes in the relationship over various horizons. We find the relation to be further complicated by the sign and consistency of the past return that also varies, somewhat sensibly, with the season and the tax environment. Accounting for these additional effects using a parsimonious technical trading rule generates surprisingly large abnormal returns, despite controlling for microstructure effects, transaction costs, and date-snooping biases. The documented variation in profits across stock characteristics, season, and tax environment appears inconsistent with existing theory, but may point to future explanations for the relation between past and expected returns.