Predictability Puzzles

Dynamic equilibrium models based on present value computation imply that returns are predictable but also generate particular patterns of predictability in asset returns. I take advantage of this to construct a set of tests of Equilibrium Generated Predictability (EGP). I apply the tests to document two puzzles: First, option implied or realized measures of volatility ought to predict returns but do not. Second, the Variance Risk Premium (VRP) predicts returns but only at long horizons. VRP fails the tests of EGP as the term structure of predictable variation is inconsistent with an equilibrium interpretation.