Subjective Expectations and Asset-Return Puzzles

Abstract

In textbook expositions of the equity-premium, riskfree-rate and equity-volatility puzzles, agents are sure of the economy's structure while growth rates are normally distributed. But because of parameter uncertainty the thin-tailed normal distribution conditioned on realized data becomes a thick-tailed Student-t distribution, which changes the entire nature of what is considered “puzzling” by reversing every inequality discrepancy needing to be explained. This paper shows that Bayesian updating of unknown structural parameters inevitably adds a permanent tail-thickening effect to posterior expectations. The expected-utility ramifications of this for asset pricing are strong, work against the puzzles, and are very sensitive to subjective prior beliefs—even with asymptotically infinite data. (JEL D84, G12)