New Entropy Restrictions and the Quest for Better-Specified Asset-Pricing Models

This article proposes the entropy of m2 (m is the stochastic discount factor) as a metric to evaluate asset-pricing models. We develop a bound on the entropy of m2 when m correctly prices a finite number of returns and consider models that pass the lower bound on m, yet fail the lower bound on m2. Interpreting our results, we elaborate on the distinction between the entropy of m2 versus the entropy of m. We further show that the entropy of m2 represents an upper bound on the expected excess (log) return of the security with the payoff of m.