We show that absence of arbitrage in frictionless markets implies a lower bound on the average of the logarithm of the reciprocal of the stochastic discount factor implicit in asset pricing models. The greatest lower boundfor a given asset menu is the average continuously compounded return on itsgrowth-optimal portfolio. We use this bound to evaluate the plausibility ofvarious parametric asset pricing models to characterize financial marketpuzzles such as the equity premium puzzle and the risk-free ratepuzzle. We show that the insights offered by the growth-optimal boundsdiffer substantially from those obtained by other nonparametric bounds.