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 bound for a given asset menu is the average continuously compounded return on its growth-optimal portfolio. We use this bound to evaluate the plausibility of various parametric asset pricing models to characterize financial market puzzles such as the equity premium puzzle and the risk-free rate puzzle. We show that the insights offered by the growth-optimal bounds differ substantially from those obtained by other nonparametric bounds.