This paper investigates how security market data can be used to restrict the admissible region for means and standard deviations of intertemporal marginal rates of substitution (IMRSs) in dynamic economic models. The approach is nonparametric and applies to a wide range of models, characterizing the duality between the mean–standard deviation frontier for IMRSs and asset returns. It also exploits the fact that IMRSs are positive random variables, providing a convenient summary of how asset market data deviate from intertemporal asset pricing theory. The paper shows that when IMRSs are constant, portfolios with the same price must have the same mean. Therefore, the existence of portfolios with the same price but different expected payoffs implies that IMRSs must vary. This observation is used to derive volatility bounds on IMRSs, which are expressed as regions of admissible mean–standard deviation pairs. The authors compare their nonparametric approach to the parametric approach used in the literature, noting that the nonparametric method can better explain why certain models are rejected by statistical tests. It also provides a common set of diagnostics for a wide range of asset pricing models and helps assess the plausibility of parametric models of asset prices. The paper illustrates these points by providing an alternative characterization of the equity premium puzzle, using annual data on stocks and bonds. It shows that the mean and standard deviation of IMRSs implied by this data fall within a restricted region. The paper also discusses the implications of restriction 1 and 2 for the mean and standard deviation of IMRSs, showing how these restrictions can be used to derive volatility bounds. The paper concludes that the nonparametric approach provides a useful complement to the parametric approach in asset pricing, allowing for a better understanding of the implications of asset market data for dynamic economic models. It also shows that the volatility bounds derived from this approach can be used to assess the plausibility of parametric models of asset prices.This paper investigates how security market data can be used to restrict the admissible region for means and standard deviations of intertemporal marginal rates of substitution (IMRSs) in dynamic economic models. The approach is nonparametric and applies to a wide range of models, characterizing the duality between the mean–standard deviation frontier for IMRSs and asset returns. It also exploits the fact that IMRSs are positive random variables, providing a convenient summary of how asset market data deviate from intertemporal asset pricing theory. The paper shows that when IMRSs are constant, portfolios with the same price must have the same mean. Therefore, the existence of portfolios with the same price but different expected payoffs implies that IMRSs must vary. This observation is used to derive volatility bounds on IMRSs, which are expressed as regions of admissible mean–standard deviation pairs. The authors compare their nonparametric approach to the parametric approach used in the literature, noting that the nonparametric method can better explain why certain models are rejected by statistical tests. It also provides a common set of diagnostics for a wide range of asset pricing models and helps assess the plausibility of parametric models of asset prices. The paper illustrates these points by providing an alternative characterization of the equity premium puzzle, using annual data on stocks and bonds. It shows that the mean and standard deviation of IMRSs implied by this data fall within a restricted region. The paper also discusses the implications of restriction 1 and 2 for the mean and standard deviation of IMRSs, showing how these restrictions can be used to derive volatility bounds. The paper concludes that the nonparametric approach provides a useful complement to the parametric approach in asset pricing, allowing for a better understanding of the implications of asset market data for dynamic economic models. It also shows that the volatility bounds derived from this approach can be used to assess the plausibility of parametric models of asset prices.