Bounds on the autocorrelation of admissible stochastic discount factors

We show how to use asset market data to restrict the admissible region for the first-order autocorrelation of the stochastic discount factor (SDF). We interpret this statistic as a measure of a model’s economic time variation across two periods. Estimating bounds for nominal and real SDFs at monthly and quarterly frequencies, we find that the admissible autocorrelations are significantly negative, but greater than −0.02, implying that the bounds impose a strong restriction on candidate SDFs. We illustrate the relevancy of these findings by showing that some widely used consumption-based models are misspecified with respect to the autocorrelation bound. Finally, we examine the implications of our results for the admissibility of linear factor models and the appropriateness of empirical pricing factors.