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 relate this statistic to the importance of the term premium compared to the risk premium prescribed by the SDF. Estimating bounds for nominal and real SDFs at monthly and quarterly frequencies, we find that the admissible autocorrelations are significantly negative, but greater than -0.01, 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. ∗School of Business, University of Alberta. Mail: Room 2-32E Business Building, Edmonton, AB, T6G 2R6. Voice: (780) 492-1684. Fax: (780) 492-3325. Email: [email protected]. I would like to thank DongHyun Ahn, Mike Cliff, Jennifer Conrad and Nadia Massoud for useful comments and discussions. I acknowledge financial support from the University of Alberta JD Muir Fellowship. The usual disclaimer applies. Please do not quote without the author’s permission. Bounds on the Autocorrelation of Admissible Stochastic Discount Factors