On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks





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    • Glosten is from Columbia University, Jagannathan is from the University of Minnesota and the Federal Reserve Bank of Minneapolis, and Runkle is from the Federal Reserve Bank of Minneapolis and the University of Minnesota. We benefitted from discussions with Tim Bollerslev, William Breen, Lars Hansen, Patrick Hess, David Hsieh, Ruth Judson, Narayana Kocherlakota, Robert McDonald, Dan Nelson, and Dan Siegel, and from comments from David Backus and René Stulz. Ruth Judson and Joe Piepgras did many of the computations. We are especially grateful for the insightful and detailed comments of the referee. The usual disclaimer regarding errors applies. Part of this research was performed while Glosten was a Visiting Economist at the New York Stock Exchange. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis, the Federal Reserve System, or the New York Stock Exchange and its members.


We find support for a negative relation between conditional expected monthly return and conditional variance of monthly return, using a GARCH-M model modified by allowing (1) seasonal patterns in volatility, (2) positive and negative innovations to returns having different impacts on conditional volatility, and (3) nominal interest rates to predict conditional variance. Using the modified GARCH-M model, we also show that monthly conditional volatility may not be as persistent as was thought. Positive unanticipated returns appear to result in a downward revision of the conditional volatility whereas negative unanticipated returns result in an upward revision of conditional volatility.