Time Variations and Covariations in the Expectation and Volatility of Stock Market Returns



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    • Stern School of Business, New York University. I would like to thank Kobi Boudoukh, Allan Kleidon, Ken Singleton, the editor, Renà Stulz, an anonymous referee, and seminar participants at the University of British Columbia, Carnegie-Mellon University, Harvard University, London Business School, New York University, Northwestern University, the University of Pennsylvania, Stanford University, and the University of Texas, Austin for helpful comments.


This article investigates empirically the comovements of the conditional mean and volatility of stock returns. It extends the results in the literature by demonstrating the role of the commercial paper—Treasury yield spread in predicting time variation in volatility. The conditional mean and volatility exhibit an asymmetric relation, which contrasts with the contemporaneous relation that has been tested previously. The volatility leads the expected return, and this time series relation is documented using offset correlations, short-horizon contemporaneous correlations, and a vector autoregression. These results bring into question the value of modeling expected returns as a constant function of conditional volatility.