There is a substantial empirical literature, beginning with Fama (1975), that utilizes regressions of the inflation rate in a given period on initial interest rates (or inflation differentials on the slope of the initial yield curve) to test the Fisher hypothesis and/or to provide forecasts of inflation. Both uses depend critically on the maintained hypothesis that asset market prices fully incorporate all relevant current information about future yields. This paper will investigate the plausibility of the rational expectations hypothesis for real returns in markets for one-period default-free bonds, will show that under normal macroeconomic assumptions it cannot be expected to hold, and will consider the consequences of its failure for the interpretation of empirical results.