Estimated real returns on nominal bonds show excess returns of some 200 bp over their index-linked equivalent. This paper considers two possible explanations for this large difference. First, we assess the likely inflation risk premium by calibrating a model of optimal bond prices under uncertainty. Employing either of CRRA or Abel (1990) relative consumption utility function to derive the stochastic discount factor and covariation risk, we suggest that the inflation risk component of this excess return is unlikely to be much above 50 bp. Secondly, we find little evidence that these excess returns can be ascribed to consistent expectational errors in predicting inflation.