Predictable variations in excess returns have often been attributed to the presence of time-varying risk premia. In this paper, we use an insight based upon new techniques from time series analysis to test whether stationary risk premia can alone explain the behavior of excess returns to long bonds relative to rolling over short rates. Surprisingly, we reject this hypothesis using U.S. T-bill returns. We then show that either permanent shocks to the risk premia and/or rationally anticipated shifts in the interest rate process could produce anomalous results.