Conditional maximum Sharpe ratios implied by fully flexible four-factor and five-factor Gaussian term structure models are astronomically high. Estimation of term structure models subject to a constraint on their Sharpe ratios uncovers properties that hold for a wide range of Sharpe ratios. These robust properties include (a) an inverse relation between a bond's maturity and its average Sharpe ratio; (b) between 15 and 20 percent of annual excess returns to bonds are predictable; and (c) variations in expected excess bond returns are driven by two factors. These factors operate at different frequencies. Nonrobust features include the mean level of the term structure. Unconstrained models imply that investors anticipated much of the decline of interest rates in the 1990s. Constrained models disagree.