I find that the standard class of affine models produces poor forecasts of future changes in Treasury yields. Better forecasts are generated by assuming that yields follow random walks. The failure of these models is driven by one of their key features: the compensation that investors receive for facing risk is a multiple of the variance of the risk. This means that risk compensation cannot vary independently of interest rate volatility. I also describe and empirically estimate a class of models that is broader than the standard affine class. These 'essentially affine' models retain the tractability of the usual models, but allow the compensation for interest rate risk to vary independently of interest rate volatility. This additional flexibility proves useful in forming accurate forecasts of future yields.