Why Long Term Forward Interest Rates (Almost) Always Slope Downwards

Abstract

The paper documents a persistent and thus far largely overlooked empirical regularity in the yield curve: the tendency for the term structure of long term forward rates to slope downwards. The persistence of this feature is demonstrated using data on US and UK Government conventional (nominal) bonds and UK Government index-linked bonds. We show that the downward slope is the result of interest rate volatility. Using a two factor Gaussian model we show that the long term forward rate curve will be downward sloping whenever the volatility of the long term zero coupon yield is sufficiently high. Using data on US Treasury STRIPs, the paper further shows that the slope of the forward rate curve predicts the volatility of long term rates and that the implied volatility from bond futures options explains the slope of the forward rate curve.