Forward rate

Abstract: Current 1 -year forward rates on 1 - to 5-year U.S. Treasury bonds are information about the current term structure of 1-year expected returns on the bonds, and forward rates track variation through time in 1-year expected returns. More interesting, 1 -year forward rates forecast changes in the 1 -year interest rate 2- to l-years ahead, and forecast power increases with the forecast horizon. We attribute this forecast power to a mean-reverting tendency in the 1-year interest rate

Abstract: We study time variation in expected excess bond returns. We run regressions of one-year excess returns on initial forward rates. We find that a single factor, a single tent-shaped linear combination of forward rates, predicts excess returns on one- to five-year maturity bonds with R2 up to 0.44. The return-forecasting factor is countercyclical and forecasts stock returns. An important component of the returnforecasting factor is unrelated to the level, slope, and curvature movements described by most term structure models. We document that measurement errors do not affect our central results. (JEL GO, G1, EO, E4) We study time-varying risk premia in U.S. government bonds. We run regressions of oneyear excess returns-borrow at the one-year rate, buy a long-term bond, and sell it in one year- on five forward rates available at the beginning of the period. By focusing on excess returns, we net out inflation and the level of interest rates, so we focus directly on real risk premia in the nominal term structure. We find R2 values as high as 44 percent. The forecasts are statistically significant, even taking into account the small-sample properties of test statistics, and they survive a long list of robustness checks. Most important, the pattern of regression coefficients is the same for all maturities. A single "return-forecasting factor," a single linear combination of forward rates or yields, describes time-variation in the expected return of all bonds.

Abstract: A class of term structure models with volatility of lognormal type is analyzed in the general HJM framework. The corresponding market forward rates do not explode, and are positive and mean reverting. Pricing of caps and floors is consistent with the Black formulas used in the market. Swaptions are priced with closed formulas that reduce (with an extra assumption) to exactly the Black swaption formulas when yield and volatility are flat. A two-factor version of the model is calibrated to the U.K. market price of caps and swaptions and to the historically estimated correlation between the forward rates.