Bond Risk Premia

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 return-forecasting 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.

Forecasting Interest Rates

“…They report R 2 s up to 44 percent when annual excess returns are predicted by five forward rates. In Table 4 the R 2 s for the 1964 through 2003 sample exceed 50 percent, both because the predictors are slightly different than those used by Cochrane and Piazzesi (2005) and because the regressions use non-overlapping observations. There is unquestionably overfitting in these regressions, since only 39 observations are explained by five variables.…”

“…However, Table 4 also includes results for the sample 1964 through 2003, which matches the sample period studied by Cochrane and Piazzesi (2005). They report R 2 s up to 44 percent when annual excess returns are predicted by five forward rates.…”

“…3 Other principal components may have information about expected future values of level, slope, and curvature. Cochrane and Piazzesi (2005) point out that a factor does not need to have a large effect on the time-t term structure in order to play an important role in time-t expectations of future yields and expected returns.…”

“…whereX t is a vector of variables known at t. The focus on monthly returns is somewhat at odds with much of the recent literature that follows Cochrane and Piazzesi (2005) by studying annual returns. But the goal here is not to generate large R 2 s, but rather to judge the statistical significance of predictability.…”

“…We take a closer look at that evidence here. We also consider one of the results in Cochrane and Piazzesi (2005), hereafter CP. The material in this section is new to the literature.…”