Bond Risk Premia

Abstract

This paper studies time variation in expected excess bond returns. We run regressions of annual excess returns on forward rates. We find that a single factor predicts 1-year excess returns on 1-5 year maturity bonds with an R 2 up to 43%. The single factor is a tent-shaped linear function of forward rates. The return forecasting factor has a clear business cycle correlation: Expected returns are high in bad times, and low in good times, and the return-forecasting factor forecasts longrun output growth. The return-forecasting factor also forecasts stock returns, suggesting a common time-varying premium for real interest rate risk. The return forecasting factor is poorly related to level, slope, and curvature movements in bond yields. Therefore, it represents a source of yield curve movement not captured by most term structure models. Though the return-forecasting factor accounts for more than 99% of the time-variation in expected excess bond returns, we find additional, very small factors that forecast equally small differences between long term bond returns, and hence statistically reject a one-factor model for expected returns.

Resolving the Spanning Puzzle in Macro-Finance Term Structure Models

“…That is, does the unspanned macro variation represent unspanned macro risk? Following standard practice-see, for example, Cochrane and Piazzesi (2005) and Ludvigson and Ng (2009)-we run predictive regressions for annual excess bond returns, using the average excess returns for bonds of different maturities (two through ten years in our case) as the dependent variable. The predictors are the first three PCs of the yield curve and each of our macroeconomic variables.…”

“…First, this may reflect the fragility of the regression evidence for the predictive power of GRO and INF in the real-world data. Second, the models' first-order Markov structure for monthly yields and macro variables can only partially capture the predictability of annual excess returns (Cochrane and Piazzesi, 2005).…”

“…However, these peaks occur early in recessions or even before the beginning of the recessions, while the economy is still expanding briskly and risk aversion and risk compensation are low. A more plausible business cycle pattern for risk premia is to be high in troughs and low at peaks (Cochrane and Piazzesi, 2005). The yields-only term premium is therefore more plausible, since it is low late in the expansion and rises throughout recessions.…”

Mortgage Risk and the Yield Curve

“…This table reports estimated coefficients from regressing annual bond excess returns constructed from ten-year Treasuries, rx 10y t,t+1y , on MBS dollar duration, the first three principal components from yields (level, slope, and curvature), the Cochrane and Piazzesi (2005) factor, expected inflation, and a growth index. Expected inflation is the consensus estimate from monthly forecasts on future inflation from Blue Chip Economic Indicators.…”

“…The annual excess bond return is then defined as rx τ t,t+1y = r τ t,t+1y − y 1y t , where y 1y t = − log Λ 1y t is the one-year yield. From the same data, we also construct a tent-shaped factor from forward rates (labeled cp t ) (see Cochrane and Piazzesi 2005). Real annual excess bond returns are denoted by rx τ * t,t+1y .…”