December 9 2004 | John H. Cochrane and Monika Piazzesi
This appendix provides additional results and analysis supporting the main paper on bond risk premia. Section A.1 presents unrestricted regression results showing that individual-bond regressions have high significance, similar to the regression of average excess returns on forward rates. Section A.2 discusses Fama-Bliss regressions, showing that they achieve a high R² that is unlikely under the expectations hypothesis, though the multiple regression provides stronger evidence against the hypothesis. Section A.3 compares the return-forecasting factor with the Fama-Bliss forward spread, showing that the return-forecasting factor subsumes all the predictability of the Fama-Bliss forward spread. Section A.4 examines the forecasting of short rate changes, showing that the return-forecasting factor has substantial power to predict short rate changes. Section A.5 adds additional lags to the model, showing that the single-factor model works just as well with additional lags as it does using only time t right hand variables. Section A.6 discusses eigenvalue factor models for yields, showing that the return-forecasting factor captures a large portion of the variance in yield changes. Section A.7 discusses eigenvalue factor models for expected excess returns, showing that the return-forecasting factor captures almost all of the variation in expected excess returns. Section A.8 discusses what measurement error can and cannot do, showing that measurement error can induce a coefficient of -1 on the one year yield and +n on the n-year yield. Section B presents robustness checks, showing that the results are stable across subsamples and that the results are stronger in the low-inflation 1990s than in the high-inflation 1970s. Section B.1 compares the results with McCulloch-Kwon data, showing that the tent-shape of γ estimates and R² are very similar across the two datasets. Section B.2 examines subsamples, showing that the pattern of coefficients is stable across different periods. Section B.3 examines real-time forecasts and trading rule profits, showing that the return-forecasting factor performs well in real-time data. Section C presents calculations for the regressions, including GMM estimates and tests. Section D discusses an affine model that captures the return-forecasting regressions exactly. The model is shown to be self-consistent and to generate the same results as the return-forecasting factor.This appendix provides additional results and analysis supporting the main paper on bond risk premia. Section A.1 presents unrestricted regression results showing that individual-bond regressions have high significance, similar to the regression of average excess returns on forward rates. Section A.2 discusses Fama-Bliss regressions, showing that they achieve a high R² that is unlikely under the expectations hypothesis, though the multiple regression provides stronger evidence against the hypothesis. Section A.3 compares the return-forecasting factor with the Fama-Bliss forward spread, showing that the return-forecasting factor subsumes all the predictability of the Fama-Bliss forward spread. Section A.4 examines the forecasting of short rate changes, showing that the return-forecasting factor has substantial power to predict short rate changes. Section A.5 adds additional lags to the model, showing that the single-factor model works just as well with additional lags as it does using only time t right hand variables. Section A.6 discusses eigenvalue factor models for yields, showing that the return-forecasting factor captures a large portion of the variance in yield changes. Section A.7 discusses eigenvalue factor models for expected excess returns, showing that the return-forecasting factor captures almost all of the variation in expected excess returns. Section A.8 discusses what measurement error can and cannot do, showing that measurement error can induce a coefficient of -1 on the one year yield and +n on the n-year yield. Section B presents robustness checks, showing that the results are stable across subsamples and that the results are stronger in the low-inflation 1990s than in the high-inflation 1970s. Section B.1 compares the results with McCulloch-Kwon data, showing that the tent-shape of γ estimates and R² are very similar across the two datasets. Section B.2 examines subsamples, showing that the pattern of coefficients is stable across different periods. Section B.3 examines real-time forecasts and trading rule profits, showing that the return-forecasting factor performs well in real-time data. Section C presents calculations for the regressions, including GMM estimates and tests. Section D discusses an affine model that captures the return-forecasting regressions exactly. The model is shown to be self-consistent and to generate the same results as the return-forecasting factor.