Recent empirical evidence has documented that some financial and macroeconomic variables can be used to predict the excess returns of the U.S. Treasury bonds. For instance, financial variables found to have such predictive power include forward rates or spreads (Fama and Bliss, 1987; Stambaugh, 1988; Cochrane and Piazzesi, 2005) and yield spreads (Campbell and Shiller, 1991). In particular, Cochrane and Piazzesi show that a tent-shaped linear combination of five forward rates can explain between 30 and 35 percent of the variation in 1-year excess returns on bonds with 2-5 years to maturity. On the other hand, Ludvigson and Ng (2008) and Duffee (2008) present empirical evidence indicating the presence of hidden factors closely related to economic activity. More specifically, Ludvigson and Ng obtain a factor (extracted from a monthly panel of 132 macroeconomic variables using dynamic factor analysis) that can explain 21-26 percent of the 1-year excess returns. Furthermore, they document that this factor plus the Cochrane-Piazzesi factor can explain 42-45 percent of the 1-year excess returns. These findings have generated a large and fast growing literature on the determinants of bond risk premia. Nonetheless, some recent studies raise concerns about the robustness of the documented power of those financial and macro variables for predicting bond risk premia (see, e.g. Duffee (2007)).
In this paper, we provide new and robust evidence on the power of macro variables for forecasting bond risk premia. Specifically, we identify a single macro factor that can explain the variation in excess returns on bonds with maturities ranging from 2 to 5 years up to 43%, which is much higher than the level of 26% documented in Ludvigson and Ng (2008, LN hereafter). In addition, this macro factor subsumes the LN factor. Our macro factor, together with the information embedded in yield curve itself, can explain as much as 88% of the time-variation in excess bond returns. Finally, our results confirm and extend those obtained by Ludvigson and Ng (2008) that bond risk premium varies countercyclically.
The reason that we are able to identify a robust macro factor with strong predicting power is that we use a supervised adaptive group “least absolute shrinkage and selection operator” (lasso) approach, that is based on a newly developed method in the statistics literature. We refer to our approach as the SAPLasso approach. This approach takes into account the cluster structure in the macroeconomic panel data to select both observed macroeconomic series and unobservable factors (grouped variables) for accurate prediction in regression.
The proposed procedures enables us to find a compromise between dimension reduction and interpretability, i.e. they could not only estimate a few factors (and a small number of individual series) from a large panel of macroeconomic measures, but also produce a model that is economically interpretable. Intuitively, SAPLasso makes use of fundamental cluster structure of macroeconomic data, selects informative factors at the group level, and thus identifies underlying economic determinants of term premia. Specifically, economic measures in employment, housing and consumer prices are found to have the strongest explanatory power for term premia. This evidence is consistent with the implication of Brandt and Wang (2003)’s model in which investors require compensation for bearing risks related to future recessions and unexpected inflation. From a practical perspective, this approach is capable of selecting important measurable variables within the selected groups, which are especially valuable for practitioners.
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Determinants of Bond Risk Premia
