THE PURPOSE OF THIS CHAPTER

In this chapter we present the salient features of empirical estimations of the term premia for nominal and real bonds that we have conducted using the data made available by the Fed.

For both nominal and real bonds we comment on their Sharpe Ratios, and we regress the excess returns on a small number of a-priori-chosen yield-curve– based regressors: the first few principal components (or their proxies), ‘carry and roll-down’, and all the forward rates in the problem. (We look at predictive regressions using macroeconomic variables as regressors in the next chapter.) Using as regressors all the forward rates in the problem constitutes the maximal (most general) set of yield-curve–based regressors. Barring information not contained in the prices, this regression must give the highest explanatory power of the observed excess returns. It is also the most vulnerable to overfitting. Therefore we pay a lot of attention to (i) how much worse the more austere and parsimonious regressors perform with respect to the maximal set of yield-curve regressors and (ii) how stable the predictions from the maximal set are.

Our conclusion will be that, both for nominal and for real rates, the second principal component by itself strikes a very good compromise between explanatory power (measured in terms of R2), parsimony and robustness when yield-curve–only regressors are used. As this conclusion is somewhat at odds with the most recent findings, we carefully compare our results with the recent literature in the next chapter.

UNDERSTANDING THE EMPIRICAL SETTING

The Empirical Questions

When we undertake empirical investigations of excess returns we normally try to answer two very important, and very different, questions.One is a question of dependence; the other is a question about the nature of the risk compensation. We explain what this means in this subsection.