A Robust Analysis of the Risk-Structure of Equilibrium Term Structures of Bond Yields

Many prominent equilibrium term structure models (ETSMs) in which the state of the economy zt follows an affine process imply that the variation in expected excess returns on bond portfolio positions is fully spanned by the set of conditional variances ςt2 of zt. We show that these two assumptions alone – spanning of excess returns by the variances ςt2 of affine processes zt – are sufficient to econometrically identify the quantities of risk that span risk premiums from the term structure of bond yields. Using this result we derive maximum likelihood estimates of ςt2 and evaluate the goodness-of-fit of the family of affine ETSMs that imply this tight link between premiums and quantities of risk. These assessments are fully robust to the values of the parameters governing preferences and the evolution of the state zt, and to whether or not the economy is arbitrage free. Our findings suggest that, to be consistent with U.S. macroeconomic and Treasury yield data, affine ETSMs should have the features that: the fundamental sources of risks, including consumption growth, inflation, and yield volatilities are driven by distinct economic shocks; consumption growth risk alone is unlikely to fully account for the predictability of excess returns on bonds; and inflation risk, and not long-run risks or variation in risk premiums arising from habit-based preferences, is likely to be the dominant risk underlying risk premiums in U.S. Treasury markets.