Is Real Interest Rate Risk Priced? Theory and Empirical Evidence

We propose a model in which real interest rates respond to both expected consumption growth and time preferences. Exposures to future consumption growth and time preference interest rate shocks are both priced relative to the Capital Asset Pricing Model (CAPM) and the Consumption Capital Asset Pricing Model (CCAPM). However, the two types of interest rate risk have different prices, and when elasticity of intertemporal substitution (EIS) is greater than one, the prices have opposite signs. Moreover, the premia for time preference risk are arbitrarily large when EIS is close to 1. We interpret this as evidence that Epstein-Zin utility with EIS close to 1 implies implausible aversion to future time preference shocks, which undermines some common Epstein-Zin calibrations. Empirically, we find little evidence that interest rate risk is priced in the cross-section of stocks. Market equity returns and treasury bonds have only small exposures to real interest rate risk.