Equilibrium asset pricing with short rate risk

I study the exact percentage price reaction (in absolute value) to changes in the short rate for long-lived assets in a tractable long-run risk equilibrium model with fluctuating expected growth rates. Calibration reveals that, under time-additive expected utility, perpetuities with constant coupons exhibit a larger effective duration than the absolute value of the stock price logarithmic derivative due to a mild positive comovement between short rates and expected dividend growth. Conversely, under Epstein-Zin preferences with unit elasticity of intertemporal substitution, the perpetuity’s effective duration is smaller due to a pronounced positive comovement between short rates and expected dividend growth. My findings suggest that strong persistence in fundamentals contributes to non-linearities in the equilibrium log prices of long-lived assets. (JEL Classification Code: G12). Keywords: equilibrium short rate, long-run risk, effective duration, stock pricing, perpetuity/consol pricing.