The Effect of Conditional Volatility, Skewness, and Excess Kurtosis on Interest Rates

Abstract

This paper examines the lognormality assumption of per capita, real consumption growth, which is a common assumption in asset pricing models. We found that shocks to household consumption growth are persistent, negatively skewed, and have excess kurtosis. Therefore, we revisited the fundamental relation between expected growth and the real risk-free rate, assuming a non-Gaussian distribution of consumption growth, and found a robust positive association between real consumption growth and real risk-free interest rate, and a negative relationship between macroeconomic uncertainty and real rates, although less in magnitude, which is consistent with both intertemporal smoothing and precautionary savings. This paper offers an answer to the puzzle of why real rates and macroeconomy appear to be empirically unrelated. Adding higher moments lowers the level of persistence of consumption growth and adds more dimensions of risk that are not captured by conditional variance. Specifically, conditional skewness amplifies the effect of intertemporal smoothing while excess kurtosis amplifies the effect of precautionary savings. The results imply that using variance as a description of uncertainty is incomplete.

Keywords: Asset Pricing, Bond Interest Rates, Term Structure

JEL Classification: G12, E43