Interest Rate Risk, Inflation, and the Cross Section of Stock Returns

We posit that the pricing mechanism of interest rate risk is contingent upon the prevailing inflation levels; in times of high (low) inflation, a positive (negative) shock to interest rates is indicative of a negative economic state. In line with this proposition, we introduce a conditional interest rate factor, defined as the shock to interest rates multiplied by the standardized inflation level. The proposed single factor effectively indicates the states of both raising interest rates to combat inflation and lowering interest rates to counteract a recession. We find supporting evidence that interest rate risk is not unconditionally priced, but rather contingent upon inflation. Specifically, the sensitivity of stock returns to interest rate innovation cannot account for the cross-section of stock returns, but when interacted with standardized inflation, it produces significant cross-sectional return differences, even after controlling for standard risk factors. Moreover, when examining standard equity portfolios as test assets, our conditional interest rate factor outperforms its unconditional counterpart in terms of pricing performance, as measured by R2 and absolute pricing error, and is comparable to the Fama-French three-factor model. Finally, we provide further validation for our proposed factor by demonstrating its ability to predict future consumption growth and achieving a Sharpe ratio comparable to the tangency portfolio