We derive a lower bound for the volatility of the permanent component of investors' marginal utility of wealth or, more generally, asset pricing kernels. The bound is based on return properties of long‐term zero‐coupon bonds, risk‐free bonds, and other risky securities. We find the permanent component of the pricing kernel to be very volatile; its volatility is about at least as large as the volatility of the stochastic discount factor. A related measure for the transitory component suggest it to be considerably less important. We also show that, for many cases where the pricing kernel is a function of consumption, innovations to consumption need to have permanent effects.