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.