Asset pricing in the frequency domain: theory and empirics

In many affine asset pricing models, the innovation to the pricing kernel is a function of innovations to current and expected future values of an economic state variable, often consumption growth, aggregate market returns, or short-term interest rates. The impulse response of the priced state variable to various shocks has a frequency (Fourier) decomposition, and we show that the price of risk for a given shock can be represented as a weighted integral over that spectral decomposition. In terms of consumption growth, Epstein-Zin preferences imply that the weight of the pricing kernel lies largely at low frequencies, while internal habit-formation models imply that the weight is shifted to high frequencies. We estimate spectral weighting functions for the equity market semi-parametrically and find that they place most of their weight at low frequencies, consistent with Epstein-Zin preferences. For Treasuries, we find that investors view increases in interest rates at low frequencies and decreases at business-cycle frequencies negatively.