Asset Pricing in the Frequency Domain: Theory and Empirics
In 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, for example consumption growth, aggregate market returns, or short-term interest rates. The impulse response of this priced variable to fundamental shocks has a frequency (Fourier) decomposition, which captures the fluctuations induced in the priced variable at different frequencies. We show that the price of risk for a given shock can be represented as a weighted integral over that spectral decomposition. The weight assigned to each frequency then represents the frequency-specific price of risk, and is entirely determined by the preferences of investors. For example, standard Epstein-Zin preferences imply that the weight of the pricing kernel lies almost entirely at extremely low frequencies, most of it on cycles longer than 230 years; internal habit-formation models imply that the weight is shifted to high frequencies. We estimate the frequency-specific risk prices for the equity market, focusing on economically interesting frequencies. Most of the pricing weight falls on low frequencies – corresponding to cycles longer than 8 years – broadly consistent with Epstein-Zin preferences.
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