Asset Pricing in the Frequency Domain: Theory and Empirics

Abstract

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.

Financial stress dynamics in the MENA region: Evidence from the Arab Spring

“…We further extend our spillover analysis by applying the Barunik and Krehlik (2015; 2018) frequency connectedness method to identify the dynamics and intensity of spillovers between the FSIs of selected MENA countries in time-frequency domain. In contrast to that of Diebold and Yilmaz (2012), this framework uses spectral representations of variance decomposition locally to retrieve time-frequency (Stiassny, 1996;Dew-becker and Giglio, 2016). For example, a shock with a strong long-term effect will have high power at low frequencies and in the cases where it transmits to other variables, it points to long-term connectedness (Barunik and Krehlik, 2018).…”

Excess Volatility: Beyond Discount Rates

“…We begin with the long run risks models of Bansal and Yaron (2004), in which log consumption growth and its volatility follow linear dynamics. The log pricing kernel is approximately linear (the linearity is exact with unit EIS, and the linear approximation is extremely accurate, as shown in Dew-Becker and Giglio (2013)). In this model the log price and the log price-dividend ratio of all consumption or dividend strips are linear functions of the model's state variables (the persistent consumption growth term x t and the conditional variance of consumption growth σ 2 t ).…”

Climate Change and Long-Run Discount Rates: Evidence from Real Estate

“…The higher z k is for long maturities, the more worried agents are about the long-run risks in the economy. For example, Dew-Becker and Giglio (2013) show that in a power utility model, only z 0 is different from zero (and equal to risk aversion γ): the agent is only worried about the oneperiod innovation in consumption. On the other hand, an Epstein-Zin investor has z 0 = γ like in the power utility model, but also z k = (γ − 1 ψ )θ k for k > 0, where ψ is the elasticity of intertemporal substitution and θ a parameter close to 1 related to the time discount factor.…”

“…Section 4 begins by providing a general decomposition of the term structure of risk and returns of the leading asset pricing models, based on Dew-Becker and Giglio (2013). This decomposition highlights that the shape of the term structure of discount rates for any asset can be attributed to the interaction of three main forces: 1) how much individuals care about long-term news relative to short-term news about consumption growth (i.e., the term structure of horizon-specific risk prices); 2) how much news about future consumption growth there is in the economy (e.g., whether the economy is subject to persistent or i.i.d.…”