Complex analytic wavelets in the measurement of macroeconomic risks

We use wavelet gain and partial gain coefficients to measure exposures to risk factors specified within popular asset pricing models with macroeconomic sources of risk. When applied to the consumption CAPM, the durable consumption model of Yogo (2006) and the model of Chen, Roll, and Ross (1986), this approach substantially influences the significance of sensitivities to macroeconomic risks, points to different frequency channels of risk transmission compared with wavelet beta coefficients and enables discovering scale-specific changes of sensitivities to macroeconomic volatility over time. Thus, taking the perspective of an investor operating at a given time scale and correcting for lead-lag effects has far reaching consequences for the choice of macroeconomic risks that should be accounted for. We find that the variables in the different models for returns can be considered as broadband or short- and long-term risk factors. Furthermore, we uncover certain trends over a long period of time, such as increasing exposure to consumption risk at business cycle frequencies or decreasing exposure to the risk premium factor at the scale corresponding to annual oscillations, which suggests that the examined quantities may not be constant over time.