Financial Proxies to Risk Aversion and Economic Uncertainty

from Bekaert, Engstrom, Xu (2020)

In "The Time Variation in Risk Appetite and Uncertainty", we develop a new measure of time-varying risk aversion that ultimately can be calculated from observable financial information at high frequencies. The general estimation philosophy is as follows:

(1) The risk aversion coefficient is utility-based, reflecting the time-varying relative risk aversion coefficient of the representative agent in a generalized habit-like model with preference shocks.

(2) Given the no-arbitrage framework, asset prices, risk premiums, and physical/ risk-neutral variances are exact functions of the state variables, including risk aversion, in the dynamic (exponential) affine model.

(3) Financial variables are observable. Thus, the market-wide risk aversion should be spanned by a judiciously-chosen instrument set of asset prices and risk variables. We use the Generalized Method of Moments to estimate their optimal linear combination given asset moment restrictions that are consistent with the dynamic no-arbitrage asset pricing model. The instrument set includes a detrended earnings yield, corporate return spread (Baa-Aaa), term spread (10yr-3mth), equity return realized variance, corporate bond return realized variance, and equity risk-neutral variance.

An advantage of the risk aversion measure we develop is that, because of its dependence on financial instruments, it can be computed at even a daily level. Unfortunately, macro-economic uncertainty (e.g., extracted from industrial production as we do in the paper) is only available at the monthly level. Here we also consider using financial instruments to approximate macro uncertainty:

(1) We estimate the monthly conditional variance of industrial production growth with a realistic Bad Environment-Good Environment innovation framework and a persistent conditional mean.

(2) Then, we project the monthly conditional variance onto the financial instruments used to span the risk aversion index. The fitted value is our uncertainty index. Our measure is 81% correlated with the Jurado-Ludvigson-Ng (2015, AER) measure, extracted from macro data, and 34% correlated with the Economic Political Uncertainty index constructed in Bake-Bloom-Davis (2016, QJE).

We track and provide up-to-date risk aversion and uncertainty indices at daily and monthly frequencies. Indices are updated biweekly. Please feel free to let us know if you have any questions!

Warm regards,

The Authors (Nancy, Eric & Geert)

This version: 2020/7/13