Sources of Entropy in Representative Agent Models

Abstract

We propose two metrics for asset pricing models and apply them to representative agent models with recursive preferences, habits, and jumps. The metrics describe the pricing kernel's dispersion (the entropy of the title) and dynamics (time dependence, a measure of how entropy varies over different time horizons). We show how each model generates entropy and time dependence and compare their magnitudes to estimates derived from asset returns. This exercise -and transparent loglinear approximations -clarifies the mechanisms underlying these models. It also reveals, in some cases, tension between entropy, which should be large enough to account for observed excess returns, and time dependence, which should be small enough to account for mean yield spreads. JEL Classification Codes: E44, G12.

Doubts and Variability: A Robust Perspective on Exotic Consumption Series

“…The persistence parameter, ϕ h is based on Wachter's (2013) parameterization (ϕ h = 1 − κ/12 where κ is the persistence parameter in her continuous time intensity process). The parameterization of χ and δ was used in Backus, Chernov, and Zin (2014) as an approximation to the multinomial distribution for consumption declines in the case of disasters, used by Wachter (2013) and Barro and Ursua (2008). In the absence of disasters, the trend growth and volatility of the Gaussian innovation are calibrated to yield mean and standard deviation of annual consumption growth of 1.80% and 1.99% respectively.…”

“…That is, the plausibility of the risk aversion required to hit desired asset-pricing targets deteriorates ash declines (and begins to approach levels that are typically though implausible -see Mehra (2003)) but the plausibility of the ambiguity aversion parameterization increases. 20 A simple implication of this is that the 'advantage' of robustness over risk aversion is greater at lowerh so that reducing the probability of a jump from our primary calibration to lower levels than in Wachter (2013) that some (such as Backus, Chernov, and Zin (2014)) prefer, would actually be in our favor.…”

Risk Pricing over Alternative Investment Horizons

“…When S t is log-normal, this notion of entropy yields one-half the conditional variance of log S t conditioned on date zero information, and Alvarez and Jermann (2005) propose using this measure as a "generalized notion of variation." Backus et al (2011) study this measure of relative entropy averaged over the initial state X 0 . They view this entropy measure for different investment horizons as an attractive alternative to the volatility of stochastic discount factors featured by Hansen and Jagannathan (1991).…”

“…They view this entropy measure for different investment horizons as an attractive alternative to the volatility of stochastic discount factors featured by Hansen and Jagannathan (1991). To relate these entropy measures to asset pricing models and data, Backus et al (2011) note that…”

“…In the construction that follows we build on ideas from Bansal and Lehmann (1997), Alvarez and Jermann (2005), and especially Backus et al (2011). The relative entropy of a stochastic discount factor functional S for horizon t is given by:…”