Asset Pricing with Fading Memory

Consumption Fluctuations and Expected Returns

“…While we emphasize the connection between our empirical analysis and the external habit model of Campbell and Cochrane (1999), our result that consumption fluctuations can predict stock returns appears consistent with other classes of asset pricing models such as learning models that can generate countercyclical variation in risk premia (Collin-Dufresne, Johannes, and Lochstoer (2016), Nagel and Xu (2018)). A series of positive fundamental shocks in a learning model induces the agent to be optimistic, which leads up to high asset prices and, in turn, low subsequent future returns.…”

“…A series of positive fundamental shocks in a learning model induces the agent to be optimistic, which leads up to high asset prices and, in turn, low subsequent future returns. For example, Nagel and Xu (2018) predict that the equity premium is negatively related to long-run weighted averages of past real per capita payout growth rates and they verify this empirically. Thus, in line with our empirical results, past growth rates of fundamentals generate slow-moving time variation in expected returns.…”

“…Out-of-sample results may differ from in-sample results due to loss of information when splitting samples in out-of-sample tests, structural breaks, and parameter uncertainty (see, e.g., Inoue and Kilian (2004), Paye and Timmermann (2006), Lettau and Van Nieuwerburgh (2008), Cochrane (2008)). Furthermore, Nagel and Xu (2018) show that in-sample predictability does not necessarily imply that out-of-sample predictability will hold in models with learning.…”

“…Thus, in line with our empirical results, past growth rates of fundamentals generate slow-moving time variation in expected returns. However, unlike the habit-based explanation of return predictability, the learning model of Nagel and Xu (2018) features constant relative risk aversion and return predictability that is induced by subjective belief dynamics rather than time-varying risk aversion.…”

Stock Price Cycles and Business Cycles

“…Bordalo, Gennaioli, and Shleifer (2018) explain how extrapolation can alternatively be obtained by postulating that agents hold diagnostic expectations. Nagel and Xu (2018) show how learning from experience by individual agents generates fading memory for the representative agent and thereby gives rise to the kind of perpetual learning present also in equation 13.…”