Asset Pricing with Return Extrapolation∗

We develop a representative agent general equilibrium model with return extrapolation and recursive preferences. Our model is the first return extrapolation model that can be taken to the data in a serious way; it allows for detailed model calibration and direct comparisons with the leading rational expectations models of the stock market. The model matches investors’ extrapolative expectations observed in surveys. It also matches facts about asset prices such as a large equity premium, low interest rate volatility, strong excess volatility and predictability for equity returns, and a low correlation between consumption growth and stock returns. Extrapolative beliefs generate perceived persistence in dividend and consumption growth that, under recursive preferences, serves as an important source of discount rate variation. ∗We thank Nicholas Barberis, Stefano Cassella, Robin Greenwood, David Hirshleifer, Jonathan Ingersoll, Theresa Kuchler, Paulo Rodrigues, Paul Sangrey, Andrei Shleifer, and seminar participants at Caltech, Maastricht University, Tilburg, University of California, Irvine, the Young Economists Symposium at Yale, and the Caltech Junior Faculty Behavioral Finance Conference for helpful comments. Please send correspondence to Lawrence J. Jin, California Institute of Technology, 1200 E. California Blvd. MC 228-77, Pasadena, CA, 91125; telephone: 626-395-4558. Email: [email protected]. †Both authors’ affiliation is the California Institute of Technology. Rational expectations models—models such as the habit formation model of Campbell and Cochrane (1999), the long-run risks models of Bansal and Yaron (2004) and Bansal, Kiku, and Yaron (2012), and the rare disasters models of Barro (2006) and Gabaix (2012)—have been the leading candidates to make sense of many stylized facts about the aggregate stock market. These facts include the equity premium puzzle of Mehra and Prescott (1985), the excess volatility puzzle of LeRoy and Porter (1981) and Shiller (1981), the evidence on predictability of equity returns documented by Campbell and Shiller (1988) and Fama and French (1988), low correlations between consumption growth and stock returns noted by Hansen and Singleton (1982, 1983), as well as negative autocorrelations of equity returns presented in Poterba and Summers (1988). However, recent survey evidence on actual investor expectations of stock market returns have raised challenges to these rational expectations models. Among others, Vissing-Jorgensen (2004), Bacchetta, Mertens, and van Wincoop (2009), Amromin and Sharpe (2013), Greenwood and Shleifer (2014), Koijen, Schmeling, and Vrugt (2015), and Kuchler and Zafar (2016) document that many individual and institutional investors have extrapolative expectations: they believe that the stock market will continue rising in value after a sequence of high past returns, and that it will continue falling in value after a sequence of low past returns. On the contrary, models with rational expectations imply that investors would expect lower or flat returns, instead of higher returns, after a sequence of high past returns. Moreover, rational expectations about future returns are positively correlated with realized returns over the same time period, whereas survey expectations are negatively correlated with realized returns. Given the discrepancy between survey expectations and models with rational expectations, there is a clear need for a behavioral benchmark model of asset pricing—one that is consistent with survey evidence on investor beliefs—that can be directly compared on quantitative grounds to more traditional asset pricing models. In this paper, we take up this challenge. We develop a Lucas-type general equilibrium model with return extrapolation and Epstein-Zin preferences. In the model, the price of the aggregate equity market and the interest rate are jointly determined in equilibrium by investor preferences and subjective beliefs. The model generates a large and countercyclical equity premium, a low and procyclical interest rate, a sizable and countercyclical Sharpe ratio, low interest rate volatility, strong excess volatility for equity, predictability of equity returns using price-dividend ratios, negative autocorrelations of equity returns, persistence of price-dividend ratios, as well as low correlations between consumption growth and stock returns. We directly compare these model implications with empirical data, and find that the majority of them quantitatively match the data. More important, the model further matches investors’ extrapolative beliefs and their memory structure derived directly from survey evidence.1 Most rational expectations models have difficulty in matching empirical predictions related to survey expectations. The basic mechanism behind our model is an endogenous two-way feedback loop: investor beliefs about returns drive asset prices, and asset prices in turn affect investor beliefs. When past returns Specifically, memory structure refers to the speed at which investors’ memory about past returns decays when these investors form beliefs about future returns.