Habits and the Term Structure of Risk Premia

Description

Since the development of the capital asset pricing model (CAPM) of Sharpe (1964) andLintner (1965), which links the risk and reward in asset returns, it has faced manychallenges. The most prominent challenges include the equity premium and risk-freerate puzzle of Mehra and Prescott (1985) and Weil (1989), the excess volatility puzzle ofShiller (1981), and the value premium puzzle of Fama and French (1992). Recentdevelopments in solving the first two puzzles involve introducing discount rate risk fromthe preferences side. The habit formation model of Campbell and Cochrane (1999) usessurplus consumption ratios to amplify variations in discount rate. The long-run riskmodel of Bansal and Yaron (2004) uses a combination of long-run risk, stochasticvolatility, and recursive preferences to increase the variations in discount rate. Anotherstrand of literature, such as Barro (2006), Gabaix (2012), and Wachter (2013), uses(time-varying) rare disasters and recursive preferences to enhance the variations indiscount rate. One common feature shared among these leading asset pricing models isthat term structures of premia and volatility are either flat or upward sloping.Despite the tremendous progress that recent developments in dynamic equilibrium assetpricing models have made in explaining some major asset pricing puzzles, some studiespost new challenges to these leading asset pricing models. They have potential difficultyin explaining the value premium, a strong empirical regularity presented in crosssectionalstock returns. As shown in Lettau and Wachter (2007, 2011) and Santos andVeronesi (2010), a key feature to explain the value premium is a downward sloping termstructure of risk premia, for which Binsbergen, Brandt and Koijen (2012) provide directempirical evidence. However, these leading asset pricing models predict otherwise.Motivated and inspired by the leading asset pricing models and the no-arbitrage modelof Lettau and Wachter (2007, 2011), we propose an equilibrium asset pricing model withtwo habits that yields a downward sloping term structure of risk premia withoutsacrificing the ability to explain key time series properties of asset returns. In addition,our model yields explicit solutions to bonds, consumption claim, and stock. Thus, we canapply our model to all three basic assets to address other challenges faced by the leadingasset pricing models; the three basic assets, as presented in Backus, Chernov and Zin(2014) and Lustig, Nieuwerburgh and Verdelhan (2013), are difficult for these models toexplain simultaneously.