Are Stocks Riskier over the Long Run? Taking Cues from Economic Theory

Abstract

We study whether stocks are riskier or safer in the long run from the perspective of Bayesian investors who employ the long-run risk, habit formation, or prospect theory models to form prior beliefs about return dynamics. Economic theory delivers important guidance for long-run investment opportunities. Specifically, incorporating prior information from the habit formation or prospect theory models reinforces beliefs in mean reversion and inferences that stocks are safer over longer horizons. Conversely, investors with long-run risk priors perceive weaker mean reversion and riskier equities. Model-based information is particularly important for inferences about uncertainty in the dividend growth component of returns. (JEL C11, G11, G12) * We thank Stijn Van Nieuwerburgh (the editor), two anonymous referees, 1 the models for long-run return dynamics, their success in matching these aspects of the data lend them credibility in this setting. The underlying assumptions in the long-run risk, habit formation, and prospect theory models about preferences and economic dynamics as well as the resulting return dynamics are quite different, which leads to interesting implications for long-horizon variance. In addition, our analysis incorporates a nonnegativity restriction on the equity premium as proposed by Campbell and Thompson (2008) and Pettenuzzo, Timmermann, and Valkanov (2014). This economic constraint has been shown to improve out-of-sample forecasting performance and sharpen estimates of model parameters. Incorporating a nonnegative equity premium is novel in the context of long-horizon return variance.We study the risk of investing in stocks by examining the predictive return variance over various investment horizons. Predictive variance is typically computed (e.g., Avramov 2002) based on the vector autoregression (VAR) framework of Campbell and Shiller (1988), Kandel and Stambaugh (1996), Campbell and Viceira (1999), and Barberis (2000), among others. Our Bayesian investors consider long-horizon risk in the context of a VAR with stock returns, dividend growth, and model-implied state variables from the long-run risk, habit formation, or prospect theory models. Specifically, the investors form prior beliefs about the VAR parameters based on asset pricing model implications. They also allow for the possibility of model misspecification, such that prior uncertainty about the VAR parameters remains. Finally, the investors combine information from the model-based prior and historical data to make inferences about long-horizon predictive variance.Incorporating model-based prior information can potentially improve inferences about risk over long horizons. As noted earlier, the perceived long-horizon return variance crucially depends on the return dynamics implied by the VAR. It has long been recognized that incorporating prior information into VARs improves the quality of prediction. In the macroeconomics literature, Litterman (1986) and Todd (1984) demonstrate improved predictions by Bayesian VARs with the "Minnesota" ...

On the Economic Value of Stock Market Return Predictors

“…Intuitively, the set of low-persistence, high-variance predictors can produce extreme changes in expected market return over short time frames, such that placing a large bet on a forecasted market return runs the risk that the conditional mean return will quickly shift to oppose the bet. Past literature (e.g., Pástor and Stambaugh (2012) and Avramov, Cederburg, and Lučivjanská (2018)) shows the long-horizon effects of uncertainty about future expected return on risk from an investor's perspective, and we add to this literature by demonstrating substantial short-term effects for low-persistence predictors.…”

“…As shown by Pástor and Stambaugh (2012) and Avramov, Cederburg, and Lučivjanská (2018), predictive variance ratios can be pushed above one by uncertainty about future expected return and estimation risk, whereas mean reversion can have a negative effect on predictive variance ratios. The predictive variance ratios for V RP are nearly uniformly greater than one across models, suggesting that uncertainty about future expected return and estimation risk are outweighing any effect of mean reversion.…”

“…Stambaugh (1999), Barberis (2000), and Avramov (2002) consider multi-period, buy-and-hold Bayesian investors similar to our setup, and Johannes, Korteweg, and Polson (2014) and Hoevenaars, Molenaar, Schotman, and Steenkamp (2014) study investors who periodically rebalance their portfolios. 6 A related literature, including studies by Pástor and Stambaugh (2012), Avramov, Cederburg, and Lučivjanská (2018), and Carvalho, Lopes, and McCulloch (2018), investigates the long-horizon predictive variance of stock market returns in the presence of market return predictability.…”

“…Avramov (2002Avramov ( , 2004 and Tu and Zhou (2010) investigate portfolio choice with multiple assets that have predictable returns. Related to these studies, Pástor and Stambaugh (2012), Avramov, Cederburg, and Lučivjanská (2018), and Carvalho, Lopes, and McCulloch (2018) consider long-horizon predictive return variance from the perspective of Bayesian investors in settings with predictable market returns.…”

From Which Consumption-Based Asset Pricing Models Can Investors Profit? Evidence from Model-Based Priors

“…Other Bayesian studies consider uncertainty about the predictive regression parameters through uninformative priors (see, for example, 2 The analytical solutions and the empirically observable state variables of the LRR model allow for additional model evaluations: the in-sample estimation proposed by Bansal, Kiku, and Yaron (2010) and Constantinides and Ghosh (2012) and the OOS fit proposed by Ferson, Nallareddy, and Xie (2013). Stambaugh (1999); Barberis (2000); Brandt, Goyal, Santa-Clara, and Stroud (2005); Penasse (2016)) or investigate how parameter uncertainty affects the long run predictive variance (see, for example, Pastor and Stambaugh (2012) and Avramov, Cederburg, and Lucivjanska (2016)). …”