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" ...
