Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles

Abstract

We model consumption and dividend growth rates as containing (i) a small long-run predictable component and (ii) fluctuating economic uncertainty (consumption volatility).These dynamics, for which we provide empirical support, in conjunction with Epstein and Zin's (1989) preferences, can explain key asset markets phenomena. In our economy, financial markets dislike economic uncertainty and better long-run growth prospects raise equity prices. The model can justify the equity premium, the risk-free rate, and the volatility of the market return, risk-free rate, and the price-dividend ratio. As in the data, dividend yields predict returns and the volatility of returns is time-varying.

Market Expectations in the Cross Section of Present Values

“…Cross-section-based estimates suggest that discount rates are less than half as persistent, and the volatility of discount rate shocks is more than twice as large, as estimates based on the aggregate book-to-market ratio. This degree of variability in return expectations is difficult to reconcile with state-of-the-art structural asset pricing models, which are calibrated to produce persistent expected market returns with mild shock volatility (e.g., Campbell and Cochrane (1999) and Bansal and Yaron (2004)). …”

Do You Save More or Less in Response to Bad News? A New Identification of the Elasticity of Intertemporal Substitution

“…Bansal and Yaron (2004) provide evidence that the presence of stochastic volatility, which is proportional to ϑ t , can impart a substantial downward bias on estimates of the EIS obtained using the method in Hall (1988).…”

“…With recursive preferences (which nest additive CRRA), this relationship affects not only the quantitative, but also the qualitative predictions of a model. For example, in the Bansal and Yaron (2004) long-run risk model, when EIS > 1, investors are willing to pay a premium to hedge against bad news about future economic growth rates. Valuation ratios are pro-cyclical, the equity premium is high, and the risk-free rate is low and stable.…”

Variance Premium and Implied Volatility in a Low-Liquidity Option Market

“…To do this, we use Bollerslev et al (2009) economic model, which is an extension of the long-run risk model of Bansal & Yaron (2004). We assume that the following closed-form equation for the variance premium holds for each t : 14…”

“…Similarly, Issler & Piqueira (2000) using data on aggregate consumption from 1975 to 1994, 14 We use their simpler equation, where they assume a constant volatility of volatility (the process q is constant at all t ). 15 We set ψ = 1.5, q = 10 −6 , κ 1 = 0.9 and ρ σ = 0.978 following the calibration in Bansal & Yaron (2004) and Bollerslev et al (2009). 16 Equation (4) is quadratic on the risk-aversion coefficient γ t .…”