The average annual rate of return on equity exceeds the average annual rate of return on short-term riskless bills by several hundred basis. There are two components to this equity premium: a risk premium and a term premium. The risk premium reflects the fact that equity is claim on stochastic payoffs, whereas a short-term riskless bill is a fixed-income security that is a claim on a known payoff. The term premium reflects the longer maturity of equity relative to short-term bills fully.
The literature on the equity premium has typically focused on the overall equity premium rather than on the separate components. In the most influential quantitative application of the Lucas (1978) fruit-tree model of asset pricing, Mehra and Prescott (1985) found that this model was incapable of producing an equity premium of more than 35 basis points when they confined attention to parameter values that they deemed plausible.
With such a small overall equity premium implied by the model, it did not much matter how much was a risk premium and how much was a term premium. However, subsequent research has produced models that can account for an equity premium of several hundred basis points per year. I will show in this paper how the equity premium in a general equilibrium model can be decomposed into a risk premium and a term premium. This decomposition provides helpful insights about the source of the equity premium and provides guidance in choosing appropriate parameter values.
The most basic application of the Lucas fruit-tree model can be used to price unlevered equity in an economy with i.i.d. consumption growth and a representative consumer with time-separable isoelastic utility. The literature has extended this basic model in many ways, and I will adopt two of these extensions, though I will combine them in a way to obtain fresh insights.
First, I will specify preferences to have the catching up with the Joneses feature introduced in Abel (1990) and used more recently by Campbell and Cochrane (1994) and Carroll, Overland, and Weil (1997). Second, I will introduce a novel tractable formulation of leverage. Despite the additional richness introduced by these extensions, I derive closed-form solutions for expected rates of return, term premia, and risk premia for a general class of assets.