Equity Premia with Benchmark Levels of Consumption: Closed-Form Results

I calculate exact expressions for risk premia, term premia, and the premium on levered equity in a framework that includes habit formation, keeping/catching up with the Joneses, and possible departures from rational expectations. Closed-form expressions for the first and second moments of returns and for the R2 of a regression of stock returns on the dividend-price ratio are derived under lognormality for the case that includes keeping/catching up with the Joneses. Linear approximations illustrate how these moments of returns are affected by parameter values and illustrate quantitatively how well the model can account for values of the equity premium, the term premium, and the standard deviations of the riskless return and the rate of return on levered equity. For empirically relevant parameter values, the linear approximations yield values of the various moments that are close to those obtained from the exact solutions.