Asset Pricing with Horizon-Dependent Risk Aversion

We study general equilibrium asset prices in a multi-period endowment economy when agents' risk aversion is allowed to depend on the maturity of the risk. In our pseudo-recursive preference framework, agents are time inconsistent for their intra-temporal decision making, though time consistent for inter-temporal decisions. We find, in the absence of jumps and under log-normal consumption growth, horizon-dependent risk aversion preferences affect the term structure of risk premia if and only if volatility is stochastic. When risk aversion decreases with the horizon (as lab experiments indicate), and the elasticity of intertemporal substitution is greater than one, our model results in a downward slopping (in absolute value) pricing of volatility risk, which, in turns, can explain the recent empirical results on the term structure of risky asset returns. We confirm this prediction using index options data.