  We study a discrete-time consumption-based capital asset pricing model under
expectations-based reference-dependent preferences. More precisely, we consider
an endowment economy populated by a representative agent who derives utility
from current consumption and from gains and losses in consumption with respect
to a forward-looking, stochastic reference point. First, we consider a general
model in which the agent's preferences include both contemporaneous gain-loss
utility, that is, utility from the difference between current consumption and
previously held expectations about current consumption, and prospective
gain-loss utility, that is, utility from the difference between intertemporal
beliefs about future consumption. A semi-closed form solution for equilibrium
asset prices is derived for this case. We then specialize to a model in which
the agent derives contemporaneous gain-loss utility only, obtaining equilibrium
asset prices in closed form. Extensive numerical experiments show that, with
plausible values of risk aversion and loss aversion, our models can generate
equity premia that match empirical estimates. Interestingly, the models turn
out to be consistent with some well-known empirical facts, namely procyclical
variation in the price-dividend ratio and countercyclical variation in the
conditional expected equity premium and in the conditional volatility of the
equity premium. Furthermore, we find that prospective gain-loss utility is
necessary for the model to predict reasonable values of the price-dividend
ratio.
