Equilibrium Asset Pricing with Time-varying Pessimism

Abstract

We study the equilibrium pricing effects of a sentiment for pessimism. Pessimism has the form of Knightian model uncertainty aversion for a neighborhood of indistinguishable model specifications that are constrained in their relative entropy from a given reference model. We fully characterise the equilibrium of a pessimistic, representative agent, exchange economy with intertemporal consumption, stochastic opportunity set, and a relative entropy constraint that can depend on the state of the economy. We find that Knightian pessimism generates substantial First Order Risk Aversion (FORA) effects that enhance excess equity returns by pushing riskfree rates down. However, we find that the structure of equity returns is virtually unaffected by a Knightian concern for model uncertainty. We compute and calibrate explicit equilibrium examples of a pessimistic economy with an amount of pessimism associated to an 11% upper probability bound of confusing the relevant worst-case model and the given reference model. Relative entropy is the key in fixing such a realistic amount of pessimism in our calibrations. Even for log utility, such small amount of pessimism generates some 55 basis points more of unconditional equity premium. Knightian pessimism provides an economically and observationally different description of excess equity returns. Our findings show that realistic amounts of both pessimism and standard risk aversion yield substantial equity premia and low riskfree rates.