Betting under subjective uncertainty

This paper shows that uncertainty-averse agents may trade extrinsic variables on efficient markets. The finding is robust to identical beliefs and strictly convex preferences. Conditional on a realization of fundamentals, the distribution of an otherwise irrelevant variable may depend on the underlying probability regime. This dependence cannot be exploited through trade on fundamentals. I provide necessary and sufficient conditions for the irrelevance of non-fundamental variables undermaxmin, smooth, and variational preferences. These conditions are found to be stringent, except formultiplier preferences (Hansen and Sargent, 2001; Strzalecki, 2011), for which it suffices that the reference priors agree conditional on fundamentals.