Robust learning in the foreign exchange market

This paper studies risk premia in the foreign exchange market when investors entertain multiple models for consumption growth. Investors confront two sources of uncertainty: (1) individual models might be misspecified, and (2) it is not known which of these potentially misspecified models is the best approximation to the actual data-generating process. Following Hansen and Sargent (Hansen, L. P., and T. J. Sargent. 2010. “Fragile Beliefs and the Price of Uncertainty.” Quantitative Economics 1 (1): 129–162.), agents formulate “robust” portfolio policies. These policies are implemented by applying two risk-sensitivity operators. One is forward-looking, and pessimistically distorts the state dynamics of each individual model. The other is backward-looking, and pessimistically distorts the probability weights assigned to each model. A robust learner assigns higher weights to worst-case models that yield lower continuation values. The magnitude of this distortion evolves over time in response to realized consumption growth. It is shown that robust learning not only explains unconditional risk premia in the foreign exchange market, it can also explain the dynamics of risk premia. In particular, an empirically plausible concern for model misspecification and model uncertainty generates a stochastic discount factor that uniformly satisfies the spectral Hansen-Jagannathan bound of Otrok et al. (Otrok, C., B. Ravikumar, and C. H. Whiteman. 2007. “A Generalized Volatility Bound for Dynamic Economies.” Journal of Monetary Economics 54 (8): 2269–2290.).