Abstract
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.).
Acknowledgments
We are grateful to Ken Kasa for intensive discussions, suggestions and advices. We also thank Wei Dong, Kimberly Berg, Oleksiy Kryvtsov, Malik Shukayev, Luba Pertersen, Huixin Bi, Pierre Guerrin, Garima Vasishtha, David Freeman, Lucas Herrenbrueck, Bertille Antoine, Xiaowen Lei, participants of SFU macrofinance group, 49th CEA conference, and seminar participants at the Bank of Canada, Ryerson University, Middlebury College, San Diego State University, Wilfrid Laurier University, Hong Kong University, and the Federal Reserve Board, for valuable comments and feedback. Comments from the editor and an anonymous referee helped to greatly improve this paper.
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