High interest rate currencies tend to appreciate relative to low interest rate currencies. This is the forward premium puzzle as one would expect that investors would demand higher interest rates on currencies expected to depreciate. This anomaly underlies the profitability of the so called carry trade, under which investors borrow in low interest rate currencies and invest in high interest rate currencies. Related to this anomaly, exchange rates often exhibit momentum in response to interest rate differential shocks. That is, when there is a positive innovation to the interest rate differential, the exchange rate appreciates at impact. The puzzle is that it continues appreciating for several months thereafter. Standard models predict an immediate appreciation followed by a depreciating path.
These patterns imply excess returns with a predictable variation over time. In principle they can be explained by either time-varying risk premia or expectational distortions. This paper concentrates on the latter explanation. It shows how a desire for robustness against some type of structured model uncertainty can explain these two anomalies. In order to be robust agents introduce a specific distortion into their model to forecast interest rate differentials. This specific distortion generates an underreaction of forecasts to news, which in equilibrium gives rise to the anomalies if the interest rate differential has high conditional persistence.
The underreaction of interest rate forecasts has been documented by Gourinchas and Tornell (2004). Using survey data on interest rate forecasts they find a substantial systemic underreaction of forecasts of interest rate differentials to news across the G7. Furthermore, they show that the estimate of this distortion in beliefs is high enough so as to generate the forward premium puzzle and momentum.
Although uncovering this link is an important step, it generates intriguing questions: why do agents systematically hold misperceptions? What supports the existence of time-varying predictable excess returns? Our contribution is to provide a microfounded framework where a desire for robustness makes optimizing agents, that hold no misperception, distort the probability distributions and behave in ways that are consistent with the anomalies we have just described. In the model, limits to arbitrage as well as time-varying predictable excess returns arise in equilibrium.
We consider a setup where agents fear that the model is misspecified (i.e., there is model uncertainty) and design robust forecasting and portfolio strategies. We show that under a specific class of structured uncertainty, underreaction of interest rate differentials’ forecasts to news is the outcome of agents’ optimization, and we link this underreaction in the bond market to the foreign exchange markets anomalies alluded to above.
