For four decades economists have been finding that the forward discount is a very biased forecast of future changes in the exchange rate. The carry trade makes money, on average. For just as long, they have been debating the appropriate interpretation of the bias. Is it evidence of an exchange risk premium? Under that interpretation, a currency that sells at a forward discount does so not because it is expected to depreciate in the future but because it is perceived as risky. Using data on survey-based expectations over 32 years across 17 currencies, we reject that interpretation of the forward bias. We find that when investors sell a currency at a forward discount, it is indeed because they expect it to depreciate. But we also find concrete evidence of a risk premium, in that expected return differentials are correlated with the VIX measure of risk — even though the risk premium can’t explain forward bias.
Back in the 1980’s, when Frankel started using survey data on currency expectations (with Kenneth Froot), there was a lot of skepticism of such data (remember, these were the days of rational expectations or bust). Since then, the use of survey data have become more widely accepted, perhaps longest in terms of inflation expectations. In the real world, many of the macro series we think of as the purview of hard-headed real-world macro people are surveys (e.g., PMI, for instance; here’s an entire conference).
Here are the time series for important variables for the USD/GBP, comparing ex post against survey (ex ante) based. First depreciation.
Notice that the two series differ substantially, with the ex ante considerably less volatile. Interestingly, unlike the usual finding, expected depreciation and the forward discount (approximately the interest differential) are positively correlated, across all currency pairs available.
The slope, while positive, is not close to unity. This suggests the existence of an exchange risk premium.
The risk premium defined using survey data naturally appears different than that defined using rational expectations.