Foreign Exchange Expectation Errors and Filtration Enlargements

Extrapolations of future market forward rates are a better predictor of the 30-days ahead BRL-USD exchange rate than forecasts from the Central Bank Focus survey of Brazilian market participants. This is puzzling because market participants observe forward rates as they submit predictions, and thus these agents perform biased forecasts even though they have access to a set of unbiased forecasts, consistent with a martingale process for the exchange rate. We argue that this rational conundrum can be explained by a mechanism through which new information enlarges the information set (a filtration), changing the underlying measure and inducing a drift into the martingale process, turning the process into a strict local martingale and generating a forecast bias. Empirical results suggest that Focus survey forecasts indeed display characteristics of a strict local martingale, while spot exchange rates and forward rates are consistent with a martingale process.

Taux d’intérêt à long terme, martingales, et marchés efficients

This note discusses some aspects of the relationship between the hypothesis that long-term bond rates follow a martingale process and the hypothesis that the bond market is efficient. It begins with some mathematics of bond prices and interest rates. It then shows that, except in one special case, the hypothesis that bond rates follow a martingale and that bond markets are efficient are theoretically inconsistent. Some empirical work is then adduced that shows that neither hypothesis is supported by the data. It concludes with some brief comments on the literature relating to this subject and some suggestions for further research.