Abstract
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.
Highlights
Imagine a rational agent that observes some information set (a filtration F = (Ft )t≥0 ) and is interested in forecasting values of some random variable
Empirical results suggest that Focus survey forecasts display characteristics of a strict local martingale, while spot exchange rates and forward rates are consistent with a martingale process
We show that the characterization of a strict local martingale through a stochastic volatility model is consistent with the behavior observed in the forecasts for the foreign exchange market studied in this article, and can be a valid explanation for the observed forecast bias
Summary
We compare survey-based forecasts from the Market Expectations System of the Central Bank of Brazil ( Focus) with future markets (B3 futures exchange markets, former BMF and BOVESPA) 30-days forward rates; and find that future markets rates are unbiased predictor of future spot rates, but Focus survey forecasts are biased predictors through a substantial portion the observed sample This is counter-intuitive because forward rates are obviously within the information set of keen market participants. Dandapani and Protter [1] explain how enlarging filtration F to G changes the underlying measure (say from P to Q), which can induce a stochastic drift in the volatility of S, turning S from an F martingale to a G strict local martingale. To our knowledge this is the first work to relate systematic prediction errors and the filtration enlargement mechanism.
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