Forward Discount Bias, Nalebuff's Envelope Puzzle, and the Siegel Paradox in Foreign Exchange

The bias of forward exchange rates as a predictor of future spot rates is typically explained or decomposed as (1) a risk premium and (2) a convexity term which accounts for the fact that, when there is stochastic inflation, nominal gains from forward currency speculation are higher than real ones and correspondingly losses are smaller. We use Nalebuff’s envelope puzzle to explain a third source of bias which involves real profits from foreign exchange speculation. Both the "real profit" bias and stochastic inflation bias arise from convexity of g(s)=1/s and so derive from Jensen's inequality as observed by Siegel (1972).

Anomalies: Foreign Exchange

In what follows, we discuss the efficiency of foreign exchange markets. To manage what would otherwise be an enormous task, the question of efficiency is viewed below from the perspective of a single type of test: the test for what is called the forward discount bias. This test is easy to understand, and since it strongly rejects the null hypothesis, statistical power is not an issue. Naturally, in discussing this particular test we mention a variety of other empirical work designed to shed light on alternative explanations of the results.