Liquidity, Information and the Size of the Forward Exchange Rate Bias

What the paper says

We first develop the theoretical rationale of the forward exchange rate unbiasedness hypothesis (FUH) for buyers of forward exchange under an assumption of risk neutrality and interest rate parity. Then by using Jensen's Inequality, we show that FUH cannot simultaneously hold true for both the sellers and buyers of the same forward currency contracts. Because of the symmetric nature of relationships among foreign exchange currency pairs, we conjecture that forward rate biases should be small. We introduce a new test statistic that averts unit root problems. This test statistic helps verify our conjectures in the empirical data. We analyze the liquidity effect of the informational content of forward exchange rates using our test statistic. We show that whether unbiasedness holds or not is driven by market conditions of crisis or non-crisis. Introduction Forward exchange rate contracts are used, among other things, to eliminate future spot exchange rate risk. (1) Currency markets are unique in the sense that there are several symmetry features among currency pairs and even among currency triplets. For example, let [S.sub.1] be the number of units of EUR per dollar; if [S.sub.2] is a model for the number of pounds per EUR, then ([S.sub.1])([S.sub.2]) is a model for pounds per dollar. Similarly, [([S.sub.1]).sup.-1] is a model for dollars per EUR, and [([S.sub.2]).sup.-1] is a model for EUR per pound. (2) Forward rates are expected to neutralize future exchange rate risk for both parties (sellers and buyers of the same currency) and, to be fair, unbiased estimators of corresponding future spot rates. (3) However, existing empirical research fails to support FUH, and such a phenomenon is referred to as the forward rate bias puzzle. There have been many attempts to unravel this puzzle, yet to our knowledge, none appears completely satisfactory. Alongside the eguity premium puzzle, the forward rate bias puzzle remains one of the unsolved mysteries of financial economics. The nature of the puzzle is succinctly spelled out by many authors. Not only is the forward rate estimator inefficient, but it predicts the future spot rate in the opposite direction. Of course because the forward rate seems to be systematically biased, it permits the existence of the carry trade. Contrary to interest rate parity theory, future spot exchange rates do not usually depreciate for high interest rate currencies and low interest rate currencies do not appreciate by as much as is expected. (4) However, the empirical evidence varies across countries, by economy type (advanced, developing and emergent economies) and by business cycle conditions. See Bansal and Dahlquist (2000) for a further discussion of these issues. Fama (1984) (5) first popularized this problem even though it had been noted by many authors like Bilson (1981), Hodrick (1987), Hansen and Hodrick(1980), Frenkel (1980), Cornell (1977) and others. (6) Fama (1984), in a study of nine industrialized countries, attributed the existence of the puzzle to the fact that the volatility of the risk premium is greater than the volatility of the realized spot rates. Bilson (1981) analyzed the speculative efficiency hypothesis wherein the null was that there were no profits to be made from pure speculation. The analyzed data led to non-acceptance of the null. Hansen and Hodrick (1980) had also rejected the simple null hypothesis of zero returns to speculation using different modeling technigues. Bansal (1997) deepened the puzzle by postulating that the puzzle was interest rate dependent. It existed only in certain environments where U.S. interest rates exceeded foreign interest rates. He also showed that dependent of the interest rate regime, the volatility of the forward premium could be greater or less than the realized future spot variation in exchange rates. Nevertheless, carry traders have continued to profit in currency markets. Goodhart, McMahon and Ngama (1992) attributed the failure of the unbiasedness hypothesis in their study to the existence of outlier data and structural breaks. …