Articles

Adrift No More
By Brian Barrett and Thomas Sanders

Page 1 of 4

The drift factor in the old U.S. Dollar Index (USDX) derived from the fact that it comprised component currencies that were expressed in European terms (foreign currency units/U.S. dollars) and that were geometrically averaged to produce an index. We have found that the USDX futures contract as respecified in response to the newly traded euro now possess only a trivial drift factor. This seems to be due to the fact that the index now is comprised largely of two currencies that are expressed in American terms, the sterling and the euro. The fact that the index remains a geometric average does not seem to introduce meaningful bias in index pricing. Thus, the bias found in previous research was undoubtedly due primarily to the specification of both sides of an arbitrage leg in Europea n terms. The results found here suggest that no systematic arbitrage can profitably be executed in the re formulated USDX futures contract.1

Introduction

Various research studies have detected systematic bias, called a "drift factor," in the U.S. Dollar Index futures contract traded on the FINEX division of the New York Board of Trade, including Redford (1986), Eytan, Harpaz and Krill (1988) and Harpar, Krull and Yagil (1990). At the time those studies were conducted, about five firms were active in arbitraging the futures contract.2 The bias or "drift" was due to the fact that the index was stated in European terms (foreign currency units/U.S. dollars) and was derived as a geometrical average of component currencies. Eytan, Harpaz and Krull, as well as Barrett and Sanders (2001), attempted to measure various drift factors in an attempt to provide a systematic correction to the futures contract.

When the euro came on the scene as a currency unit in January 1999, the USDX had to, of course, be re-specified. The index is now comprised of six component currencies instead of ten, and the formulation has been redone. The old base exchange rates as of 1973 have been dropped.3 The new USDX futures index is now specified as:

where the futures contracts are in European terms and the coefficients are the trade weights officially specified by the Federal Reserve System in 1973, representing the relative amount of foreign trade with the U.S. from each country. The various x indicate that the mathematical terms are to be multiplied.

The futures index is easy to compute since all of the component futures are individually traded on the FINEX. For example, on May 12, 2000, the index futures contract was computed as:

Note that the Sterling and euro rates are taken in the reciprocal, since these two futures contracts are actually traded on the FINEX in American terms (U.S. dollars/foreign currency); the remainder of the futures contracts are traded in European terms. Of course, with the inversions in the third and seventh terms, the index futures contract still is totally in European terms.

One wonders if the old methods for correcting for the drift factor as specified in the literature still apply, since the USDX formulation now has changed and the euro itself is a basket of currencies. Any method detailed in previous research studies can be examined. The purpose of this paper is to apply the rollover method as provided in Barrett and Sanders to determine drift factors on the new index. Presumably, a priori, knowledge of systematic drift factors could be utilized by traders to arbitrage the futures contract.

Our research has come to a surprising result. When all of the trading costs are considered, the new USDX futures contract as re-specified is no longer significantly biased, so the chance for economic arbitrage has disappeared. Also, we applied the data to the previous specification of the USDX futures contract and likewise found that, on a daily rollover basis, even the old contract cannot be economically arbi-traged.4

Rollover Model

Under the rollover model of Barrett and Sanders, a daily arbitrage position at time t is set long on the futures index and long on the respective individual component futures contracts. If the dollar rises at t +1, the index makes money and the individual futures contracts lose money. But the offsets are not exact due to the drift factor bias in index pricing. Previous research suggested that, because the index is mathematically biased, such arbitrage profits would continue indefinitely because the long-long position did not serve to bring together the legs of the arb position.

Measuring the size of the drift factor can determine the size of the arbitrage profit potential. To obtain this measurement, the index at t+1 is "fixed up." That is, a drift factor is determined iteratively after the fact that would have sufficiently reduced the index at time so that the index p rofit is forced to equal the individual futures aggregate loss.