The drift factor in biased futures index pricing models: A new look

The presence of bias in index futures prices has been investigated in various research studies. Redfield(11) asserted that the U.S. Dollar Index (USDX) futures contracttraded on the U.S. Cotton Exchange (now the FINEX division of the New York Board of Trade) could besystematically arbitraged for nontrivial returns because it is expressed in so‐called “Europeanterms” (foreign currency units/U.S. dollar). Eytan, Harpaz, and Krull (4) (EHK) developed a theoretical factor using Brownian motion to correct for theEuropean terms and the bias due to the USDX index being expressed as a geometric average. Harpaz, Krull, and Yagil(5) empirically tested the EHK index. They used the historical volatility toproxy the EHK volatility specification. Since 1990, it has become more commonplace to use option‐impliedvolatility for forecasting future volatility. Therefore, we have substituted option implied volatilities intoEHK's correction factor and hypothesized that the correction factor is “better” exante and therefore should lead to better futures model pricing. We tested this conjecture using twelvecontracts from 1995 through 1997 and found that the use of implied volatility did not improve the bias correctionover the use of historical volatility. Furthermore, no matter which volatility specification we used, the modelfutures price appeared to be mis‐specified. To investigate further, we added a simple naïve δbased on a modification of the adaptive expectations model. Repeating the tests using this naïve“drift” factor, it performed substantially better than the other two specifications. Our conclusion isthat there may be a need to take a new look at the drift‐factor specification currently in use. © 2002Wiley Periodicals, Inc. Jrl Fut Mark 22:579–598, 2002