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 contract traded on the U.S. Cotton Exchange (now the FINEX division of the New York Board of Trade) could be systematically arbitraged for nontrivial returns because it is expressed in so‐called “European terms” (foreign currency units/U.S. dollar). Eytan, Harpaz, and Krull ( 4 ) (EHK) developed a theoretical factor using Brownian motion to correct for the European 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 to proxy the EHK volatility specification. Since 1990, it has become more commonplace to use option‐implied volatility for forecasting future volatility. Therefore, we have substituted option implied volatilities into EHK's correction factor and hypothesized that the correction factor is “better” ex ante and therefore should lead to better futures model pricing. We tested this conjecture using twelve contracts from 1995 through 1997 and found that the use of implied volatility did not improve the bias correction over the use of historical volatility. Furthermore, no matter which volatility specification we used, the model futures price appeared to be mis‐specified. To investigate further, we added a simple naïve δ based 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 is that there may be a need to take a new look at the drift‐factor specification currently in use. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:579–598, 2002