Implied Betas for the Frankel-Wei Regression Framework

The Frankel-Wei regression framework measures the relationship between one currency and another currency solely by using foreign exchange rates as regression variables, where investors choose a common numéraire for the foreign exchange rates. When the common numéraire is a single currency, the foreign exchange rates are bilateral exchange rates. Option implied volatilities are easily estimated from listed option prices for bilateral exchange rates. In this paper, we use the implied volatilities to estimate implied betas for the Frankel-Wei regression framework. We show that both the average betas and the average implied betas for a system of currencies are exactly 0.5, which provides strong evidence of a bias in the estimator of the betas when single currencies are used as the common numéraire