On the Realized Risk of Foreign Exchange Rates: A Fractal Perspective

Abstract

While well-established literature argues that realized variances are close to a lognormal distribution, this study follows Benoit Mandelbrot by taking a fractal perspective. Using power laws to model realized foreign exchange rate variances, our findings indicate that power laws offer an alternative to the lognormal in terms of goodness-of-fit tests. Further, our analysis shows that estimated power law exponents for seven out of nine realized FX variances are α^<3, which indicates that the variance of realized variance is statistically undefined. We conclude that the foreign exchange rate market is far riskier than earlier believed. By implication, documented research in an enormous body of literature that draws conclusions from variance analyses stands on shaky grounds.