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

Masoumeh Fathi, Klaus Grobys and James W. Kolari ()
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Masoumeh Fathi: Finance Research Group, School of Accounting and Finance, University of Vaasa, Wolffintie 34, 65200 Vaasa, Finland
Klaus Grobys: Finance Research Group, School of Accounting and Finance, University of Vaasa, Wolffintie 34, 65200 Vaasa, Finland
James W. Kolari: Department of Finance, Mays Business School, Texas A&M University, College Station, TX 77843-4218, USA

JRFM, 2024, vol. 17, issue 2, 1-14

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.

Keywords: foreign exchange rates; Pareto distributions; power laws; second moment; variance; variance of variance (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2024
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