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

Author

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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
    Innovation and Entrepreneurship (InnoLab), 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)

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.

Suggested Citation

  • Masoumeh Fathi & Klaus Grobys & James W. Kolari, 2024. "On the Realized Risk of Foreign Exchange Rates: A Fractal Perspective," JRFM, MDPI, vol. 17(2), pages 1-14, February.
    • Handle: RePEc:gam:jjrfmx:v:17:y:2024:i:2:p:79-:d:1340654
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    References listed on IDEAS

    as
    1. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
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    3. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    4. Torben G. Andersen & Tim Bollerslev & Nour Meddahi, 2004. "Analytical Evaluation Of Volatility Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(4), pages 1079-1110, November.
    5. Eugene F. Fama, 1963. "Mandelbrot and the Stable Paretian Hypothesis," The Journal of Business, University of Chicago Press, vol. 36, pages 420-420.
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