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On the Estimation of Optimal Cutoffs for Power Laws and the Cross Section of Realized Foreign Exchange Rate Variances

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  • Klaus Grobys

    (University of Vaasa, Finance Research Group, School of Accounting and Finance
    University of Vaasa, Innovation and Entrepreneurship (InnoLab))

Abstract

Extending recent research, this study introduces a novel testing procedure based on modern block bootstrap techniques and maximum likelihood estimation to investigate whether the universal power-law process governing the cross-section of realized foreign exchange (FX) rate variances exhibits a conjoint cutoff. The analysis posits that the maximum likelihood estimator for the exponent of a power law is intrinsically dependent on the selected cutoff. Our innovative test, calibrated to the cross-section of realized daily FX variances, provides evidence for the existence of such a universal cutoff. The findings have significant implications for FX risk management. Specifically, they indicate that (a) the benefits of FX risk diversification may be more constrained than previously assumed, and (b) the extent of power-law behavior in the realized variance risk of the FX market may be substantially underestimated when conventional single-equation models are employed to determine the optimal cutoff for a power law.

Suggested Citation

  • Klaus Grobys, 2026. "On the Estimation of Optimal Cutoffs for Power Laws and the Cross Section of Realized Foreign Exchange Rate Variances," Computational Economics, Springer;Society for Computational Economics, vol. 68(2), pages 1245-1292, August.
    • Handle: RePEc:kap:compec:v:68:y:2026:i:2:d:10.1007_s10614-025-11064-2
    DOI: 10.1007/s10614-025-11064-2
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    References listed on IDEAS

    as
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    10. Grobys, Klaus, 2024. "A universal exponent governing foreign exchange rate risks," International Review of Financial Analysis, Elsevier, vol. 95(PB).
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    14. Grobys, Klaus & Junttila, Juha, 2021. "Speculation and lottery-like demand in cryptocurrency markets," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 71(C).
    15. Luis M. Viceira & Ricardo Gimeno, 2010. "The euro as a reserve currency for global investors," Working Papers 1014, Banco de España.
    16. Jinghong Shu & Jin E. Zhang, 2006. "Testing range estimators of historical volatility," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 26(3), pages 297-313, March.
    17. 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.
    18. Grobys, Klaus, 2021. "What do we know about the second moment of financial markets?," International Review of Financial Analysis, Elsevier, vol. 78(C).
    19. 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.
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    22. Opie, Wei & Riddiough, Steven J., 2020. "Global currency hedging with common risk factors," Journal of Financial Economics, Elsevier, vol. 136(3), pages 780-805.
    23. Grobys, Klaus, 2023. "Correlation versus co-fractality: Evidence from foreign-exchange-rate variances," International Review of Financial Analysis, Elsevier, vol. 86(C).
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    Keywords

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    JEL classification:

    • F31 - International Economics - - International Finance - - - Foreign Exchange
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

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