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

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.