A universal exponent governing foreign exchange rate risks

Departing from previous studies, this paper uses power laws to model foreign exchange rate risks in terms of realized foreign exchange rate (FX) variances for daily and weekly data. Empirical tests based on daily data provide strong evidence for emergent market risk behavior manifested in a common power-law exponent governing the cross section of realized FX variances. We show that this emergent market risk behavior is invariant across various time frequencies. Based on modern bootstrapping techniques, we derive a novel joint test for investigating the presence of total invariance—that is, invariance of emergent market risk behavior across time frequencies and over time. Our novel test provides strong evidence for total invariance of realized FX variances. We argue that the results are in line with the theory of complex systems—that is, even though FX risk exhibits idiosyncratic features that may originate from market-distinct factors (inflation, interest rates, public debts, etc.), emergent market behavior manifests itself in a universal power-law exponent governing the cross section of FX risks.