An empirical multivariate extension of random-exponent fractal modeling: joint distribution and portfolio risk in cross-asset ETFs

Antunes de Araujo, Fernando Henrique and Kojić, Milena (2026) An empirical multivariate extension of random-exponent fractal modeling: joint distribution and portfolio risk in cross-asset ETFs. The North American Journal of Economics and Finance, 86. ISSN 1879-0860

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Abstract

This article develops an empirical multivariate extension of the random-exponent fractal logic in the reference univariate study (Frezza, 2018). The empirical target is the joint distribution of nine cross-asset ETF returns observed from 2012-03-01 to 2026-02-27, a span that covers the COVID-19 pandemic, the Russia-Ukraine invasion, the Israel-Hamas war and two major tariff shocks. The proposed specification combines a rolling local roughness proxy, a vector autoregression for that state, asset-level conditional scales and a multivariate t-copula dependence layer that is re-estimated at each rolling origin and held fixed over the forecast window. Relative to the closest univariate-style benchmark, namely the independent fractal specification, the proposed model reduces energy distance by 13.2%, 18.5% and 21.8% at the 32-, 64- and 126-day horizons, while cutting correlation RMSE by 48.3% at 64 days and 52.3% at 126 days. Paired-bootstrap inference shows that the gains over the independent fractal benchmark are stable for energy distance and correlation RMSE at all horizons, while co-exceedance gains are not statistically distinguishable once overlap among forecast windows is preserved. All strong benchmarks, including DCC-GARCH, are evaluated on the same 66-origin grid and with the same simulation budget. After within-family Holm correction, the proposed model reduces 1% equal-weight portfolio quantile error relative to the historical block bootstrap by 12.4%, 15.0% and 21.5% across the three horizons; DCC-GARCH retains significantly lower co-exceedance RMSE at all horizons and lower 32-day correlation RMSE. Neither 5% quantile loss nor joint VaR-ES loss establishes systematic dominance. Conditional-coverage tests confirm that the 5% equal-weight VaR of the proposed model passes where the independent fractal and t-copula-without-H benchmarks fail, and the proposed model also passes for risk parity where DCC-GARCH fails. These findings do not imply universal dominance over every multivariate competitor: t-copula, historical bootstrap and DCC-GARCH benchmarks remain competitive. The contribution is more specific. Jointly modeling local roughness and cross-asset dependence materially improves the natural multivariate scaling of the original univariate design in both joint-distribution fit and portfolio-risk calibration.

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