Geopolitical risk and the multi-scale leadership of oil and Bitcoin over global equities: a triangular wavelet–connectedness approach

This study asks whether Brent crude oil (“black gold”) and Bitcoin (“digital gold”) act as substitutes or as complementary channels when shocks reach equity markets, and how this balance shifts across horizons, geopolitical regimes, and between oil exporters and importers. The empirical design relies on a triangular system in which oil and Bitcoin are potential shock transmitters and equities are the final object of interest. The framework combines continuous wavelet coherence and phase, wavelet-based local projections, and frequency-domain connectedness within a single multi-scale setting and introduces a Substitution Index that tracks, over time and frequency, whether equity risk is predominantly oil-led or Bitcoin-led. The analysis uses daily data from 2020 to 2024 for the Europe Brent spot price, Bitcoin, and benchmark equity indices for selected G7, BRICS, and GCC economies, together with a global geopolitical risk index. In the band-filtered decomposition, oil carries the larger share of medium- to long-horizon equity risk, roughly between one and a half and 6 months, whereas Bitcoin matters mainly at short horizons during crypto-specific episodes. Periods of high geopolitical risk coincide with a stronger oil–equity link and a weaker Bitcoin channel, moving the Substitution Index toward oil, and the tilt is more pronounced for net oil exporters (Canada, Russia, Saudi Arabia, and United Arab Emirates) than for importers (euro area, Japan, India, and China). Both patterns depend on how the decomposition is computed: under a single unfiltered VAR, the index is nearly identical across bands and the exporter–importer difference is not statistically significant, so we report them as descriptive. The “digital vs. black gold” question therefore has no unconditional answer. In the baseline, whether oil or Bitcoin leads, and whether the two act as substitutes or as complements, depends on the investment horizon and on the level of geopolitical risk.