Beyond Magnitude: Lacunarity of Cross-Asset Correlation Images as a Structural Measure of Systemic Dependence

Standard scalar indicators of systemic dependence, such as the mean pairwise correlation, the absorption ratio, and the dispersion of the eigenvalue spectrum, summarise the magnitude of co-movement but are by construction blind to its spatial arrangement. We propose treating the time-varying cross-asset correlation matrix as a greyscale image and quantifying its spatial organisation with the multiscale gliding-box lacunarity. Using a controlled block-factor generative model in which the average correlation is held fixed while the sectoral block strength is varied, we show that lacunarity recovers the planted block structure almost perfectly (partial Spearman ρ=0.92 at fixed mean correlation), a recovery that persists under fat-tailed innovations, time-varying loadings, and overlapping communities, whereas the mean correlation and the absorption ratio remain flat. Applied to twenty years of daily data for sixty-two sector-spanning United States equities, lacunarity tracks a model-free index of block heterogeneity after controlling for correlation magnitude (partial Spearman ρ=0.46, ninety-five percent bootstrap interval [0.33,0.58]) and improves the out-of-sample prediction of block structure beyond the magnitude baselines. We are explicit about two boundaries. A simple permutation-invariant dispersion statistic, the standard deviation of the off-diagonal correlations, tracks block heterogeneity even more strongly than lacunarity, so lacunarity is not the most efficient estimator of that quantity; its distinct role, confirmed by a scrambling test, is that it responds to the spatial arrangement of dependence, which dispersion measures are invariant to, and it remains informative under a canonical clustering or spectral ordering. The measure is descriptive rather than predictive of future drawdowns. The results position correlation-image lacunarity as an interpretable, computationally light, and arrangement-sensitive complement to the existing magnitude and dispersion descriptors of systemic dependence.