Multifractal Scaling in Cross-Sectoral Financial Markets: Connections with Diffusion and Chaos

Abstract

Financial returns are known to depart from Gaussian, uniform-scaling behaviour,yet standard risk models, Gaussian value-at-risk, mean-variance optimisation,still assume it, systematically mispricing tail risk. This paper does not re-establishthat departure; it isolates the specific channels through which it arises, since eachchannel implies a different fix. Across 50 assets in six sectors (2010–2026), weseparate correlation-driven multifractal scaling, directional asymmetry betweengains and losses, short-horizon leptokurtosis, and geometric path complexity.The generalised Hurst exponent H(q) is non-constant for every asset, directlyfalsifying the constant-volatility-of-volatility assumption embedded in BlackScholes-style pricing and in weak-form efficiency claims. A surrogate-validateddecomposition attributes this scaling to genuine temporal correlation, not heavytails alone, in 36 of 50 assets, including defensive consumer staples (KO, PEP,JNJ) whose low headline volatility masks structural non-linearity. Symmetricfluctuation analysis isolates the leverage effect’s asymmetric footprint, favouringmeasures such as Expected Shortfall over symmetric alternatives. A cumulantdiagnostic finds short-horizon non-Gaussian tail structure in 43 of 50 assets, concentrated in financials and traceable to 2008–2009, with direct implications forcalibrating risk models to sufficiently turbulent periods. Finally, a box-countinganalysis tests and rejects one specific deterministic-chaos explanation, ruling outthat mechanism while leaving the diffusion finding, and its risk implications,intact.