Hidden Coupling: Rethinking Commodity Diversification with Mutual Information

The case for commodity diversification is usually argued from linear correlation, yet allocation decisions can be questioned precisely when correlation misses nonlinear co-movement. This paper asks: do commodities truly diversify equities when it matters, and can we size exposure accordingly? Using daily ETFs from 2020–2025, I compare absolute Pearson correlation with mutual information (MI) and benchmark observed MI against its Gaussian-implied value at the prevailing correlation. Two results stand out. In calm or trending markets, both commodity-laden and non-commodity mixes explain very little of SPY’s uncertainty: correlation overstates the practical distinctiveness of commodities. In systemic stress (e.g., 2020), portfolios can exhibit low correlation yet sharply elevated MI, revealing hidden, nonlinear coupling consistent with financialization, even as commodity sleeves deliver right-tail payoffs. I then operationalize MI in a sizing overlay that caps the commodity sleeve when market-scaled MI exceeds its Gaussian benchmark. In out-of-sample tests (2020–2024), the MI rule delivers very small, directionally favorable reductions in expected shortfall and drawdown relative to an identically constrained correlation trigger, but with materially lower turnover. MI is thus a practical complement to correlation, useful for detecting regime shifts and sizing commodity exposure when dependence intensifies near the left tail.