Working papers, notes, and methodological writing.

On the β-Spectrum of Cross-Sectional Equity Returns

We estimate the liquidity elasticity β, governing how quickly market-maker depth withdraws as volatility rises, across 1,543 instruments — 43 CME futures from tick microstructure and 1,500 US equities from ten years of minute bars via Corwin–Schultz spreads. The estimated elasticities form a continuous spectrum from β = +2.00 (leveraged ETFs) to β = −0.33 (Treasury-bill ETFs), with coherent sector differentiation and a single sector — Treasury-bill ETFs — exhibiting uniformly significant negative β: the predicted safe-haven stabilizing regime.

We interpret this spectrum through a capital-weighted Kuramoto phase-oscillator model whose coupling K(r) emerges endogenously from a microstructural feedback loop, with β partitioning the dynamics into stabilizing, withdrawing, and destabilizing regimes. During the March 2020 crash, the aggregate Kuramoto order parameter peaks at 0.14 — far below the calibrated activation threshold — confirming that the endogenous feedback remains latent even under extreme stress. Against a rolling-correlation benchmark, the Kuramoto measure significantly outperforms for drawdown prediction (paired t = 3.04, p = 0.002) and captures orthogonal information.

Power Gridlock: Portfolio Construction in Electrical Grid Equities

Construction of a long-only portfolio over the universe of listed electrical grid operators, with a discussion of sector concentration, capacity constraints, and the structural drivers of grid-equity returns through capacity-tightening cycles.