Strategic Alpha Identification in Ultra-High-Dimensional Markets: Equilibrium-Quotient Econometrics and Zero-Sum Rotational Strategies

An identification-first framework for extracting equilibrium-relevant structure when the market state is wider than the available sample.

Working Paper · Forthcoming

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Ultra-high-dimensional strategic markets create a structural identification problem before they create a prediction problem. When the number of empirically relevant state coordinates exceeds the number of independent observations, many primitive payoff systems can reproduce the same observed equilibrium. This paper therefore replaces unrestricted primitive recovery with an equilibrium quotient: the equivalence class of structural systems that generate the same equilibrium behavior on the empirically supported state domain. The empirical application uses institutional Form 13F holdings to ask how much economically meaningful structure remains identifiable inside a market with thousands of securities but only a small number of repeated cross sections.

Research question

Which economic objects remain point identified when p greatly exceeds n, and can those identified objects support disciplined strategic analysis of institutional allocation, transition dynamics, residual ownership structure, and portfolio exposure without pretending that every primitive payoff coefficient is recoverable?

Method

The paper combines equilibrium-quotient identification, row-space functionals, strategic-rank arguments, spectral dimension reduction, repeated institutional-holdings cross sections, low-dimensional transition operators, and symmetric-skew decomposition. The empirical design uses a balanced panel of 200 institutional investors and 6,736 persistent securities across three SEC Form 13F report dates, with Marchenko-Pastur screening, parallel analysis, effective-rank diagnostics, subspace comparisons, transition estimation, residual-security analysis, and constrained exposure-neutralization experiments.

Main findings

Supported dimension

12–14

In the audited balanced panel, Marchenko-Pastur screening selects 12 directions at every date and parallel analysis selects 13 or 14, despite an ambient universe of 6,736 persistent securities.

Effective dimension

≈31

Spectral entropy implies an effective dimension close to 31 across all three dates, showing a compact leading core together with a broader but still highly compressed spectral shoulder.

Explained structure

≈64%

The hard-threshold low-dimensional subspace explains about 64 percent of standardized holdings variation, indicating persistent common institutional allocation geometry without requiring one exact universal rank.

Dynamic persistence

R² > 0.978

Adjacent rank-13 transition operators fit the evolution of low-dimensional investor coordinates with R² above 0.978, while their spectral radii sit near the unit boundary.

Operator geometry

>99% symmetric

More than 99 percent of transition energy is symmetric in the conservative rank-13 specification, while the rotational component is small. The result supports a precise distinction between norm-changing and rotational dynamics without converting matrix geometry into an unsupported causal trading claim.

Why it matters

The paper's central contribution is methodological discipline under severe underidentification. Rather than letting a regularizer decide which primitive story is called structural, the equilibrium quotient isolates the functionals that every observationally equivalent system must share. The empirical evidence then shows that a market can be ultra-high dimensional in its primitive representation yet remain strongly organized in a persistent low-dimensional allocation geometry. That distinction creates a defensible foundation for strategic-risk analysis, counterfactual support diagnostics, and future return or propagation tests while keeping residual holdings structure separate from realized alpha until those return tests are actually performed.

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