arXiv subjects

Marc da Costa Nunes

Publications and source records attributed to Marc da Costa Nunes.

3 recordsLinked to original sources

arXiv2026

Cities of Signals: Compression, Separation, and the Geometry of Novelty

A cross-sectional signal is a forecast vector over $d$ assets at each date; demeaned and normalized, it is a point on a sphere. Its city is the direction of its time-averaged vector in a common target-aligned frame, a compressed summary. When is the angle between two cities a conservative estimate of the angle between the histories? For independent uniform histories, the probability that the history angle is at least the city angle tends to one when the city angle is at most 90 degrees, with an $O(T^{-1/2})$ error bound uniform in dimension. Selecting for positive average information coefficient (IC) changes the unconditional limit to $γ_q>1/2$, about 56% for 20 assets. The bound extends to independent, rotationally symmetric histories with temporal dependence; summable products of lag correlations preserve the conditional limit. A stationary ergodic theorem allows shared signal movement and identifies the population margin determining the limiting ordering. Among 266,815 positive-IC pairs in AlphaNova's Competition May 2026, the history angle is at least the city angle for 58.9% overall, 74.1% at city angles up to 90 degrees, and 1.5% beyond. These frequencies describe the observed library and do not validate the uniform null: residual agreement is mostly positive, and an empirical second-moment diagnostic cannot be matched within that null by adjusting temporal dependence alone. On the full 776-signal sample, a city angle of at least 60 degrees selects pairs with a 94.3% success rate at the same history-angle threshold, against an 85.0% base rate, and retains 72.5% of pairs. Explicit constructions show the limits of direction-only summaries, retained lengths give sharp bounds, and shared time blocks recover missing information, here only at fine resolution. Persistent positive IC confines cities and bounds their motion; convergence also requires a stable mean direction.

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arXiv2026

Separated Signal Libraries: Packing, Saturation, and Joint Spectral Limits

We study libraries of cross-sectional signals: at each date, a forecast vector over $d$ assets intended to predict the next period's cross-sectional return. Demeaned and unit-normalized, a signal is a point on a sphere and its $T$-date history a point on a product of $T$ spheres. A pairwise correlation cap on histories is a minimum angular separation on that product, so growing a library under such a cap is a packing problem. If a large library is not too pairwise correlated and is equally weighted, does the equally weighted sum (EWS) tend to a known principal-component quantity as it grows? We answer this under explicit assumptions on how the library is filled. Separation alone guarantees nothing: it fixes no limiting distribution; a saturated library covers the sphere yet can carry a biased count; and near-maximum packing on a fixed domain forces uniform volume, which on the unrestricted sphere gives zero mean and no distinguished principal component (PC1). Alignment depends on the admission rule and candidate distribution. Under the uniform product-volume benchmark, screening on positive average information coefficient (IC) yields a nonzero, target-aligned mean but an isotropic second moment, whereas a positive IC margin $β$ makat every finite $T$, with athree-level spectrum whose leading eigenvalue tends to $β^2$ while residual levels decay as $1/T$; margins of order $T^{-1/2}$ keep a positive admission rate but a vanishing eigengA finite residual-spectrum criteS-PC1 alignment.Gilbert-Varshamov codes show separation permits both outcomes: exponentially large positive-IC libraries exist whose EWS is PC1, and others whose EWS is orthogonal to PC1. $\log J=o(T)$ suffices for uniform estimation among $J$ candidates from $T$ iid dates. Derived results are proved and checked numerically; no market data are used.

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arXiv2026

Large Signal Libraries: Equal-Weight Limits and the Divergent Spectra of Signals and PnL

An ensemble of roughly 3,000 signals over 20 assets was reported to have approximately 90% correlation with the leading component of the asset-space return structure. Does having about 158 signals per available linear dimension explain that alignment? The population answer depends on the research process's design distribution and its relation to returns: crowding alone imposes neither a nonzero mean nor agreement with a principal component. The population theory developed here distinguishes four objects: the equal-weight signal, signal principal components, equal-weight profit and loss (PnL), and PnL principal components. The return operator in the motivating observation is a separate object. Independent libraries converge to their design mean; exchangeable libraries can retain a random conditional mean. Cross-sectional signals over $d$ assets, once demeaned and normalized, lie on the unit sphere $S^{q-1}$ of a $q$-dimensional space, $q=d-1$. Under axial symmetry, their nonzero mean is signal-cloud PC1 exactly when its longitudinal second moment exceeds $1/q$, the isotropic energy share. Residual-and-gap bounds quantify approximate alignment. Combining design weights into signals contracts the tangent of their angle to PC1 to at most $\sqrt{λ_2/λ_1}$ times its value, where $λ_1>λ_2$ are the leading signal-kernel eigenvalues; the factor is sharp. A target-aligned frame separates transverse signal geometry, which PnL discards, from dispersion weighting and temporal centering, which also change the spectrum. A reproducible synthetic example illustrates the geometric threshold, and a proposed empirical program separates library growth from limited-history estimation. No market-data empirical results are presented.

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