Nonlinear Factor Compression in Crowded Equity Repricing

Periods of crowded positioning produce nonlinear compression of the realised factor covariance, in which seemingly orthogonal factors co-move under degrossing pressure. We interpret this as a topological collapse of the effective factor manifold and discuss its consequences for risk decomposition during stress windows.

Realised factor covariance Σ_t = U_t Λ_t U_t^T. Compression is observed as a fall in the effective rank rank_eff(Σ_t) = (Σ λ_i)^2 / Σ λ_i^2 during degrossing episodes.

Conventional risk models that hold factor structure constant overstate diversification precisely when diversification is most needed. Position sizing that ignores compression is procyclical.

Risk frameworks should report effective-rank time series alongside conventional factor risk attributions.

Identification of degrossing episodes is ex-post; live identification carries lag.