End-to-End Neural Shrinkage of Indefinite Pairwise Correlation Matrices for Small-Cap-Inclusive Portfolios

01 摘要

Small-cap-inclusive equity universes contain recently listed and intermittently traded securities, so enforcing a common look-back discards a substantial fraction of the available information. Pairwise-complete estimation preserves the longest overlap for each asset pair, but the resulting correlation matrix can be indefinite because its entries are computed on different samples. This prevents direct use in Markowitz optimization and falls outside the assumptions of standard random-matrix shrinkage. We adapt a rotation-invariant neural covariance estimator to this setting. The model computes mask-aware marginal moments and a pairwise correlation matrix proxy, processes its signed spectrum, and uses a bidirectional gated recurrent unit conditioned on factor-aligned effective sample lengths derived from the overlap matrix and eigenvector loadings. It maps all eigenvalues, including negative ones, to a positive inverse spectrum. The reconstructed covariance is positive definite and is trained end-to-end to minimize five-day realized global-minimum-variance risk. We evaluate 26 expanding-window models from 2000 to 2025 on up to 1,500 U.S. equities in a closing-auction simulator with po

02 关键点

1. Small-cap-inclusive equity universes contain recently listed and intermittently traded securities, so enforcing a common look-back discards a substantial fraction of the available information.
2. Pairwise-complete estimation preserves the longest overlap for each asset pair, but the resulting correlation matrix can be indefinite because its entries are computed on different samples.
3. This prevents direct use in Markowitz optimization and falls outside the assumptions of standard random-matrix shrinkage.