Overview

Metrics for the Individual × Continuous cell — one continuous factor score per (date, asset_id), evaluated cross-sectionally per date and aggregated over time.

Metric	Page
Spearman rank correlation, the canonical signal-quality summary	ic
Per-date ordinary least squares (OLS) slope \(\lambda\), Newey-West (NW) heteroskedasticity-and-autocorrelation-consistent (HAC) \(t\) on its mean	fm_beta
Long-short quintile spread (equal- and value-weighted)	quantile
Pairwise ordering accuracy for small allocation universes	directional_pair_accuracy
Quintile-return monotonicity rank test	monotonicity
HHI-style top-bucket concentration	concentration
Turnover, breakeven cost, net spread	tradability
Spanning \(\alpha\) vs an existing factor pool	spanning

ic and fm_beta are the two inferential entry points (each carries a \(p\)-value); the rest are descriptive / risk diagnostics that profile the same factor without contributing to the inferential test.

For when each applies see Reference § Metric applicability. The discipline behind the inferential SEs (NW HAC bandwidth, Shanken EIV) is consolidated in Reference § Statistical methods.