PCA-APT Stress Index for Market Drawdowns

This study develops a leakage-safe PCA–APT framework that constructs an idiosyncratic market-stress index from cross-sectional residual dispersion and evaluates its usefulness for anticipating equity drawdowns. Using daily adjusted prices for SPY and 11 U.S. sector ETFs from 2020–2025, we compute sector excess returns (sector minus SPY), estimate a low-dimensional common component via principal component analysis (PCA), and define residual stress as the cross-sectional root-mean-square magnitude of PCA reconstruction residuals. To prevent look-ahead bias, the PCA mapping is estimated using information available only through t−1, stress is computed out-of-sample at t, and stress regimes are identified using a rolling train-only quantile threshold that is shifted forward by one trading day. Drawdown-warning performance is assessed using drawdown-onset events and early-warning classification metrics (ROC-AUC, PR-AUC, and horizon-H precision/recall). Empirically, residual stress spikes cluster around drawdown onsets and provides predictive information, although a volatility-based benchmark remains stronger on average across discrimination metrics. Importantly, residual stress exhibits state-dependent complementarity with volatility: conditional on low volatility, high residual stress is associated with a materially higher probability of a drawdown onset within the next H=21 trading days (approximately 17% vs. 8%), and the joint high-stress/high-volatility regime identifies the highest-risk states (approximately 36% onset probability). Event-level overlap diagnostics further indicate that residual stress can flag a subset of drawdown onsets not captured by a volatility-threshold rule, while some onsets are not preceded by either signal. Economic relevance is examined under transaction costs through (i) a residual-ranked sector long–short portfolio and (ii) stress-managed SPY overlays that reduce exposure during detected regimes. In the baseline sample, a volatility-managed overlay improves drawdown control relative to buy-and-hold, whereas the residual-stress overlay does not reduce maximum drawdown and the residual-ranked long–short strategy is not robustly profitable after costs. Overall, the paper contributes a reproducible, leakage-safe evaluation pipeline linking cross-sectional residual dispersion to drawdown risk and clarifies when residual stress serves as a complementary market-structure risk indicator alongside standard volatility-based signals.