Algorithmic Monitoring: Measuring Market Stress with Machine Learning

TL;DR

The paper tackles the challenge of measuring latent market stress in real time by constructing the Market Stress Probability Index (MSPI), an equity-only, cross-sectional signal derived from CHSP data. It maps a rich set of monthly cross-sectional fragility signals into a one-month-ahead stress probability using an $L_1$-regularized logistic regression within an expanding-window framework, and compares it against a parsimonious benchmark and nonlinear learners. The study emphasizes transparent measurement and calibration, showing that MSPI delivers superior probability forecasts (calibration, Brier score, and log loss) while maintaining competitive discrimination, and it interprets MSPI as both a forward-looking risk state variable and a tool for stress-risk innovations via residuals and local projections. The findings have practical implications for real-time monitoring in electronic markets and macro-finance analyses, offering a reproducible, auditable input that can be integrated into risk management, volatility forecasting, and policy-like monitoring frameworks.

Abstract

I construct a Market Stress Probability Index (MSPI) that estimates the probability of high stress in the U.S. equity market one month ahead using information from the cross-section of individual stocks. Using CRSP daily data, each month is summarized by a set of interpretable cross-sectional fragility signals and mapped into a forward-looking stress probability via an L1-regularized logistic regression in a real-time expanding-window design. Out of sample, MSPI tracks major stress episodes and improves discrimination and accuracy relative to a parsimonious benchmark based on lagged market return and realized volatility, delivering calibrated stress probabilities on an economically meaningful scale. Further, I illustrate how MSPI can be used as a probability-based measurement object in financial econometrics. The resulting index provides a transparent and easily updated measure of near-term equity-market stress risk.

Figures (6)

• Figure 1: MSPI out-of-sample. The solid line plots the predicted probability that the next month is a stress month. Dots mark months for which stress is realized in the subsequent month under the definition in equation \ref{['eq:stress_def']}.
• Figure 2: Out-of-sample stress probability - model horse race (calibrated). MSPI (black) is the L1-logit probability of next-month stress. Random forest (blue) and gradient boosting (orange) are estimated under the same expanding-window design and Platt-calibrated in real time within each training window to place forecasts on a comparable probability scale.
• Figure 3: Stress phase diagram. Each point plots MSPI$_t$ against next-month realized market volatility $\sigma^{mkt}_{t+1}$. The strong positive association supports interpreting MSPI as a forward-looking risk state variable.
• Figure 4: ROC curves out-of-sample (raw scores). Curves are computed from uncalibrated model scores to measure discrimination; the dashed $45^\circ$ line corresponds to random classification.
• Figure 5: Precision--recall curves out-of-sample (raw scores). Curves are computed from uncalibrated model scores; precision--recall is informative here because stress months are relatively infrequent (event rate 15.9%).