Mechanism for Identifying Market Regimes Based on a Gaussian Mixture Model

This project develops and evaluates a data-driven mechanism for identifying market regimes in U.S. equity markets using Gaussian Mixture Models (GMMs). The moti- vation stems from the growing need for interpretable, unsupervised methods that can capture the complex, nonstationary, and regime-dependent behavior of financial returns. Traditional econometric models—such as Markov-Switching frameworks—often rely on strong parametric assumptions about transition probabilities and are sensitive to struc- tural breaks. In contrast, GMMs offer a probabilistic, flexible, and transparent approach that allows for overlapping regimes and non-linear relationships between risk and return. The study applies the model to daily returns and 30-day realized volatility of the SPDR SP 500 ETF (SPY) from 2000 to 2024, standardizing features to ensure numer- ical stability and comparability. Model selection is guided by the Bayesian Information Criterion (BIC), which consistently favors a three-regime specification corresponding to empirically recognizable “bull,” “neutral,” and “bear” market states. Each regime is sta- tistically characterized by its mean, volatility, skewness, and kurtosis, and economically linked to historical market events such as the 2008 financial crisis and the 2020 Covid-19 shock. The probabilistic (“soft”) classification provided by the GMM enables continuous regime probabilities rather than abrupt, binary transitions, reflecting the inherently grad- ual nature of market shifts. These probabilities can be directly incorporated into portfolio- management and risk-control frameworks, supporting adaptive asset-allocation, volatility- targeting, and hedging strategies. The research demonstrates that regime-aware ap- proaches based on GMM signals can reduce drawdowns and enhance risk-adjusted per- formance relative to static allocation benchmarks. Beyond its empirical findings, this project contributes a transparent and reproducible analytical framework built entirely in Python, following data-science best practices. The 3 open-source implementation facilitates extension to other markets or features (e.g., option- implied volatility, macro indicators), bridging academic research and professional appli- cation. Overall, the work highlights how interpretable machine-learning methods like GMMs can strengthen the link between statistical modeling and practical decision-making in modern quantitative finance.