Uncommon Factors for Bayesian Asset Clusters

We introduce the Bayesian Clustering Model (BCM), a new general framework combining decision tree and Bayesian variable selection for modeling panel data with grouped heterogeneity, with an emphasis on economic guidance and interpretability. We apply BCM to estimating uncommon-factor models for data-driven yet economically motivated asset clusters and macroeconomic regimes, utilizing marginal likelihood to address parameter/model uncertainties and overfitting in tree growth. We find strong evidence for (i) cross-sectional heterogeneity linked to (nonlinear interactions of) idiosyncratic volatility, size, and value, and (ii) structural changes in factor relevance predicted (i.e., macro-instrumented) by market volatility and valuation. We identify MKTRF and SMB as common factors, together with multiple uncommon factors across characteristics-managed, market-timed clusters. The learned grouped heterogeneity also helps explain volatility- or size-related anomalies, offers effective test assets, and renders many popular factors irrelevant (thus mitigating the "factor zoo'' problem). Overall, BCM outperforms benchmark common-factor models, e.g., achieving an out-of-sample cross-sectional R² exceeding 25% for multiple clusters and an investment Sharpe ratio tripling that of the tangency portfolios built from Fama-French double-sorted portfolios.