Asset Pricing with Panel Tree under Global Split Criteria
60 Pages Posted: 27 Oct 2021 Last revised: 15 Sep 2022
Date Written: April 15, 2022
We introduce a class of interpretable tree-based models (P-Tree) for analyzing (unbalanced) panel data, with iterative and global (instead of recursive and local) split criteria. We apply P-Tree to split the cross section of asset returns under the no-arbitrage condition, generating a stochastic discount factor model and diversified test portfolios for asset pricing. P-Tree visualizes nonlinear feature interactions, accommodates time-series splits, and allows interactions between macroeconomic states and asset characteristics. In an empirical study of U.S. equities, data-driven P-Tree reveals that long-term reversal, volume volatility, and industry-adjusted market equity interact to drive cross-sectional return variation, and that inflation constitutes the most critical regime-switching when interacting with firm characteristics. P-Tree models consistently outperform known observable and latent factor models at pricing individual asset and portfolio returns, while delivering profitable and transparent trading strategies utilizing characteristic interactions. Notably, the efficient portfolio on P-Tree factors generates a monthly risk-adjusted alpha of 2.46% and an annualized Sharpe ratio of 1.71 out of sample. The methodology is broadly applicable in building trees with vectorized outcomes and economic restrictions as split criteria to guard against overfitting and improve model performance.
Keywords: CART, Cross-Sectional Returns, Interpretable AI, Latent Factor, Machine Learning.
JEL Classification: C1, G11, G12
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