Asset Pricing with Panel Trees under Global Split Criteria
53 Pages Posted: 27 Oct 2021 Last revised: 23 Nov 2021
Date Written: November 1, 2021
We introduce a class of interpretable tree-based models (P-Trees) for analyzing panel data, with iterative and global (instead of recursive and local) splitting criteria to avoid overfitting and improve model performance. We apply P-Tree to generate a stochastic discount factor model and test assets for cross-sectional asset pricing. Unlike other tree algorithms, P-Trees accommodate imbalanced panels of asset returns and grow under the no-arbitrage condition. P-Trees also graphically capture nonlinearity and interaction effects and accommodate regime-switching and interactions between macroeconomic states and firm characteristics. For example, P-Tree identifies inflation as the most important macro predictor with regime-switching in U.S. equity data. Based on multiple pricing, prediction, and investment metrics, we find that (boosted or time-series) P-Trees outperform standard factor models and PCA latent factor models. An equal-weighted portfolio for five factors generated by P-Trees delivers an excess alpha of 1.09% against the Fama-French 3-factor benchmark, producing an annualized Sharpe ratio of 1.98 out of sample. Data-driven cutpoints in P-Trees reveal that long-run reversal, volume volatility, and industry-adjusted market equity drive cross-sectional return variations, consistent with variable importance analysis using random forests.
Keywords: CART, Cross-Sectional Returns, Latent Factor Model, Machine Learning, Panel Data, Stochastic Discount Factor, Tree Ensembles.
JEL Classification: C1, G1
Suggested Citation: Suggested Citation