# Growing the Efficient Frontier on Panel Trees

arXiv: https://arxiv.org/abs/2501.16730 · HTML: https://mlsanity.com/paper/2501.16730/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 54 references that are in the map.
- First posted on arXiv 28 Jan 2025.

## Builds on (most cited first, 6 of 6)

- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [Surprises in High-Dimensional Ridgeless Least Squares Interpolation](https://mlsanity.com/paper/1903.08560/) (2019)
- [Deep Learning in Asset Pricing](https://mlsanity.com/paper/1904.00745/) (2019)
- [Stochastic tree ensembles for regularized nonlinear regression](https://mlsanity.com/paper/2002.03375/) (2020)
- [Deep Learning in Characteristics-Sorted Factor Models](https://mlsanity.com/paper/1805.01104/) (2018)
- [Power Enhancement in High Dimensional Cross-Sectional Tests](https://mlsanity.com/paper/1310.3899/) (2013)

## Built on by (most cited first, 2 of 2)

- [Alpha-R1: Alpha Screening with LLM Reasoning via Reinforcement Learning](https://mlsanity.com/paper/2512.23515/) (2025)
- [LambdaRankIC: Directly Optimizing Rank IC for Financial Prediction](https://mlsanity.com/paper/2605.00501/) (2026)

## Abstract (arXiv)

We introduce a new class of tree-based models, P-Trees, for analyzing (unbalanced) panel of individual asset returns, generalizing high-dimensional sorting with economic guidance and interpretability. Under the mean-variance efficient framework, P-Trees construct test assets that significantly advance the efficient frontier compared to commonly used test assets, with alphas unexplained by benchmark pricing models. P-Tree tangency portfolios also constitute traded factors, recovering the pricing kernel and outperforming popular observable and latent factor models for investments and cross-sectional pricing. Finally, P-Trees capture the complexity of asset returns with sparsity, achieving out-of-sample Sharpe ratios close to those attained only by over-parameterized large models.