Regression Tree for Portfolio Optimization and Imbalanced Data

Description

Investors face the problem of how to allocate capital among investible assets to optimize their portfolio according to their own utilities all the time. The common practice is to estimate the mean and covariance of returns from historical data and create meanvariance efficient portfolios or using more advanced strategies. However, a critical problem is that the cross-sectional data of returns is imbalanced. For example, investing in ETFs has become increasingly important for the rise of robot advisors, and we have witnessed hundreds of ETFs created in the recent two decades. First, given many ETFs are created for similar purposes for different demands of investors, grouping them into the same leaf portfolio helps ease the high-dimensional investment decision. Second, many ETFs have been introduced, restructured, or replaced in recent decades, and our P-Tree helps with this imbalanced data issue.This proposed research project aims to provide a novel approach to optimize portfolio using imbalanced data by the customized regression trees named Panel Tree, or P-Tree. Our approach is applicable to various groups of assets such as individual stocks, ETFs, bonds, industry portfolios, etc. Furthermore, the P-Tree framework is flexible enough to incorporate existing methods on shrinkage estimation of mean and variance, and robust portfolio optimizations.We aim to provide a unified model originated from the Classification and Regression Tree (CART) model (Breiman et al., 1984) in machine learning, with a bespoke split criterion using economic intuition from portfolio optimization. The tree partitions the cross-sectional data of assets into non-overlapping groups by the asset characteristics, each group is economically a portfolio (leaf portfolio), which could be equal weighted or value weighted portfolio of asset within the leaf. Besides, our framework can incorporate the above approaches on shrinkage estimator, robust portfolio or regularization on weights straightforwardly.