Asset-Pricing Trees with Pruning

Introduction

This repository contains the implementation of the paper Forest through the Trees: Building Cross-Sections of Stock Returns.

The project is largely based on the official R prototype, available on the official webpage.

Method Overview

Asset Pricing trees

Based on the set of stock characteristics, cross-sections of asset returns could be build using the Asset-Pricing tree algorithm:

1. The firms are categorized into two (n_splits parameter) equally sized groups according to the high/low value of a characteristic variable (For example, Size)
2. Within each group, stocks are further splitted into two equally sized subgroups by another characteristic (For example, value).
3. Step 2 repeats until the algorithm reaches the maximum tree_depth value.

In total, with tree depth of 4 and n_splits of 2, there are 2^4 = 16 different subgroups built at the end of the tree.

An example of AP-tree provided in the paper:

Tree Pruning with ElasticNet ML model

While the set of basis assets built by AP-tree does reflect the relevant information conditional on stock characteristics, one could face the curse of dimensionaly problem:

• With only 2 characteristics,the number of basis functions will be equal to 64. (given n_splits and tree_depth equal to 2 and 3, respectively)

Thus, the researchers proposed a technique that not only lowers the dimension of the basis assets, but also retain both the relevant information from the characteristics and portfolio interpretability.

In particular, the model solves mean-variance portfolio construction problem with elastic net:

The hyperparameters (mean shrinkage, L1 and L2 regularization lambdas) are tuned on the validation set using Time-Series cross-validation technique, and the model is finally evaluated on the test set.

Comparison

The comparison between implementations is made based on out-of-sample Sharpe ratio as a function of tuning parameters for AP-Trees on Size, Investment and Operating Profitability. In the paper, the lineplot looks as follows:

In this implementation, the lineplot looks as follows:

Setup

Install the required packages for Python3.7+:

pip install -r requirements.txt

Usage

Download the required dataset from the link.

Place all the files from the directory into characteristics folder.

All the parameters, such as the tree depth or the number of split per node could be set under the corresponding fields in src/constants.py file.

To build tree portfolios, run the command:

python build_trees.py

To prune the resulted trees, run the command:

python prune_trees.py

To plot test SR, run the command:

python plot_test_sr.py --feature_combination {e.g. lme_op_investment}