# Entropy-Augmented Forecasting and Portfolio Construction at the Industry-Group Level: A Causal Machine-Learning Approach Using Gradient-Boosted Decision Trees

## TL;DR

This paper shows that using entropy measures in machine learning improves financial forecasts and investment strategies for industry groups.

## Contribution

The novel use of entropy measures with gradient-boosted decision trees improves both profitability and interpretability in industry-group portfolio construction.

## Key findings

- A weekly maximum-profit model with Shannon entropy achieved over 30,000% accumulated return.
- Entropy-based models showed lower volatility and better downside protection on monthly and quarterly horizons.
- Profit strategies focused on cyclical industries, while risk strategies favored defensive sectors.

## Abstract

This paper examines whether information-theoretic complexity measures enhance industry-group return forecasting and portfolio construction within a machine-learning framework. Using daily data for 25 U.S. GICS industry groups spanning more than three decades, we augment gradient-boosted decision tree models with Shannon entropy and fuzzy entropy computed from recent return dynamics. Models are estimated at weekly, monthly, and quarterly horizons using a strictly causal rolling-window design and translated into two economically interpretable allocation rules, a maximum-profit strategy and a minimum-risk strategy. Results show that the top performing strategy, the weekly maximum-profit model augmented with Shannon entropy, achieves an accumulated return exceeding 30,000%, substantially outperforming both the baseline model and the fuzzy-entropy variant. On monthly and quarterly horizons, entropy and fuzzy entropy generate smaller but robust improvements by maintaining lower volatility and better downside protection. Industry allocations display stable and economically interpretable patterns, profit-oriented strategies concentrate primarily in cyclical and growth-sensitive industries such as semiconductors, automobiles, technology hardware, banks, and energy, while minimum-risk strategies consistently favor defensive industries including utilities, food, beverage and tobacco, real estate, and consumer staples. Overall, the results demonstrate that entropy-based complexity measures improve both economic performance and interpretability, yielding industry-rotation strategies that are simultaneously more profitable, more stable, and more transparent.