Entropy-Based Portfolio Optimization in Cryptocurrency Markets: A Unified Maximum Entropy Framework

Area of Science:

• Quantitative Finance
• Information Theory
• Computational Economics

Background:

• Traditional mean-variance portfolio optimization is insufficient for volatile cryptocurrency markets due to extreme volatility and unstable correlations.
• Variance is an inadequate risk measure for cryptocurrencies, necessitating alternative approaches for portfolio construction.

Purpose of the Study:

• To propose a unified entropy-based portfolio optimization framework using the Maximum Entropy Principle (MaxEnt).
• To offer a robust and distribution-free alternative to classical variance-based portfolio optimization for cryptocurrencies.

Main Methods:

• Formally derived Shannon entropy, Tsallis entropy, and Weighted Shannon Entropy (WSE) using Lagrange multipliers within a MaxEnt framework.
• Interpreted portfolio diversification as an inference problem under uncertainty, with entropy acting as a structural regularizer.
• Empirically illustrated the framework using Bitcoin, Ethereum, Solana, and Binance Coin weekly return data.

Main Results:

• Different entropy measures induce systematic diversification behaviors: Shannon entropy favors uniform allocations, Tsallis entropy enhances tail risk robustness, and WSE allows asset-specific weights.
• Entropy-based criteria yield stable and interpretable allocations in turbulent market conditions.
• The MaxEnt formulation unifies various entropy measures, clarifying entropy's role in regularizing diversification.

Conclusions:

• The proposed entropy-based framework provides a flexible and robust alternative to classical portfolio optimization for cryptocurrencies.
• The MaxEnt approach offers a theoretically coherent and practically applicable method for portfolio construction under uncertainty.
• The framework is extendable to dynamic multi-period settings and alternative entropy formulations, paving the way for future research.