Mean–Variance–Entropy Framework for Cryptocurrency Portfolio Optimization

Florentin Șerban () and Bogdan-Petru Vrînceanu
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Florentin Șerban: Department of Applied Mathematics, Bucharest University of Economic Studies, 010374 Bucharest, Romania
Bogdan-Petru Vrînceanu: Master Business Analytics, Bucharest University of Economic Studies, 010374 Bucharest, Romania

Mathematics, 2025, vol. 13, issue 10, 1-10

Abstract: Portfolio optimization is a fundamental problem in financial theory, aiming to balance risk and return in asset allocation. Traditional models, such as Mean–Variance optimization, are effective, but often fail to account for diversification adequately. This study introduces the Mean–Variance–Entropy (MVE) model, which integrates Tsallis entropy into the classic Mean–Variance framework to enhance portfolio diversification and risk management. Entropy, specifically second-order entropy, penalizes excessive concentration in the portfolio, encouraging a more balanced and diversified allocation of assets. The model is applied to a portfolio of five major cryptocurrencies: Bitcoin (BTC), Ethereum (ETH), Solana (SOL), Cardano (ADA), and Binance Coin (BNB). The performance of the MVE model is compared with that of the traditional Mean–Variance model, and results demonstrate that the entropy-enhanced model provides better diversification, although with a slightly lower Sharpe ratio. The findings suggest that while the entropy-adjusted model results in a slightly lower Sharpe ratio, it offers better diversification and a more resilient portfolio, especially in volatile markets. This study demonstrates the potential of incorporating entropy into portfolio optimization as a means to mitigate concentration risk and improve portfolio performance. The approach is particularly beneficial for markets such as cryptocurrency, where volatility and asset correlations fluctuate rapidly. This paper contributes to the growing body of literature on portfolio optimization by offering a more diversified, robust, and risk-adjusted approach to asset allocation

Keywords: portfolio optimization; entropy-based models; risk diversification; cryptocurrency investment; robust asset allocation; mean–variance framework (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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