IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i10p1693-d1661283.html
   My bibliography  Save this article

Mean–Variance–Entropy Framework for Cryptocurrency Portfolio Optimization

Author

Listed:
  • 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)

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

Suggested Citation

  • Florentin Șerban & Bogdan-Petru Vrînceanu, 2025. "Mean–Variance–Entropy Framework for Cryptocurrency Portfolio Optimization," Mathematics, MDPI, vol. 13(10), pages 1-10, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:10:p:1693-:d:1661283
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/10/1693/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/10/1693/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
    2. Fama, Eugene F & French, Kenneth R, 1992. "The Cross-Section of Expected Stock Returns," Journal of Finance, American Finance Association, vol. 47(2), pages 427-465, June.
    3. Black, Fischer, 1972. "Capital Market Equilibrium with Restricted Borrowing," The Journal of Business, University of Chicago Press, vol. 45(3), pages 444-455, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sudi Sudarsanam & Ashraf A. Mahate, 2003. "Glamour Acquirers, Method of Payment and Post‐acquisition Performance: The UK Evidence," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 30(1‐2), pages 299-342, January.
    2. Dimitri Vayanos & Paul Woolley, 2023. "Asset Management as Creator of Market Inefficiency," Atlantic Economic Journal, Springer;International Atlantic Economic Society, vol. 51(1), pages 1-11, March.
    3. Shiyang Huang & Xin Liu & Dong Lou & Christopher Polk, 2024. "The Booms and Busts of Beta Arbitrage," Management Science, INFORMS, vol. 70(8), pages 5367-5385, August.
    4. Stefan Nagel, 2013. "Empirical Cross-Sectional Asset Pricing," Annual Review of Financial Economics, Annual Reviews, vol. 5(1), pages 167-199, November.
    5. Fernando Rubio, 2005. "Estrategias Cuantitativas De Valor Y Retornos Por Accion De Largo," Finance 0503029, University Library of Munich, Germany.
    6. Attiya Yasmeen Javid, 2000. "Alternative Capital Asset Pricing Models: A Review of Theory and Evidence," PIDE Research Report 2000:3, Pakistan Institute of Development Economics.
    7. Frankfurter, George M. & McGoun, Elton G., 2002. "Resistance is futile: the assimilation of behavioral finance," Journal of Economic Behavior & Organization, Elsevier, vol. 48(4), pages 375-389, August.
    8. Amit Goyal, 2012. "Empirical cross-sectional asset pricing: a survey," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 26(1), pages 3-38, March.
    9. Eugene F. Fama & Kenneth R. French, 2004. "The Capital Asset Pricing Model: Theory and Evidence," Journal of Economic Perspectives, American Economic Association, vol. 18(3), pages 25-46, Summer.
    10. Rolf Bühner, 1998. "Unternehmensspaltung — Motive und Aktienmarktreaktionen," Schmalenbach Journal of Business Research, Springer, vol. 50(9), pages 809-840, September.
    11. Philip Gharghori & Ronald Lee & Madhu Veeraraghavan, 2009. "Anomalies and stock returns: Australian evidence," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 49(3), pages 555-576, September.
    12. Antonio Zoratto Sanvicente & Renato Teles Delgado, 2010. "Learning Theory and Equity Valuation: an Empirical Analysis," Brazilian Review of Finance, Brazilian Society of Finance, vol. 8(2), pages 113-139.
    13. Sonntag, Dominik, 2018. "Die Theorie der fairen geometrischen Rendite [The Theory of Fair Geometric Returns]," MPRA Paper 87082, University Library of Munich, Germany.
    14. Fernando Rubio, 2005. "Eficiencia De Mercado, Administracion De Carteras De Fondos Y Behavioural Finance," Finance 0503028, University Library of Munich, Germany, revised 23 Jul 2005.
    15. Committee, Nobel Prize, 2013. "Understanding Asset Prices," Nobel Prize in Economics documents 2013-1, Nobel Prize Committee.
    16. Frankfurter, George M. & McGoun, Elton G. & Allen, Douglas E., 2004. "The prescriptive turn in behavioral finance," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 33(4), pages 449-468, September.
    17. Christopher Kantos & Dan diBartolomeo, 2020. "How the pandemic taught us to turn smart beta into real alpha," Journal of Asset Management, Palgrave Macmillan, vol. 21(7), pages 581-590, December.
    18. Asgar Ali & K. N. Badhani, 2021. "Beta-Anomaly: Evidence from the Indian Equity Market," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 28(1), pages 55-78, March.
    19. Kaserer Christoph & Hanauer Matthias X., 2017. "25 Jahre Fama-French-Modell: Erklärungsgehalt, Anomalien und praktische Implikationen," Perspektiven der Wirtschaftspolitik, De Gruyter, vol. 18(2), pages 98-116, June.
    20. Kim, Jeong-Ryeol, 2002. "The stable long-run CAPM and the cross-section of expected returns," Discussion Paper Series 1: Economic Studies 2002,05, Deutsche Bundesbank.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:13:y:2025:i:10:p:1693-:d:1661283. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.