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Cryptocurrencies on the Balance Sheet: Insights from Strategy—Bitcoin Interactions

  • Sabrina Aufiero 1,*,   
  • Antonio Briola 1,   
  • Tesfaye Salarin 2,   
  • Silvia Bartolucci 1,   
  • Fabio Caccioli 1,3,   
  • Tomaso Aste 1

Received: 30 Sep 2025 | Revised: 18 Jun 2026 | Accepted: 03 Jul 2026 | Published: 27 Jul 2026

Abstract

This paper investigates the evolving link between cryptocurrency and equity markets in the context of the recent wave of corporate Bitcoin (BTC) treasury strategies. We assemble a dataset of 39 publicly listed firms holding BTC, from their first acquisition through April 2025. Using daily logarithmic returns, we first document significant positive co-movements via Pearson correlations and single factor model regressions, discovering an average BTC beta of 0.62, and isolating 12 companies, including Strategy (formerly MicroStrategy, MSTR), exhibiting a beta exceeding 1. We then classify firms into three groups reflecting their exposure to BTC, liquidity, and return co-movements. We use transfer entropy (TE) to capture the direction of information flow over time. Transfer entropy analysis consistently identifies BTC as the dominant information driver, with brief, announcement-driven feedback from stocks to BTC during major financial events. Our results highlight the critical need for dynamic hedging ratios that adapt to shifting information flows. These findings provide important insights for investors and managers regarding risk management and portfolio diversification in a period of growing integration of digital assets into corporate treasuries.

References 

  • 1.

    Ray, K. Bitcoin’s 2024 Performance as An Asset Class. Forbes 2025. Available online: https:// www.forbes.com/sites/digitalassets/2025/02/21/bitcoins-2024-performance-as-an-asset-class/ (accessed on 17 June 2026).

  • 2.

    Meynkhard, A. Fair market value of bitcoin: Halving effect. Invest. Manag. Financ. Innov. 2019, 16, 72.

  • 3.

    M’bakob, G.B. Bubbles in Bitcoin and Ethereum: The role of halving in the formation of super cycles. Sustain. Futur. 2024, 7, 100178.

  • 4.

    Fabus, J.; Kremenova, I.; Stalmasekova, N.; et al. An empirical examination of Bitcoin’s halving effects: Assessing cryptocurrency sustainability within the landscape of financial technologies. J. Risk Financ. Manag. 2024, 17, 229.

  • 5.

    Reuters. Global crypto market tops 3 trillion on hopes of Trump-fuelled boom. 2024. Available online: https://www.reuters.com/technology/crypto-market-capitalisation-hits-record-32-trillion-coingecko-says-2024-11-14/ (accessed on 17 June 2026).

  • 6.

    CoinDesk. TradFi Investors Piled $38.7B Into Bitcoin ETFs, Three Times More Than Previous Quarter, 2025. Available online: https://www.coindesk.com/markets/2025/02/19/tradfi-investors-piled-usd38-7b-into-bitcoin-etfs-three-times-morethan-previous-quarter (accessed on 17 June 2026).

  • 7.

    Lipschultz, B.; Menton, J.; Dey, E. ‘This Is Madness’: The 15 Minutes That Rocked Stock Markets. Bloomberg 2025. Available online: https://www.bloomberg.com/news/articles/2025-04-07/-this-is-madness-the-15-minutes-that-rocked-stockmarket-desks (accessed on 17 June 2026).

  • 8.

    Torres, M.P.M. Bitcoin’s CorrelationWith Tech Stocks Jumps to Highest Level Since August. Bloomberg 2024. Available online: https://www.bloomberg.com/news/articles/2024-05-17/bitcoin-s-correlation-with-tech-stocks-jumps-to-highest-levelsince-august?utm_medium=cpc_search&utm_campaign=NB_ENG_DSAXX_DSAXXXXXXXXXX_EVG_XXXX_XXX_Y0629_EN_EN_X_BLOM_GO_SE_XXX_XXXXXXXXXX&gclsrc=aw.ds&gad_source=1&gad_campaignid=21359970428&gbraid=0AAAAAD9e5yrir2xdil_gQkOszfU8J_kid&gclid=Cj0KCQjw39zSBhDhARIsANammDtT-YAupeALxM1Xm02pm_ywQvsKI89xLMt6MqLIVc2ZTRmjH2ANHqIaAn0nEALw_wcB (accessed on 17 June 2026).

  • 9.

    Watorek, M.; Kwapien, J.; Drozdz, S. Cryptocurrencies are becoming part of the world global financial market. Entropy 2023, 25, 377.

  • 10.

    Phillips, P.J.; Pohl, G. MicroStrategy, Bitcoin Yield, Complete Markets. SSRN 2024, http://dx.doi.org/10.2139/ssrn.5038109.

  • 11.

    Hyatt, J. The Richest Crypto and Bitcoin Billionaires in the World 2024. 2024. Available online: https://www.forbes.com/sites/johnhyatt/2024/04/02/the-richest-crypto-and-bitcoin-billionaires-in-the-world-2024/ (accessed on 17 June 2026).

  • 12.

    Pan, D.; Lipschultz, B. Michael Saylor’s Big Bet on Bitcoin Is Inspiring Copycat CEOs. Bloomberg 2025. Available online: https://www.bloomberg.com/news/articles/2025-02-19/michael-saylor-s-big-bet-on-bitcoin-is-inspiring-copycatceos (accessed on 17 June 2026).

  • 13.

    French, A. Bitcoin Hoarder’s Stock Soars 4800% in Japan After Crypto Rally. Bloomberg 2025. Available online: https://www.bloomberg.com/news/articles/2025-02-10/bitcoin-btc-hoarder-s-stock-soars-4-000-in-japan-after-crypto-rally (accessed
    on 17 June 2026).

  • 14.

    Bitcoin Treasuries. Bitcoin Treasuries—Current Crypto Assets Held by Institutions. 2025. Available online: https://bitcointreasuries.net (accessed on 17 June 2026).

  • 15.

    Investing.com News. FLD Stock Touches 52-Week Low at $3.65 Amid Market Challenges. Investing.com 2025. Available online: https://www.investing.com/news/company-news/fld-stock-touches-52week-low-at-365-amid-market-challenges-93CH-3981592 (accessed on 17 June 2026).

  • 16.

    Ghosh, S. A 325% Stock Surge Greets a Tiny Company’s Strategy to Buy Solana. Bloomberg 2025. Available online: https://www.bloomberg.com/news/newsletters/2025-04-22/a-325-stock-surge-greets-a-tiny-company-s-strategy-to-buysolana (accessed on 17 June 2026).

  • 17.

    Mantegna, R.N. Hierarchical structure in financial markets. Eur. Phys. J.-Condens. Matter Complex Syst. 1999, 11, 193–197.

  • 18.

    Onnela, J.P.; Chakraborti, A.; Kaski, K.; et al. Dynamics of market correlations: Taxonomy and portfolio analysis. Phys. Rev. E 2003, 68, 056110.

  • 19.

    Kullmann, L.; Kertész, J.; Kaski, K. Time-dependent cross-correlations between different stock returns: A directed network of influence. Phys. Rev. E 2002, 66, 026125.

  • 20.

    Plerou, V.; Gopikrishnan, P.; Rosenow, B.; et al. Universal and nonuniversal properties of cross correlations in financial time series. Phys. Rev. Lett. 1999, 83, 1471.

  • 21.

    Jung, W.S.; Chae, S.; Yang, J.S.; et al. Characteristics of the Korean stock market correlations. Phys. A Stat. Mech. Its Appl. 2006, 361, 263–271.

  • 22.

    Briola, A.; Vidal-Tomás, D.; Wang, Y.; et al. Anatomy of a Stablecoin’s failure: The Terra-Luna case. Financ. Res. Lett. 2023, 51, 103358.

  • 23.

    Vidal-Tomás, D.; Briola, A.; Aste, T. FTX’s downfall and Binance’s consolidation: The fragility of centralised digital finance. Phys. A Stat. Mech. Its Appl. 2023, 625, 129044.

  • 24.

    Briola, A.; Aste, T. Dependency structures in cryptocurrency market from high to low frequency. Entropy 2022, 24, 1548.

  • 25.

    Briola, A. Deep Complex Networks: Applications in Financial Systems Modeling. Ph.D. Thesis, University College London, London, UK, 2024.

  • 26.

    Shannon, C.E. A mathematical theory of communication. Bell Syst. Tech. J. 1948, 27, 379–423.

  • 27.

    Bossomaier, T.; Barnett, L.; Harré, M.; et al. Transfer Entropy. In An Introduction to Transfer Entropy; Springer: Berlin/Heidelberg, Germany, 2016.

  • 28.

    Aste, T. Probabilistic Data-Driven Modeling; Cambridge University Press: Cambridge, UK, 2025.

  • 29.

    Granger, C.W. Investigating causal relations by econometric models and cross-spectral methods. Econometrica 1969, 37, 424–438.

  • 30.

    Bressler, S.L.; Seth, A.K. Wiener–Granger causality: A well established methodology. Neuroimage 2011, 58, 323–329.

  • 31.

    Lin, H.; Ren, M.; Barucca, P.; et al. Granger Causality Detection with Kolmogorov-Arnold Networks. arXiv 2024, arXiv:2412.15373.

  • 32.

    Schreiber, T. Measuring information transfer. Phys. Rev. Lett. 2000, 85, 461.

  • 33.

    Marschinski, R.; Kantz, H. Analysing the information flow between financial time series: An improved estimator for transfer entropy. Eur. Phys. J.-Condens. Matter Complex Syst. 2002, 30, 275–281.

  • 34.

    Baek, S.K.; Jung, W.S.; Kwon, O.; et al. Transfer entropy analysis of the stock market. arXiv 2005, arXiv:physics/0509014.

  • 35.

    Dimpfl, T.; Peter, F.J. Using transfer entropy to measure information flows between financial markets. Stud. Nonlinear Dyn.
    Econom. 2013, 17, 85–102.

  • 36.

    Sandoval Jr., L. Structure of a global network of financial companies based on transfer entropy. Entropy 2014, 16, 4443–4482.

  • 37.

    He, J.; Shang, P. Comparison of transfer entropy methods for financial time series. Phys. A Stat. Mech. Its Appl. 2017, 482, 772–785.

  • 38.

    Dimpfl, T.; Peter, F.J. Group transfer entropy with an application to cryptocurrencies. Phys. A Stat. Mech. Its Appl. 2019, 516, 543–551.

  • 39.

    Peng, S.; Han, W.; Jia, G. Pearson correlation and transfer entropy in the Chinese stock market with time delay. Data Sci. Manag. 2022, 5, 117–123.

  • 40.

    Neto, J.d.P.N.; Figueiredo, D.R. Ranking influential and influenced stocks over time using transfer entropy networks. Phys. A Stat. Mech. Its Appl. 2023, 630, 129119.

  • 41.

    Mungo, L.; Bartolucci, S.; Alessandretti, L. Cryptocurrency co-investment network: token returns reflect investment patterns. EPJ Data Sci. 2024, 13, 11.

  • 42.

    Ma, H. Volatility dynamics analysis of Bitcoin (BTC-USD) and MicroStrategy (MSTR). In Proceedings of ICFTBA 2024 Workshop: Human Capital Management in a Post-Covid World: Emerging Trends and Workplace Strategies; EWA Publishing: Oxford, UK, 2025. https://doi.org/10.54254/2754-1169/2024.ld19045.

  • 43.

    Bollerslev, T. Generalized autoregressive conditional heteroskedasticity. J. Econom. 1986, 31, 307–327.

  • 44.

    Krause, D. Ponzi or Pioneer? Evaluating the Viability of MicroStrategy’s Bitcoin-Focused Model. SSRN 2025. http://dx.doi.org/10.2139/ssrn.5079326.

  • 45.

    Newey, W.K.; West, K.D. Automatic lag selection in covariance matrix estimation. Rev. Econ. Stud. 1994, 61, 631–653.

  • 46.

    BBC News. Bitcoin price falls below $6000 as sell-off continues. BBC News 2018. Available online: https://www.bbc.com/news/technology-42958325 (accessed on 17 June 2026).

  • 47.

    Partington, R. Bitcoin Price Hits All-Time High of More Than $20,000. The Guardian 2020. Available online: https://www.theguardian.com/technology/2020/dec/16/bitcoin-price-hits-all-time-high-of-more-than-20000 (accessed on 17 June 2026).

  • 48.

    He, J. Brutal Month for Bitcoin as June Ends With Biggest Drop in 11 Years. CoinDesk 2022. Available online: https://www.coindesk.com/markets/2022/07/01/brutal-month-for-bitcoin-as-june-ends-with-biggest-drop-in-11-years (accessed on 17 June 2026).

  • 49.

    Yerushalmy, J. The SEC has approved bitcoin ETFs. What are they and what does it mean for investors? The Guardian 2024. Available online: https://www.theguardian.com/technology/2024/jan/11/bitcoin-etf-approved-sec-explained-meaningsecurities-regulator-tweet (accessed on 17 June 2026).

  • 50.

    Ray, S. Bitcoin Surges Past $100,000 for the First Time. Forbes 2024. Available online: https://www.forbes.com/sites/siladityaray/2024/12/04/bitcoin-surges-past-100000-for-the-first-time/ (accessed on 17 June 2026).

  • 51.

    The White House. Establishment of the Strategic Bitcoin Reserve and United States Digital Asset Stockpile. 2025. Available online: https://www.whitehouse.gov/presidential-actions/2025/03/establishment-of-the-strategic-bitcoin-reserve-and-unitedstates-digital-asset-stockpile/ (accessed on 17 June 2026).

  • 52.

    Choueifaty, Y.; Froidure, T.; Cabrol, A. Accounting for the performance of Microstrategy First decomposition. SSRN 2025, http://dx.doi.org/10.2139/ssrn.5172347.

  • 53.

    MicroStrategy Incorporated. Form 8-K: Current Report Pursuant to Section 13 or 15(d) of the Securities Exchange Act of 1934. 2025. https://www.sec.gov/Archives/edgar/data/1050446/000119312525310607/mstr-20251117.html (accessed on 17 June 2026).

  • 54.

    Behrendt, S.; Dimpfl, T.; Peter, F.J.; et al. RTransferEntropy—Quantifying information flow between different time series using effective transfer entropy. SoftwareX 2019, 10, 100265. https://doi.org/10.1016/j.softx.2019.100265.

  • 55.

    Fama, E.F.; French, K.R. Common risk factors in the returns on stocks and bonds. J. Financ. Econ. 1993, 33, 3–56.

  • 56.

    Amihud, Y. Illiquidity and stock returns: Cross-section and time-series effects. J. Financ. Mark. 2002, 5, 31–56.

  • 57.

     Coinbase. What is a Bitcoin Futures ETF? 2021. Available online: https://www.coinbase.com/en-gb/learn/crypto-basics/whatis-a-bitcoin-futures-etf (accessed on 17 June 2026).

  • 58.

    Miller, R. MicroStrategy’s Software Business Turns Profitable As Bitcoin Stash Appreciates. Forbes 2023. Available online: https://www.forbes.com/sites/rosemariemiller/2023/02/02/microstrategys-software-business-turns-profitable-asbitcoin-stash-appreciates/ (accessed on 17 June 2026).

  • 59.

    Saylor, M. Interview—Michael Saylor, President of MicroStrategy: We Buy as Many Bitcoins as Possible. MarketScreener 2023. https://uk.marketscreener.com/quote/stock/STRATEGY-INC-10105/news/INTERVIEW-Michael-Saylor-Presidentof-MicroStrategy-We-buy-as-many-bitcoins-as-possible-44499915/ (accessed on 17 June 2026).

  • 60.

    Van Straten, J.; Braun, H. Strategy Raising Another $21B to Buy Bitcoin, Posts Large Q1 Loss on BTC Price Decline. CoinDesk 2025. Available online: https://www.coindesk.com/markets/2025/05/01/strategy-raising-another-21b-to-buybitcoin-posts-large-q1-loss-on-btc-price-decline (accessed on 17 June 2026).

  • 61.

    MacKinlay, A.C. Event studies in economics and finance. J. Econ. Lit. 1997, 35, 13–39.

  • 62.

    Politis, D.N.; Romano, J.P. The stationary bootstrap. J. Am. Stat. Assoc. 1994, 89, 1303–1313.

  • 63.

    Briola, A.; Bartolucci, S.; Aste, T. HLOB–Information persistence and structure in limit order books. Expert Syst. Appl. 2025, 266, 126078.

  • 64.

    Wang, Y.; Briola, A.; Aste, T. Topological portfolio selection and optimization. In Proceedings of the Fourth ACM International Conference on AI in Finance, Brooklyn, NY, USA, 27–29 November 2023; pp. 681–688.

  • 65.

    Wang, Y.; Briola, A.; Aste, T. Homological neural networks: A sparse architecture for multivariate complexity. In Proceedings of 2nd Annual Workshop on Topology, Algebra, and Geometry in Machine Learning (TAG-ML), Honolulu, HI, USA, 28 July 2023; pp. 228–241.

  • 66.

    Briola, A.; Wang, Y.; Bartolucci, S.; et al. Homological convolutional neural networks. arXiv 2023, arXiv:2308.13816.

  • 67.

    Wang, Y.; Aste, T. Network filtering of spatial-temporal GNN for multivariate time-series prediction. In Proceedings of the Third ACM International Conference on AI in Finance, New York, NY, USA, 2–4 November 2022; pp. 463–470.

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Aufiero, S.; Briola, A.; Salarin, T.; Bartolucci, S.; Caccioli, F.; Aste, T. Cryptocurrencies on the Balance Sheet: Insights from Strategy—Bitcoin Interactions. Journal of Social Physics 2026. https://doi.org/10.53941/jsp.2026.100008.
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