IDEAS home Printed from https://ideas.repec.org/a/spr/futbus/v11y2025i1d10.1186_s43093-025-00551-5.html
   My bibliography  Save this article

The risk–return trade-off of Bitcoin: Evidence from regime-switching analysis

Author

Listed:
  • Chikashi Tsuji

    (Chuo University)

Abstract

Despite its importance, there has been little research on the relationship between Bitcoin’s risk and returns. Therefore, it is necessary to investigate the risk–return trade-off of Bitcoin. In the existing limited literature, a negative risk–return relationship in Bitcoin for high-frequency intraday time-series data has been reported. In this paper, we use lower time–frequency data and suitable models for the data frequency to examine the risk–return trade-off of Bitcoin. Specifically, this paper examines the time-series volatility risk–return trade-off of Bitcoin using standard Markov switching (MS) and MS–GARCH models with weekly Bitcoin data from 2010 to 2024. Consequently, the study reveals several new findings. Firstly, the volatility risk–return trade-off relationship is identified for Bitcoin’s log returns. Secondly, the risk–return trade-off is also found for Bitcoin’s simple returns. Thirdly, the risk–return trade-off is uncovered for Bitcoin’s risk premiums as well. Fourthly, the study shows that the risk–return trade-off relationships for Bitcoin’s log returns, simple returns, and risk premiums hold true for all business days from Monday to Friday, indicating the robustness of the results. Furthermore, the study presents significant interpretations, implications, and discussion. We emphasize that we have discovered positive weekly risk–return relationships for Bitcoin using Markov switching models for the first time. This demonstrates the novelty of our work.

Suggested Citation

  • Chikashi Tsuji, 2025. "The risk–return trade-off of Bitcoin: Evidence from regime-switching analysis," Future Business Journal, Springer, vol. 11(1), pages 1-25, December.
    • Handle: RePEc:spr:futbus:v:11:y:2025:i:1:d:10.1186_s43093-025-00551-5
    DOI: 10.1186/s43093-025-00551-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1186/s43093-025-00551-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1186/s43093-025-00551-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Turner, Christopher M. & Startz, Richard & Nelson, Charles R., 1989. "A Markov model of heteroskedasticity, risk, and learning in the stock market," Journal of Financial Economics, Elsevier, vol. 25(1), pages 3-22, November.
    2. Campbell, John Y. & Hentschel, Ludger, 1992. "No news is good news *1: An asymmetric model of changing volatility in stock returns," Journal of Financial Economics, Elsevier, vol. 31(3), pages 281-318, June.
    3. Tsuji, Chikashi, 2020. "Correlation and spillover effects between the US and international banking sectors: New evidence and implications for risk management," International Review of Financial Analysis, Elsevier, vol. 70(C).
    4. Yaya, OlaOluwa S. & Lukman, Adewale F. & Vo, Xuan Vinh, 2022. "Persistence and volatility spillovers of bitcoin price to gold and silver prices," Resources Policy, Elsevier, vol. 79(C).
    5. Syed Jawad Hussain Shahzad & Elie Bouri & Mobeen Ur Rehman & David Roubaud, 2022. "The hedge asset for BRICS stock markets: Bitcoin, gold or VIX," The World Economy, Wiley Blackwell, vol. 45(1), pages 292-316, January.
    6. Baillie, Richard T. & DeGennaro, Ramon P., 1990. "Stock Returns and Volatility," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(2), pages 203-214, June.
    7. Wang, Jianxin & Yang, Minxian, 2013. "On the risk return relationship," Journal of Empirical Finance, Elsevier, vol. 21(C), pages 132-141.
    8. Jia, Boxiang & Shen, Dehua & Zhang, Wei, 2024. "Bitcoin market reactions to large price swings of international stock markets," International Review of Economics & Finance, Elsevier, vol. 90(C), pages 72-88.
    9. Farman Ullah Khan & Faridoon Khan & Parvez Ahmed Shaikh, 2023. "Forecasting returns volatility of cryptocurrency by applying various deep learning algorithms," Future Business Journal, Springer, vol. 9(1), pages 1-11, December.
    10. Jiang, Shangrong & Li, Yuze & Lu, Quanying & Wang, Shouyang & Wei, Yunjie, 2022. "Volatility communicator or receiver? Investigating volatility spillover mechanisms among Bitcoin and other financial markets," Research in International Business and Finance, Elsevier, vol. 59(C).
    11. Chaim, Pedro & Laurini, Márcio P., 2018. "Volatility and return jumps in bitcoin," Economics Letters, Elsevier, vol. 173(C), pages 158-163.
    12. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    13. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    14. Raza, Syed Ali & Khan, Komal Akram & Guesmi, Khaled & Benkraiem, Ramzi, 2023. "Uncertainty in the financial regulation policy and the boom of cryptocurrencies," Finance Research Letters, Elsevier, vol. 52(C).
    15. Ghysels, Eric & Santa-Clara, Pedro & Valkanov, Rossen, 2005. "There is a risk-return trade-off after all," Journal of Financial Economics, Elsevier, vol. 76(3), pages 509-548, June.
    16. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-131, February.
    17. Liu, Xiaochun, 2017. "Unfolded risk-return trade-offs and links to Macroeconomic Dynamics," Journal of Banking & Finance, Elsevier, vol. 82(C), pages 1-19.
    18. Bouri, Elie & Azzi, Georges & Dyhrberg, Anne Haubo, 2017. "On the return-volatility relationship in the Bitcoin market around the price crash of 2013," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 11, pages 1-16.
    19. Urquhart, Andrew, 2016. "The inefficiency of Bitcoin," Economics Letters, Elsevier, vol. 148(C), pages 80-82.
    20. Conrad, Jennifer & Kaul, Gautam, 1988. "Time-Variation in Expected Returns," The Journal of Business, University of Chicago Press, vol. 61(4), pages 409-425, October.
    21. Ahmed, Walid M.A., 2020. "Is there a risk-return trade-off in cryptocurrency markets? The case of Bitcoin," Journal of Economics and Business, Elsevier, vol. 108(C).
    22. Ravi Bansal & Hao Zhou, 2002. "Term Structure of Interest Rates with Regime Shifts," Journal of Finance, American Finance Association, vol. 57(5), pages 1997-2043, October.
    23. Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70.
    24. Andrew W. Lo, A. Craig MacKinlay, 1988. "Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification Test," The Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 41-66.
    25. Köchling, Gerrit & Schmidtke, Philipp & Posch, Peter N., 2020. "Volatility forecasting accuracy for Bitcoin," Economics Letters, Elsevier, vol. 191(C).
    26. Bouri, Elie & Molnár, Peter & Azzi, Georges & Roubaud, David & Hagfors, Lars Ivar, 2017. "On the hedge and safe haven properties of Bitcoin: Is it really more than a diversifier?," Finance Research Letters, Elsevier, vol. 20(C), pages 192-198.
    27. Han, SeungOh, 2024. "Nonlinear relationship between cryptocurrency returns and price sensitivity to market uncertainty," Finance Research Letters, Elsevier, vol. 68(C).
    28. Hachmi Ben Ameur & Zied Ftiti & Waël Louhichi, 2024. "Interconnectedness of cryptocurrency markets: an intraday analysis of volatility spillovers based on realized volatility decomposition," Annals of Operations Research, Springer, vol. 341(2), pages 757-779, October.
    29. Bajra, Ujkan Q. & Aliu, Florin, 2023. "Deciphering the cryptocurrency conundrum: Investigating speculative characteristics and volatility," Finance Research Letters, Elsevier, vol. 58(PC).
    30. Nick Taylor, 2023. "The Determinants of Volatility Timing Performance," Journal of Financial Econometrics, Oxford University Press, vol. 21(4), pages 1228-1257.
    31. Yu, Miao, 2019. "Forecasting Bitcoin volatility: The role of leverage effect and uncertainty," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 533(C).
    32. McQueen, Grant & Thorley, Steven, 1991. "Are Stock Returns Predictable? A Test Using Markov Chains," Journal of Finance, American Finance Association, vol. 46(1), pages 239-263, March.
    33. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    34. Almeida, José & Gonçalves, Tiago Cruz, 2023. "A systematic literature review of investor behavior in the cryptocurrency markets," Journal of Behavioral and Experimental Finance, Elsevier, vol. 37(C).
    35. Salvador, Enrique & Floros, Christos & Arago, Vicent, 2014. "Re-examining the risk–return relationship in Europe: Linear or non-linear trade-off?," Journal of Empirical Finance, Elsevier, vol. 28(C), pages 60-77.
    36. Hedegaard, Esben & Hodrick, Robert J., 2016. "Estimating the risk-return trade-off with overlapping data inference," Journal of Banking & Finance, Elsevier, vol. 67(C), pages 135-145.
    37. Chou, Ray Yeutien, 1988. "Volatility Persistence and Stock Valuations: Some Empirical Evidence Using Garch," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 3(4), pages 279-294, October-D.
    38. Kumar, Anoop S. & Anandarao, S., 2019. "Volatility spillover in crypto-currency markets: Some evidences from GARCH and wavelet analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 448-458.
    39. Khalfaoui, Rabeh & Gozgor, Giray & Goodell, John W., 2023. "Impact of Russia-Ukraine war attention on cryptocurrency: Evidence from quantile dependence analysis," Finance Research Letters, Elsevier, vol. 52(C).
    40. French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, vol. 19(1), pages 3-29, September.
    41. Dastgir, Shabbir & Demir, Ender & Downing, Gareth & Gozgor, Giray & Lau, Chi Keung Marco, 2019. "The causal relationship between Bitcoin attention and Bitcoin returns: Evidence from the Copula-based Granger causality test," Finance Research Letters, Elsevier, vol. 28(C), pages 160-164.
    42. Corbet, Shaen & Lucey, Brian & Urquhart, Andrew & Yarovaya, Larisa, 2019. "Cryptocurrencies as a financial asset: A systematic analysis," International Review of Financial Analysis, Elsevier, vol. 62(C), pages 182-199.
    43. Bansal, Ravi & Lundblad, Christian, 2002. "Market efficiency, asset returns, and the size of the risk premium in global equity markets," Journal of Econometrics, Elsevier, vol. 109(2), pages 195-237, August.
    44. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
    45. Mensi, Walid & Al-Yahyaee, Khamis Hamed & Kang, Sang Hoon, 2019. "Structural breaks and double long memory of cryptocurrency prices: A comparative analysis from Bitcoin and Ethereum," Finance Research Letters, Elsevier, vol. 29(C), pages 222-230.
    46. Roberto C. Gutierrez & Eric K. Kelley, 2008. "The Long‐Lasting Momentum in Weekly Returns," Journal of Finance, American Finance Association, vol. 63(1), pages 415-447, February.
    47. Filipova, Kameliya & Audrino, Francesco & De Giorgi, Enrico, 2014. "Monetary policy regimes: Implications for the yield curve and bond pricing," Journal of Financial Economics, Elsevier, vol. 113(3), pages 427-454.
    48. Dirk G. Baur & Thomas Dimpfl, 2021. "The volatility of Bitcoin and its role as a medium of exchange and a store of value," Empirical Economics, Springer, vol. 61(5), pages 2663-2683, November.
    49. Wang, Zijun & Khan, M. Moosa, 2017. "Market states and the risk-return tradeoff," The Quarterly Review of Economics and Finance, Elsevier, vol. 65(C), pages 314-327.
    50. Cai, Jun, 1994. "A Markov Model of Switching-Regime ARCH," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 309-316, July.
    51. Katsiampa, Paraskevi & Corbet, Shaen & Lucey, Brian, 2019. "Volatility spillover effects in leading cryptocurrencies: A BEKK-MGARCH analysis," Finance Research Letters, Elsevier, vol. 29(C), pages 68-74.
    52. Hamilton, James D. & Susmel, Raul, 1994. "Autoregressive conditional heteroskedasticity and changes in regime," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 307-333.
    53. Shahzad, Syed Jawad Hussain & Bouri, Elie & Roubaud, David & Kristoufek, Ladislav & Lucey, Brian, 2019. "Is Bitcoin a better safe-haven investment than gold and commodities?," International Review of Financial Analysis, Elsevier, vol. 63(C), pages 322-330.
    54. Gozgor, Giray & Tiwari, Aviral Kumar & Demir, Ender & Akron, Sagi, 2019. "The relationship between Bitcoin returns and trade policy uncertainty," Finance Research Letters, Elsevier, vol. 29(C), pages 75-82.
    55. Lundblad, Christian, 2007. "The risk return tradeoff in the long run: 1836-2003," Journal of Financial Economics, Elsevier, vol. 85(1), pages 123-150, July.
    56. repec:bla:jfinan:v:44:y:1989:i:1:p:1-17 is not listed on IDEAS
    57. Jiqian Wang & Feng Ma & Elie Bouri & Yangli Guo, 2023. "Which factors drive Bitcoin volatility: Macroeconomic, technical, or both?," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 42(4), pages 970-988, 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. Liu, Jingzhen, 2019. "Impacts of lagged returns on the risk-return relationship of Chinese aggregate stock market: Evidence from different data frequencies," Research in International Business and Finance, Elsevier, vol. 48(C), pages 243-257.
    2. Barroso, Pedro & Maio, Paulo, 2024. "The risk–return tradeoff among equity factors," Journal of Empirical Finance, Elsevier, vol. 78(C).
    3. Tsuji, Chikashi, 2020. "Correlation and spillover effects between the US and international banking sectors: New evidence and implications for risk management," International Review of Financial Analysis, Elsevier, vol. 70(C).
    4. Yao, Jing & Yang, Yiwen, 2023. "Risk-return tradeoff and serial correlation in the Chinese stock market: A bailout-driven crash feedback hypothesis," Economic Modelling, Elsevier, vol. 129(C).
    5. Farooq Malik, 2015. "Revisiting the relationship between risk and return," Review of Quantitative Finance and Accounting, Springer, vol. 44(1), pages 25-40, January.
    6. Turan Bali & Kamil Yilmaz, 2009. "The Intertemporal Relation between Expected Return and Risk on Currency," Koç University-TUSIAD Economic Research Forum Working Papers 0909, Koc University-TUSIAD Economic Research Forum, revised Nov 2009.
    7. Dimitrios Koutmos, 2015. "Is there a Positive Risk†Return Tradeoff? A Forward†Looking Approach to Measuring the Equity Premium," European Financial Management, European Financial Management Association, vol. 21(5), pages 974-1013, November.
    8. Chang, Kuang-Liang, 2016. "Does the return-state-varying relationship between risk and return matter in modeling the time series process of stock return?," International Review of Economics & Finance, Elsevier, vol. 42(C), pages 72-87.
    9. Bali, Turan G., 2008. "The intertemporal relation between expected returns and risk," Journal of Financial Economics, Elsevier, vol. 87(1), pages 101-131, January.
    10. Lundblad, Christian, 2007. "The risk return tradeoff in the long run: 1836-2003," Journal of Financial Economics, Elsevier, vol. 85(1), pages 123-150, July.
    11. Keunbae Ahn, 2021. "Predictable Fluctuations in the Cross-Section and Time-Series of Asset Prices," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2021, January-A.
    12. Hatemi-J, Abdulnasser & Irandoust, Manuchehr, 2011. "The dynamic interaction between volatility and returns in the US stock market using leveraged bootstrap simulations," Research in International Business and Finance, Elsevier, vol. 25(3), pages 329-334, September.
    13. Thomas C. Chiang & Jiandong Li, 2012. "Stock Returns and Risk: Evidence from Quantile," JRFM, MDPI, vol. 5(1), pages 1-39, December.
    14. Ahmed, Walid M.A., 2020. "Is there a risk-return trade-off in cryptocurrency markets? The case of Bitcoin," Journal of Economics and Business, Elsevier, vol. 108(C).
    15. Cathy Yi†Hsuan Chen & Thomas C. Chiang, 2016. "Empirical Analysis of the Intertemporal Relationship between Downside Risk and Expected Returns: Evidence from Time†varying Transition Probability Models," European Financial Management, European Financial Management Association, vol. 22(5), pages 749-796, November.
    16. Wang, Wenzhao, 2018. "Investor sentiment and the mean-variance relationship: European evidence," Research in International Business and Finance, Elsevier, vol. 46(C), pages 227-239.
    17. Andrew Harvey & Rutger-Jan Lange, 2015. "Modeling the Interactions between Volatility and Returns," Cambridge Working Papers in Economics 1518, Faculty of Economics, University of Cambridge.
    18. Cenesizoglu, Tolga, 2022. "Return decomposition over the business cycle," Journal of Banking & Finance, Elsevier, vol. 143(C).
    19. Nikolaos A. Kyriazis, 2021. "A Survey on Volatility Fluctuations in the Decentralized Cryptocurrency Financial Assets," JRFM, MDPI, vol. 14(7), pages 1-46, June.
    20. Peter F. Christoffersen & Francis X. Diebold, 2006. "Financial Asset Returns, Direction-of-Change Forecasting, and Volatility Dynamics," Management Science, INFORMS, vol. 52(8), pages 1273-1287, August.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:spr:futbus:v:11:y:2025:i:1:d:10.1186_s43093-025-00551-5. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.