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Tracking ‘Pure’ Systematic Risk with Realized Betas for Bitcoin and Ethereum

Author

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  • Bilel Sanhaji

    (Economics Department, Université Paris 8 (LED), 2 rue de la Liberté, 93526 Saint-Denis, France
    These authors contributed equally to this work.)

  • Julien Chevallier

    (Economics Department, Université Paris 8 (LED), 2 rue de la Liberté, 93526 Saint-Denis, France
    These authors contributed equally to this work.)

Abstract

Using the capital asset pricing model, this article critically assesses the relative importance of computing ‘realized’ betas from high-frequency returns for Bitcoin and Ethereum—the two major cryptocurrencies—against their classic counterparts using the 1-day and 5-day return-based betas. The sample includes intraday data from 15 May 2018 until 17 January 2023. The microstructure noise is present until 4 min in the BTC and ETH high-frequency data. Therefore, we opt for a conservative choice with a 60 min sampling frequency. Considering 250 trading days as a rolling-window size, we obtain rolling betas < 1 for Bitcoin and Ethereum with respect to the CRIX market index, which could enhance portfolio diversification (at the expense of maximizing returns). We flag the minimal tracking errors at the hourly and daily frequencies. The dispersion of rolling betas is higher for the weekly frequency and is concentrated towards values of β > 0.8 for BTC ( β > 0.65 for ETH). The weekly frequency is thus revealed as being less precise for capturing the ‘pure’ systematic risk for Bitcoin and Ethereum. For Ethereum in particular, the availability of high-frequency data tends to produce, on average, a more reliable inference. In the age of financial data feed immediacy, our results strongly suggest to pension fund managers, hedge fund traders, and investment bankers to include ‘realized’ versions of CAPM betas in their dashboard of indicators for portfolio risk estimation. Sensitivity analyses cover jump detection in BTC/ETH high-frequency data (up to 25%). We also include several jump-robust estimators of realized volatility, where realized quadpower volatility prevails.

Suggested Citation

  • Bilel Sanhaji & Julien Chevallier, 2023. "Tracking ‘Pure’ Systematic Risk with Realized Betas for Bitcoin and Ethereum," Econometrics, MDPI, vol. 11(3), pages 1-36, August.
    • Handle: RePEc:gam:jecnmx:v:11:y:2023:i:3:p:19-:d:1214066
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    as
    1. Z. Merrick Li & Oliver Linton, 2022. "A ReMeDI for Microstructure Noise," Econometrica, Econometric Society, vol. 90(1), pages 367-389, January.
    2. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(1), pages 122-150, February.
    3. Ole E. Barndorff-Nielsen & Neil Shephard, 2006. "Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation," Journal of Financial Econometrics, Oxford University Press, vol. 4(1), pages 1-30.
    4. Esam Mahdi & Ameena Al-Abdulla, 2022. "Impact of COVID-19 Pandemic News on the Cryptocurrency Market and Gold Returns: A Quantile-on-Quantile Regression Analysis," Econometrics, MDPI, vol. 10(2), pages 1-14, June.
    5. Mancini, Cecilia & Gobbi, Fabio, 2012. "Identifying The Brownian Covariation From The Co-Jumps Given Discrete Observations," Econometric Theory, Cambridge University Press, vol. 28(2), pages 249-273, April.
    6. Andrew J. Patton & Michela Verardo, 2012. "Does Beta Move with News? Firm-Specific Information Flows and Learning about Profitability," The Review of Financial Studies, Society for Financial Studies, vol. 25(9), pages 2789-2839.
    7. Pankaj Agrrawal & Faye W. Gilbert & Jason Harkins, 2022. "Time Dependence of CAPM Betas on the Choice of Interval Frequency and Return Timeframes: Is There an Optimum?," JRFM, MDPI, vol. 15(11), pages 1-18, November.
    8. Konstantin Häusler & Hongyu Xia, 2022. "Indices on cryptocurrencies: an evaluation," Digital Finance, Springer, vol. 4(2), pages 149-167, September.
    9. Tim Bollerslev & Jonathan H. Wright, 2001. "High-Frequency Data, Frequency Domain Inference, And Volatility Forecasting," The Review of Economics and Statistics, MIT Press, vol. 83(4), pages 596-602, November.
    10. Xin Huang & George Tauchen, 2005. "The Relative Contribution of Jumps to Total Price Variance," Journal of Financial Econometrics, Oxford University Press, vol. 3(4), pages 456-499.
    11. Andersen, Torben G. & Dobrev, Dobrislav & Schaumburg, Ernst, 2012. "Jump-robust volatility estimation using nearest neighbor truncation," Journal of Econometrics, Elsevier, vol. 169(1), pages 75-93.
    12. Seth Armitage & Janusz Brzeszczynski, 2011. "Heteroscedasticity and interval effects in estimating beta: UK evidenceÂ," CFI Discussion Papers 1103, Centre for Finance and Investment, Heriot Watt University.
    13. Jiang, George J. & Oomen, Roel C.A., 2008. "Testing for jumps when asset prices are observed with noise-a "swap variance" approach," Journal of Econometrics, Elsevier, vol. 144(2), pages 352-370, June.
    14. Baur, Dirk G. & Hoang, Lai, 2021. "The Bitcoin gold correlation puzzle," Journal of Behavioral and Experimental Finance, Elsevier, vol. 32(C).
    15. José Almeida & Tiago Cruz Gonçalves, 2022. "Portfolio Diversification, Hedge and Safe-Haven Properties in Cryptocurrency Investments and Financial Economics: A Systematic Literature Review," JRFM, MDPI, vol. 16(1), pages 1-25, December.
    16. Jia Li & Viktor Todorov & George Tauchen & Huidi Lin, 2019. "Rank Tests at Jump Events," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(2), pages 312-321, April.
    17. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    18. Engle, Robert F. & Gallo, Giampiero M., 2006. "A multiple indicators model for volatility using intra-daily data," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 3-27.
    19. Kalman J. Cohen & Gabriel A. Hawawini & Steven F. Maier & Robert A. Schwartz & David K. Whitcomb, 1983. "Estimating and Adjusting for the Intervalling-Effect Bias in Beta," Management Science, INFORMS, vol. 29(1), pages 135-148, January.
    20. Tian Xie, 2019. "Forecast Bitcoin Volatility with Least Squares Model Averaging," Econometrics, MDPI, vol. 7(3), pages 1-20, September.
    21. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Jin Wu, 2005. "A Framework for Exploring the Macroeconomic Determinants of Systematic Risk," American Economic Review, American Economic Association, vol. 95(2), pages 398-404, May.
    22. Matkovskyy, Roman & Jalan, Akanksha & Dowling, Michael & Bouraoui, Taoufik, 2021. "From bottom ten to top ten: The role of cryptocurrencies in enhancing portfolio return of poorly performing stocks," Finance Research Letters, Elsevier, vol. 38(C).
    23. Jean Jacod & Yingying Li & Xinghua Zheng, 2017. "Statistical Properties of Microstructure Noise," Econometrica, Econometric Society, vol. 85, pages 1133-1174, July.
    24. Christian T. Brownlees & Giampiero M. Gallo, 2010. "Comparison of Volatility Measures: a Risk Management Perspective," Journal of Financial Econometrics, Oxford University Press, vol. 8(1), pages 29-56, Winter.
    25. Diaa Noureldin & Neil Shephard & Kevin Sheppard, 2012. "Multivariate high‐frequency‐based volatility (HEAVY) models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(6), pages 907-933, September.
    26. Seth Armitage & Janusz Brzeszczynski, 2011. "Heteroscedasticity and interval effects in estimating beta: UK evidence," Applied Financial Economics, Taylor & Francis Journals, vol. 21(20), pages 1525-1538.
    27. Toshiaki Watanabe, 2012. "Quantile Forecasts Of Financial Returns Using Realized Garch Models," The Japanese Economic Review, Japanese Economic Association, vol. 63(1), pages 68-80, March.
    28. Christian Contino & Richard H. Gerlach, 2017. "Bayesian tail‐risk forecasting using realized GARCH," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 33(2), pages 213-236, March.
    29. Bollerslev, Tim & Patton, Andrew J. & Quaedvlieg, Rogier, 2016. "Exploiting the errors: A simple approach for improved volatility forecasting," Journal of Econometrics, Elsevier, vol. 192(1), pages 1-18.
    30. Trimborn, Simon & Härdle, Wolfgang Karl, 2018. "CRIX an Index for cryptocurrencies," Journal of Empirical Finance, Elsevier, vol. 49(C), pages 107-122.
    31. Vitali Alexeev & Mardi Dungey & Wenying Yao, 2016. "Continuous and Jump Betas: Implications for Portfolio Diversification," Econometrics, MDPI, vol. 4(2), pages 1-15, June.
    32. Neil Shephard & Kevin Sheppard, 2010. "Realising the future: forecasting with high-frequency-based volatility (HEAVY) models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(2), pages 197-231.
    33. Dirk G. Baur & Thomas Dimpfl, 2019. "Price discovery in bitcoin spot or futures?," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(7), pages 803-817, July.
    34. Ole E. Barndorff-Nielsen & Neil Shephard, 2004. "Econometric Analysis of Realized Covariation: High Frequency Based Covariance, Regression, and Correlation in Financial Economics," Econometrica, Econometric Society, vol. 72(3), pages 885-925, May.
    35. Robert Engle, 2002. "New frontiers for arch models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 425-446.
    36. Carol Alexander & Jaehyuk Choi & Heungju Park & Sungbin Sohn, 2020. "BitMEX bitcoin derivatives: Price discovery, informational efficiency, and hedging effectiveness," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(1), pages 23-43, January.
    37. Yuan-Hung Hsu Ku & Ho-Chyuan Chen & Kuang-Hua Chen, 2007. "On the application of the dynamic conditional correlation model in estimating optimal time-varying hedge ratios," Applied Economics Letters, Taylor & Francis Journals, vol. 14(7), pages 503-509.
    38. Kroner, Kenneth F. & Sultan, Jahangir, 1993. "Time-Varying Distributions and Dynamic Hedging with Foreign Currency Futures," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(4), pages 535-551, December.
    39. Cohen, Kalman J. & Hawawini, Gabriel A. & Maier, Steven F. & Schwartz, Robert A. & Whitcomb, David K., 1983. "Friction in the trading process and the estimation of systematic risk," Journal of Financial Economics, Elsevier, vol. 12(2), pages 263-278, August.
    40. Robert F. Engle, 2000. "The Econometrics of Ultra-High Frequency Data," Econometrica, Econometric Society, vol. 68(1), pages 1-22, January.
    41. Będowska-Sójka, Barbara & Kliber, Agata, 2021. "Is there one safe-haven for various turbulences? The evidence from gold, Bitcoin and Ether," The North American Journal of Economics and Finance, Elsevier, vol. 56(C).
    42. Bollerslev, Tim & Zhang, Benjamin Y. B., 2003. "Measuring and modeling systematic risk in factor pricing models using high-frequency data," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 533-558, December.
    43. Kroner, Kenneth F & Ng, Victor K, 1998. "Modeling Asymmetric Comovements of Asset Returns," The Review of Financial Studies, Society for Financial Studies, vol. 11(4), pages 817-844.
    44. Hasbrouck, Joel, 1995. "One Security, Many Markets: Determining the Contributions to Price Discovery," Journal of Finance, American Finance Association, vol. 50(4), pages 1175-1199, September.
    45. Tian, Shuairu & Hamori, Shigeyuki, 2015. "Modeling interest rate volatility: A Realized GARCH approach," Journal of Banking & Finance, Elsevier, vol. 61(C), pages 158-171.
    46. Lintner, John, 1969. "The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets: A Reply," The Review of Economics and Statistics, MIT Press, vol. 51(2), pages 222-224, May.
    47. Peter Reinhard Hansen & Asger Lunde & Valeri Voev, 2014. "Realized Beta Garch: A Multivariate Garch Model With Realized Measures Of Volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(5), pages 774-799, August.
    48. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    49. Andersen, Torben G, 2000. "Some Reflections on Analysis of High-Frequency Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(2), pages 146-153, April.
    50. Fabian Hollstein & Marcel Prokopczuk & Chardin Wese Simen, 2020. "The Conditional Capital Asset Pricing Model Revisited: Evidence from High-Frequency Betas," Management Science, INFORMS, vol. 66(6), pages 2474-2494, June.
    51. Pierre J. Venter & Eben Maré, 2020. "GARCH Generated Volatility Indices of Bitcoin and CRIX," JRFM, MDPI, vol. 13(6), pages 1-15, June.
    52. Doan, Bao & Lee, John B. & Liu, Qianqiu & Reeves, Jonathan J., 2022. "Beta measurement with high frequency returns," Finance Research Letters, Elsevier, vol. 47(PA).
    53. Yukun Liu & Aleh Tsyvinski, 2021. "Risks and Returns of Cryptocurrency," The Review of Financial Studies, Society for Financial Studies, vol. 34(6), pages 2689-2727.
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    1. Julien Chevallier & Bilel Sanhaji, 2023. "Jump-Robust Realized-GARCH-MIDAS-X Estimators for Bitcoin and Ethereum Volatility Indices," Stats, MDPI, vol. 6(4), pages 1-32, December.

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