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Properties of VaR and CVaR Risk Measures in High-Frequency Domain: Long–Short Asymmetry and Significance of the Power-Law Tail

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  • Tetsuya Takaishi

    (Department of Liberal Arts, Hiroshima University of Economics, Hiroshima 731-0192, Japan)

Abstract

This study investigates the properties of risk measure, value at risk (VaR) and conditional VaR (CVaR), using high-frequency Bitcoin data. These data allow us to conduct a high statistical analysis. Our findings reveal a disparity in VaR and CVaR values between the left and right tails of the return probability distributions. We refer to this disparity as “long–short asymmetry”. In the high-frequency domain, the tail distribution can be accurately described by a power-law function. Moreover, the ratio of CVaR to VaR is expected to be determined solely by the power-law exponent. Through empirical analysis, we confirm that this ratio property holds true for high confidence levels. Furthermore, we investigate the relationship between risk measures (VaR and CVaR) and realized volatility. We observe that they trace a trajectory in a two-dimensional plane. This trajectory changes gradually, indicating periods of both high and low risk.

Suggested Citation

  • Tetsuya Takaishi, 2023. "Properties of VaR and CVaR Risk Measures in High-Frequency Domain: Long–Short Asymmetry and Significance of the Power-Law Tail," JRFM, MDPI, vol. 16(9), pages 1-13, September.
    • Handle: RePEc:gam:jjrfmx:v:16:y:2023:i:9:p:391-:d:1231324
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    References listed on IDEAS

    as
    1. Tetsuya Takaishi, 2017. "Statistical properties and multifractality of Bitcoin," Papers 1707.07618, arXiv.org, revised May 2018.
    2. 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.
    3. Stanis{l}aw Dro.zd.z & Robert Gk{e}barowski & Ludovico Minati & Pawe{l} O'swik{e}cimka & Marcin Wk{a}torek, 2018. "Bitcoin market route to maturity? Evidence from return fluctuations, temporal correlations and multiscaling effects," Papers 1804.05916, arXiv.org, revised Jul 2018.
    4. P. Gopikrishnan & M. Meyer & L.A.N. Amaral & H.E. Stanley, 1998. "Inverse cubic law for the distribution of stock price variations," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 3(2), pages 139-140, July.
    5. Dora Almeida & Andreia Dionísio & Isabel Vieira & Paulo Ferreira, 2022. "Uncertainty and Risk in the Cryptocurrency Market," JRFM, MDPI, vol. 15(11), pages 1-17, November.
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