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Spectral risk for digital assets

Author

Listed:
  • Meng-Jou Lu

    (Asia University)

  • Matúš Horváth

    (Masaryk University)

  • Xingjia Wang

    (Humboldt Universität zu Berlin)

  • Wolfgang Karl Härdle

    (Humboldt Universität zu Berlin
    Charles University
    National Yang Ming Chiao Tung University
    Singapore Management University)

Abstract

Digital assets (DAs) are a unique asset class that presents investors with opportunities and risks that are contingent upon their particular characteristics such as volatility, type, and profile, among other factors. Among DAs, cryptocurrencies (CCs) have emerged as the most liquid asset class, holding this distinction for almost a decade. However, while CCs offer a high level of liquidity, investors must be aware of the potential risks and rewards associated with investing in this asset class, and should conduct a thorough evaluation before making any investment decisions. Our study examines the risk profile of CCs through portfolio analysis, utilizing Spectral Risk Measures (SRMs) as the commonly applied method. In this study, we investigate the application of SRMs in assessing the risk structure of CC portfolios, and their alignment with investors’ risk preferences. We employ SRMs to evaluate the CC index CRIX and portfolios constructed from the most liquid 10 CCs from the Blockchain Research Center (BRC), optimizing different SRMs.Our empirical findings suggest that various optimal portfolio allocations can be formulated to meet the unique risk appetites of individual investors. All Quantlets (macros, code snippets) are available via quantlet.com and instructive educational element are available on quantinar.com .

Suggested Citation

  • Meng-Jou Lu & Matúš Horváth & Xingjia Wang & Wolfgang Karl Härdle, 2025. "Spectral risk for digital assets," Review of Quantitative Finance and Accounting, Springer, vol. 64(2), pages 537-574, February.
    • Handle: RePEc:kap:rqfnac:v:64:y:2025:i:2:d:10.1007_s11156-024-01313-0
    DOI: 10.1007/s11156-024-01313-0
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    References listed on IDEAS

    as
    1. Prodosh Simlai, 2021. "Accrual mispricing, value-at-risk, and expected stock returns," Review of Quantitative Finance and Accounting, Springer, vol. 57(4), pages 1487-1517, November.
    2. Cotter, John & Dowd, Kevin, 2006. "Extreme spectral risk measures: An application to futures clearinghouse margin requirements," Journal of Banking & Finance, Elsevier, vol. 30(12), pages 3469-3485, December.
    3. Kevin Dowd & John Cotter & Ghulam Sorwar, 2008. "Spectral Risk Measures: Properties and Limitations," Journal of Financial Services Research, Springer;Western Finance Association, vol. 34(1), pages 61-75, August.
    4. Acerbi, Carlo, 2002. "Spectral measures of risk: A coherent representation of subjective risk aversion," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1505-1518, July.
    5. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    6. Green, Richard C & Hollifield, Burton, 1992. "When Will Mean-Variance Efficient Portfolios Be Well Diversified?," Journal of Finance, American Finance Association, vol. 47(5), pages 1785-1809, December.
    7. Chanwit Phengpis & Peggy Swanson, 2011. "Optimization, cointegration and diversification gains from international portfolios: an out-of-sample analysis," Review of Quantitative Finance and Accounting, Springer, vol. 36(2), pages 269-286, February.
    8. Michael Fung, 2013. "A trade-off between non-fundamental risk and incentives," Review of Quantitative Finance and Accounting, Springer, vol. 41(1), pages 29-51, July.
    9. Benjamin Mögel & Benjamin R. Auer, 2018. "How accurate are modern Value-at-Risk estimators derived from extreme value theory?," Review of Quantitative Finance and Accounting, Springer, vol. 50(4), pages 979-1030, May.
    10. Trimborn, Simon & Härdle, Wolfgang Karl, 2018. "CRIX an Index for cryptocurrencies," Journal of Empirical Finance, Elsevier, vol. 49(C), pages 107-122.
    11. Brandtner, Mario, 2013. "Conditional Value-at-Risk, spectral risk measures and (non-)diversification in portfolio selection problems – A comparison with mean–variance analysis," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 5526-5537.
    12. Fei Leng & Gregory Noronha, 2019. "Relative value in corporate bond sectors," Review of Quantitative Finance and Accounting, Springer, vol. 52(3), pages 717-735, April.
    13. Adam, Alexandre & Houkari, Mohamed & Laurent, Jean-Paul, 2008. "Spectral risk measures and portfolio selection," Journal of Banking & Finance, Elsevier, vol. 32(9), pages 1870-1882, September.
    14. Petukhina, Alla & Klochkov, Yegor & Härdle, Wolfgang Karl & Zhivotovskiy, Nikita, 2024. "Robustifying Markowitz," Journal of Econometrics, Elsevier, vol. 239(2).
    15. Behr, Patrick & Guettler, Andre & Miebs, Felix, 2013. "On portfolio optimization: Imposing the right constraints," Journal of Banking & Finance, Elsevier, vol. 37(4), pages 1232-1242.
    16. Victor DeMiguel & Francisco J. Nogales, 2009. "Portfolio Selection with Robust Estimation," Operations Research, INFORMS, vol. 57(3), pages 560-577, June.
    17. Massimiliano Barbi & Silvia Romagnoli, 2014. "A Copula‐Based Quantile Risk Measure Approach to Estimate the Optimal Hedge Ratio," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 34(7), pages 658-675, July.
    18. Kevin Dowd & David Blake, 2006. "After VaR: The Theory, Estimation, and Insurance Applications of Quantile‐Based Risk Measures," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(2), pages 193-229, June.
    19. Cai, Jun & Tan, Ken Seng & Weng, Chengguo & Zhang, Yi, 2008. "Optimal reinsurance under VaR and CTE risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 185-196, August.
    20. Alla Petukhina & Simon Trimborn & Wolfgang Karl Härdle & Hermann Elendner, 2021. "Investing with cryptocurrencies – evaluating their potential for portfolio allocation strategies," Quantitative Finance, Taylor & Francis Journals, vol. 21(11), pages 1825-1853, November.
    21. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    22. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
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    More about this item

    Keywords

    Spectral risk measure; Value-at-risk; Expected shortfall; Digital assets; CRIX; Portfolio;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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