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How accurate is the square-root-of-time rule in scaling tail risk: A global study

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  • Wang, Jying-Nan
  • Yeh, Jin-Huei
  • Cheng, Nick Ying-Pin

Abstract

The square-root-of-time rule (SRTR) is popular in assessing multi-period VaR; however, it makes several unrealistic assumptions. We examine and reconcile different stylized factors in returns that contribute to the SRTR scaling distortions. In complementing the use of the variance ratio test, we propose a new intuitive subsampling-based test for the overall validity of the SRTR. The results indicate that serial dependence and heavy-tailedness may severely bias the applicability of SRTR, while jumps or volatility clustering may be less relevant. To mitigate the first-order effect from time dependence, we suggest a simple modified-SRTR for scaling tail risks. By examining 47 markets globally, we find the SRTR to be lenient, in that it generally yields downward-biased 10-day and 30-day VaRs, particularly in Eastern Europe, Central-South America, and the Asia Pacific. Nevertheless, accommodating the dependence correction is a notable improvement over the traditional SRTR.

Suggested Citation

  • Wang, Jying-Nan & Yeh, Jin-Huei & Cheng, Nick Ying-Pin, 2011. "How accurate is the square-root-of-time rule in scaling tail risk: A global study," Journal of Banking & Finance, Elsevier, vol. 35(5), pages 1158-1169, May.
  • Handle: RePEc:eee:jbfina:v:35:y:2011:i:5:p:1158-1169
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    References listed on IDEAS

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    Cited by:

    1. Stavros Degiannakis & Pamela Dent & Christos Floros, 2014. "A Monte Carlo Simulation Approach to Forecasting Multi-period Value-at-Risk and Expected Shortfall Using the FIGARCH-skT Specification," Manchester School, University of Manchester, vol. 82(1), pages 71-102, January.
    2. Sbrana, Giacomo & Silvestrini, Andrea, 2013. "Aggregation of exponential smoothing processes with an application to portfolio risk evaluation," Journal of Banking & Finance, Elsevier, vol. 37(5), pages 1437-1450.
    3. Alexander, Carol & Lazar, Emese & Stanescu, Silvia, 2013. "Forecasting VaR using analytic higher moments for GARCH processes," International Review of Financial Analysis, Elsevier, vol. 30(C), pages 36-45.
    4. Del Brio, Esther B. & Mora-Valencia, Andrés & Perote, Javier, 2014. "VaR performance during the subprime and sovereign debt crises: An application to emerging markets," Emerging Markets Review, Elsevier, vol. 20(C), pages 23-41.
    5. repec:eee:revfin:v:34:y:2017:i:c:p:86-98 is not listed on IDEAS
    6. repec:oup:jfinec:v:15:y:2017:i:4:p:649-677. is not listed on IDEAS
    7. Erik Kole & Thijs Markwat & Anne Opschoor & Dick van Dijk, 2017. "Forecasting Value-at-Risk under Temporal and Portfolio Aggregation," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 15(4), pages 649-677.
    8. Luca Spadafora & Marco Dubrovich & Marcello Terraneo, 2014. "Value-at-Risk time scaling for long-term risk estimation," Papers 1408.2462, arXiv.org.
    9. Balaban, Ercan & Lu, Shan, 2016. "Forecasting the term structure of volatility of crude oil price changes," Economics Letters, Elsevier, vol. 141(C), pages 116-118.

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