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

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

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


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.

Original languageEnglish
Pages (from-to)1158-1169
Number of pages12
JournalJournal of Banking and Finance
Issue number5
StatePublished - May 2011


  • Heavy-tail
  • Jumpiffusion
  • Serial dependence
  • Square-root-of-time rule
  • Subsampling-based test
  • Value at risk
  • Volatility clustering


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