On time-scaling of risk and the square–root–of–time rule

Jon Danielsson and Jean-Pierre Zigrand

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: Many financial applications, such as risk analysis and derivatives pricing, depend on time scaling of risk. A common method for this purpose, though only correct when returns are iid normal, is the square–root–of–time rule where an estimated quantile of a return distribution is scaled to a lower frequency by the square-root of the time horizon. The aim of this paper is to examine time scaling of risk when returns follow a jump diffusion process. It is argued that a jump diffusion is well-suited for the modeling of systemic risk, which is the raison d’etre of the Basel capital adequacy proposals. We demonstrate that the square–root–of–time rule leads to a systematic underestimation of risk, whereby the degree of underestimation worsens with the time horizon, the jump intensity and the confidence level. As a result, even if the square–root–of–time rule has widespread applications in the Basel Accords, it fails to address the objective of the Accords.

Keywords: square-root-of time rule; time-scaling of risk; value-at-risk; systemic risk; risk regulation; jump diffusions (search for similar items in EconPapers)
JEL-codes: D81 G18 G20 (search for similar items in EconPapers)
Pages: 32 pages
Date: 2003-03
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http://eprints.lse.ac.uk/24827/ Open access version. (application/pdf)

Related works:
Journal Article: On time-scaling of risk and the square-root-of-time rule (2006)
Working Paper: On time-scaling of risk and the square–root–of–time rule (2003)
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Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:24827

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