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

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  • Danielsson, Jon
  • Zigrand, Jean-Pierre

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.
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Suggested Citation

  • Danielsson, Jon & Zigrand, Jean-Pierre, 2006. "On time-scaling of risk and the square-root-of-time rule," Journal of Banking & Finance, Elsevier, vol. 30(10), pages 2701-2713, October.
  • Handle: RePEc:eee:jbfina:v:30:y:2006:i:10:p:2701-2713
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    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G18 - Financial Economics - - General Financial Markets - - - Government Policy and Regulation
    • G20 - Financial Economics - - Financial Institutions and Services - - - General

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