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

Author

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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.

Suggested Citation

  • Danielsson, Jon & Zigrand, Jean-Pierre, 2003. "On time-scaling of risk and the square–root–of–time rule," LSE Research Online Documents on Economics 24827, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:24827
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    More about this item

    Keywords

    square-root-of time rule; time-scaling of risk; value-at-risk; systemic risk; risk regulation; jump diffusions;
    All these keywords.

    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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