A first important observation is that VaR applies to the extreme lower tail of the return distribution, i.e. large losses far way from the mean. Bank regulators have recognized this and typically chosen a (the confidence level) equal to 99%. This number obviously reflects regulators’ natural tendency for conservativeness in their prudential supervision of banks. The same tendency also comes out in Basle regulators’ choice of holding period, the second important model parameter. A 10-day horizon is prescribed on the assumption that positions cannot be liquidated quicker than within 10 business days. To compute the 10-day VaR, the application of a simple square-root-of-time rule is permitted, ie. 10-day VaR is derived as the product of square root of 10 and the 1-day VaR. For the purpose of setting adequate capital, the Basle accord provides, in addition, a multiplicative factor of 3 by which the computed VaR for the 10-day period should be multiplied. It is important to mention here that the square-root-of-time rule is the appropriate scaling factor for deriving multi-day VaR figures from 1-day figures only under the assumption of normality. Once we take into consideration the fat-tail property of underlying risk factors, the scale factor would be a-root-of-time, where a is the tail index. A point of interest in this context is that while simple models, such as Normal, under-estimate the 1-day VaR when the return series have ‘fat’ tails, they over estimate the multi-day VaR because the square-root rule turns out to be too conservative for fat tailed series. For a more detailed discussion on this and an empirical illustration see the technical document available.


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