A remark concerning value-at-risk

Over the past two decades Value-at-Risk (VaR) became arguably the most popular measure of financial risk. Major banks calculate VaR on daily basis in order to determine the amount of capital a bank needs to offset the market risk. Banks use calculation methods of their choice, and many estimations are based on the assumption that portfolio rates of return have normal distribution. The important question is whether the chosen method of VaR calculation is accurate. As the light-tail property of the normal distribution can cause significant underestimation of VaR, the Basel Committee suggested to calculate the amount of capital needed by multiplying the bank's internal estimate of VaR by the factor 3. It's also common to use the so-called "square root of time" rule when evaluating VaR over a longer time horizon. This article aims to refine Stahl's argument behind the "factor 3" rule and say a word of caution concerning the "square root of time" rule.