Whats statistics got to do with it?
VaR is actually a piece of information about the distribution of possible future losses on a portfolio. The actual gain or loss won’t be known until it happens. Until then it’s uncertain; a random variable. Information about the behavior of a random variable is called a statistic. As you may guess, there are many statistics about a portfolio returns, for example the expected return. The VaR is a very useful statistic for risk managers, but it’s unlikely that it’s the only statistic that has some usefulness. Nevertheless, it is the statistic focused on almost exclusively. Now for the tricky stuff. VaR itself is a random variable, because not only is the portfolio’s future return unknown, but the distribution of the portfolio’s return must be guessed at by inference from observable data. That means that the calculated VaR is really itself just an estimate of the true VaR. So you could estimate a VaR of the distribution of the VaR! Most people are content with estimating confidence interv
