What’s the old saying? There are lies, damn lies, and statistics. “Value at Risk works” is arguably, from a statistical point of view, an accurate statement. But as with many statistics, we need to understand what’s truly at work.
If you are measuring VaR, for example, at the 95% level, you’re saying that the worst loss is $XXX, at that level; meaning that 5% of the time the loss can be worse. Another way to view this is that 19 out of 20 times the loss won’t be above $XXX, but one out of twenty it will be.
In reality, you may find that it’s much less than one out of 20 times. The problem is that sometimes, when it’s that one time, it is a far greater loss than one would have expected. It’s not three, four, or perhaps even five standard deviations away from the mean; it’s 10, 15, or 20 standard deviations away! And perhaps this is because of the failure to truly know what lies ahead. VaR’s estimates are based on historical information, and if the only thing we know is history, we don’t know what lies around the corner.
Again, caution must be exercised when using this statistic. It’s not going away and arguably works fine, except that the losses can be a tad worse than one would have anticipated.