From Why Banks Failed the Stress Test:
Back in August 2007, the Chief Financial Officer of Goldman Sachs, David Viniar, commented to the Financial Times:
“We are seeing things that were 25-standard deviation moves, several days in a row”
To provide some context, assuming a normal distribution, a 7.26-sigma daily loss would be expected to occur once every 13.7 billion or so years. That is roughly the estimated age of the universe.
A 25-sigma event would be expected to occur once every 6 x 10^124 lives of the universe. That is quite a lot of human histories. When I tried to calculate the probability of a 25-sigma event occurring on several successive days, the lights visibly dimmed over London and, in a scene reminiscent of that Little Britain sketch, the computer said “No”. Suffice to say, time is very unlikely to tell whether Mr Viniar’s empirical observation proves correct.
Fortunately, there is a simpler explanation – the model was wrong. Of course, all models are wrong. The only model that is not wrong is reality and reality is not, by definition, a model. But risk management models have during this crisis proved themselves wrong in a more fundamental sense. They failed Keynes’ test – that it is better to be roughly right than precisely wrong. With hindsight, these models were both very precise and very wrong.