I had mentioned this level of movement last year at several lectures. Mr. Viniar who was the CFO of Goldman Sachs said in 2007, we are seeing things that were 25 standard deviation moves, several days in a row.
What does a 25 Standard Deviation mean? Does it really mean anything? These chaps actually tried to put some context around this 25 SD move. I am going to quote some extracts:
a 5-sigma event corresponds to an expected occurrence of less than just one day in the entire period since the end of the last Ice Age; a 6-sigma event corresponds to an expected occurrence of less than one day in the entire period since our species, Homo Sapiens, evolved from earlier primates; and a 7-sigma event corresponds to an expected occurrence of just once in a period approximately five times the length of time that has elapsed since multicellular life first evolved on this planet
So we are at 7 sigma and we are already way back into the mists of time on this planet. “ok ok, so get on with it”
These numbers are on truly cosmological scales, and a natural comparison is with the number of particles in the Universe, which is believed to be between 1.0e+73 and 1.0e+85 (Clair, 2001). Thus, a 20-event corresponds to an expected occurrence period measured in years that is 10 times larger than the higher of the estimates of the number of particles in the Universe. For its part, a 25-sigma event corresponds to an expected occurrence period that is equal to the higher of these estimates but with the decimal point moved 52 places to the left!
They explain this in a different way.
UK National Lottery is currently was offering a prize of £2.5m for a ticket costing £1. Assuming it to be a fair bet, the probability of winning the lottery on any given attempt is therefore 0.0000004. The probability of winning the lottery n times in a row is therefore 0.0000004 n , and the probability of a 25 sigma event is comparable to the probability of winning the lottery 21 or 22 times in a row.
And we should not forget Goldman’s losing streak – Goldman did not just experience a single 25-sigma event, but experienced several in a row – or forget that other institutions also experienced 25-sigma events. If the probability of a single 25-sigma event is low, the odds of two or more such events are truly infinitesimal. For example, the odds of two 25-sigma events on consecutive days are equal to 3.057e-136 squared, which is 9.3450e-272. This is as likely as winning the lottery about 42 times in a row. The corresponding expected occurrence period is the square of 1.309e+135 years – that is, 1.713e+270 years – a number so vast that it dwarves even cosmological figures. As Oscar Wild might have put it: to experience a single 25-sigma event might be regarded as a misfortune, but to experience more than one does look like carelessness
So before you decide to beat up the banks, have a think about what they were faced with. But then again, one can question, just what kind of a business are you running where extremes of this kind are present? How do design contingencies of this nature? Or put in scenario’s of this kind? Scenario Analysis is one of the most common ways of trying to analyse how things might happen in the future, but if you had to have some scenario’s of wildly cosmologically oriented events like this will need several universe sized computers to analyse.
The mind boggles.