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But when [[Mrs. Pinterman]] then cries, “fire” the situational dynamic is very different: ''everyone'' tries to leave at once. Even those who didn’t hear Mrs. Pinterman directly, because they instinctively copy everyone else, who did. | But when [[Mrs. Pinterman]] then cries, “fire” the situational dynamic is very different: ''everyone'' tries to leave at once. Even those who didn’t hear Mrs. Pinterman directly, because they instinctively copy everyone else, who did. | ||
When assessing probabilities, therefore, pay attention to the dependency of the events. If two events can influence each other — you bought a stock, it went up in price, so I bought it too, kind of thing — ''[[normal distribution]]s do not apply. | When assessing probabilities, therefore, pay attention to the dependency of the events. If two events can influence each other — you bought a stock, it went up in price, so I bought it too, kind of thing — ''[[normal distribution]]s do not apply.'' | ||
This seems an obvious lesson; the JC feels less patronising about stating it since failure to heed it led to the collapse of [[LTCM]] ''and'' the [[global financial crisis]]. This from someone who really should have known better: | This seems an obvious lesson; the JC feels less patronising about stating it since failure to heed it led to the collapse of [[LTCM]] ''and'' the [[global financial crisis]]. This from someone who really should have known better: | ||
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{{Quote|“We were seeing things that were 25-standard deviation moves, several days in a row.” | {{Quote|“We were seeing things that were 25-standard deviation moves, several days in a row.” | ||
:—David Viniar, Chief Financial Officer, [[Goldman]]}} | :—David Viniar, Chief Financial Officer, [[Goldman]]}} | ||
''Twenty five'' [[Standard deviation|standard deviations]]. That makes [[LTCM]]’s feeble ''ten'' sigma event seem a | ''Twenty five'' [[Standard deviation|standard deviations]]. That makes [[LTCM]]’s feeble ''ten'' sigma event seem a virtual certainty. We have it on good authority that the probability of a 25 standard deviation move is 1.309 x 10<sup>130</sup>. <ref>Good [https://www.nottingham.ac.uk/business/who-we-are/centres-and-institutes/gcbfi/documents/cris-reports/cris-paper-2008-3.pdf paper on this from Nottingham University].</ref> That looks a big number, but to a lay person, it doesn’t really have the same impact as writing it out, so let’s do that: | ||
{{Quote|1 day in 1.3 billion billion billion billion billion billion billion billion billion billion billion billion billion billion days. | {{Quote|1 day in 1.3 billion billion billion billion billion billion billion billion billion billion billion billion billion billion days. | ||
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By comparison, the earth is 1 658 000 000 000 days old, and the universe itself ten times older than that (16 580 000 000 000 000 days). So the [[Goldman]] [[CFO]] was talking about an event that you would only expect once in several trillion trillion trillion trillion lives of the universe, happening ''several days in a row''. | By comparison, the earth is 1 658 000 000 000 days old, and the universe itself ten times older than that (16 580 000 000 000 000 days). So the [[Goldman]] [[CFO]] was talking about an event that you would only expect once in several trillion trillion trillion trillion lives of the universe, happening ''several days in a row''. | ||
So, no, Mr Viniar: you weren’t seeing cosmos-defying anomalies. ''Your models were wrong''. But enough already of the chutzpah.<ref>But, [[get your coat]], you know?</ref> The practical lesson is that, unless you are dealing with normally-distributed events, normal probabilities are a ''really'' bad proxy at the extremes. ''Ninety-nine per cent of the way there is nowhere. It isn’t good enough''. | So, no, Mr Viniar: you weren’t seeing cosmos-defying anomalies. ''Your models were wrong''. | ||
But enough already of the chutzpah.<ref>But, [[get your coat]], you know?</ref> The practical lesson is that, unless you are dealing with normally-distributed events, normal probabilities are a ''really'' bad proxy at the extremes. ''Ninety-nine per cent of the way there is nowhere. It isn’t good enough''. | |||
''All'' existential crises sit in the last 1 per cent — last 0.01 per cent, even — because the defining feature of an existential crisis is ''everyone panicking and selling at once''. These are, by definition, the events a normal distribution says will not happen, because events in a normal distribution are independent of each other. | ''All'' existential crises sit in the last 1 per cent — last 0.01 per cent, even — because the defining feature of an existential crisis is ''everyone panicking and selling at once''. These are, by definition, the events a normal distribution says will not happen, because events in a normal distribution are independent of each other. | ||