Normal distribution: Difference between revisions

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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:


{{Quote|“We were seeing things that were 25-standard deviation moves, several days in a row.”
{{Quote|{{viniarquote}}
:—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 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:
''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: