There is no fully satisfactory way to apply probability theory to the real world, because our estimate of probabilities depends on assumptions that are often likely to be untrue in the real world. So we cannot say that an incredibly unlikely event just happened; all we can say is that we misunderestimated the probability. —Dan -----Original Message-----
From: Charles Greathouse <charles.greathouse@case.edu> Sent: Jun 27, 2016 2:32 PM To: math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] GBP/USD exchange rate made 12-sigma move last Friday
Was anyone actually using the standard deviation of the previous 100 days' daily returns (or similar) as a risk model? I agree that this would be a silly model, and it's it hard to imagine that it would misrepresent the odds of such an event, but unless someone is using it this is just a strawman.
On Monday, June 27, 2016, Henry Baker <hbaker1@pipeline.com> wrote:
FYI -- Such an event is expected to happen every 2.2516410228987967E+30 YEARS, or about phi*10^20 times the current age of the universe. (Thanks, Maxima).
Oops! Time to fire some more bank regulators & helicopter some more $$$$$ onto Wall Street.
Some models may be useful, but not these.
I'd say that the following announcement may be greeted with raspberries:
http://www.cnbc.com/2016/06/27/us-banks-stress-tests-may-offer-comfort-in-br...
"The stress tests created for banks by U.S. regulators after the 2008 financial crisis may prove their worth this week, providing a timely message on banks' hardiness in the midst of turbulence over last week's vote by Britain to leave the European Union."
"The Federal Reserve will release the second set of results from stress tests it has conducted annually on large banks since 2009 on Wednesday. The tests look at how strong banks would be in the event of an unforeseen crisis, with economies in freefall, stock markets dropping precipitously and market counterparties at risk of failure."
"And while the stresses that the Fed is testing for in this case are imagined, analysts say *the results should be reassuring to investors* worried about banks' exposure to Brexit, an outcome that took the world and markets by surprise."
https://en.wikipedia.org/wiki/Age_of_the_universe
----
http://www.zerohedge.com/news/2016-06-27/these-brexit-market-moves-were-bigg...
"However, on Friday various markets saw volatile moves that put 2008 in the dust: in fact, the historic collapse in GBPUSD was not only far greater than any such move seen in history, but was an unprecedented 12-sigma move."
"A Ten Sigma event happens in one day out of 524,900,000,000,000,000,000 YEARS
"A Fifteen Sigma event happens in one day out of 3,671,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 YEARS
"A Twelve Sigma Event is somewhere in between.
https://arxiv.org/ftp/arxiv/papers/1103/1103.5672.pdf
"The Universe is supposedly 15,000,000,000 YEARS old for comparison's sake."
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