tag:blogger.com,1999:blog-5071936218849577375.post4741132951979601147..comments2024-03-19T23:20:47.782-07:00Comments on Unintentional Irony: Central LimitJames Killushttp://www.blogger.com/profile/08265296146264452333noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-5071936218849577375.post-70168130341079014012015-08-10T08:16:21.891-07:002015-08-10T08:16:21.891-07:00I think you hit the point at the end when you said...I think you hit the point at the end when you said "there certainly are traders who are as stupid as he describes". <br /><br />In Taleb's defence, I think he is pretty aware that the CLT isn't about the tails but rather that 'finance people' assume the CLT and then carry on as though 'everything' is hunky-dory...it's perhaps more the erroneous jump in reasoning he is railing against i.e. they then think they are capturing 'risk'.<br /><br />MarkAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-5071936218849577375.post-62042354010605326512007-09-03T12:53:00.000-07:002007-09-03T12:53:00.000-07:00Now, reread the conditions on the CLT. The critica...<EM>Now, reread the conditions on the CLT. The critical one is "sum has finite variance".</EM><BR/><BR/>That does bring up an interesting point. One of the salient features of a "random walk" is that it is, in fact, an example of a distribution with an unbounded variance; it grows without limit over time. That gives rise to the phenomenon of "spurious correlations" when random walk variables are regressed against other variables.<BR/><BR/>That's a main reason for the "correlations" that have been found for the stock market against such oddities as sunspots and skirt hems. It also means that the Wall Street "quants," who use spreadsheet multivariate regressions at every opportunity, delude themselves on a regular basis.<BR/><BR/>I will note that Taleb is at least aware that something is wrong. And recent events have shown that, whatever Taleb's errors in mathematics, science, and statistics, there certainly are traders who are as stupid as he describes.James Killushttps://www.blogger.com/profile/08265296146264452333noreply@blogger.comtag:blogger.com,1999:blog-5071936218849577375.post-13150173903341797472007-09-02T21:33:00.000-07:002007-09-02T21:33:00.000-07:00The CLT is about the distribution of the mean.Now,...The CLT is about the distribution of the mean.<BR/><BR/>Now, reread the conditions on the CLT. The critical one is "sum has finite variance".<BR/><BR/>The whole point about "extremistan" variables is that they don't.<BR/><BR/>ie. CLT doesn't apply. (Or actually, it does sort of apply, resulting in something that sort of looks Gaussian, but also has a fat tail!)<BR/><BR/>The other underlying assumption with Taleb is he is an investor. He looks at the sum of his gains and losses over the years. An whilst this "almost CLT" drives the probability distributions of his wealth, the fat tail wags that dog.Anonymousnoreply@blogger.com