--- In FairfieldLife@yahoogroups.com, off_world_beings <[EMAIL PROTECTED]> wrote: > > Even though I do not consider stock markets a measure of anything > significant, do you really thingk that 30 year Statistician Maestro > Maxwell Rainforth
He was not listed as having done the study. > did not account for this layman's mistake? > Don't kid yourself...he accounted for it. > > OffWorld But OK then. If you are sure. Even though this "layman's mistake" is made by many. Its common to assume normality of distrubutions without testing specifically for such. Often, results are not too distorted. Except as, stated, when dealing with extremes at the tail of the distribution. So if my hypothesis is incorrect as to why their analysis was so far off, by a factor of 5000, then perhaps you can explain why they could be so far off. They "found" a 1/50,00 chance of a market rise such as the currently one, when such naturally occurs about 5 out of any 52 starting weeks, on average in any given year. That is, a 12.9% gain or better for a 17 weeks period it has occurred on average 4.98 times year, going back to 1960, . > --- In FairfieldLife@yahoogroups.com, new.morning <no_reply@> > wrote: > > > > A recent MUM press release states tha "advanced econometric models" > > show something like a 1/50,000 chance for normal occurance of > recent > > market increases since the start of IA -- thus opening the door for > > claims of some special new effect. > > > > A well-known mistake that can be made in studies of financial > markets > > is to using analysis and models that assume a normal distribution. > > Distributions of the returns for most financial markets, certainly > the > > S&P 500 -- the proxy for all US markets -- has "fat tails" and a > > lower peak than a normal distribution. More like the top half of a > > somewhat flattened circle -- aka an elipse, than the classic "bell" > > shape of a normal (aka guassian) distribution. > > > > For some analysis, in the main body of the distriubtion, the > > difference is not to substantial. However, when analyzing the > tails, > > the extreme events, the normal distribution extremely > underestimates > > the occurence of extreme gains or losses, that is the top or > bottom > > 1% or more accutely, the top .1%. > > > > Such laxness in using normal distribution assumptiosn when modeling > > financial markets is one reason for the famous, dramatic collapse > of > > the hedge fund LTC -- Long Term Capital -- built and managed by > some > > of the best academic minds on Wall St. They simply underestimated > the > > probability of "the perfect storm". Instead of being a one in 500 > or > > so year event, it occurs far more "frequently" -- and did so on > their > > watch, collapsing 100 billion dollar portfolios to nothing within > weeks. > > > > That MUM's recent analysis may be falling into similar trap > occurred > > to me this morning when doing some calculations to answer Turq's > question. > > > > Looking at just 13 years of S&P 500 data, assuming a normal > > distribution -- as is the case when applying most tests of > > significance in statistics, the top return day, is overestimated in > > its rarity, by a factor of 15,000. The third top day by a factor of > > 5000. The top 10th day by a factor of 250. The rarity of the top 80 > > days are overstated by assuming the S&P 500 is normally > distributed, > > though the factor of overstatement declines rapidly from the top > down > > to the 80th highest daily return. The same occurs on the left tail, > > the lowest, or most negative returns. And in the middle of the > > distribution, the "rarity" of returns is underestimated. > > > > MUM was trying to assess how rare is the recent run-up in the S&P > > 500. While they did not disclose what tests or methods they used, > it > > is likely they used methods that assume a normal distribution -- as > > most methods in most statistical software do. And such loose > > assumptions of normality works ok, except when dealing with the > very > > extremes of the "tails" of financial distributions. > > > > They are looking at the rarity of the returns over 13+ weeks, the > same > > principle applies: A normal distribution will underestimate the > > frequency of extreme events -- certainly the top 1 or 2, or 10 or > so. > > In other words, it will deem such a tail event much rarer than it > > really is, Thus, the 1/50,000 probability might be overestimated > by a > > factor of 1000 or even 10,000. > > > > On top of that, if the MUM researchers over specificed > the "pattern" > > of the last 13 week rise, that is, over qualified it in ways that > are > > not essential to its "description", this too would make the recent > > rise appear statistically much rare than it is. > > > > Thus, the caveat to always eye-ball the underlying data and > results. > > Does looking at the recent rise in the context of the last 4-5 > years > > seem quite unique? No, similar reversals have occured about once > every > > year. > > > > Perhaps the MUM press release should states that "advanced > econometric > > models", run by not so advanced econometricians, showed ... the > > following misleading results." > > >
