Comments on: Misbehavior of the Markets and other things
http://ask.metafilter.com/55739/Misbehavior-of-the-Markets-and-other-things/
Comments on Ask MetaFilter post Misbehavior of the Markets and other thingsThu, 25 Jan 2007 11:35:30 -0800Thu, 25 Jan 2007 11:35:30 -0800en-ushttp://blogs.law.harvard.edu/tech/rss60Question: Misbehavior of the Markets and other things
http://ask.metafilter.com/55739/Misbehavior-of-the-Markets-and-other-things
I have a few questions about Benoit Mandelbrot's "(Mis)behavior of the Markets", fractal finance and Gaussian distribution. <br /><br /> (1) Does this school (which seems to be very aligned with Taleb's Popperian skepticism in its approach) of thought have a name for it? It seems to successfully reject Bachelier's original paper and all papers and equations that rely on the Gaussian distribution (or take it as a given).<br>
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(2) Are his findings widely accepted among academics? Or practitioners (e.g., most leading Wall Street institutions)? It seems that true Gaussian distribution was never widely accepted, but used anyway as it works until it doesn't.<br>
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(3) While his antithesis of modern finance seems quite convincing, are his fractals applicable? I am trying to figure out if he manages to prove anything beyond constructing a visually pleasing example of a stock chart. Fractal generation manages to show the similar bubbles and long-tails that are characteristic of a real market (and not in some platonic Brownian market), but that does not prove that fractals can be used to better manage risk.<br>
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I've read a few papers on Mandelbrot's site, but nothing explaining a little more in depth his ideas. I studied the Black–Scholes model in school and was taught on using models which in their forms are based on a normal Gaussian distribution. I never liked this for reasons that Mandelbrot and Taleb managed to express. Any journals that I can subscribe to which follow that line of thought more closely? I have been reading the JFE but will take on more if they are interesting.post:ask.metafilter.com,2007:site.55739Thu, 25 Jan 2007 10:55:35 -0800geoff.mandelbrotfractalfinancebrowniantalebquantitativefinanceBy: yoyo_nyc
http://ask.metafilter.com/55739/Misbehavior-of-the-Markets-and-other-things#838890
This is on my list. I have not read it yet but it might interest you:<br>
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Fractals and Scaling In Finance<br>
by Benoit B. Mandelbrot<br>
Publisher: Springer; 1 edition (April 20, 2005)<br>
ISBN-10: 0387983635<br>
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I think his research is well known. One of the problems is that BS works with the assumption that stocks follow a Brown-motion but a Levi flight would actually be a better describtion. However, AFAIK the mathematics get to tricky to get this into the BS model.comment:ask.metafilter.com,2007:site.55739-838890Thu, 25 Jan 2007 11:35:30 -0800yoyo_nycBy: Mutant
http://ask.metafilter.com/55739/Misbehavior-of-the-Markets-and-other-things#838937
<i>"Gaussian distribution was never widely accepted, but used anyway as it works until it doesn't."</i><br>
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I'm not sure I totally agree with this statement. We use the Gaussian distribution because it's simple, and easily defined in terms of two moments - the mean and the standard deviation.<br>
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But we all know it doesn't <i>truly</i> describe the distribution of returns in many markets - for example equities. The 1987 stock market crash - a single drop of roughly 22% or some 520 points - according to a normal distribution would be 20 standard deviation event (IIRC)!! Or something that should only happen once every billion years or so. <br>
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Then there is the asymmetry of returns, again particularly in the equity markets; we know they move a hell of a lot faster DOWN than they do up. This is the entire idea behind Asymmetric GARCH models, for example. This reality hardly is consistent with the simplified, not to mention symmetrical Gaussian view.<br>
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But getting back to <i>why</i> the normal distribution is used - its a simple concept and easily explained. Who reading this doesn't understand the Bell Curve? And tools exist to convert a normal distribution to certain other distributions (accounting for skewness and kurtosis of course), so analysis can be carried out using a normal distribution and the results converted. <br>
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Finally, and perhaps most importantly - keep in mind under Basel II and other regulatory regimes, models must be explained to regulators. If you've got a precise idea of the <i>true</i> return distribution of an asset class, you've probably spent a crapload of money arriving at this conclusion and the last thing you want to do is explain your research to a Central Bank. You're gonna trade the hell out of this advantage. So many desks <i>do</i> understand more precise return distributions of the assets traded, and they ain't talking.comment:ask.metafilter.com,2007:site.55739-838937Thu, 25 Jan 2007 12:19:51 -0800MutantBy: b1tr0t
http://ask.metafilter.com/55739/Misbehavior-of-the-Markets-and-other-things#838969
Taleb and Mandelbrot are both popular over at the <a href="http://www.wilmott.com/">Wilmott</a> forums, one of the most reputable groups of quants I've found on the 'net.<br>
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Wilmott himself has a few books on <a href="http://www.amazon.com/exec/obidos/ASIN/0471498629/metafilter-20/ref=nosim/">quantitative </a> <a href="http://www.amazon.com/exec/obidos/ASIN/0470018704/metafilter-20/ref=nosim/">finance</a>. The intorducing book starts out by deriving BS, then moves on to methods for improving BS.<br>
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Note that there are some great MP3 podcasts on quantitative finance over at Wilmott. You have to register to see anything, but once you do there is plenty of interesting free stuff.comment:ask.metafilter.com,2007:site.55739-838969Thu, 25 Jan 2007 12:46:48 -0800b1tr0tBy: CrunchyFrog
http://ask.metafilter.com/55739/Misbehavior-of-the-Markets-and-other-things#838980
Mathematician here, not an economist.<br>
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The justification for the Gaussian distribution is the <a href="http://en.wikipedia.org/wiki/Central_limit_theorem">Central Limit Theorem</a>. Basically, if some random variable is a combination of many different same- (or similarly-) distributed random variables, the combined one tends towards being Gaussian.comment:ask.metafilter.com,2007:site.55739-838980Thu, 25 Jan 2007 13:00:58 -0800CrunchyFrog