
Benoit B. Mandelbrot: How Fractals Can Explain What's Wrong with Wall Street - prakash
http://www.sciam.com/article.cfm?id=multifractals-explain-wall-street&print=true
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mitko
As Mandelbrot stated :

These techniques do not come closer to forecasting a price drop or rise on a
specific day on the basis of past records. But they provide estimates of the
probability of what the market might do and allow one to prepare for
inevitable sea changes.

In my opinion multifractals can explain the Dow and Nasdaq fluctuations, but
it is not enough to predict them. That the market has fractal structure as
Mandelbrot noticed is probably very good assumption, but it depends on so many
factors that the dimentionality of the fractal will be enormous, and one of
the dimencions would be time. Also every stock history, every index, or
whatever other value used is just a function of that fractal structure with
respect to current and past time. Knowing the values of these functions can
give a lot information about the structure of the market to estimate what
would be their future values but this is not sure to happen. However some
trends could be estimated but their time scale cannot be known for sure ( we
have multifractal in which the time can be streched ). So we can say we expect
that there will be crisis between 3 and 6 months from now on but we may never
the exact that until it hits us.

Very similar is the situation with earthquake predictions, but there we have I
believe much more knowledge about the underlying fractal structure (the Earth,
continents, continental drift, internal Earth energy etc.) We can say there
would be big earthquake in Cali every several decades but short term
predictions are hard to make.

I will be happy to hear your opinion about fractals and stock market.

~~~
Anon84
People seem to be in the habit of mistaking _"description"_ with
_"explanation"_ or _predictive power_. I have no doubt that you can _describe_
short term stock market fluctuations in many different ways (fractals and
multi-fractals being one of them) that still doesn't get you anywhere close to
_explaining or predicting_ those fluctuations. There is good reason for this,
of course. Mainly, that short term behavior is mostly psychological. If
investors are happy (confident, bull, whatever you want to call it) prices go
up, if they are unhappy (scared, bearish, etc) prices go down. To this short
time scale behavior you have to add the long time scale component that makes
the average market value increase at roughly 10% a year, and the "invisible
hand" effect that makes individual stock prices converge (eventually) to the
correct value.

IMHO, It's the combination of these three effects that make (short term) stock
market fluctuations practically unpredictable.

Here's an hilarious description of this "market sentiment"...

    
    
          “You have to remember two things about the markets.
          One is that they are made up of very sharp and 
          sophisticated people, these are the greatest brains. 
          And the second thing you have to remember, is that 
          the financial markets, to use the common phrase, are 
          driven by sentiment.
    
          What does that mean?
    
          What does that mean? Well, things, lets say, are just
          going along as normal in the market. And then, 
          suddenly, out ot the blue, one of these very sharp 
          and sophisticated people says “MY GOD, SOMETHING 
          AWFUL IS GOING TO HAPPEN! WE LOST EVERYTHING! OH MY 
          GOD, WHAT ARE WE GOING TO DO, WHAT ARE WE GOING TO 
          DO?!? SHALL I JUMP OUT OF THE WINDOW? LET’S ALL JUMP 
          OUT OF THE WINDOW! SELL, SELL, SELL! Precisely. And 
          then, a few days later, this same, sophisticated 
          person says ‘you know, I think things are going 
          rather well’ and everybody else says ‘I agree with 
          you, I think we’re rich.’ [...] And that’s what we 
          call market sentiment.”
    
    

<http://www.dailymotion.com/video/k2rLNuMggOKSJWHSpY>

~~~
mitko
very nice video. Surely, psychology factors play quite a part in the way
market works. And also having several variables determined by such factors in
chain you can expect to have big fluctuations - exactly the ones that the
Gaussian("normal distribution") portfolios fail to explain.

the last part of the video explains an example of such chain- and the effect-
the subprime crisis.

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ctkrohn
The problem of "fat tails" has been known in finance for a long time, and
there are plenty of models in which the distribution of price increments has a
higher kurtosis than a Gaussian distribution. Interestingly enough, fractal
models are not commonly used at all. Stochastic vol models are a lot more
widespread. I'm a trader, not a quant, so I can't comment on why fractals were
never in favor -- anyone else know?

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joe_the_user
"Editor's Note: This story was originally published in the February 1999
edition of Scientific American. We are posting it in light of recent news
involving Lehman Brothers and Merrill Lynch."

And Mandlebrot's original research was done in the 1960's before Black,
Scholes and Merton were getting prizes and destroying hedge funds in the
1990s. Moreover, Mandlebrot was certainly renowned by the 1970's. You would
think people would pay attention to his ideas.

Just goes to show the appeal of research which tells people what they _want_
to hear..

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cakeface
Interesting article. If this was originally written in 1999 then someone must
have tried to create a fractal generator on historical market data for the Dow
or Nasdaq. I wonder if it helped anyone prepare for the current stock market
troubles.

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neilk
Hilarity: when I loaded it, on the page was one of Chrysler's "thanks for your
investment" ads.

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fizx
Lost me when he confused the normal distribution with the plain English
meaning of normal.

~~~
wynand
From <http://www.andrews.edu/~calkins/math/webtexts/stat06.htm>:

    
    
      Normal in statistics generally refers to the gaussian distribution or the "normal" way we would expect errors to be distributed.
    

When Mandelbrot says: "Granted, the bell curve is often described as
normal—or, more precisely, as the normal distribution. But should financial
markets then be described as abnormal?", he has reason. But I don't think he
even meant it as a very serious remark.

~~~
barrkel
Yes, I do believe he was making a pun.

