5 ms·

Benoit B. Mandelbrot: How Fractals Can Explain What's Wrong with Wall Street

24 points by prakash 18y ago

neilk 18y ago
Hilarity: when I loaded it, on the page was one of Chrysler's "thanks for your investment" ads.
fizx 18y ago
Lost me when he confused the normal distribution with the plain English meaning of normal.
- wynand 18y ago
  From http://www.andrews.edu/~calkins/math/webtexts/stat06.htm 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 18y ago
    Yes, I do believe he was making a pun.
cakeface 18y ago
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.
mitko 18y ago
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 18y ago
  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 http://www.dailymotion.com/video/k2rLNuMggOKSJWHSpY
  - mitko 18y ago
    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.
ctkrohn 18y ago
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?
joe_the_user 18y ago
"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..

24 points by prakash 18y ago

neilk 18y ago

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

fizx 18y ago

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

wynand 18y ago
From http://www.andrews.edu/~calkins/math/webtexts/stat06.htm 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 18y ago
  Yes, I do believe he was making a pun.

cakeface 18y ago

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.

mitko 18y ago

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 18y ago
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 http://www.dailymotion.com/video/k2rLNuMggOKSJWHSpY
- mitko 18y ago
  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.

ctkrohn 18y ago

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?

joe_the_user 18y ago

"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..