Investing in Stock Markets: Fat Tails, Persistence, Multifractals & Turbulence

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Discussion Overview

The discussion revolves around the concepts of fat tails, persistence, multifractals, and turbulence in the context of stock market behavior. Participants explore the implications of these concepts on market efficiency and the statistical methodologies used to analyze stock returns, including Rescaled Range Analysis and the Hurst exponent.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants question the relationship between fat tails and the Efficient Market Hypothesis (EMH), suggesting that fat tails do not necessarily disprove EMH but indicate potential misleading results from standard distribution models.
  • There is mention of a meta-study that critiques the interpretation of Rescaled Range Analysis in identifying long-term memory in stock market returns.
  • One participant discusses the existence of fat tails and the development of metrics like Value at Risk (VAR) to assess outlier risk, noting that stock returns over long periods do not follow a normal distribution.
  • Concerns are raised about the assumption of long-term stationary distributions in the context of fat tails, with a suggestion that this assumption may be false.
  • Market inefficiency is discussed in relation to simulated trading strategies, with references to historical research that explores this topic.
  • Participants express interest in the relationship between chaos theory and market behavior, with some skepticism about the validity of chaos models in finance.
  • Fractal geometry is proposed as a potentially relevant framework for understanding financial markets, with references to the Hurst exponent and multifractal models.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the implications of fat tails for market efficiency or the validity of various statistical methods. Multiple competing views remain regarding the interpretation of results and the relevance of different models.

Contextual Notes

Limitations include the dependence on specific statistical methodologies and the unresolved nature of the assumptions regarding market behavior and distribution characteristics.

wigglywoogly
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Does anyone here know much about these topics? I understand they surround the absence of normally distrubted returns, excessive kurtosis. Fat tails somehow disprove the EMH? Can anyone explain this argument?

I've been advised that there are links to turbulence in fluid dynamics, joined by the overarching maths of fractals. Could anyone talk me through this proof of a result from Kolmogorov (perhaps in a PM):

http://www.sjsu.edu/faculty/watkins/kolmo.htm

Thanks and regards to you all.
 
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"Fat tails somehow disprove the EMH?"

Don't think so, it just means that popular assumption in models of standard distribution can lead to misleading results.
 
With regard to fractals, there have been quite a few papers and many books published on this subject all claiming to have found the hidden structure of stock market returns in terms of persistence or long term memory. The usual methodology used by these authors is "Rescaled Range Analaysis", a statistical procedure borrowed from hydrology. I did a meta-study of these papers and found that their interpretation of the results of Rescaled Range Analysis is flawed. I wrote this up in a paper and posted it online at the ssrn research sharing site. Here is the link to the download button:

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2448648.

If you have the time to read it I would be grateful for your comments and feedback.
 
jamalmunshi said:
With regard to fractals, there have been quite a few papers and many books published on this subject all claiming to have found the hidden structure of stock market returns in terms of persistence or long term memory. The usual methodology used by these authors is "Rescaled Range Analaysis", a statistical procedure borrowed from hydrology. I did a meta-study of these papers and found that their interpretation of the results of Rescaled Range Analysis is flawed. I wrote this up in a paper and posted it online at the ssrn research sharing site. Here is the link to the download button:

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2448648.

If you have the time to read it I would be grateful for your comments and feedback.
I will do, really appreciate your input. I'll let you know once I get a chance to read it. Thanks.
 
Fat tails certainly exist and investment managers have developed metrics to assess what they call "outlier risk" I think one method is called VAR analysis.

Technically, the term fat tails means fat compared to a normal distribution. Analysis shows that over long time periods, stock returns are not normally distributed. One should note that this implicitly assumes that there is some long term stationary distribution and this may be false.

I do not think that fat tails imply market inefficiency. A normal distribution would only be expected if increments in returns were independent and stationary. But there is much evidence that this is not the case. One idea of an efficient market is that all available information is incorporated fairly into the current price. The current price then is the expected future price and can change only with new information. Mathematically, this means that stock prices follow a Martingale. Martingales can have non-stationary increments and therefore can have fat tails.

Market inefficiency can be statistically detected through simulated trading strategies. A famous paper of Barr Rosenberg in the Journal of Portfolio Management describes some of these strategies.

http://www.iijournals.com/doi/abs/10.3905/jpm.1985.409007

I don't know about Chaos in the markets but I do know that it went through a hot topic period and there were many snake oil peddlers who tried to get people to invest in purported chaos theory models. If you know of some scientifically proved examples of chaos in the market I would love to see the research.
 
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Thank you for the link to the Rosenberg paper which I had read a few decades ago but I will read it again as I have forgotten. I believe it is one of those value investing papers that were popular back then. I will write again after I have read the paper. Again, thank you for the link.
 
jamalmunshi said:
Thank you for the link to the Rosenberg paper which I had read a few decades ago but I will read it again as I have forgotten. I believe it is one of those value investing papers that were popular back then. I will write again after I have read the paper. Again, thank you for the link.

Yes the paper was written for portfolio mangers but I think it is based on rigorous research.
 
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I read your paper Jamal. It seems like you have some criticisms of the R/S approach, but that's only one method of estimating the Hurst exponent. Persistence and long memory is part of it, but also clustering volatility and intermittent large outliers. The multifractal formalism has been shown to provide all of these effects parsimoniously.
I don't know about chaos exactly, but there's good reason to think fractal geometry has something to say about finance. (After all, Brownian motion and the simplest financial time series model are themselves rich fractal phenomena.)

Here's Mandelbrot's paper on multifractal asset returns.
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=78588
The Hurst exponent can also be inferred from the estimated multifractal spectrum
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=78588
And this more robust, stationary model (Markov Switching Multifractal):
http://www.tandfonline.com/doi/abs/10.1198/073500107000000403