The random walk and fractals

Long-Term Capital Management,  the theory of fractals and the Hurst Exponent lead me to question that markets are random and rational in the debate recently given a nudge by the awarding of the Nobel Prize in economics to economists on either side of this question.

For me the timing of the award was good because I have just finished reading When Genius Failed: The Rise and Fall of Long-Term Capital Management by Roger Lowenstein.

Long-Term Capital Management was an attempt to make money  out of a belief that markets are rational.  The company employed academics in economics/mathematics to trade according to models run on computers.  It worked for a while and this company became one of the most successful hedge funds and two of its board members were awarded the Nobel prize in economics.  But one of the reasons it failed was because the markets did not always behave as they had been modelled.  They behaved like fractals.

Another reason the company failed is that its employees were not really geniuses.  I have a theory that genius is 90 percent plagiarism.  Thus anyone can be 90 percent genius so long as they listen.  Those who don’t listen are stuck down below 10 percent. This would suggest that to be a genius you have to listen.    It is clear from the book that these guys were not listeners.   They were caught with the idea that you can prove how smart you are by how much money you can make.

The author of this book figures the way to make sure there isn’t another LTCM is with greater regulation.  Rather than regulation governments should require financial institutions to publish detailed information about their operations.  These guys were extremely secretive and refused to provide their associates with information which would have revealed their operations as being much riskier than anyone believed.  Their customers should have refused to work with them but the company was making so much money no one wanted to be left out.

I didn’t learn about fractals until sometime after I had studied economics. Now I think they provide a good model for a lot of human activity including markets and economics.

The classic example of a fractal is the sea-shore with its ins and outs and more ins and outs within the major ones.  Think of the song about a wheel within a wheel within a wheel.  The Elliott wave theory is a fractal, just remove the fives.  Markets and the economy can be seen as a series of trends with trends within trends.  They also have major turning points rather than following the straight line of regression analysis.

So the problem for somebody trying to forecast markets or the economy is to identify turning points, especially the major ones.

There is a concept of fractal dimension which indicates the extent of the trends and it can be calculated with the formula 2 – H where H is the Hurst Exponent.  Changes in fractal dimension indicate turning points.

Edwin Hurst was a hydraulic engineer working on the Nile River in the first half of the twentieth century.  He wanted to prove the different annual river flows were random and developed a way of testing a series of numbers to determine whether or not they were random.  To his surprise they were not.

The same test can be applied to any time series including market and economic data.  The Hurst exponent can now be calculated with as few as 32 data points and it varies considerably with each calculation, most indicating the numbers are not random.  This by itself is a strong indication that there are problems with the random walk theory.

I suspect a lot of the “quants”  who are currently using “black boxes” to play the markets, apparently with some success, are using the Hurst Exponent.

The importance of the debate about random walk may depend upon how much we want to understand about how markets and the economy actually work.  It may be that some people don’t want to understand how things actually work.  For those of us who do I think fractals are more promising.  And one should never place one’s savings with fund managers who don’t listen.


One Response

  1. The problem regarding theories which explain human behavior is that human behavior changes as a result of this knowledge. If the funds that can determine the market trends are convinced that the Hurst exponent can read the market they will use it to invest and they will make it a self-fulfilled prophecy. Until some other funds struggling to make great profits will risk to play against the Hurst exponent – causing a severe blow to its credibility.
    Thus, every model that works, works just for the pioneers.

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