RIP: Benoit Mandelbrot, 20 November 1924 – 14 October 2010

Mandelbrot was most famous for his work in mathematics, specifically fractal geometry. Fractal geometry is how designs and patterns repeat themselves across scale, like a snowflake.  An example would be an atom which is over 99% space, is like the solar system which is over 99% space and the Galaxy, which is over 99% space, which is like the Universe.  An example of a fractal zoom can be seen below. 

However, it was his work in finance that most interests me.  Mandelbrot did not support the foundations of modern mathematical finance.  His big gripe was the development of statistical tools to measure risk.  Using quantitative methods to measure risk is not just incomplete, it is dangerous.  The whole premise of modern portfolio theory rests upon the statistical application of the bell curve.  The problem is, returns do not follow the bell curve. 

Stock returns are leptokurtic, negatively skewed.  That's just a fancy way of saying that returns have fat tails and that the downside tail is even fatter than the upside tail. 

A big supporter of the Mandelbrotian mathematical reality was Nassim Taleb, the author of the Black Swan. He has chapters from his book devoted to Mandelbrotian finance. Taleb has been making a fortune off the economic crisis, which he predicted and profited from. They both say that we are really screwed, with Taleb saying that things could be worse than the great depression.


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