Benoit Mandelbrot

 

Sebastian Mallaby., More money than god : hedge funds and the making of a new elite, 2010.   

 • the modeling of abnormal distributions was a problem largely unsolved in mathematics.

 • For non-nerds, this distribution is often called the bell-curve.  For nerds, it is the normal distribution.  For nerds who like to show-off, the distribution is Gaussian., Tails of the unexpected, Paper by Andrew G Haldane (and) Benjamin Nelson, Given at “The Credit Crisis Five Years On: Unpacking the Crisis”, conference held at the University of Edinburg Business School, 8-9 June 2012.

 

 • The trouble with [Benoit] Mandelbrot's insight was that it was too awkward to live with; it rendered the statistical tools of financial economics useless, since the modeling of abnormal distributions was a problem largely unsolved in mathematics.

 • Eugene Fama, the father of efficient-market theory, who got to know Mandelbrot at the time, conducted tests on stock-price changes that confirmed Mandelbrot's assertion.  If price changes had been normally distributed, jumps greater than five standard deviations should have shown up in daily price data about once every 7,000 years.  

 • Instead, they [price changes greater than five standard deviations] cropped up about once every three to four years. 

 • Having made this discovery, Fama and his colleagues buried it.  

 • the ... hypothesis did not apply to moments of crisis. 

pp.104-105

The efficient-market hypothesis had always been based on a precarious assumption:  the price changes conformed to a “normal” probability distribution ── the one represented  by the familiar bell curve, in which numbers at and near the median crop up frequently while numbers in the tails distribution are rare to the point of vanishing.  Even in the early 1960s, a maverick mathematician named Benoit Mandelbrot argued that the tails of the distribution might be fatter than the normal bell curve assumed; and Eugene Fama, the father of efficient-market theory, who got to know Mandelbrot at the time, conducted tests on stock-price changes that confirmed Mandelbrot's assertion.  If price changes had been normally distributed, jumps greater than five standard deviations should have shown up in daily price data about once every 7,000 years.  Instead, they cropped up about once every three to four years. 

   Having made this discovery, Fama and his colleagues buried it.  The trouble with Mandelbrot's insight was that it was too awkward to live with; it rendered the statistical tools of financial economics useless, since the modeling of abnormal distributions was a problem largely unsolved in mathematics.

p.105

Paul Cootner, complained that “Mandelbrot, like Prime Minister Churchill before him, promises us not utopia but blood, sweat, toil and tears. If he is right, almost all of our statistical tools are obsolete ── least squares, spectral analysis, workable maximum-likelihood solutions, all our established sample theory, closed distribution functions. Almost without exception, past econometric work is meaningless.”66  

p.105

To prevent itself from toppling into this intellectual abyss, the economics profession kept its eyes trained the other way, especially since the mathematics of normal distributions was generating stunning breakthroughs.  

p.105

In 1973 a trio of economists produced a revolutionary method for valuing options, and a thrilling new financial industry was born.  Mandelbrot's objections were brushed off. 

p.105

   The crash of 1987 forced the economics profession to reexamine that assertion. 

p.105

To put that probability into perspective, it meant that an event such as the crash would not be anticipated to occur even if the stock market were to remain open for twenty billion years, the upper end of the expected duration of the universe, 

p.106

   As well as challenging the statistical foundation of financial economists' thinking, Black Monday forced a reconsideration of their institutional assumptions. 

p.106

In the chaos of the market meltdown, brokers' phone lines were jammed with calls from panicking sellers; it was hard to get through and place an order. 

p.106

And, most important, the sheer weight of selling made it too risky to go against the trend.  When the whole world is selling, it doesn't matter whether sophisticated hedge funds believe that prices have fallen too far.  Buying is crazy. 

   At a minimum, it seemed, the efficient-market hypothesis did not apply to moments of crisis. 

pp.106-107

But the crash raised a further question too:  If markets were efficient, why had the equity bubble inflated in the first place?  Again, the answer seemed to lie partly in the institutional obstacles faced by speculators.  In the summer of 1987, investors could see plainly that stocks were selling for higher multiples of corporate earnings than they had historically; but if the market was determined to value them that way, it would cost money to buck it. 

   (More money than god : hedge funds and the making of a new elite / Sebastian Mallaby.,  1. hedge funds., 2. investment advisors.,  HG4530.M249  2010, 332.64'524──dc22, 2010, )

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