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The (Mis)behavior of Markets by Benoit Mandelbrot and Richard L. Hudson, Basic Books, 2006. $17.00
Benoit Mandelbrot was the first person to realize that prices are not normally distributed, not distributed as a bell-shaped curve.This was a subtle and incredibly important observation.Price distributions certainly looked normal.The deviations from normal were rare and easy to ignore.More important, perhaps, there were strong mathematical reasons why prices should be normally distributed.And if prices were not normally distributed, there would be consequences; trading would be much, much riskier than conventional theory asserted.
Mandelbrotís observations were more or less ignored until late in 1987.I discussed the issues in my books and articles and made suggestions (i.e., robust statistics, graphic techniques) for alleviating the problem, but not too many others did.I was beaten up by the editors of MAR, among others, for my positions.This was unpleasant, but not completely unreasonable.No one was completely sure Mandelbrot was right.Even assuming he was right, no one knew how prices were really distributed. Until you know how prices are distributed, you canít really manage risk, at least, not the way you are telling your clients you are.
On October 19, 1997, the market slipped a bit.According to Mandelbrot, the probability of that drop, given standard financial industry assumptions and given the behavior of the Dow from 1916 to 2003, was less than one in fifty billion.Suddenly, almost everyone saw that the old assumption of normality was wrong.Academics began researching distributions anew.Bankers and portfolio managers began stress testing their portfolios.Things got better.No, thatís wrong.As far as catastrophic risk was concerned, things got a little, tiny, shadow of a faint impression better.Long Term Capital Management crashed and burned in August 1998.At one time, LTCM had 25 PhDs on its payroll, including several of the finest investment minds in the world.I suspect that they were, at least, partially familiar with the issue.Now, there may have been many reasons why LTCM imploded but one of the reasons, surely, was that the markets were riskier than their models assumed.If a group as smart and educated and motivated as the staff of LTCM cannot manage this issue where does this leave the rest of us?
Mandelbrot does a good job of laying out the issues.This much is known: prices are not normally distributed, the markets are much riskier than our models indicate, many of our oldest and most trusted tools (portfolio theory, the capital asset pricing model, options theory and others) are deeply flawed.Beyond that, well, no one is really certain.Mandelbrot believes that price distributions follow multifractal laws.Mandelbrot invented fractals, a numerical/computer technique that, among other things, produces artificial, but amazingly lifelike drawings of mountains and coastlines.Roughly speaking, multifractals are the interactions of several fractal processes.Other investment academicians have other opinions.If we are lucky, the academicians will find consensus in a decade or two.
Mandelbrot provides no solutions to the problems he raises.In the meantime, therefore, those of us who are not willing to delay trading for a couple of decades need to worry.We need to review our legal statements to make sure what we claim to be doing can really be done.And we need to review every aspect of research, trading and portfolio management.A prudent director of research needs to ask himself what assumptions underlie his techniques and what the risks are if his assumptions are wrong.When his techniques assume normal distributions, which they will more often than not, he should probably replace them.(Exceptions that come to mind involve auditing and diagnostics.)In a few cases, mathematically trustworthy techniques are available now.For example, the state of the art for statistical testing is quite advanced (and completely ignored by those who sell shrink wrapped packages for developing trading methods.)When trustworthy techniques are not available, the manager must use the most robust techniques available (i.e., stress testing and Monte Carlo simulations) and then supplement them with graphic techniques that show what is happening without making assumptions.
Mandelbrotís book is quite readable.Richard L. Hudson, the co-author, was managing director of the Wall Street Journalís European edition.Unfortunately, the book is still confusing and repetitious.There is way too much of Mandelbrot in this book and not enough of the other people working in this field.I donít believe that this is Mr. Hudsonís fault.Mr. Mandelbrot sounds like he is very difficult to work with.If you are a quant or you manage quants, you need to read this book.At the very least, you need to understand that you have problems and you need to know what they are.
An earlier version of this article was published in MARHedge.
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