Investors blinded by science

Richard Beddard
15.11.04

Benoit Mandelbrot uses the word "ridiculous" with alarming frequency. It would be comical if the subject was not the mathematics underpinning the financial markets, but it is.

The professor is better known for changing the way we look at the natural world. He is best known for the infinitely iterative fractal images of the Mandelbrot Set. But in his book, The (mis)Behaviour of Markets he and co-author Richard Hudson say mathematicians do not understand the risk of ruin. Their models, used by fund managers, bankers and businessmen the financial world over, all understate risk.

The maths is not faulty, says Mandelbrot. It simply does not apply to markets.

Risk

"Risk is the dominant theme in markets," says Hudson. "We see that in the collapse of the internet bubble, we see that in every news event, we see that in 11 September - not the event itself but the way the markets reacted to it, we see that in the '87 crash."

Prices, says Mandelbrot, are much more variable than the 'Random Walk' assumed by conventional models. The Random Walk says prices move timidly around the mean, and extreme events are exceedingly rare; so rare they are easily ignored. Back in the real world prices hardly change for long periods. Then suddenly they make frightening moves; far larger and far more often than convention suggests.

While developing their competing models at IBM in the 1960s Mandelbrot and Harry Markowitz, the inventor of modern portfolio theory, would meet in the corridors: "I would ask him: 'You still believe in this nonsense about mean variance?'" says Mandelbrot, "And he would reply: 'You still believe in this nonsense about doing better?'"

According to standard theory you would not expect to see a 6.8% fall in the Dow Jones Industrial Average in 100,000 years of trading says Mandelbrot in his book. It fell 6.8% on 31 August 1998. It also fell heavily on two earlier occasions that month (odds of all three: one in 500 billion) and on 19 October 1987, just a decade earlier, it dropped 29%. The odds of that? "You could span the powers of ten from the smallest sub-atomic particle to the breadth of the measurable universe - and still never meet such a number."

Markowitz's theory and others that developed out of the Random Walk are attractive, says Mandelbrot, because they are reassuring. Bad things do not happen very often, and the mathematics is conventional and comparatively easy: "The formulas are simple. You can put them in a calculator."

But, like a badly designed software program, mathematicians have spent the last 40 years patching the theory to bridge the reality gap.

Champion of roughness

The degree to which things vary, or roughness, is complex. And Mandelbrot made it his life's work. Whether it is the surface of a metal, the coastline of the UK, or the inside of the human lung, Mandelbrot has measured its roughness using the fractal geometry he invented.

The maths is not easy. It is new and requires powerful computer programs. Mandelbrot only recently tied it together. Neither is it reassuring. Although fractal finance simplifies reality, it does not shirk it.

"It tries to look at the roughness of the world straight in the face," he says. In doing so, it describes what anyone who reads the business pages instinctively knows: "The risk of a company collapsing is viewed as infinitesimal by (modern finance) theory, is known not to be infinitesimal by practitioners and is acknowledged to be very significant by fractal theory."

Imagine the stock pickers crowing. Ever since the Random Walk gained acceptance active investors questioned it. In assuming a series of prices is modelled by a random sequence of coin tosses Mandelbrot says mathematicians made another dangerous assumption; that today's price change has no bearing on tomorrow's.

Accept that, and you accept you cannot beat the market because the price of a stock, currency or commodity embodies everything that is known about it.

"Is it true that every morning is a fresh beginning? It is ridiculous," says Mandelbrot, "Nobody believes in it." But millions invest in the index tracking funds the theory inspired.

Mandelbrot says a big rise today increases the chances of a big rise, or a big fall tomorrow. Volatility clusters, prices trend on people's expectations and correct as reality bites. Anomalies exist. In fact it is the anomalies that are important because that is where the serious money is made or lost.

Faking it

He says the proof is in the pictures. Try to fake a sequence of prices with a Random Walk and the resulting chart is tame. It only resembles a real market. A fractal simulation of a market is 'wild' and indistinguishable from the real thing, like the fractal landscapes that decorate idling computer screens.

You cannot ignore the palpable risk of ruin.

Mandelbrot says this is what Long Term Capital Management did. The hedge fund blew-up in 1998. It had borrowed heavily to buy Russian bonds and, though each bet it made was risky, theoretically the risks cancelled each other out because the prices were uncorrelated. They moved in different directions.

That was until August 1998 when the Russian government defaulted. Suddenly nobody wanted the bonds at any price, global markets fell into step, and LTCM could not ride-out its losses.

Despite having two Nobel Prize winning architects of modern finance theory on the team, they did not possess the mathematical tools to understand the risks they faced, says Mandelbrot. "They did not even conceive of the possibility." Fractal finance would have put them in the right "ballpark" he says.

Many UK investors underestimated the risks in 2001. And the companies that designed and sold them split-capital investment trusts and precipice bonds make their excuses. They claim nobody could have foreseen events, or a three-year bear market of such magnitude was wildly improbable.

Not so, says Mandelbrot: "The trouble with any model is it affects the way people think about reality... they know the market well but they are feeling that somehow it is simpler than it seems. That somebody has simplified matters miraculously to allow you to make money whether rain or shine."

Legacy

On Saturday Professor Mandelbrot will be eighty years old: "Either I will be six feet above, or six feet under," he says, "Now I feel I should make my main points very strongly… I do view that as part of my legacy."

A book on the markets is a small part of the rich intellectual bounty Mandelbrot is amassing. But he will leave a model that challenges mathematicians to understand the markets better and, he says, gives them the tools to do it. In the meantime he reminds us that to put money in the markets is to put it at risk of ruin. The irony is investors knew that all along. But some were blinded by science.