Posted on 03/31/2005 11:34:57 AM PST by nickcarraway
Assume that City slickers are dumb and their effects on markets can be reproduced, according to complexity theory. Roger Highfield reports
You might be forgiven for wondering if the best way to invest in stock markets is to consult a chimpanzee first - it has long been suspected that City hotshots are just lucky, overpaid fools who work in an industry where chance rules.
Aping it: buying and selling shares is as much a matter of luck as rational thought
Now science is beginning to support the idea that randomness, not rationality, exerts surprising sway over the markets. The insights have come from researchers who are interested in complexity, where the simple behaviour of many traders in a market governed by various rules can produce highly complex "emergent" behaviour (the waxing and the waning of share prices).
The effect is driven by non-linearity, which abounds in nature. To put it simply, a linear world is an idealised one where one plus one makes two. A nonlinear world - the one we live in - is where one thousand plus one thousand oranges could lead to something quite different from two thousand oranges, such as a marmalade factory.
One of the leading exponents of applying complexity theory to the markets is Prof Doyne Farmer of the Santa Fe Institute in New Mexico, where much of the pioneering work in the field was done. In work in the institute, and for the Prediction Company which he founded, he has tried to model human traders as simple software programs - called agents - to see if they can reproduce the behaviour of the London Stock Exchange.
With his colleagues, including Dr Paolo Patelli and Ilija Zovko, Prof Farmer decided to start out with the simplest model of all. They assumed that their software traders place orders to buy and sell at random, subject only to trading rules in a typical financial market. This "is something you can teach your dog", said Prof Farmer. "You can program your computer to do it in one line."
They tested their simple minded traders on 21 months of data on 11 stocks from the London Stock Exchange. The model did not predict prices, but it did reflect, to a surprising degree, the variation from stock to stock, the spread - the difference between buying and selling prices - and the price diffusion rate, how actively prices were moving around, two basic market properties.
Although most economic models stress the role of strategy in financial market transactions, this study shows that it is possible for a computer to reproduce the variations in stocks by dropping assumptions of rationality nearly altogether. The predictive power of this "zero intelligence" model will fuel suspicions that fund managers rely more on luck than judgment.
But the success of this model does not imply that stock traders are devoid of any intelligent thought, as they try to outwit each other, said Mr Zovko. The rise and fall of stock prices is also deeply affected by the rules of trading, and their effects can be arbitrary in the same way that calls handled by a telephone exchange can be modelled randomly, even though most people have a good reason to pick up the phone.
"The prevailing view in economics about how markets function is that you have a rational investor rationally processing all the information that arrives," said Prof Farmer. "Our analysis challenges that view by saying that maybe a lot of price movement is more or less mechanical."
The study reinforces the conclusions of an earlier study by Prof Farmer, working with Dr Fabrizio Lillo and Prof Rosario Mantegna at the University of Palermo, Italy. After analysing transactions and quotes at the New York Stock exchange for the 1,000 most capitalised stocks between 1995 and 1998, they found regularity in the way market prices respond to new orders.
The study found a "master curve" of the mean price change (known by specialists as the market impact function) caused by a single transaction of a given volume in the sea of seemingly random fluctuations in the supply and demand of stocks. But, once again, their results were consistent with some aspects of trading having the same statistical properties found in idealised computer models of a stock market populated by "zero-intelligence" traders.
Meanwhile, another pioneer in complexity science has gone so far as to claim that the edifice of financial theory that has been erected by economists over the past century rests on faulty foundations, placing investors at much greater risk of ruin than they realise.
Prof Benoit Mandelbrot of Yale University, New Haven, is the maverick 80-year-old father of fractal geometry, the mathematics of roughness. The most famous example of fractals, the Mandelbrot Set (see above), has been replicated on millions of posters, T-shirts and albums and his work has had a profound impact on a range of fields, from art to pure mathematics.
A fractal, from the Latin for "broken", is a shape that can be broken into smaller parts, each an echo of the whole. A cauliflower is fractal: each floret is, itself, a cauliflower in miniature. Similarly, fractal geometry can describe a statistical pattern, such as the patterns in a stock-price chart.
Mandelbrot's fractal models can reduce the complex gyrations of IBM's stock price, the FTSE 100, cotton trading and exchange rates to more straightforward formulae that yield a more accurate description risk. As a consequence, Prof Mandelbrot is credited with pioneering the application of physics techniques to economics - what is today called "econophysics".
Recently, Prof Mandelbrot launched an attack on financial theory in The (Mis)behaviour of Markets: A Fractal View of Risk, Ruin and Reward, written with Richard L Hudson, the former managing editor of the European edition of the Wall Street Journal, who lives in Brussels.
"Standard financial theories, as taught in business schools around the world, are fundamentally wrong," said Mr Hudson. "They under-estimate the real risk of stock, bond, commodity and other asset markets." By contrast, a "fractal" financial theory offers better understanding of how markets work, of risk and "how it is that we gain and lose fortunes with such frightening rapidity," he said.
Current financial theory - modern portfolio theory, by which stock portfolios can be built; the capital asset pricing model, to price securities and value acquisitions; the Black-Scholes formula to price stock and other options contracts; and the efficient market hypothesis - the theory behind the growth of stock-index funds - rest on work by French mathematician Louis Bachelier, who pioneered the "random walk hypothesis" for stock prices.
These modern models adopt Bachelier's assumption that a "bell curve" describes how much prices vary up or down, with few big movements and lots of little movements constrained within a fairly narrow range. But, as Prof Mandelbrot first demonstrated four decades ago and other economists have since confirmed, prices vary much more wildly than the bell curve.
They follow so-called "power-law" distributions and change discontinuously. These distributions are everywhere. They are found in the size of earthquakes, where there are lots of small events, a few big ones and an intermediate number of average-sized ones. The law also rules the links between sites on the internet. And a power law rules the stock market.
Sharp price swings - crashes and booms - are far more common than the standard models assume. And price changes in the past affect markets today; they are not "independent" from one another, as standard models also assume.
"The mathematics behind a lot of the most common financial calculations - how to balance a portfolio of stocks and bonds, how to decide whether an acquisition is priced right, how to hedge a dollar/sterling currency exposure - can be dangerously off-base," said Mr Hudson. "It can, for instance, underestimate the risk of going broke by several orders of magnitude."
The alternative, "fractal finance", offers, they believe, a more powerful tool for reducing the way a particular price varies - a cotton price, a stock chart or a dollar-euro exchange rate - to a few simple mathematical ideas.
Prof Mandelbrot's analysis suggests that bubbles, such as the internet boom, are an inevitable part of markets and that even substantial-looking patterns can, in fact, be the product of mere fractal chance. That explains why most people miss market trends or imagine them where none exist - to their own financial grief.
Some fund managers around the world are now playing with Prof Mandelbrot's ideas. However, when asked whether he is now rich as a result of using them, the fractal wizard declined to put his mouth where his money is: "I never discuss politics, religion, sex or my portfolio.''
Roger Highfield will judge Fame Lab at the Cheltenham Science Festival, which takes place from June 8-12. Booking opens March 14 - for a brochure call 01242 237377, email boxoffice@cheltenham.gov.uk or visit www.cheltenhamfestivals.org.uk. We have negotiated a rate of £110 for a double/twin room (£65 for a single) per night B&B in Cheltenham's four star Queen's Hotel, located two minutes walk from most of the Festival venues. Prices are based on a minimum two-night stay between Thursday 9 and Sunday 12 June, 2005. Call Cheltenham TIC to book on 01242 517110, quoting Telegraph Science reader offer.
The (Mis)behaviour of Markets: A Fractal View of Risk, Ruin and Reward by Benoit Mandelbrot with Richard L Hudson (Basic Books) is available for £27.50 plus £2.25 p&p. To order, please call Telegraph Books Direct on 0870 155 7222
Interesting.
I just finished it. I highly reccomend it to anyone who has spent years learning modern finance theory in school, or studying for the CFA. This book will blow your mind.
...but the democrats don't think we're smart enough to manage private social security accounts.
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