Science reports on agent based models of financial leverage –Leverage: The Root of All Financial Turmoil:

Given that in the buildup to the recent global economic meltdown hedge funds had been leveraging their deals by ratios of 30-to-1 (that is, borrowing $30 for every $1 of their own that they put in), it may seem obvious that massive leverage leads to trouble. But Stefan Thurner, an econophysicist and director of the complex systems research group at the Medical University of Vienna, Austria, and colleagues say their model shows that many of the distinctive statistical properties of financial markets emerge together as rates of leverage climb. “Leverage is the driver,” Thurner says. “That wasn’t obvious.”

Financial markets behave in ways that, econophysicists say, classical economic theory cannot explain. Classical economics assumes that the fluctuations in stock prices conform to a so-called Gaussian distribution—a bell curve that gives little probability to large swings. In reality, the distribution has “fat tails” that make big changes more likely, and the shapes of those tails conform to a mathematical formula known as a power law. Classical economics assumes that the fluctuations are uncorrelated from one moment to the next, whereas big swings in prices tend to come together in the so-called clustering of volatility.

To try to explain those characteristics, over the past 5 years Thurner and colleagues have developed an “agent-based model” of a market. In such a computer model, virtual agents of various types interact according to certain rules, like robots playing a game. The researchers included hedge funds that could borrow to make their investments; banks to loan the money; “noise investors” who, like day traders, simply react to the market and have no other insight into the value of assets; and general investors who played the role of, for example, state pension funds.

The model contains more than a dozen adjustable parameters. However, Thurner and colleagues found that the maximum level of leverage exerts a curious, unifying effect. If they forbade leverage, the market behaved largely as classical economics would predict. But as they increased the maximum leverage, the characteristics of real markets emerged together. “We can explain the fat tails, the right [power law], the clustering of volatility, all this,” Thurner says. And when the leverage limit climbed to levels of 5-to-1 and beyond, the market became unstable and hedge funds went bust much more often.

“I thought it was rather brilliant,” says Christoph Jan Hamer, an econophysicist with Solvency Fabrik in Köln, Germany. Hamer says he was impressed with a detail of the model: If leverage is high, then a tiny fluctuation created by the noise traders can trigger a much bigger swing. But Christian Hirtreiter of the University of Regensburg says, “I would think that leverage itself is not the problem. I would think it is a symptom of the problem.”

Thurner, who managed a hedge fund that tanked, says that limiting leverage should help prevent crashes. He admits, however, that he would not have embraced that idea when the market was still going strong.