36 | NewScientist | 6 June 2009

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Bubble math

The human factor

The current financial crisis started with

an enormous housing bubble in the US,

UK and elsewhere. People borrowed

ever more against the value of their

homes and lenders sold the risk on,

in an impenetrable web of financial

transactions. Common sense might

have pointed to a brewing catastrophe.

Yet amazingly, some financial

institutions were assessing their risks

with models that ignored the possibility

that housing prices might fall.

The reason was a mixture of

shortsightedness – a decade or more

of continuous growth had obscured

the longer-term reality of market

fluctuations – and rampant greed: if

there are megabucks to be made today,

why worry too much about tomorrow?

That’s why we need objective signs

of trouble building, says physicist Didier

Sornette of the Swiss Federal Institute

of Technology (ETH) in Zurich. He heads

a new lab at ETH called the Financial

Crisis Observatory , which aims to detect

developing market bubbles from the

mathematical patterns they throw up.

His work indicates that can be done

by looking for any quantity, such as

housing or stock values, that is rising

faster than exponentially over a period

of time . That is an indication, he

suggests, of potentially dangerous

positive feedback, in which confidence

engendered by upward moves on a

market encourages ever more people to

invest – without any objective increase

in the worth of what is being traded.

That sort of behaviour can be

identified by plotting the logarithm

of prices in a given market over time.

Anything greater than a straight-line

increase is a danger signal. Despite

its simplicity, this is an approach that

hasn’t been applied before – and there

is evidence it works. In 2005, Sornette

and his colleague Wei-Xing Zhou found

the signature of a fast-growing bubble

in US housing data over the previous

two years, especially in the north-east

and the west of the country, and

predicted a bursting point of mid-2006

that turned out to be fairly accurate

(Physica A, vol 361, p 297).

“With the right monitoring, it would

have been clear that the last 15 years

of excesses were leading to an

unsustainable regime that could only

blow up,” says Sornette. His group is

now developing similar techniques for

monitoring, for example, the stock

values of the 500 largest US companies.

Estimated global credit

write-down 2009-10

trillion4$

6 June 2009 | NewScientist | 37

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Purely mathematical approaches such as

Sornette’s have a big drawback: the irrational

behaviour of people. In any bubble, those

making big profits will find arguments as to

why this time the underlying maths should

be different. Before the dotcom bubble burst

10 years ago, the reasoning was that the

internet had created a “new economy”; in the

build-up to the current crisis, people said that

financial engineering had made mortgage

risk a thing of the past.

That’s why renowned economists Karl Case

of Wellesley College in Massachusetts and

Robert Shiller of Yale University suggest that

if we are to identify bubbles before they

burst, their brethren need to get a lot more

psychological in their approach. Traditionally,

economists rarely ask people about the

thinking behind their decisions. Some even

argue that one should never do so, as people’s

assessments of their own motivations are so

skewed as to be scientifically worthless.

Case and Shiller’s research, however,

suggests that bubbles show up most easily

through probes of individual attitudes to

economic reality. “The notion of a bubble is

really defined in terms of people’s thinking,”

says Shiller. Their large-scale surveys show,

for instance, that the current crisis came

about when people started believing that

future rises in property values would largely

pay for their other investments, relieving

them of any need to save for a rainy day.

“If you word questions carefully,” says

Shiller, “you can learn what people are

thinking and how they’re making their

decisions. You need this kind of information

to detect a bubble.” Coupled with more

mathematical approaches, that might provide

just enough warning for politicians and

regulators to step in and mitigate the worst

of crashes before they happen.

Bubbles are nothing new (see “The madness of

crowds”, page 42). Now, though, a bubble in just

one country can cause the whole world’s economy

to collapse. Globalisation would be hard to roll

back – so how do we contain its dangers?

Economists have been worrying about this kind

of “systemic risk” since the bank failures of the Great

Depression in the 1930s. Regulations introduced soon

afterwards required banks to hold adequate reserves,

and governments guaranteed many bank deposits.

For 70 years, that avoided a repeat.

The present crisis owes much to the emergence

of a globally interlinked “shadow banking system” –

investment banks, hedge funds, mutual funds,

insurance companies and the like – not subject to

these safeguards. Producing policy prescriptions this

time will mean penetrating that complex web to find

out how it was woven – and what made it break.

The essential tool will be network theory –

a branch of applied mathematics used to tease

out complex relationships in areas from computing

to biology. Last year, for example, economists

Domenico Delli Gatti of the Catholic University of

Milan, Italy, and his colleagues, including Nobel

prizewinner Joseph Stiglitz of Columbia University in

New York, used the approach to show how a few

banks in a network generally emerge as connecting

hubs with an outsized share of links.

“Financially robust lenders can supply credit at

better conditions and therefore tend to increase

their market share, attracting a higher number of

links,” says Delli Gatti. That’s good in the short term

for people looking for money, but it suggests

systemic risk grows naturally as a system becomes

dependent on a few pivotal institutions. Their failure

can trigger avalanches of further trouble.

Financial food websthat conclusion is borne out by research from John

Geanakoplos of Yale University and his colleagues.

They studied how hedge funds compete to attract

investors by seeking high leverage – borrowing

heavily to amplify the funds they can invest, as well

as their potential profits. In simulations of market

activity, the researchers show how this creates

enormous credit dependencies between banks and

hedge funds that can push markets through an

abrupt “phase transition” from stability to instability,

much as solid ice abruptly melts into liquid water.

So how might we engineer our financial networks

more robustly? Some scientists think that answers

lie in areas where similar risks emerge. Ecologists,

for instance, have spent decades getting to grips

Network solutions

Global chaos began with

home repossessions

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