The man who broke the world?

Apr 27th, 2009 | By | Category: International

Headache inducing calculations of how much extra tax will be payable through the self-assessment system on 31st October; the permanently miserable visage of Taoiseach Brian Cowen; the strike by Dublin bus drivers against cutbacks; the fact that the Luas will not run from just down the road this year; a friend’s loss of his job last month; the anxiety amongst pensioners about what other reductions they face; the derelict properties along our road; the bigger class sizes in the primary school; the prospect of having no prospect of retiring at the age of 65 – the list of the consequences of the Crisis, both small and large, both personal and universal could go on and on and on.  And if things are bad here, what must they be like for those in Africa whose lives are already on a knife edge?

How did we get where we are?

The conspiracy theorists offer their usual fantastic solutions.  The Left believe it is the end of capitalism.  Even Christian writers have come up with some extraordinary stuff – the idolatry of Mammon and other such suggestions, (though it is odd how so many of them seem quite happy to point the finger at others while leading their own comfortable middle class lives).

The Crisis seems to stem not from conspiracies or spiritual forces, but from the much more mundane matter of doing the wrong sums.  The actuarial calculation that suggested that, for instance, Johnny Cash would die of a ‘broken heart’ soon after his partner was used as a basis for calculating what might be reasonable levels of lending on the world’s financial markets.

Sam Jones brilliant analysis “Of couples and copulas” in the weekend Financial Times magazine should be published as a leaflet and sent to every home in the country.  It is seems almost incredible that the work of one Chinese mathematician should have laid the foundation for the explosion of credit and the implosion of the world’s financial system.

David Li had worked in actuarial science, that field of life insurance and pensions work that calculates when we are likely to die.  He went to work in New York ten years ago, where there had been a great influx of physicists, the so-called ‘quants’ who were attracted by the salaries and the challenges of applying their mathematical skills to the financial markets.  Li’s contribution was to devise a mathematical model of how things were linked.  Sam Jones’ writes:

Borrowing from his work in actuarial science and insurance and his knowledge of the broken-heart syndrome, he attempted to solve one of Wall Street quants’ most intractable problems: default correlation.

Markets do not function in laboratory-like isolation. They are linked, correlated . . . Suppose, for example, that a bank loans money to two outfits – a dairy farm and a dairy. The farm, according to ratings agencies, has a 10 per cent chance of going bust and the dairy a 5 per cent chance. But if the farm does go under, the chances that the dairy will follow will rise above 5 per cent – quickly and steeply – if the farm was its main milk supplier.

And it gets more complicated from there. How correlated are the default probabilities on bonds issued by our Irish dairy farm and those issued by a software company in Malaysia? Not at all, you might think: the businesses not only provide totally different products and services, they’re also geographically remote from each other. Suppose, though, that both companies have been lent money by the same troubled bank that is now calling in its loans . . .

Financial institutions needed to know if their investment was a reasonable risk and Li was to present what appeared to be a foolproof model on which to base decisions.

“Suddenly I thought that the problem I was trying to solve [as an actuary] was exactly the problem these guys were trying to solve. Default [on a loan] is like the death of a company.” And if he could apply the broken hearts maths to broken companies, he’d have a way of mathematically modelling the effect that one company’s default would have on the chance of default for others.

He decided to use a very standard type of curve – the Gaussian copula, which is better known as a bell curve, or normal distribution – to map and determine the correlation on any given portfolio of assets. In the same way that actuaries could tell their employers the chances of Johnny Cash dying soon after June Carter without knowing anything about Cash other than the fact of his recent widowhood, so quants could tell their employers the effect one company defaulting might have on another doing the same – without knowing anything about the companies themselves. From this point on, it really could be, would be, a number-crunching game . . .

In November 2003, Sam Jones describes Li’s moment of triumph:

The presentation was a riot of equations, mathematical lemmas, arching curves and matrices of numbers. The questions afterwards were deferential, technical. Li, it seemed, had found the final piece of a risk-management jigsaw that banks had been slowly piecing together since quants arrived on Wall Street.

Of course, the wheels came off the  machine.  Calculating when someone might die is a far more precise business than calculating economic behaviour.

How had Li’s formula failed to anticipate this? The problem was that it assumed events tended to cluster heavily around an average – a “normal” state. In actuarial science, Li’s formula could adequately capture binary outcomes such as life or death, but in the messy world of mortgages and economics, it faltered. The range of possible outcomes here was more complicated, and indeed, random, than those facing an insurance company’s clients. Markets – particularly the mortgage market – were far more prone to extreme correlation scenarios than were insurers. Death from a broken heart, for all its poetic associations, is far easier to predict than the more prosaic, but ultimately unknowable, interrelatedness of markets.

None of which changes the reality of where we are, but perhaps offers a more sanguine prospect of the future.  We are not in the hands of conspirators or demons, we are the victims of simple mistakes.  As Sir Bernard Ingham once commented, “Many journalists have fallen for the conspiracy theory of government. I do assure you that they would produce more accurate work if they adhered to the cock-up theory.”

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  1. Wow Ian this is very interesting and I normally have a brain freeze when you discuss economics. One thing he doesn’t seem to factor in is ‘fear’ and ’emotional investing’ despite the mathematical and logical reasons for this current meltdown, add journalists and negative reporting into the equation and you have an unreasonable fear of buying back into the markets. Despite US confidence that they’ve bottomed, I’m not so sure . . there’s still a whole heap of uncertainty out there that even the most stalward economic equation can’t factor in.

  2. I suppose there was always uncertainty in the actuarial market, but spread across a sufficiently large number, the sums turned out correctly. I find fascinating the idea that economics is even more uncertain than life and death – shows how much worth one can attach to the ‘expert’ opinions.

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