The Financial Crisis: Time for mathematicians to stand up and be counted

When something goes wrong in our society, there are usually three stages to its analysis: Stage 1 is a rant in the media, usually with petrol poured on the fire by politicians looking for scape-goats and a deflection of attention from their own contribution. After a few weeks or months we move to stage two, where we get more useful facts and start to understand the matter. Stage three follows after many decades when the historians feel able to give a proper perspective, perhaps in the light of the release of confidential papers after the real rogues are long dead. The transition from stage 1 to stage 2 is a fascinating affair. If we look at the recent removal of the speaker, Michael Martin was initially vilified for his attempts to slow the release of information – now we are starting to find out that possibly he was leant on to do things against his own instincts.

So here we are struggling to move to stage 2 of our understanding of the financial crisis. We cannot wait for a historical analysis, as we need to repair things now.

Amongst all the scape-goating we should remember a very clear point. This crisis was triggered by a failure of regulation and lending, in which banks were allowed to lend to poorer clients without proper regulation. The banks did so in an environment of artificially low interest rates, to clients who failed to make the payments when rates went back up. This failure of not a matter of ‘rocket science’. It is not ‘A’-level maths. It is basic common sense.

Do not forget the root cause – a regulation failure

The biggest problem was in the US, but we should not allow ourselves to be distracted away from the corresponding problems in the UK. If you invest some money in a variety of regulated investment schemes you are given illustrations of what you might get back if the typical returns are 4, 6 or 8% (they used to be higher but the regulators changed their minds).

If you borrow money instead there is usually no such regulated and clear scenario analysis. I recall taking out a mortgage at 12.4% in around 1989. It is lucky for me that I remember that figure. Ordinary and “sub-prime” (higher risk) clients were recently allowed to borrow money on the basis of affordability calculated on the basis of historically low interest rate levels and were not routinely provided with proper and compulsory illustrations at, e.g. 8% and 12% as well as the proposed figures at around 4% or less. In May 2005 the UK FSA issued a lame statement saying they wanted to see improvements in mortgage Key Facts documents. Their good practice factsheet merely encouraged intermediaries to have customers have a “buffer”. Some recent “Key Facts” documents tell clients how much their payments will increase if rates go up by 1%, but for many unfortunate borrowers, the truth of their situation only becomes clear when they get a revised monthly payment demand and realize they might lose their home.

This is not ‘rocket science’. It is a spectacular failure of regulation. This failure permeates the financial regulation administration in this country, and is a direct result of appointing bankers to the regulator. Poachers turned gamekeeper are well known for letting their pals off.

It applies not just to mortgage and other loans, but in other scenarios of products that are linked to market volatility – this is the `rocket science’ of market folklore. Mr and Mrs Britain can buy from ads in the back of the Sunday newspapers that are complex financial products. You can find all kinds of exotic products, but the corresponding relevant scenarios, in this case comprising both return and volatility scenarios, are not given, nor, so far as I am aware, have the regulators asked for them. Why not? Perhaps, because it might upset the industry?

A detailed study of the “Madness of Mortgage Lenders” has been published in May 2009 by King’s Professor of Human Geography and leading expert on housing, Chris Hamnett – it is summarized here.

Politics 101: First create your scapegoat

Instead of grasping the importance of these basic causes there has been instead an orgy of mis-directed blame. As is traditional in such circumstances the blame is being directed at the group that the politicians and media think is the most vulnerable – the scientists. They tend not to get involved with the media so often, do not vigorously defend themselves and are more interested in quietly finding out the facts than influencing the headlines.

In the current crisis it is the ‘quants’ and financial mathematicians who are feeling the heat. The politicians have been allowed to construct this blame deflection because some of the mechanisms for transmitting the crisis that was originally created by regulation failure, involved products requiring mathematical analysis. So what should we say about mathematical colleagues who worked on mortgage-backed securities? Throw them in jail and lock away the key? Actually, no. Like any other human being with a job, mortgage and family, they responded to the profit-focused demands of their managers, their organization and its remuneration policy.

We need to re-define the remuneration of such people according to their success at risk control rather in terms of short-term profit. The reality is also that there were too few mathematicians in positions of sufficient responsibility to even argue, e.g., at board level, where they might be listened to, that the risk characteristics of products were too dangerous, and the personal risks they faced were often too high to speak out at all in the face of the search for profit. The history of science is littered with persecution of the individual who speaks out. Joseph Rotblat was subject to trumped up spying charges after he was the only physicist to leave the Manhattan (atomic bomb) project on grounds of conscience. Objectors and whistle blowers in the financial industry suffer a severe financial penalty, as has been well noted elsewhere.

The reality

The real, and bigger picture is that the financial mathematics part of the scientific community has worked on research to improve the modelling of risk and the nature of price changes in financial markets. We work on improving our understanding of the likelihood of extreme events, and of the means to hedge against them. Derivatives were introduced in order to allow companies to control their risk, for example by allowing a UK exporter to control its income from foreign sales in a market where exchange rates are volatile. Credit derivatives were introduced to allow organizations to protect themselves against defaults of other companies.

Some reckless folk then speculated on these products in an inadequately regulated market. Nick Leeson famously brought down Barings with his trading. It was a complicated situation but at the heart of it was a failure to take account of the basic maths of hedging. Leeson did not just ignore the mathematical rules – he went in the opposite direction of what they said he should do.

More recently, even the Chief Financial Officer of Goldman Sachs, which has in fact survived the crisis better than many organizations, was heard complaining in 2008 about experiencing “25 sigma events” (i.e. highly extreme events) three days in a row, as if this was so unlikely that they could not reasonably have expected it.

For just how long have mathematicians being trying to get the banks to do it properly?

In fact the mathematical finance community has been aware of the greater likelihood of extreme events for a very long time and continues to write about it. In 2006 a paper appeared in my own journal, Applied Mathematical Finance, by K. Fergusson and E. Platen, explaining that the daily returns on major world indices were modelled well by a “Student t distribution with four degrees of freedom”. You do not need to know exactly what this means. What you do need to know is that the likelihood of a “25 sigma” event is over 10 to the power 130 times more likely in that model than in the standard models used by many banks (based on Gaussian distributions). That is, 1 followed by over 130 zeroes, or, an “awful lot” more likely. The mathematical and statistical knowledge of the presence of kurtosis in asset returns actually go back decades, to the work of Mandelbrot in the 1960s and beyond, but were routinely ignored by banks and continue to be ignored, while calculating “Value at Risk” on the basis of old and naïve Gaussian assumptions. My own contributions to this area have focused on providing simple mathematical methods to allow risk to be assessed using models allowing more for extreme values – you can even find my own 2006 formula (published in the Journal of Computational Finance) for simple sampling of the key distribution observed earlier that year, on Wikipedia under “Quantile Function” – but in fact the basic ideas of sampling these “fat-tailed” objects that model extreme events goes back to 1970 and the work of G.W. Hill, and R. Bailey published a paper in 1994 that made it crystal clear how to make a simple modification, to an algorithm common in banking (Box-Muller, e.g. as in the Numerical Recipes books), to allow for the same effects. Professor P. Embrechts has been arguing from Switzerland for the proper use of maths to model extreme values for many years, and he, I and many other colleagues in the mathematical community have been pushing the cause of such models, and for models of dependency that capture the domino effect, for many years.

In the FT of 10^th June 2009, Lord Turner, Chair of the FSA, is quoted as follows:

The problem, he said, was that banks' mathematical models assumed a "normal" or "Gaussian" distribution of events, represented by the bell curve, which dangerously underestimated the risk of something going seriously wrong.

So we can see that it was known how to sort this out ages ago, and mathematicians have repeatedly explained how to do it. Other researchers have other “fat-tailed” distributions to be applied to other situations (hyperbolic, stable…). So the problem is not the intrusion of mathematics into banking. It is, rather, that there are too few mathematicians in the system, especially at the top levels of banking, finance and regulation. No-one should pretend that fixing this alone is a cure-all, but the financial system might then have a little more rationality and a bit more stability.