Long View: When it's time to ask for whom the bell curve tolls
By John Authers, Investment Editor
Published: May 2 2008 21:31 | Last updated: May 2 2008 21:31
"Do you know what a bell curve is? It's a curve, shaped like a bell."
London mayoral candidate Boris Johnson, speaking at the Oxford Union in 1985
As investors we put a lot of weight on the bell curve, perhaps too much weight, and certainly more than we realise. Our investment and risk decisions depend on it. Mr Johnson was describing what statisticians call the "normal distribution," which frequently recurs in nature. As the diagram shows it is, indeed, shaped like a bell.
In nature, all kinds of phenomena – from the height of humans to the number of peas in a pod – follow this distribution. And the assumption that investment returns also follow a bell curve is the building block for a system which is central to the way fund managers approach risk. Known as "Value at Risk" or "VaR", all MBA students learn about it early on at business school.
The diagram shows how it works. Armed with a good sample of past results, statisticians can predict future results with some confidence. Most will be clustered around the mean in the centre. Typically for stocks, this will be a moderate profit. Better returns to this are on the right side of the bell, with outlying strokes of great fortune on the far right. The really nasty losses will all be on the left hand side of the bell, known as the tail.
Using statistical techniques that work in the natural sciences, a risk manager can now work out the risk of such a loss. The line in the diagram shows the level of losses which will happen only 1 per cent of the time. In the jargon, a risk manager can now say that "with 99 per cent confidence" their value at risk is the amount of money that is lost at that point. There is a 99 per cent chance that the investment will do better than that.
If the VaR at this point is too much to swallow, then the risk manager will take steps to move to reduce their risks. It can be a useful common sense tool for thinking about risk.
The problem is that VaR has become ubiquitous. Regulators and ratings agencies allow banks to decide how much capital they should have using VaR models. Since the credit crisis started, VaR has come in for criticism. One problem is that it is backward looking. If the past sample of investment returns was gleaned from
a period of low volatility and strong stock returns, as we had from 2003 to 2007, they will not be much use in navigating the current situation. UBS, which has needed to raise more capital, blamed this in part on its VaR model which was "based on five years of data, whereby the data were sourced from a period of relatively positive growth".
VaR also does not take account of what are now known as "black swans"
– extreme events that have not happened in the past. These can lead to extreme results, or change the shape of the bell for the future. The unprecedented fall in US national house prices may be such a black swan.
Still another argument is that if everyone moves to the same place on the bell curve – where they expect a good return for little risk – they will change the shape of the curve. If everyone crowds into the same investments, they will create the conditions for sudden reversals and extra volatility. That inflicted bad losses on many fund managers last summer.
A new objection which I saw aired last month for the first time is even more profound. Even if we do follow a bell curve, VaR can lead to excessive risk.
David Einhorn, a New York hedge fund manager, offers the following example: you are offered odds of 127 to one on $100 that when you toss a coin, heads will not come up seven times in a row. The chance that you will win is 99.2 per cent. So you can say with 99 per cent confidence that you have no value at risk. Using a VaR model, a bank could hold no capital to guard against a loss on this bet.
But in fact there is a 0.8 per cent chance (not an unimaginable black swan) that they will lose $12,700.
What risk managers need to know, according to Mr Einhorn, is what will happen in the "tail" – the 1 per cent of the time when things go wrong. By ignoring the tails, he says, "it creates an incentive to take excessive but remote risks". It also "creates
a false sense of security". Where does this leave us? Risk managers have made horrible mistakes in the past year. But VaR might still have its uses. Academics are working on improvements to VaR, using computers to "stress test" their assumptions for black swan events, or trying to model the effects when many investors make the same decisions. Critics, such as James Montier of Société Générale, lambast VaR as "pseudoscience". "Simply because something can be quantified doesn't mean that it is sensible," he says. "There is no substitute for rigorous critical or sceptical thinking."
He is right about this. But like other tools taught at business school, quantifying risks can be useful, provided they do not take the place of common sense, or imagination. In future, risk managers and investors should use their quantitative tools, and then think much more carefully about what could go wrong.
Copyright The Financial Times Limited 2008
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