Banks now employ thousands of highly-qualified mathematicians to quantify risk for them. So why did they not foresee the credit crunch? Quantitative finance lecturer Paul Wilmott explains how a failure to see beyond the numbers might be to blame.
More or Less, Radio 4
Friday 5 December at 1330 GMT
Repeated Sunday at 2000 GMT
We have learned the hard way how important it is to measure and manage risk.
Despite the thousands of mathematics and science PhDs working in risk management nowadays we seem to be at greater financial and economic risk than ever before.
To show you one important side of banking I would like you to follow me in an exercise with parallels in risk management.
You are in the audience at a small, intimate theatre, watching a magic show.
The magician hands a pack of cards to a random member of the audience, asks him to check that it is an ordinary pack, and to give it a shuffle.
The magician turns to another member of the audience and asks her to name a card at random. "Ace of Hearts," she says.
Pick a card, any card
The magician covers his eyes, reaches out to the pack of cards, and after some fumbling around he pulls out a card.
The question to you is what is the probability of the card being the Ace of Hearts?
Think about this question while I talk a bit about risk management.
Feel free to interrupt me as soon as you have an answer.
Oh, you already have an answer? What is that, one in 52, you say? On the grounds that there are 52 cards in an ordinary pack.
It certainly is one answer.
But aren't you missing something, possibly crucial, in the question?
Ponder a bit more.
Risk managers employed by banks are often highly-qualified mathematicians
One aspect of risk management is that of 'scenario analysis.' Risk managers in banks have to consider possible future scenarios and the effects they will have on their bank's portfolio.
Assign probabilities to each event and you can estimate the distribution of future profit and loss. Not unlike our exercise with the cards. Of course, this is only as useful as the number of scenarios you can think of.
You have another answer for me already?
You had forgotten that it was a magician pulling out the card.
Well, yes, I can see that might make a difference.
So your answer is now that it will be almost 100% that the card will be the Ace of Hearts - the magician is hardly going to get this trick wrong.
Are you right?
Think just a while longer while I tell you more about risk and its management.
The risks of probabilities
Sometimes the impact of a scenario is quite easy to estimate. For example, a bank might ask what will happen to the value of their assets if interest rates rise by 1%.
After some mathematical analysis they will come up with an answer - which will depend, for example, on how many bonds they hold.
But estimating the probability of that interest rate rise in the first case might be quite tricky. And more complex scenarios might not even be considered.
What about the effects of combining rising interest rates, rising mortgage defaults and falling house prices in America?
Hmm, it is rather looking like that scenario didn't get the appreciation it deserved.
Back to our magician friend.
Are those the only two possible answers? Either one in 52 or 100%? Suppose you had billions of dollars of hedge fund money riding on the outcome of this magic trick - would you feel so confident in your answers?
(A hedge fund betting on the outcome of a magic show, how unrealistic! But did you know that there is at least one hedge fund that 'invests' in poker players, funding their play and taking a cut of their winnings? So who knows what they will think of next?)
When I ask finance people this question, I usually get either the one in 52 answer or the 100% answer.
Some will completely ignore the word 'magician,' hence the first answer.
Some will say "I'm supposed to give the maths answer, aren't I? But because he's a magician he will certainly pick the Ace of Hearts."
Rather frighteningly, some people trained in the higher mathematics of risk management still don't see the second answer even after being told.
This is really a question about whether modern risk managers are capable of thinking beyond maths and formulas.
Do they appreciate the human side of finance, the herding behaviour of people, the unintended consequences - what I think of as all the fun stuff?
The human side of finance
There is no correct answer to our magician problem.
The exercise is to think of as many possibilities as you can.
For example, when I first heard this question an obvious answer to me was zero.
There is no chance that the card is the Ace of Hearts.
This trick is too simple for any professional magician.
Maybe the trick is a small part of a larger effect - getting this part 'wrong' is designed to make a later feat more impressive...the Ace of Hearts is later found inside someone's pocket.
Or maybe on the card are the winning lottery numbers - which are drawn randomly 15 minutes later on live TV.
Or maybe the magician was Tommy Cooper.
When I ask non mathematicians, this is the sort of answer I get.
Once you start thinking outside the box of mathematical theories the possibilities are endless.
And although a knowledge of advanced mathematics is important in modern finance I do rather miss the days when banking was populated by managers with degrees in History, who had been leaders of the school debating team.
A lot of mathematics is no substitute for a little bit of commonsense and an open mind.
You can hear more on the risks of risk management on BBC Radio 4's More or Less on Friday, 5 December 2008 at 1330 GMT (repeated on Sunday 7 December at 2000 GMT). To subscribe to the podcast or listen again, visit the More or Less website.