Beware financial models

Creating a financial formula might win you the Nobel Prize for Economics, but such models offer dangerous comfort

Hari Seldon, professor of maths at Streeling University, excels at two things: martial arts and using probablism to predict the future of markets, economies and empires with astonishing accuracy. Hari can't rescue us from recession – he's a fictional hero created by sci-fi guru Isaac Asimov. But the credit crunch should prompt directors to ask if today's mathematical financial models are any better than science fiction.

Take the mother of all financial mathematical equations for analyzing equity-market data, Black-Scholes. By successfully putting a value on an option, the model makes it seem that risk is defined and controlled. But like any model, Black-Scholes makes assumptions, one being that the drifting value of an equity emulates Brownian motion.

Imagine, for example, a huge ball on the concourse of Tokyo's Shinjuku station. Busy commuters are rushing in all directions for trains, coffee, exits. The ball takes many hits but they mostly cancel each other out, so it goes nowhere fast, unpredictably. The commuters represent lots of fast transactions; the ball is the Brownian drift of the equity's value.

If there's a panic at Shinjuku, commuters dash for the exits en masse. When the market reaches crisis point, everyone wants out at once. Black-Scholes can't handle that – it was never meant to model unpredictable human behaviour. 

Black-Scholes was a huge advance that created more liquidity, but paved the way for  CDOs (Collateralised Debt Obligations) – sophisticated financial tools that repackage individual loans into a sellable product.

Did the model fail? Mathematical high-brows Emanuel Derman and Paul Wilmott say all models sweep dirt under the rug, but a good model makes the absence of dirt visible. Black-Scholes does this beautifully, but CDOs were so complex they could hide a lot of dirt. This prompted Derman and Wilmott to draft their Hippocratic Oath for Modelers which, in edited form, may help those obliged to use these models at work:

1. Don't be seduced or overawed by elegant equations. To confuse a model with the real world is to embrace a future disaster driven by the belief that humans obey mathematical rules.

2. If you don't understand what a model assumes, don't use the model.

3. When the assumptions stop applying to reality, stop applying the model to reality. Otherwise, your actions may have enormous effects on your job, your business and the economy, many of them beyond your comprehension.

Some CFOs have gone further than Derman and Wilmott, turning to simpler models derived from traffic lights – three levels of alert that highlight escalating potential for disruption – or developing scenario budgets that run alongside normal budgets and give early warning that forecast and reality are diverging dangerously.

Irving Wladawsky-Berger, chairman of IBM's academy of technology, believes businesses need to become smarter, and braver, as they spin scenarios: "Like meteorologists tracking a hurricane, you want to leverage advanced technologies and real-time information to figure out different scenarious and keep re-running the models as new information comes in. But you need to assemble people with a diverse set of skills and opinions. The best decisions are based on quantification and numbers and human judgement, especially from experienced managers who intuitively feel when something is not quite right."

The Modelers' Oath, simple warning tools, and the right blend of IT and instinct could help limit the damage until a real Hari Seldon comes along.