My knowledge of statistics is decent; my knowledge of economics is not. But even I (after a little reading) can tell that the sub-prime loans crisis was due to people forgetting that probabilities need to be independent for simple maths to work on them.
Here's an example:
Let's say the probability of Man Utd winning the Premiership is 1/3, the probability of me getting over 60% on my patristics exam is 1/2 and the probability of Arsenal finishing outside the top two of the Premiership is 1/4.
Now how I do in my exams is pretty much independent of what goes on in football, so I can say that the chance of Man Utd winning the Premiership and of me getting over 60% on my patristics exam is 1/3 x 1/2 = 1/6.
But the chance of Man Utd winning and Arsenal finishing outside the top two aren't independent. If one happens, the other is more likely to happen. So the probability of that isn't just 1/3 x 1/4 = 1/12. It's going to be more than that.
That's roughly what happened with the sub-prime mortgages. They took lots of events which actually were connected to each other, in this case the chances of poor people in America being unable to pay their mortgages, but just multiplied the probabilities when assessing the risks. If someone had done that in a GCSE maths class I was teaching, I'd have told them off. But when they're doing it with the global economy, they probably deserve to be sacked and sued until they can't get any kind of mortgage, especially because the people their incompetence hurts most will be the poor. It pretty much always is.
As a result of America's mortgage crisis, we have learnt that, to play in banking's premier league, you need much more than a degree from Harvard Business School, the morals of an alley cat and an unbridled lust for riches. These attributes help, but the sine qua non of a seat at the top table is a willingness to suspend disbelief until junk loans to trailer-dwelling welfare claimants can be diced, sliced, spiced and resold as triple-A securities. This takes some doing, as the business - quite clearly - makes no sense.
It is like a restaurateur opening up cans of dog-meat, sprinkling it with herbs, presenting the mix as steak tartare, and charging £25 a portion for something that will poison most of his customers. The difference is, passing off chopped donkey for Aberdeen Angus would be illegal; the repackaging of toxic sub-prime mortgages as high-quality investments was not.