Pardon for another non-technical post, but I thought it may be interesting. A friend of mine, a professor at the University of Texas, presented an article of his student, introducing some mathmatical theory explaining the roots of today crisis in economy. And I could not resist to answer. If you know all this, please, understand. Afetr all, if some professors don't get it, it may be interesting to a fair share of people around...
So, here it is:
Do you think that may be this article is a little au contrare to Occam's razor principle?
You see, subprime mortgages per se are not what's the real reason of today's crisis. If it would be so, the cost of handling it would not be $700 bln+, but only around $40-50 bln to help people stay in homes and let the real estate bubble go down slower without big economical or social impact.
The real problems is derivatives based on these subprime mortgages. You don't need a mathematical theory or even Excel to explain it. Although, I admit, there was straightforward and intentional mathematical error in the middle, all right. In a case, somebody missed how it was done, let me explain with an example. Imagine a fleet of 1000 cars going over very long bridge which has a 50% chance to collapse in a next few minutes. Owner of this fleet, scared of the possibility, asks you to buy the whole fleet at a very attractive price. Now, you think, the chances that bridge will collapse is 50%, hence the chance to lose each specific car is 50%, now if I have 1000 cars then the chances that at least 10% of cars survive is much greater than that. You know, say for two cars probability that at least one to survive is p1+p2-p1*p2 = 0.5 + 0.5 - 0.5*0.5 = 0.75, that is 75%. And for a 1000 cars it's much much better. So if the part which will survive will cover the cost, you are good. You see the problem? Dependent events were represented as independent. A mistake unforgivable to a college student, but somehow ok for Wall Street CEOs.
If it's still not clear, let's say the fleet is 10 cars and owner offers you price of 10% of fair value. The chance that at least one car will survive if events are independent is 99.95%, so it looks like a sure shot. So you are entering the game with the expectations of 99.95% chance of not losing money and great expectation of making money. In fact, the chance of losing money is still 50%.
What they did was packaging a lot of subprime mortgages and applying the logic above. Then they issued the bonds based on, say, 10% of those mortgages, _whichever will survive_. And they got AAA rating to these bonds. And then, in expectation of profit, they issued bonds on these bonds with leverage ($1 in original bonds produced $10 in next derivatives) exceeding total annual planetary gross product in times. What was ignored is that the risk of subprime mortgages is not merely financial state of borrowers, but the state of the real estate bubble, which was going to burst with not even 50%, but with 100% probability, everybody knew that ahead. And financial state of the borrowers was not that independent either.
So, you see, no need for extra math or even Excel (although, I used it to calculate probabilities above). What we deal with is cheating and larceny, nothing a good cop could not handle in time without a need for extra math. Unfortunately, neither Greenspan, nor Bernanke proved themselves to be good cops.