Thursday, September 18, 2008

Let's take it down a notch

Okay, that last post ended up being way too long and more complex than I wanted. Let's try again with an even simpler example.

I am a bookie. I have taken a bet for $100 that the St. Louis Rams will win the Super Bowl, at odds of 100,000 to 1. That is, if the Rams do win the Super Bowl, I have to pay out $10,000,000. I don't have $10,000,000, so I have a few options on how to cover this possibility.

a) I could sell counter-bets. That is, I could get 100 people to bet me $100,000 each that the Rams won't win the Super Bowl. If the Rams win, then I owe one person $10,000,000, and I have $100,000 x 100 = $10,000,000 in hand to pay this off. If the Rams lose, I pay back the 100 original bettors their money, plus $1 each. I can cover that with the $100 from the original bet on the Rams.

b) I could lay off the risk to someone else. That is, I could take the original $100 and lay a bet with a different bookie on the Rams at 100,000 to 1. If the Rams win, then bookie B will pay me $10,000,000, and I'll use that to pay off the original bettor.

c) I could take a lot of other 100,000 to 1 bets on different events. That is, I can take a $100 bet that the Pittsburgh Pirates will win the World Series. If I take 100,000 more bets with these odds, all at $100, then I've got $10,000,000 in hand. If it so happens that the Rams win the Super Bowl, I'm alright.

So what happened? Well, not only did the Rams win the Super Bowl, but the Pirates won the World Series as well. How do I pay back the $20,000,000 I owe? Well, if I pursued option c), then I've only got $10,000,000 on hand, and I can't cover the bets. If I used option b), then I should be cashing in my own bets on the Rams and the Pirates, and I should be okay.

So some firms got into trouble right away, because they used option c), and got burned by two low probability events. The firms that used option b) went to their bookies and asked to get paid off, except that their bookies were the ones using option c). So the firms using option b) ended up not being able to get paid off either. So in the end the firms could not make good the original bets.

Who is to blame? Firms using option c) seem culpable - but the chances that two 1/100,000 events happen at once is 1 in 100,000,000,000 - so maybe they were just unlucky. Firms using b) were trying to be careful, but maybe they should have paid more attention to whom they were betting with.

All the firms were stupid in one sense. They did not consider that some of the 1 in 100,000 events were correlated. That is, it sure seems like the Pirates and Rams have nothing to do with each other. They play different sports. Except that a little research would have shown that they are owned by the same company, and a new training regimen imposed by the company made the players on both teams better. If they had known this, then the probability of both events happening is much better than 1 in 100,000,000,000.

In real life, firms didn't consider enough that mortgage defaults are correlated with each other. Defaults could be correlated because they are related to general housing conditions, which affect everyone. Firms got caught out when defaults went way higher than they expected (i.e. both the Rams and the Pirates won), and since they all were exposed the same way, no one could pay anyone else off.

Now none of the firms (bookies) are willing to take any bets until they figure out how much they will actually get paid back. No bookies, no bets = no loans, no economic expansion.

1 comment:

Diane Vollrath said...

surprisingly, I got it the first time


But sports analogies aren't my thing - I still like the cupcakes best