Friday, October 3, 2008

Martingales and the Financial Crisis

This article compares the developments on Wall Street to placing a martingale bet. In the martingale game you bet, say, $100 on a coin flip, and keep doubling down if you lose. The game seems to offer certain gain for no risk. If you lose on the first flip you bet $200 on the next, if it comes heads you are up $100 ($200 minus the $100 you lost on the first flip). Just hang around till you get a heads. Seems a sure thing. The problem, of course, is that it is always possible that you get a run of tails that could wipe you out before you win. This is the "law of gambler's ruin."

What is interesting about the game is that you have a high probability of winning a relatively small amount, and a small probability of losing a huge amount. Notice that as long as you don't have the cataclysmic event you are earning positive profits with seemingly no risk. You are a financial genius. You are imitated by other financial geniuses. You get a large bonus for your invention of a strategy that produces such high risk-adjusted returns.

Only you haven't really earned super risk-adjusted returns. You just have not yet experienced the run that produces the big losses. After all, a run of say 10 tails in a row is not all that likely with a fair coin. In the meantime you are the Lord of Wall Street and a Master of the Universe. You probably are playing this game with a lot of leverage too. So when you do crash, you can take others down with you.

Why do smart Wall Street types play this game? There are various explanations, but one obvious one is that while you earn the good returns you are accumulating bonuses that you do not lose when the crash occurs. The incentive schemes of hedge funds and financial institutions in general encourage risk taking. Given that they do it should not be surprising that financial managers take excessive risks.

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