Interesting article in Slate Magazine today, “We’re Down $700 Billion. Let’s Go Double or Nothing! How the financial markets fell for a 400-year-old sucker bet,” written by Jordan Ellenberg, warns that the prospect of a bail out may have contributed to reckless behavior on Wall Street.
Ellenberg is Associate Professor of Mathematics at The University of Wisconsin. He has a Ph.D from Harvard. As a teenager Ellenberg became known as a math prodigy, winning many math competitions. When he was 17 (in 1988) The National Enquirer featured him in an articled entitled, “America’s Top Math Whiz Kid.” He writes a regular column for Slate.
Jordan Ellenberg
Ellenberg explains the math of his thinking in detail in the article and says that Wall Street’s recent behavior resembles a betting strategy that involves doubling one’s bet, until you win — a strategy that comes down through history and is called “the matingale.” He writes, “Here’s how to make money flipping a coin. Bet 100 bucks on heads. If you win, you walk away $100 richer. If you lose, no problem; on the next flip, bet $200 on heads, and if you win this time, take your $100 profit and quit. If you lose, you’re down $300 on the day; so you double down again and bet $400. The coin can’t come up tails forever! Eventually, you’ve got to win your $100 back.
“This doubling game offers something for nothing—certain profits, with no risk. You can see why it’s so appealing to gamblers. But five more minutes of thought reveals that the martingale can lead to disaster. The coin will come up heads eventually—but “eventually” might be too late. Most of the time, one of the first few flips will land heads and you’ll come out on top. But suppose you get 10 tails in a row. Just like that, you’re out $204,700. The next step is to bet $204,800—if you’ve got it. If you’re out of cash, the game is over, and you’re going home 200 grand lighter. …
“But wait a minute, maybe somebody will loan you the $200,000 you need to stay in the game. After all, you’ve got a great track record; up until this moment, you’ve always ended up ahead! If people keep staking you money, you can just keep betting until, eventually, you win big time.”
Ellenberg continues, “The carefully synthesized financial instruments now seeping toxically from the hulls of Lehman Bros. and Washington Mutual are vastly more complicated than the martingale. But they suffer the same fundamental flaw: They claim to create returns out of nothing, with no attendant risk. That’s not just suspicious. In many cases, it’s mathematically impossible.”
Ellenberg concludes his article by saying, “This is what makes some people queasy about the federal bailout of the banks. It just might be that the prospect of a bailout—which could make a total collapse no worse for the banks than a garden-variety bear market—could have helped cause the martingale boom. There seems to be little question that the country needs the bailout now. But unless some real pain for the martingalers is built in, we’d better be ready for a return to maverick finance down the road.”
