Post by zuolun on Feb 16, 2015 11:14:03 GMT 7
The Gambler's Fallacy
Gambling with Other People’s Money
Imagine a superb poker player who asks you for a loan to finance his nightly poker playing. For every $100 he gambles, he’s willing to put up $3 of his own money. He wants you to lend him the rest. You will not get a stake in his winning. Instead, he’ll give you a fixed rate of interest on your $97 loan.
The poker player likes this situation for two reasons. First, it minimizes his downside risk. He can only lose $3. Second, borrowing has a great effect on his investment — it gets leveraged. If his $100 bet ends up yielding $103, he has made a lot more than 3 percent — in fact, he has doubled his money. His $3 investment is now worth $6.
But why would you, the lender, play this game? It’s a pretty risky game for you. Suppose your friend starts out with a stake of $10,000 for the night, putting up $300 himself and borrowing $9,700 from you. If he loses anything more than 3 percent on the night, he can’t make good on your loan.
Not to worry — your friend is an extremely skilled and prudent poker player who knows when to hold ,em and when to fold ,em. He may lose a hand or two because poker is a game of chance, but by the end of the night, he’s always ahead. He always makes good on his debts to you. He has never had a losing evening. As a creditor of the poker player, this is all you care about. As long as he can make good on his debt, you’re fine. You care only about one thing — that he stays solvent so that he can repay his loan and you get your money back.
But the gambler cares about two things. Sure, he too wants to stay solvent. Insolvency wipes out his investment, which is always unpleasant — it’s bad for his reputation and hurts his chances of being able to use leverage in the future. But the gambler doesn’t just care about avoiding the downside. He also cares about the upside. As the lender, you don’t share in the upside; no matter how much money the gambler makes on his bets, you just get your promised amount of interest.
If there is a chance to win a lot of money, the gambler is willing to take a big risk. After all, his downside is small. He only has $3 at stake. To gain a really large pot of money, the gambler will take a chance on an inside straight.
As the lender of the bulk of his funds, you wouldn't want the gambler to take that chance. You know that when the leverage ratio — the ratio of borrowed funds to personal assets — is 32–1 ($9700 divided by $300), the gambler will take a lot more risk than you’d like. So you keep an eye on the gambler to make sure that he continues to be successful in his play.
But suppose the gambler becomes increasingly reckless. He begins to draw to an inside straight from time to time and pursue other high-risk strategies that require making very large bets that threaten his ability to make good on his promises to you. After all, it’s worth it to him. He’s not playing with very much of his own money. He is playing mostly with your money. How will you respond?
You might stop lending altogether, concerned that you will lose both your interest and your principal. Or you might look for ways to protect yourself. You might demand a higher rate of interest. You might ask the player to put up his own assets as collateral in case he is wiped out. You might impose a covenant that legally restricts the gambler’s behavior, barring him from drawing to an inside straight, for example.
Gambling with Other People’s Money
Imagine a superb poker player who asks you for a loan to finance his nightly poker playing. For every $100 he gambles, he’s willing to put up $3 of his own money. He wants you to lend him the rest. You will not get a stake in his winning. Instead, he’ll give you a fixed rate of interest on your $97 loan.
The poker player likes this situation for two reasons. First, it minimizes his downside risk. He can only lose $3. Second, borrowing has a great effect on his investment — it gets leveraged. If his $100 bet ends up yielding $103, he has made a lot more than 3 percent — in fact, he has doubled his money. His $3 investment is now worth $6.
But why would you, the lender, play this game? It’s a pretty risky game for you. Suppose your friend starts out with a stake of $10,000 for the night, putting up $300 himself and borrowing $9,700 from you. If he loses anything more than 3 percent on the night, he can’t make good on your loan.
Not to worry — your friend is an extremely skilled and prudent poker player who knows when to hold ,em and when to fold ,em. He may lose a hand or two because poker is a game of chance, but by the end of the night, he’s always ahead. He always makes good on his debts to you. He has never had a losing evening. As a creditor of the poker player, this is all you care about. As long as he can make good on his debt, you’re fine. You care only about one thing — that he stays solvent so that he can repay his loan and you get your money back.
But the gambler cares about two things. Sure, he too wants to stay solvent. Insolvency wipes out his investment, which is always unpleasant — it’s bad for his reputation and hurts his chances of being able to use leverage in the future. But the gambler doesn’t just care about avoiding the downside. He also cares about the upside. As the lender, you don’t share in the upside; no matter how much money the gambler makes on his bets, you just get your promised amount of interest.
If there is a chance to win a lot of money, the gambler is willing to take a big risk. After all, his downside is small. He only has $3 at stake. To gain a really large pot of money, the gambler will take a chance on an inside straight.
As the lender of the bulk of his funds, you wouldn't want the gambler to take that chance. You know that when the leverage ratio — the ratio of borrowed funds to personal assets — is 32–1 ($9700 divided by $300), the gambler will take a lot more risk than you’d like. So you keep an eye on the gambler to make sure that he continues to be successful in his play.
But suppose the gambler becomes increasingly reckless. He begins to draw to an inside straight from time to time and pursue other high-risk strategies that require making very large bets that threaten his ability to make good on his promises to you. After all, it’s worth it to him. He’s not playing with very much of his own money. He is playing mostly with your money. How will you respond?
You might stop lending altogether, concerned that you will lose both your interest and your principal. Or you might look for ways to protect yourself. You might demand a higher rate of interest. You might ask the player to put up his own assets as collateral in case he is wiped out. You might impose a covenant that legally restricts the gambler’s behavior, barring him from drawing to an inside straight, for example.