Financial Theory: Lecture 21 Transcript
November 12, 2009
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Professor John Geanakoplos:
So time to start. So let me begin by reviewing a little bit of the dynamic
hedging which I could have described a little bit more clearly last time. It's a very important idea and I made
a little bit of a mess of it.
I didn't make that big a mess of it, but a little bit of a mess of it. So let's be a little bit careful now about who
knows what and what you're doing. So we said imagine somebody who knows that the probability the
Yankees are going to win the World Series is 60 percent, and therefore each game of the World Series is 60
percent, and knows that the probability the Phillies win the game is 40 percent. So suppose that he finds
somebody who is willing to bet with him on the Phillies. So he can win 100 dollars if the Yankees win. He
has to pay 100 dollars if the Yankees lose.
Now, his expected payoff is 20. He should take the bet because if the person's willing to bet at even odds, the
Phillies fan's willing to bet at even odds and he knows the odds are 60/40, on expectation he's going to make
20. So it's clear what he should do, but the problem is he's subject to risk.
Although he's right about the odds he could still, even though he's done the smart thing, he could still end up
losing 100 dollars which could be a disaster for him. So what he would like to do is to hedge his bets.
Now, what does it mean hedge his bet? Well, suppose there was another bookie who was willing to bet at
60/40 odds in either direction then what should he do? Well, if he can find another bookie who was willing to
bet at 60/40 odds he should try and lock in 20 dollars no matter what.
So he should do this bet. He should bet with the other bookie 80 dollars. He'd be willing to give up 80 dollars
if the Yankees won in order to win 120 dollars if the Phillies win, and that's a fair bet according to the other
bookie because it's 60/40 odds, 60 percent of this and 40 percent of that, this is 3 to 2 odds so it's a fair bet.
So in other words, he makes money by taking advantage of the Philly fan to bet on the Yankees, but that
subjects him to risk. So in order to minimize the risk he hedges his bet. That's where the expression came
from. He hedges that bet by betting in the opposite direction, on--betting on the Phillies with his bookie, in
the opposite direction, but standing to lose less than he, you know, he's betting in this proportion, in this
amount so that he gets 20 no matter what. So he's locked in his 20-dollar profit. So that was where we began.
Now, let's just think about it a little bit more carefully than I did before.
Somebody, in fact, basically asked this question. Is he really making money because he understands better the
odds of the Yankees winning the game? Is he making money because he knows the odds are 60/40 and the
poor Philly fan thinks they're 50/50? The answer is no. That's not why he's making money.