Financial Theory: Lecture 15 Transcript
October 27, 2009
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Professor John Geanakoplos:
Okay, I think I'll start. So we considered for a long time a world of certainty.
Hope something's okay. Considered a world of certainty where we assumed we could foresee the future
perfectly, and we still managed to figure out fairly interesting things.
But the world is much more complicated than that. It's a world of uncertainty, and in a world of uncertainty,
economics comes into its own, I think, as a fascinating subject. So I spent a little time reviewing some
mathematics for you last time that many of you already knew, so I'm going to take that for granted going
forward and just start over, this time from an economic perspective instead of a mathematical perspective.
So suppose today that we assume that you could buy a stock today whose price tomorrow could be 104 or 98
with 50:50 probabilities and we assume that everybody knew the probabilities. Know probabilities and
maximize expected payoff next period, okay? Well, + payoff this period.
If we assumed--and we're going to drop this assumption, but I'm going to keep it for a little while--if we
assumed that all people cared about was their expected payoff next period and of course they care about their
payoff this period, what would the value of the stock have to be? Well, under the simple rule for how people
act, you'd take 1 half times 104 + 1 half times 98, and that would give you--what would that give you? It'd
give you 101, okay, because this is + 4 times 1 half is + 2; - 2 times 1 half which is - 1, so it's + 1, so that'd
give you 101.
So you would say that the price of the stock today would have to be 101. Now we could slightly refine this
utility function and say people maximize the discounted expected payoff next period + the payoff this period.
And if the discount is 100 over 101, then we're going to have to multiply this by 100 over 101 and we'll get a
price of 100.
Okay, so that's the basic first step. We can incorporate uncertainty by assuming people replace the uncertain
outcomes with certain outcomes in their head, and then discount, just like we've seen before. Of course,
before we had utility functions but I'm not going to do that quite yet. I'm just going to say, suppose that we
just did that, right? That would give us a theory of how people manage uncertainty and react to uncertainty
and how they set the prices. So it's the expected--expectation theory of pricing.
Now before we complicate the theory, I want to just take this literally as true and make some inferences from
it. Well, the first inference you can make is that today's price would then be the discounted expectation of
tomorrow's price. That's just repeating the same thing, but what's an implication of that? The implication of
that is, if you didn't know tomorrow's price, know the expectation of tomorrow's price, you could guess
today's price.