Financial Theory: Lecture 24 Transcript
December 1, 2009
Professor John Geanakoplos:
Anyhow, so today I'm going to try and wrap up a few loose ends. So I'm
going to try and talk about the high water mark of finance which is basically CAPM and Black-Scholes, both
of which we've almost talked about, almost finished talking about, and I'm going to talk in the middle about
Social Security which we never finished, my Social Security plan. So I hope to deal with all three of these
So just to wrap up the CAPM, the CAPM had two main ideas. The first idea was diversification and the
second main idea, as we said, was the tradeoff between risk and return.
Shakespeare had both of these ideas. He understood that you're safer if you've got each of your boats on a
different ocean, and he understood that if you're going to take a high risk you'd better get a high return
otherwise nobody is willing to take it. And so he made that very clear.
In fact I think the whole point of the play is about economics, The Merchant of Venice, and he made both of
these principles very clear, but he couldn't quantify them and he couldn't mathematize them, and the Capital
Asset Pricing Model gives a mathematical, quantifiable form to both and a quite shocking recommendation in
So just to draw those two pictures, for those of you who didn't hear it last night, if you do Tobin's famous
picture, this is the Markowitz-Tobin Capital Market Line they called it. It's very important to keep straight
what's on the diagram. There's the standard deviation of any asset per dollar. So here I'm writing the price. So
it's per dollar, and here is the expectation of the asset per dollar. So pi of Y, I'm calling that the price. So this
is per dollar.
And I'm not going to go over what we derived before, but we noticed that if you took all the risky assets, any
risky asset's going to have per dollar, if it's priced, some standard deviation and some expectation. You can
write down all the risky assets, and you can combine them, and you'll get a possibility set that looks like this.
So the diversification already shows up in this picture because if you combine this asset and this asset you're
going to get possibilities by putting half of your money in each, not on the straight line between them, but on
some curved line that's much better because you're reducing your risk.
So Markowitz already had that curve and this picture in mind. Tobin added the riskless asset, which he put
here, and then he said, well, if there's a riskless asset everybody's going to do the same thing and everyone's
going to choose the same point. It's better for everybody, so this is the optimal risky portfolio and it has to be
equal to the market, because if everybody's smart enough to figure out what to do they're all going to do the
same thing, and whatever everybody holds that's by definition the market. So Tobin showed that everybody
should choose something on this capital market line and so everybody should split his money between the
market and a riskless asset.