Financial Theory: Lecture 10 Transcript
October 6, 2009
Professor John Geanakoplos:
Time to start. So this class and the next class and a half are going to be about
Fisher's theory of present value and the interest rate, and then we're going to move to uncertainty.
So up until now what we've done is we found out first, if you know the whole economic system, how to solve
for equilibrium. To figure out from the primitives of people's tastes, their impatience, the technology, the
economy, how to figure out the real rate of interest if provided there is no uncertainty in the world and people
can forecast what is going to happen later.
We've found that once you've done that, the price of every asset, if people are rational and looking forward to
the future, the price of every asset is going to be the present value of the future payments of the asset. So if
you think of the payments as real payments, which is what Fisher always recommended, you discount by the
real interest rate. If you think of them as cash payments then you discount by the nominal interest rate. So
every asset corresponds to its present value of its dividends either discounted by the real rate or the nominal
Now, this thinking is surprisingly powerful and leads you to unexpected conclusions. So the next two classes
is about that. Mostly I'm going to talk about Social Security, but I'm going to begin today by finishing off a
subject we didn't quite get through last time.
So you see, if you realize that the price of every asset is just the present value of its dividends, and you also
suppose you know what the dividends are going to be and what the future interest rates are going to be, then
it follows that you know what the price of the asset is going to be, not just today, but next year, and the year
after and the year after that. So your theory of asset pricing today, which was based on the assumption that
you can forecast the future, necessarily implies the theory of asset pricing in the future. So you can tell
something about how asset prices are going to change, and of course you can also test the theory because the
theory implicitly is forecasting something about the future, and therefore you can test the theory.
So let's just take a couple examples that are in the notes. So we said at the top, if you can read it, I hope it's
not too small--I want to move a little quickly so I could be writing this on the board, but if you can see it and
you look at the top line it says that the present value of the assets is just the discount of future dividends. So
maybe I'll start one line up, actually, in these notes. So if you look in the middle here the present value today,
suppose you have an asset, maybe I'm going to write on the board after all.