WEBVTT

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Prof: Anyhow,
so today I'm going to try and

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wrap up a few loose ends.

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So I'm going to try and talk
about the high water mark of

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finance which is basically CAPM
and Black-Scholes,

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both of which we've almost
talked about,

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almost finished talking about,
and I'm going to talk in the

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middle about Social Security
which we never finished,

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my Social Security plan.

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So I hope to deal with all
three of these things today.

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So just to wrap up the CAPM,
the CAPM had two main ideas.

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The first idea was
diversification and the second

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main idea, as we said,
was the tradeoff between risk

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and return.

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Shakespeare had both of these
ideas.

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He understood that you're safer
if you've got each of your boats

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on a different ocean,
and he understood that if

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you're going to take a high risk
you'd better get a high return

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otherwise nobody is willing to
take it.

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And so he made that very clear.

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In fact I think the whole point
of the play is about economics,

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The Merchant of Venice,
and he made both of these

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principles very clear,
but he couldn't quantify them

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and he couldn't mathematize
them,

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and the Capital Asset Pricing
Model gives a mathematical,

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quantifiable form to both and a
quite shocking recommendation in

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both cases.

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So just to draw those two
pictures,

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for those of you who didn't
hear it last night,

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if you do Tobin's famous
picture, this is the

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Markowitz-Tobin Capital Market
Line they called it.

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It's very important to keep
straight what's on the diagram.

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There's the standard deviation
of any asset per dollar.

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So here I'm writing the price.

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So it's per dollar,
and here is the expectation of

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the asset per dollar.

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So pi of Y, I'm calling that
the price.

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So this is per dollar.

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And I'm not going to go over
what we derived before,

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but we noticed that if you took
all the risky assets,

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any risky asset's going to have
per dollar,

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if it's priced,
some standard deviation and

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some expectation.

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You can write down all the
risky assets,

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and you can combine them,
and you'll get a possibility

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set that looks like this.

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So the diversification already
shows up in this picture because

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if you combine this asset and
this asset you're going to get

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possibilities by putting half of
your money in each,

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not on the straight line
between them,

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but on some curved line that's
much better because you're

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reducing your risk.

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So Markowitz already had that
curve and this picture in mind.

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Tobin added the riskless asset,
which he put here,

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and then he said,
well, if there's a riskless

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asset everybody's going to do
the same thing and everyone's

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going to choose the same point.

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It's better for everybody,
so this is the optimal risky

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portfolio and it has to be equal
to the market,

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because if everybody's smart
enough to figure out what to do

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they're all going to do the same
thing,

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and whatever everybody holds
that's by definition the market.

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So Tobin showed that everybody
should choose something on this

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capital market line and so
everybody should split his money

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between the market and a
riskless asset.

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Put your money in the bank or
own the entire market.

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That was his recommendation and
that was the beginning of the

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whole idea of index investing.

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So that was the first idea,
first, most important idea.

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Now, how could you test this?

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Well, you could simply test
every fund in history and

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compare so called experts and
see if those guys could get you

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above this line.

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So by the way,
the slope of the line,

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one more thing,
is the slope equals Sharpe

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ratio.

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So everybody's trying to get
the highest Sharpe ratio they

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can,
and if you have this portfolio

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you've made a mistake,
you haven't held the optimal

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one, then the slope of your
performance will be a lower

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Sharpe ratio than that.

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The slope of this,
which is the Sharpe ratio of

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that point, is worse than the
slope of that,

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which is the Sharpe ratio of
this point.

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And the Sharpe ratio,
remember, is (the expectation

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per dollar minus what you can
get in the riskless asset per

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dollar) divided by the started
deviation of Y per dollar,

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let's say.

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So that's just the slope of
this line.

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So we can measure performance
of a portfolio manger by the

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Sharpe ratio.

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Everyone should try and get the
highest Sharpe ratio.

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The upshot of diversification
is you should buy a little bit

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of every stock in the economy no
matter how small,

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no matter how big,
no matter how safe,

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no matter how risky,
you should spread your money

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across everything.

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That's the recommendation of
Tobin.

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And it relies,
of course, on everybody else

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being rational,
so everybody else is choosing

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the right thing.

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Then you can just piggyback and
do what everybody else is doing.

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So that's the first thing.

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Very shocking,
as I said, at first glance

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you'd think someone who loves
risk would just invest in risky

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stocks and people who are very
risk averse would just invest in

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safe stocks.

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Tobin says, no, no, no, no.

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If you're risk averse you
should just put most of your

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money in the bank and hold a
little bit of every stock.

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So you're here somewhere.

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If you're very risk tolerant
you shouldn't just concentrate

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on the risky stocks.

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You should buy the same
proportion of all stocks as

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everyone else,
but you should borrow the money

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to do it and maybe way up here.

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And people who borrow money to
invest that's called leveraging.

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So that's idea number one,
the crucial idea.

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There are a lot of ideas mixed
in that,

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and as I said,
you can test it by seeing if

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anyone can beat the market--
is there anyone historically

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that has had a higher Sharpe
ratio than the market.

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In 1967 when all of this was
being tested there was a famous

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book called A Random Walk Down
Wall Street written by Malkiel,

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which I recommend you read.

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He gives the history of tests
of whether people could beat the

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market.

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Of course many people beat the
market for short periods of

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time.

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Then they totally collapse.

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And then some people beat the
market for 20 years in a row and

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then retire,
but there are so few of those

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people that it looks like just
by random dumb luck you could

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get almost those people.

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On the other hand there are
some people like Warren Buffet

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who seem to beat the market for
40 or 50 years.

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It's really hard to believe
that that's all just luck.

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And so that's one test of the
thing.

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The second idea of the Capital
Asset Pricing Model is risk and

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return.

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And so now if we assume--so all
this graph,

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by the way, assumed quadratic
utilities,

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quadratic or mean variance
utilities,

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quadratic utility and common
probabilities.

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So everybody knew what the
probabilities were of the

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different states,
so you know how to measure the

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covariance and the variance and
all that because you know what

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the probabilities are to measure
over.

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So here, having assumed that,
it turns out that you just

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apply the principle that we saw
the first few days of class,

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that the price is going to
equal the marginal utility,

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not the total utility.

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Price is going to equal
marginal utility and if the

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price equals the marginal
utility the marginal utility is

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going to be--
depends, according to this

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assumption of quadratic
utilities as we showed,

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depends on expectation.

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So this is the price of Y,
so let's just call it pi of Y

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like I did before.

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It depends on the expectation
of Y and it depends on the

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covariance of Y with the market.

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We've assumed with quadratic
utilities that people only care

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about the mean and the variance,
so you'd have expected the

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marginal utility of any single
asset to depend on its mean and

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its variance,
but it's the marginal utility.

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It's what it adds to what
you've already got.

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So it adds expectation because
expectation's additive,

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but when you add another stock
to what you already have,

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the variance of the whole
portfolio changes according to

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the covariance of the new thing
with what you already had,

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and everybody already had the
market.

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So given that you know that the
price,

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mathematically therefore,
the price has to equal

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something times the expectation
of Y plus something times the

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covariance of Y with the market.

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But that's true for all Y.

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In particular it's true for the
riskless asset.

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So the riskless asset pays 1
for sure, has no covariance with

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anything like the market,
and its price is 1 over (1 r).

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So therefore A has to be 1 over
(1 r).

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So we know that this has to be
(1 r).

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And then B could be whatever it
is.

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The covariance,
by the way, is going to be bad,

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so this is minus.

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And then B, you have to figure
B out.

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So you don't know what B is a
priori.

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You don't know what the
interest rate is either.

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You had to see that in the
market.

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Once you know the price of one
asset,

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and you know its correlation
with the market,

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if you knew this price,
and you know the expectation of

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Y,
and you know the covariance

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with the market that will tell
you B.

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So once you've given one price
of a risky asset,

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like of the market as a whole,
you're going to be able to

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figure out the price of every
other asset because from that

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one price you can deduce B,
and once you have B you can

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price everything.

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So that's the second idea,
risk and return.

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And you can see it graphically
and more dramatically,

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because if I take that same
equation,

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this is called the covariance
pricing formula,

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you take that and divide by pi
of Y you get 1 equals

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expectation of Y divided by the
price of Y--

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dividing both sides by pi of
Y-- minus B times the covariance

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of (Y over the price of Y) with
M.

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So that just tells me the
expectation and the covariance

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of a dollar's worth,
just like this was a dollar's

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worth.

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This was per dollar and this is
per dollar,

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so if you put the covariance of
Y and the pi of Y down here,

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and M over here,
and here you put expectation Y

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over pi of Y,
this just says this is just a

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constant,
and this is a constant,

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so it says this and this are
linearly related.

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These are all securities who
have price 1.

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There has to be a linear
relationship between their

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expectation per dollar and their
covariance per dollar with the

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market.

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And as the covariance gets
higher the return gets higher.

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So if you take a stock with a
high covariance it's going to

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have to have a high expected
return.

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That's exactly what Shakespeare
said.

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If it's more risky people won't
hold it unless it's got a higher

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return, which means you can buy
it for a cheap price.

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So its price is less than its
expectation.

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But the difference with
Shakespeare is we've quantified

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risk.

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It's not what you would have
thought, variance,

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it's covariance.

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And that's it.

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Those are the two big ideas and
you could test--

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so this is called the Security
Market Line,

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and you could test this by
asking is every stock--

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so if you look at every stock
last year,

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you look at its covariance,
you put a point here,

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then you look this year at its
expected return,

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of course some stocks are going
to be wild,

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but you average over a bunch of
stock and a bunch of years.

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Do you get things that lie in a
straight line or close to a

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straight line?

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And Sharpe, in 1967,
found that amazingly when you

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did that you got--so I described
last night exactly what his test

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was.

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You got something that looked
incredibly close to a straight

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line like that.

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So this was the greatest
triumph in the history of the

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social sciences,
it was called,

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because you had huge amounts of
data,

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huge capacity to test things,
a shocking conclusion,

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a shockingly precise theory to
test,

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and it fit the line so
incredibly closely.

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And it just swept,
it made a huge impression in

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finance and in economics and
lots of Nobel Prizes were given

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for this.

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Sharpe won a Nobel Prize.

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Markowitz won a Nobel Prize.

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Tobin won a Nobel Prize.

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Lintner died.

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He would have won a Nobel Prize
too.

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So this was the first major
triumph, the most important

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triumph of finance,
the Capital Asset Pricing

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Model.

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Now, as it happens,
as the theory's been tested

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over and over again every year
since 1967 it's performed more

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and more poorly.

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And so now when you do this you
get points that look like this,

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and like that,
and like this,

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and they don't seem to lie on a
straight line at all,

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and it's pretty shocking how up
until '67 or the early '70s that

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it seemed to work out perfectly
and now it doesn't work very

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well.

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And this business they've also
discovered, according to this

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you couldn't beat the market.

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So how do you test whether
something beats the market?

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You can pick a bunch of people
and say,

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"Could they beat the
market,"

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or you can actually just make
up a strategy yourself like buy

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only new stocks.

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Just every year buy the stocks
that have come onto the S&P

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500 for the first time,
or just buy the stocks that are

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the biggest 10 percent.

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And it turns out some of those
strategies actually do beat the

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market.

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So I don't have time to go into
the details, you know,

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that is they lie above or below
here.

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So the theory has come into--so
theory and doubt.

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And so what I'm going to talk
about next week is,

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and it certainly doesn't
explain the current crisis,

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so I want next week to explain
crisis.

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So next week I'm going to end
by giving another theory which

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is going to explain the crisis
and be different from this one,

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but of course it hasn't been
tested over 30 years or 50 years

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like CAPM.

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CAPM looked great for the first
20 years,

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so whatever I say next week
will probably turn out to be 90

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percent wrong,
but at the moment it looks

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pretty good.

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And I didn't want to spend half
the course on it in case in 20

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years it seemed to be
ridiculous.

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But anyway, I'm going to
present it anyway to those of

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you who want to hear it next
week,

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and it'll be,
I think, understandable and

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down to earth and it'll invoke a
very basic thing.

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Nowhere in this model did we
take into account,

15:34.984 --> 15:37.674
you know, when we say people
leverage that means they're

15:37.667 --> 15:39.957
borrowing money and choosing to
go up here.

15:39.960 --> 15:43.570
We haven't taken into account
that they have to pay the money

15:43.570 --> 15:47.180
back, and who's going to trust
them to pay the money back?

15:47.178 --> 15:49.508
And forcing them to do
something to guarantee they're

15:49.509 --> 15:52.239
going to pay the money back is
going to change the theory in a

15:52.243 --> 15:54.883
critical way,
which I'll get to next week.

15:54.879 --> 15:56.819
Now, one last thing about the
theory,

15:56.820 --> 16:00.790
as I say, you test it by
seeing--nobody should be above

16:00.792 --> 16:04.472
this line and nobody should be
above this line,

16:04.470 --> 16:06.910
but of course you can find
people above this line.

16:06.908 --> 16:10.738
Swensen, to take a famous Yale
example, is above this line.

16:10.740 --> 16:16.520
And you can find people above
this line, Ellington.

16:16.519 --> 16:18.839
So Ellington,
let's say, above this line.

16:18.840 --> 16:20.440
All right, so hedge funds.

16:20.440 --> 16:27.090
Let's call it an anonymous
hedge fund since we're on camera

16:27.090 --> 16:30.760
now, hedge fund,
hedge fund E.

16:30.759 --> 16:33.039
So the question is,
is that luck,

16:33.039 --> 16:37.529
they just did it a few years in
both cases like 15 years apiece,

16:37.530 --> 16:39.670
or does it mean something?

16:39.668 --> 16:42.408
All right, well,
so you can measure the,

16:42.408 --> 16:44.968
you know, if you believe this
theory and you just say,

16:44.970 --> 16:47.590
okay, let's say the theory's 99
percent true,

16:47.590 --> 16:50.070
it's just that there are a few
people who really do beat the

16:50.068 --> 16:52.278
market,
then you can decide by looking

16:52.279 --> 16:56.159
at these graphs just how good is
Swensen relative to the market?

16:56.158 --> 16:59.318
How good is this hedge fund
relative to the market?

16:59.320 --> 17:02.480
And so you have a way of
calibrating and measuring how

17:02.476 --> 17:03.486
well people do.

17:03.490 --> 17:06.520
So I don't have time to get
into that, but I would measure

17:06.516 --> 17:09.646
the quality of a hedge fund by
its marginal Sharpe ratio.

17:09.650 --> 17:12.010
How much does having access to
this hedge fund,

17:12.006 --> 17:14.406
if you added it to your
portfolio, increase your

17:14.413 --> 17:17.133
portfolio hedge ratio
[correction: Sharpe ratio]?

17:17.130 --> 17:19.430
That's, I think,
the right measure of how good a

17:19.426 --> 17:20.206
hedge fund is.

17:20.210 --> 17:23.460
And the right measure of how
good Swensen is,

17:23.455 --> 17:25.665
is, what's his Sharpe ratio?

17:25.670 --> 17:27.530
And so there's a different
criterion.

17:27.529 --> 17:28.769
I keep emphasizing this.

17:28.769 --> 17:32.639
Swensen is managing an entire
portfolio so you have to measure

17:32.644 --> 17:35.994
him on how's he done for Yale,
because Yale's not going to

17:35.986 --> 17:37.506
combine him with something else.

17:37.509 --> 17:39.429
It's just holding what he holds.

17:39.430 --> 17:41.290
So it's his Sharpe ratio.

17:41.288 --> 17:42.958
But Ellington,
you're going to combine

17:42.961 --> 17:44.501
Ellington with some other stuff.

17:44.500 --> 17:47.020
So Swensen might invest in
Ellington, but ten million other

17:47.019 --> 17:47.409
things.

17:47.410 --> 17:51.050
And so you have to say how much
is Ellington going to help

17:51.051 --> 17:52.651
Swensen's Sharpe ratio?

17:52.650 --> 17:55.430
So instead of Swensen's Sharpe
ratio how much is Ellington

17:55.434 --> 17:57.394
going to help the market Sharpe
ratio?

17:57.390 --> 18:01.810
So that's how you should
measure a hedge fund,

18:01.805 --> 18:06.805
its marginal Sharpe ratio,
and Swensen by his Sharpe

18:06.807 --> 18:07.787
ratio.

18:07.788 --> 18:20.388
So I'd say measure Swensen
performance by Sharpe ratio,

18:20.390 --> 18:30.530
measure hedge fund performance
by marginal Sharpe ratio,

18:30.528 --> 18:35.268
because you'd be crazy to put
all your money in a hedge fund.

18:35.269 --> 18:37.909
The only people who do it are
the partners of the hedge fund

18:37.905 --> 18:40.495
who are sort of forced to do it
because that's how they can

18:40.498 --> 18:43.308
persuade investors that they're
really paying attention to their

18:43.313 --> 18:46.763
fund,
because all their money's at

18:46.757 --> 18:47.377
risk.

18:47.380 --> 18:48.110
So that's it.

18:48.109 --> 18:49.369
That's the basic bottom line.

18:49.368 --> 18:54.838
So are there any questions
before I now move on from this?

18:54.838 --> 18:57.718
We talked about this last night
and we talked about it for the

18:57.723 --> 18:58.673
last two lectures.

18:58.670 --> 19:01.040
All right, so it's a high water
mark as I say;

19:01.038 --> 19:05.308
incredibly precise prediction
and incredibly close to the

19:05.314 --> 19:08.754
facts, at least in 1967 but not
after that.

19:08.750 --> 19:12.980
Now, I want to move to an aside
of Social Security before I come

19:12.980 --> 19:17.080
back to Black-Scholes which is
the last high water mark of the

19:17.076 --> 19:18.416
standard theory.

19:18.420 --> 19:23.690
Remember the upshot of what
we've talked about so far.

19:23.690 --> 19:38.210
The upshot of this is that the
market will get a higher return.

19:38.210 --> 19:39.700
Oh, by the way,
I'd say one other thing.

19:39.700 --> 19:45.360
What is the standard critique
of this theory?

19:45.358 --> 19:47.598
So of course everybody else has
seen that the theory doesn't

19:47.603 --> 19:47.873
work.

19:47.868 --> 19:50.318
So what is their explanation
for why?

19:50.318 --> 19:53.218
What's the old explanation for
why the theory isn't working so

19:53.217 --> 19:53.737
well now?

19:53.740 --> 19:57.380
The explanation is that in the
old days what was thought of as

19:57.375 --> 19:59.875
the market was just all American
stocks.

19:59.880 --> 20:02.190
But now it's pretty obvious,
in fact it should have been

20:02.191 --> 20:03.411
obvious from the beginning.

20:03.410 --> 20:07.450
And so Swensen realized it
early on that Markowitz's advice

20:07.446 --> 20:09.776
is to diversify,
diversify, diversify,

20:09.782 --> 20:11.522
not just into all American
stocks,

20:11.519 --> 20:14.219
into everything all over the
world and all kinds of assets

20:14.221 --> 20:15.551
that aren't stocks at all.

20:15.548 --> 20:18.588
So what you measure as the
market shouldn't just be

20:18.594 --> 20:19.694
American stocks.

20:19.690 --> 20:22.720
It should be the world
portfolio, but how do you

20:22.717 --> 20:24.647
measure the world portfolio?

20:24.650 --> 20:27.210
That's hard to do,
and so people have tried to

20:27.207 --> 20:30.497
maintain that the reason the
theory doesn't work is because

20:30.503 --> 20:33.293
we've got the wrong M in all
these equations.

20:33.288 --> 20:37.008
So that would be a nice way of
fixing the theory.

20:37.009 --> 20:39.699
I doubt if that's going to help
in the end.

20:39.700 --> 20:43.550
So my problem about collateral
is a different look at it.

20:43.548 --> 20:47.888
But anyhow, so the market
according to the theory will get

20:47.887 --> 20:52.147
a higher return than bonds,
and of course that's true.

20:52.150 --> 20:56.900
The market has a very high
positive covariance with itself

20:56.900 --> 20:59.400
so a very low price up here.

20:59.400 --> 21:02.100
It's high covariance with
itself, so a low price.

21:02.098 --> 21:04.368
Compared to its expectation the
price is low,

21:04.369 --> 21:06.949
so you're paying much less than
the expectation.

21:06.950 --> 21:10.000
So then when you see what
actually happens it's going to

21:10.000 --> 21:11.610
look much higher than that.

21:11.609 --> 21:12.709
It's not just this.

21:12.710 --> 21:16.050
The price is lower therefore
the final outcome's going to be

21:16.053 --> 21:17.473
much bigger on average.

21:17.470 --> 21:21.670
So to put it another way,
if you had two possibilities

21:21.674 --> 21:24.694
which you knew were equally
likely,

21:24.690 --> 21:28.880
1 half and 1 half,
and the market paid off

21:28.878 --> 21:33.578
something good here and
something bad here,

21:33.578 --> 21:36.288
so everybody's rich here and
everybody's poor here.

21:36.288 --> 21:39.168
The price of the Arrow security
of this state is going to be

21:39.172 --> 21:42.302
much lower than the price of the
Arrow security of this state.

21:42.298 --> 21:45.118
So this state is going to have
a price,

21:45.118 --> 21:49.138
let's say .8,
and this one might have a price

21:49.136 --> 21:53.906
.2 because here the bad state,
that's when everybody's poor,

21:53.906 --> 21:56.286
so you're going to,
you know, this formula

21:56.288 --> 21:59.108
basically tells you that if
you're paying off here you're

21:59.112 --> 22:01.232
negatively correlated with the
market,

22:01.230 --> 22:03.750
you're going to have to pay a
very high price for it because

22:03.752 --> 22:04.482
you're hedging.

22:04.480 --> 22:08.020
By buying this security you're
balancing off what you have with

22:08.018 --> 22:08.758
the market.

22:08.759 --> 22:13.379
By buying the market,
people don't like that because

22:13.375 --> 22:17.445
it adds more risk to what you
already have.

22:17.450 --> 22:21.590
And so people don't like it so
they're not going pay very much,

22:21.594 --> 22:25.744
so the price will be much less
than the actual probability of 1

22:25.738 --> 22:26.338
half.

22:26.338 --> 22:28.048
So that's the conclusion of
what we've done.

22:28.048 --> 22:30.538
I want to now connect this to
Social Security.

22:30.538 --> 22:36.378
So you remember in our Social
Security model we had land that

22:36.383 --> 22:40.003
went here,
here, here, paid 1,1,

22:39.998 --> 22:43.798
1,1, 1, and we had these
people,

22:43.798 --> 22:47.248
overlapping generations-people
like that.

22:47.250 --> 22:51.020
And we discovered a very
important thing.

22:51.019 --> 22:54.949
The reason why Social Security
seems to be broke is because we

22:54.952 --> 22:59.082
gave away so much money to the
people in the first generation.

22:59.078 --> 23:01.788
It's not that Social Security
wastes money like George Bush

23:01.786 --> 23:03.836
seems to imply whenever he talks
about it.

23:03.838 --> 23:05.528
It's not like they just throw
it away.

23:05.528 --> 23:09.318
It's that we gave a huge gift
to the people in the '40s,

23:09.317 --> 23:13.307
the '50s and the '60s and so
everyone after that has to pay

23:13.309 --> 23:14.549
for that gift.

23:14.548 --> 23:19.098
But there's a little bit more
to George Bush's story than I've

23:19.104 --> 23:22.394
allowed so far,
which is that he wants to put

23:22.387 --> 23:24.327
the money into stocks.

23:24.328 --> 23:29.068
And we know that stocks are
going to get a higher return

23:29.068 --> 23:30.188
than bonds.

23:30.190 --> 23:32.450
That's the whole point of this
theory.

23:32.450 --> 23:35.160
You put money in stocks,
the expected return on stocks

23:35.157 --> 23:37.507
is higher than the expected
return on bonds.

23:37.509 --> 23:41.279
So if you want to make this
mathematical we have to add the

23:41.276 --> 23:45.236
possibility of risk and stocks
and it looks like it's going to

23:45.237 --> 23:48.797
be hopelessly complicated,
but we can do it very easily.

23:48.798 --> 23:54.168
So I'm going to reproduce the
same picture with uncertainty in

23:54.171 --> 23:57.571
stocks in it,
and then we're going to come

23:57.574 --> 24:01.634
back to Social Security and
spend 15 minutes talking about

24:01.634 --> 24:04.844
what's the right plan for Social
Security.

24:04.838 --> 24:08.158
So how could I take this simple
model,

24:08.160 --> 24:10.450
which already seemed
complicated, it's already a

24:10.452 --> 24:13.562
pretty complicated model,
had no uncertainty,

24:13.556 --> 24:16.386
and now put uncertainty in it?

24:16.390 --> 24:23.140
Well, I'm going to suppose that
land--so this is the land

24:23.138 --> 24:27.718
dividends I'm now going to
describe.

24:27.720 --> 24:29.460
And by the way,
I had people with endowments

24:29.457 --> 24:29.737
here.

24:29.740 --> 24:31.720
They were (3,1) and (3,1).

24:31.720 --> 24:34.440
Remember, this is their
endowments, but we didn't say

24:34.439 --> 24:36.269
where those endowments came
from.

24:36.269 --> 24:37.819
So I'm going to take the land
dividends.

24:37.818 --> 24:41.108
I'm going to suppose the
dividend of the land today is 1,

24:41.107 --> 24:44.217
but things might get better or
worse in the future.

24:44.220 --> 24:48.480
Maybe the dividend goes to 2 or
down to 1 half,

24:48.482 --> 24:49.042
say.

24:49.038 --> 24:53.058
I'm taking some extreme case
where it doubles or halves,

24:53.058 --> 24:56.898
and maybe after that it could
double again or it could go back

24:56.900 --> 25:00.740
to 1 and here it could go to 1
or it could go to 1 quarter.

25:00.740 --> 25:04.010
So what dividends are doing is
a random walk.

25:04.009 --> 25:08.679
If the economy starts getting
more productive then it's in a

25:08.683 --> 25:11.573
better position,
and from that point things get

25:11.569 --> 25:14.239
even more productive or maybe go
back to where they were.

25:14.240 --> 25:16.780
If things get worse they're
worse, but maybe things will

25:16.776 --> 25:19.216
start to get better again or
continue to get worse.

25:19.220 --> 25:24.480
So this is what I imagine as my
process of dividends.

25:24.480 --> 25:30.150
So if you own the land you get
all these dividends in the whole

25:30.154 --> 25:32.814
infinite future,
all right?

25:32.808 --> 25:36.218
And now let's say that there's
labor as well,

25:36.215 --> 25:37.605
so labor income.

25:37.608 --> 25:41.498
So I have to make an assumption
about labor income.

25:41.500 --> 25:48.390
So I'm going to assume only
young work.

25:48.390 --> 25:50.570
So here we kind of made the
same assumption.

25:50.568 --> 25:53.288
You get a lot when you're young
and not much when you're old.

25:53.288 --> 25:55.748
I'm going to assume only the
young work,

25:55.750 --> 26:01.160
and I'm going to assume that
this productivity gains or

26:01.157 --> 26:02.697
losses,
and by the way,

26:02.704 --> 26:04.164
you might think you never go
backwards.

26:04.160 --> 26:07.470
Maybe it goes from 1 to 2 or 1
to 1.1.

26:07.470 --> 26:11.720
So it's always growing,
but random.

26:11.720 --> 26:15.260
But I'm just going to keep it
here since I solved this example

26:15.256 --> 26:16.006
last night.

26:16.009 --> 26:18.889
I might as well stick to that
one, but there's no reason

26:18.892 --> 26:21.782
why--I could have made the thing
always, no matter what,

26:21.775 --> 26:23.815
either stay the same or get
better.

26:23.818 --> 26:25.878
That might have been a better
example to do,

26:25.880 --> 26:29.180
more realistic because we don't
really have tremendous

26:29.182 --> 26:32.692
productivity declines,
but anyway, all I mean to do is

26:32.686 --> 26:34.506
to put some randomness here.

26:34.509 --> 26:42.509
So only young work and wages
proportional to dividends,

26:42.509 --> 26:50.959
so let's just assume this,
so I'm assuming--this is what's

26:50.955 --> 26:56.285
called neutral technical change.

26:56.288 --> 26:58.918
So presumably the reason why
productivity is going up,

26:58.920 --> 27:01.210
the dividends are getting
higher, is there are more

27:01.207 --> 27:03.447
discoveries improving the
product of the land,

27:03.450 --> 27:05.910
but they're probably also
improving the product of labor,

27:05.910 --> 27:08.380
and so let's say they have same
effect on both.

27:08.380 --> 27:12.080
So I'm going to assume that
labor is actually--put the 1

27:12.080 --> 27:12.620
above.

27:12.618 --> 27:20.318
Let's say labor always gets 3
times what dividends are.

27:20.318 --> 27:25.468
So this is a 6 and this will be
3 halves, and this will be 12

27:25.472 --> 27:29.772
and 3 again and 3 quarters,
so that's what labor is

27:29.768 --> 27:32.258
getting, so labor income.

27:32.259 --> 27:38.039
I shouldn't have switched
colors, labor income.

27:38.038 --> 27:43.368
So that's my complicated world,
way more complicated than it

27:43.374 --> 27:44.554
was before.

27:44.548 --> 27:47.118
So if you own the land you get
all the dividends in the future.

27:47.118 --> 27:50.678
People live two periods,
so I'm going to assume that

27:50.681 --> 27:54.041
utility--
so you're going to live when

27:54.037 --> 27:58.837
you're young and then when
you're old and up and when

27:58.844 --> 28:00.974
you're old and down.

28:00.970 --> 28:04.120
So you're going to live--let's
say a guy born here,

28:04.121 --> 28:06.581
he's young here,
or she's young here.

28:06.578 --> 28:10.028
She can work here,
and then she's going to be old

28:10.032 --> 28:12.982
here and here,
but when she's old it's not

28:12.983 --> 28:16.873
clear how good her investment's
going to turn out.

28:16.868 --> 28:20.058
So this is going to just be our
simple log.

28:20.058 --> 28:27.548
I'll call this 1 half log Y 1
quarter log Z_up 1

28:27.554 --> 28:31.634
quarter log Z_down.

28:31.630 --> 28:34.760
So you don't discount the
future, let's say,

28:34.759 --> 28:37.499
you just take log of
consumption today plus

28:37.500 --> 28:41.220
probability 1 half of log
consumption in the up state,

28:41.220 --> 28:43.120
1 half log consumption in the
down state.

28:43.118 --> 28:47.028
So the probabilities here are 1
half.

28:47.029 --> 28:50.629
These are the objective
probabilities.

28:50.630 --> 28:54.000
So maybe I should have written
the utility--maybe better it

28:54.000 --> 28:56.850
would have been to write the
utility like that.

28:56.848 --> 29:00.778
That's what people know,
what the probabilities are.

29:00.779 --> 29:01.759
So that's it.

29:01.759 --> 29:05.069
That's my set up.

29:05.069 --> 29:07.819
So what should the economy do?

29:07.819 --> 29:08.679
What should people do?

29:08.680 --> 29:13.700
You see, if you buy--if you're
some person like this woman

29:13.703 --> 29:16.503
here,
she could decide to hold bonds,

29:16.497 --> 29:20.737
and she could get whatever the
interest rate turns out to be,

29:20.740 --> 29:22.240
which we're going to compute in
a minute,

29:22.240 --> 29:25.350
or she could hold stock in
which case she's going to get--

29:25.349 --> 29:28.479
let's start her off here, maybe.

29:28.480 --> 29:31.950
She could buy land;
buy stock.

29:31.950 --> 29:33.290
Now we don't know what the
price is yet.

29:33.289 --> 29:34.239
We have to compute that.

29:34.240 --> 29:36.920
But if she buys the stock
she'll get a dividend of 2 here

29:36.916 --> 29:39.256
and be able to sell the land for
a high price,

29:39.259 --> 29:41.729
because from here on it's
obviously pretty productive,

29:41.730 --> 29:45.050
better than it was back here,
or she might get unlucky and

29:45.045 --> 29:47.415
the price might,
you know, the dividend might be

29:47.421 --> 29:48.761
really terrible,
just 1 half,

29:48.762 --> 29:51.882
and not only that but the land
she sells when she's old is also

29:51.878 --> 29:53.788
going to have a really lousy
price.

29:53.788 --> 29:57.058
So if she holds land she's
going to get a high dividend and

29:57.060 --> 29:59.880
a high capital return,
or else a low dividend and a

29:59.882 --> 30:01.182
low capital return.

30:01.180 --> 30:04.110
It's really risky for her,
or she could just buy a bond at

30:04.107 --> 30:07.087
whatever interest rate it turns
out to be and get something

30:07.086 --> 30:07.546
safe.

30:07.548 --> 30:12.298
So what should she do,
and will that be a good thing

30:12.299 --> 30:17.799
for the economy or can we make
everybody better off by using

30:17.796 --> 30:19.656
Social Security?

30:19.660 --> 30:29.560
So how can we solve this?

30:29.558 --> 30:31.988
So it looks like a really
complicated model to solve

30:31.986 --> 30:34.076
because we've got a generation
born here,

30:34.078 --> 30:36.628
another one born here,
the same generation might be

30:36.625 --> 30:38.965
born up here under different
circumstances,

30:38.970 --> 30:41.960
and then this generation here
could be born under any of three

30:41.957 --> 30:47.287
different circumstances,
so there's a lot to solve for.

30:47.288 --> 30:51.378
But what we know is that when
we compute the Arrow price,

30:51.380 --> 30:54.640
starting from any point,
this Arrow price is going to be

30:54.642 --> 30:57.962
bigger than 1 half and this
one's going to be less than 1

30:57.963 --> 31:01.293
half because the economy is
doing much worse down here so

31:01.286 --> 31:04.666
people know they're all going to
get screwed down here and

31:04.667 --> 31:06.267
consume a lot less.

31:06.269 --> 31:08.879
So to hedge that they're all
going to want to buy,

31:08.884 --> 31:12.144
they're going to be desperate
to buy consumption down here.

31:12.140 --> 31:14.870
Of course they can't all do
that, so it's got to be the

31:14.869 --> 31:17.949
price that's more than 1 half
that discourages them from doing

31:17.953 --> 31:18.413
that.

31:18.410 --> 31:21.160
And they don't really need that
much to buy up here because

31:21.159 --> 31:23.199
their dividends,
they're going to be so rich

31:23.198 --> 31:23.718
anyway.

31:23.720 --> 31:27.380
So the price of the Arrow
security is going to be less

31:27.383 --> 31:31.463
than 1 half because there's so
much that they have to end up

31:31.460 --> 31:34.640
holding and that'll encourage
them to buy.

31:34.640 --> 31:36.550
I mean, sorry,
I said the logic backwards.

31:36.548 --> 31:38.638
There's so much that they're
going to have to end up

31:38.641 --> 31:40.651
consuming because the economy is
so productive.

31:40.650 --> 31:43.480
How can you get them to plan to
consume that much up there?

31:43.480 --> 31:45.860
It's by having a low Arrow
security price.

31:45.858 --> 31:48.388
So even in advance they know
that they're going to end up

31:48.385 --> 31:51.045
consuming a lot and they're
happy to do that because they're

31:51.048 --> 31:53.798
willing to buy Arrow securities
because they're so cheap.

31:53.799 --> 31:58.339
So how do we solve all this?

31:58.338 --> 32:00.058
So everybody following the
problem?

32:00.058 --> 32:02.708
It's quite a complicated
problem, but it turns out to

32:02.711 --> 32:04.141
have a very simple answer.

32:04.140 --> 32:04.670
Yep?

32:04.670 --> 32:08.980
Student: So the down
state, the price of consumption

32:08.980 --> 32:11.880
is high but the price of land is
low?

32:11.880 --> 32:12.980
Prof: Right, so.

32:12.980 --> 32:17.690
Well, so if you start--starting
from here the price of

32:17.686 --> 32:20.636
consumption--
if you want to buy at this

32:20.643 --> 32:22.833
point, consumption at this
point,

32:22.828 --> 32:25.648
you're going to have to pay
more than 1 half to get it,

32:25.650 --> 32:29.830
but you know that once you get
here the price of land is going

32:29.827 --> 32:31.057
to have dropped.

32:31.059 --> 32:32.259
So yes, I'm agreeing with you.

32:32.259 --> 32:35.129
Student: I understand
the first part because the CAPM

32:35.133 --> 32:35.623
price...

32:35.618 --> 32:37.208
Prof: Right,
now why should the price of

32:37.211 --> 32:37.941
land be lower here?

32:37.940 --> 32:42.610
Remember, the price of land is
always in terms of the

32:42.606 --> 32:45.386
consumption good that period.

32:45.390 --> 32:48.770
Every period I might as well
take an apple to have a price of

32:48.773 --> 32:49.003
1.

32:49.000 --> 32:52.510
So you see, the land here is
producing an entire apple,

32:52.505 --> 32:56.135
and on average going forward
it's going to be producing 1

32:56.140 --> 32:56.790
apple.

32:56.788 --> 32:59.398
The geometric average of all
these numbers is 1 starting at

32:59.404 --> 32:59.994
this point.

32:59.990 --> 33:03.590
Once you've gone down to here
production has deteriorated.

33:03.588 --> 33:05.928
The land is only producing 1
half an apple here,

33:05.930 --> 33:08.290
and in the future instead of
producing 12 it's going to

33:08.286 --> 33:10.726
produce 3 apples here and only 3
quarters of an apple.

33:10.730 --> 33:13.410
So it's crummier land down
here, so you're going to pay

33:13.414 --> 33:14.414
less for the land.

33:14.410 --> 33:17.950
Any other questions?

33:17.950 --> 33:21.430
But I'm going to tell you
exactly what you'll pay for the

33:21.433 --> 33:21.873
land.

33:21.869 --> 33:23.429
So we're going to solve this.

33:23.430 --> 33:37.980
So need to solve for land price
in each state,

33:37.980 --> 33:56.370
and interest rate at each
state, and price of up Arrow

33:56.365 --> 34:06.105
security,
and price of down Arrow

34:06.107 --> 34:11.927
security at each state.

34:11.929 --> 34:14.109
So how can we do all that?

34:14.110 --> 34:17.230
Well, first of all you notice
that the Arrow securities are

34:17.226 --> 34:18.136
always the key.

34:18.139 --> 34:21.779
Once you solve for those you
can figure out everything else.

34:21.780 --> 34:28.050
So we just have to solve for
these, the price of the up and

34:28.052 --> 34:32.272
down Arrow securities in every
state.

34:32.268 --> 34:41.988
Oh, this was me in a previous
class today.

34:41.989 --> 34:43.529
I didn't erase it.

34:43.530 --> 35:00.240
I figured the next guy would do
it, serves me right.

35:00.239 --> 35:03.469
So how can we solve this?

35:03.469 --> 35:15.699
Well, we can guess,
let's do it up here,

35:15.697 --> 35:27.297
guess that these prices,
Arrow prices,

35:27.300 --> 35:36.080
the same at every state.

35:36.079 --> 35:38.489
So what do I mean by that?

35:38.489 --> 35:41.359
I mean, here,
how many apples would you pay

35:41.358 --> 35:42.928
to get an apple here?

35:42.929 --> 35:47.409
I'm guessing that that's the
same amount you would pay here

35:47.405 --> 35:49.175
to get an apple here.

35:49.179 --> 35:53.049
And what you'd pay in apples at
this point to get an apple down

35:53.050 --> 35:56.980
here is going to be the same as
this generation would pay to get

35:56.983 --> 35:58.423
an apple down here.

35:58.420 --> 35:59.250
That's a guess.

35:59.250 --> 36:00.770
We have to verify that that's
going to work.

36:00.768 --> 36:10.158
It seems like everything is
sort of homogeneous,

36:10.161 --> 36:22.551
and so guess that price of land
is proportional to dividends in

36:22.552 --> 36:25.552
that state.

36:25.550 --> 36:28.240
Well, the whole thing is sort
of homogeneous and everything,

36:28.239 --> 36:32.489
so if the land here is 4 times
as good as the land here,

36:32.489 --> 36:36.119
the land here is 4 times as
good as the land here,

36:36.119 --> 36:39.339
because the dividends are
always 4 times higher if you go

36:39.338 --> 36:40.198
up one thing.

36:40.199 --> 36:42.579
So this is 4 times that,
that's 4 times that.

36:42.579 --> 36:46.499
So why not guess that the price
of land is 4 times here than it

36:46.503 --> 36:49.483
is here, 4 times higher here
than it is here.

36:49.480 --> 36:51.320
Sounds possible,
anyway, and of course these are

36:51.322 --> 36:52.972
going to turn out to be correct
guesses.

36:52.969 --> 36:57.729
So once you make these guesses
it's going to be very simple to

36:57.728 --> 37:01.788
find the equilibrium,
and then we can verify that the

37:01.786 --> 37:03.656
guesses are correct.

37:03.659 --> 37:07.389
So what does this guy want to
do here?

37:07.389 --> 37:09.409
So assume you only work when
you're young.

37:09.409 --> 37:10.559
So what's your income?

37:10.559 --> 37:13.639
What's anybody's income like
this young guy here?

37:13.639 --> 37:19.749
Young at time 1,
so this is time 1 here,

37:19.746 --> 37:26.156
time 2, time 3,
time 4, so at time 1 their

37:26.164 --> 37:34.154
income is 3 because that's what
their wage was.

37:34.150 --> 37:37.590
They work when they're young
and they've got three.

37:37.590 --> 37:38.090
That's it.

37:38.090 --> 37:39.460
They don't own the land when
they're born.

37:39.460 --> 37:42.760
They're going to buy the land
but they don't own it now,

37:42.760 --> 37:44.740
and so what do they want to do?

37:44.739 --> 37:46.789
They want to consume when
they're young,

37:46.786 --> 37:48.146
their utility,
remember?

37:48.150 --> 37:51.030
So what's their budget set?

37:51.030 --> 37:55.540
Their budget set is they can
consume Y, that's consuming

37:55.543 --> 37:58.913
here, or they can consume here
or here.

37:58.909 --> 38:03.139
So they can consume
P_up times

38:03.135 --> 38:09.305
Z_up P_down
times Z_down.

38:09.309 --> 38:12.289
That's what they can do with
those Arrow securities.

38:12.289 --> 38:15.529
So what are they trying to
maximize?

38:15.530 --> 38:22.800
They're trying to maximize 1
half log Y 1 quarter log

38:22.798 --> 38:29.508
Z_up 1 quarter log
Z_down.

38:29.510 --> 38:32.180
That's what they're trying to
do.

38:32.179 --> 38:34.619
So what do we have to do?

38:34.619 --> 38:37.979
We have to clear this market
and this market given what the

38:37.980 --> 38:40.530
young are going to do in the
next period,

38:40.530 --> 38:43.030
but let's see what this guy's
going to do when he's young.

38:43.030 --> 38:46.360
Everybody is going to face a
similar, basically a scaled up

38:46.358 --> 38:47.848
version of this problem.

38:47.849 --> 38:49.659
So this is what the guy is
doing here.

38:49.659 --> 38:52.909
He's got an income of 3 and
there's the price of up and down

38:52.911 --> 38:53.961
Arrow securities.

38:53.960 --> 38:57.700
That's going to tell him what
to consume here and what to plan

38:57.695 --> 38:59.835
to consume up here and down
here.

38:59.840 --> 39:01.690
Student: Do you change
your utility function?

39:01.690 --> 39:03.350
Prof: So utility
function is the same one as

39:03.347 --> 39:03.577
this.

39:03.579 --> 39:06.639
I just multiplied through by 1
half, right?

39:06.639 --> 39:09.679
So I put 1 half,
1 quarter, 1 quarter to get

39:09.684 --> 39:10.184
that.

39:10.179 --> 39:14.229
So I've just multiplied it all
by a constant.

39:14.230 --> 39:16.470
So now the coefficients add up
to 1;

39:16.469 --> 39:18.039
1 half, 1 quarter and 1 quarter.

39:18.039 --> 39:20.619
That's his budget constraint,
but what's the budget

39:20.619 --> 39:22.889
constraint going to be of a guy
down here?

39:22.889 --> 39:24.179
It's exactly the same.

39:24.179 --> 39:28.079
He's going to maximize the same
utility function and his budget

39:28.079 --> 39:30.419
constraint,
since the prices of the Arrow

39:30.420 --> 39:34.050
securities are the same,
the only difference is going to

39:34.045 --> 39:36.805
be that he's only got 3 halves
here.

39:36.809 --> 39:39.079
So they're pretty similar
problems.

39:39.079 --> 39:41.829
So let's see what the guy at
time 1 is going to do.

39:41.829 --> 39:49.029
That's going to imply that Y =
(Cobb-Douglas) 1 half times (his

39:49.030 --> 39:55.420
income) 3 divided by the price
of Y which is just 1,

39:55.420 --> 40:03.110
so 1 half of 3 over 1 which is
3 halves.

40:03.110 --> 40:06.750
And what's he going do when
he's old?

40:06.750 --> 40:09.740
Z_up is going to
be--well,

40:09.739 --> 40:15.029
his Cobb-Douglas is 1 quarter,
and then his income is still 3,

40:15.030 --> 40:18.240
and then the price is
P_up of the Arrow

40:18.242 --> 40:18.982
security.

40:18.980 --> 40:26.110
In the down case he's going to
have 1 quarter times 3 (that's

40:26.114 --> 40:31.114
his income) divided by
P_down.

40:31.110 --> 40:33.950
So to clear this market what do
we have to do?

40:33.949 --> 40:37.379
We have to clear the market by
doing what?

40:37.380 --> 40:40.100
Z_up,
that's this guy,

40:40.096 --> 40:44.906
so 1 quarter (so this is the
old guy) times 3 divided by

40:44.914 --> 40:46.584
P_up.

40:46.579 --> 40:49.419
That's what this guy wants to
consume up here,

40:49.422 --> 40:53.092
plus what the young are going
to do there, but we know what

40:53.088 --> 40:55.298
the young are going to do here.

40:55.300 --> 40:58.740
This young person is doing
exactly what this guy did,

40:58.739 --> 41:02.379
except instead of having a
starting wealth of 3 he has a

41:02.376 --> 41:04.026
starting wealth of 6.

41:04.030 --> 41:07.550
So instead of consuming young 3
halves he's going to consume

41:07.554 --> 41:08.574
young 6 halves.

41:08.570 --> 41:12.450
So this is going to be plus 3.

41:12.449 --> 41:15.679
He's going to consume half of
his wages just like this guy

41:15.682 --> 41:18.352
consumed half of his wages when
he was young.

41:18.349 --> 41:21.409
So this new young guy,
the young guys are always going

41:21.409 --> 41:24.989
to consume in the first period
half of what their wages are.

41:24.989 --> 41:26.679
That's what this equation tells
us.

41:26.679 --> 41:29.189
If this is your budget set,
this is your income,

41:29.192 --> 41:32.082
this is what your budget set is
and this is what you're

41:32.077 --> 41:32.877
maximizing.

41:32.880 --> 41:36.180
This is a very special
Cobb-Douglas case where you have

41:36.182 --> 41:40.132
endowments only in one good,
so it's clear that in that good

41:40.134 --> 41:43.384
you'll always consume the
Cobb-Douglas coefficient

41:43.380 --> 41:47.210
fraction of it,
1 half of that, so 3 halves.

41:47.210 --> 41:52.210
And this guy's going to consume
1 half of 6 which is 3.

41:52.210 --> 41:55.800
So the old up here are going to
consume that number.

41:55.800 --> 42:03.400
The young are going to consume
3, and what's the total that's

42:03.403 --> 42:07.463
available for them to consume?

42:07.460 --> 42:08.640
What's available?

42:08.639 --> 42:10.729
Student: 6.

42:10.730 --> 42:12.940
Prof: No, more.

42:12.940 --> 42:13.990
Student: 8.

42:13.989 --> 42:17.879
Prof: 8;
the young got 6 apples and the

42:17.884 --> 42:24.444
land paid 2 apples in dividends,
so the total number of apples

42:24.440 --> 42:25.300
is 8.

42:25.300 --> 42:26.650
So that's it.

42:26.650 --> 42:31.690
And so we can solve that and
that's going to imply that

42:31.690 --> 42:36.800
multiplying--
so that's 5 and multiplying by

42:36.795 --> 42:39.405
4 is 20,
so P_U,

42:39.414 --> 42:42.844
of course I'm going to screw
this up now.

42:42.840 --> 42:48.560
P_U is 3 over 20,
because if you put 3 over 20 in

42:48.563 --> 42:54.783
here you get the 3s cancel and
you get 20 over 4 which is 5,

42:54.780 --> 42:57.860
and 5 3 is 8, so it's 3 over 20.

42:57.860 --> 43:00.430
Now meanwhile,
what are we going to have in

43:00.431 --> 43:01.351
the up state?

43:01.349 --> 43:02.729
In the up state...

43:02.730 --> 43:03.480
Student: In the down
state.

43:03.480 --> 43:04.020
Prof: Down state.

43:04.019 --> 43:05.369
That was the up state.

43:05.369 --> 43:13.749
In the down state the guy's
going to do 1 quarter 3 over

43:13.751 --> 43:16.191
P_D.

43:16.190 --> 43:18.150
What is this other guy going to
do?

43:18.150 --> 43:24.250
The young person here is going
to consume what?

43:24.250 --> 43:26.060
So in the downstate what are we
going to have?

43:26.059 --> 43:31.069
The equation of the downstate
is going to be--

43:31.070 --> 43:38.150
so this one 1 quarter 3 divided
by P_down plus what's

43:38.152 --> 43:43.182
this guy going to consume when
he's young?

43:43.179 --> 43:47.169
Well, his income,
his wages are 3 halves and he's

43:47.168 --> 43:51.488
going to consume half of that so
it's 3 quarters,

43:51.489 --> 43:54.149
right, because when you're
young you always end up

43:54.150 --> 43:57.800
consuming half of your wages,
so 3 quarters and that has to

43:57.802 --> 44:03.892
equal--
what's the total?

44:03.889 --> 44:07.879
2?

44:07.880 --> 44:11.680
2, so what does that leave us?

44:11.679 --> 44:15.449
That leaves us 3 quarters,
that's 5 fourths,

44:15.452 --> 44:16.772
so let's see.

44:16.768 --> 44:22.588
So 5 fourths equals 3 quarters
over P_D,

44:22.590 --> 44:30.380
so P_D is going to
equal 3 fifths,

44:30.380 --> 44:32.840
right, because the 4s drop out
and you put P_D up and

44:32.842 --> 44:34.432
the 5 down,
it's 3 fifths.

44:34.429 --> 44:35.279
So that's it.

44:35.280 --> 44:37.790
So now we've got--we've figured
out the prices.

44:37.789 --> 44:39.929
So this Arrow security was 1
half.

44:39.929 --> 44:42.229
I mean, the probabilities are 1
half, 1 half,

44:42.228 --> 44:44.368
but the prices,
the Arrow security prices,

44:44.369 --> 44:47.399
are going to be less than 1
half and more than 1 half.

44:47.400 --> 44:52.420
I forgot what they were
already, 3 twentieths,

44:52.420 --> 44:55.210
3 over 20 and 3 over 5.

44:55.210 --> 44:56.510
Those are the Arrow prices.

44:56.510 --> 44:58.610
By the way, you notice they
don't add up to 1.

44:58.610 --> 45:03.510
So what's the interest rate?

45:03.510 --> 45:07.010
So if you want to get--a
riskless bond pays 1 in each of

45:07.014 --> 45:09.964
these two states,
so how much is that worth,

45:09.963 --> 45:13.833
1 over (1 r) equals (You have
to buy both Arrow securities.

45:13.829 --> 45:15.089
We've done this before.)

45:15.090 --> 45:20.740
3 twentieths 3 fifths which
equals 15 twentieths,

45:20.737 --> 45:27.087
which equals 3 fourths,
so therefore 1 r = 4 thirds.

45:27.090 --> 45:30.550
So r is 33 percent.

45:30.550 --> 45:31.950
So that's what we did.

45:31.949 --> 45:36.349
We've got the probabilities,
3 twentieths and 3 fifths.

45:36.349 --> 45:39.179
Just as we thought the price of
the down Arrow security is going

45:39.177 --> 45:41.907
to be much bigger than the price
of the up Arrow security even

45:41.914 --> 45:44.254
though objectively they have
50/50 probability,

45:44.250 --> 45:45.550
and why is that?

45:45.550 --> 45:49.030
Because everyone who's rational
is going to realize that they

45:49.034 --> 45:52.524
have to plan to consume much
more up here than down here,

45:52.518 --> 45:56.628
but they're not going to want
to do that unless the price is

45:56.634 --> 45:57.684
much cheaper.

45:57.679 --> 45:59.099
So that's how we got the price.

45:59.099 --> 46:00.749
So now what's the price of land?

46:00.750 --> 46:03.760
That's the only last thing we
have to figure out,

46:03.764 --> 46:05.214
so the price of land.

46:05.210 --> 46:11.920
So the price of land at time 1
equals what?

46:11.920 --> 46:14.510
Well, what if you buy the land?

46:14.510 --> 46:17.510
What do you get?

46:17.510 --> 46:23.460
You get 3 twentieths,
then you get the dividend which

46:23.458 --> 46:28.838
is 2, but then you get to sell
the land which is

46:28.835 --> 46:31.805
P_land^(up).

46:31.809 --> 46:36.169
And then plus if you get the
down state you get a

46:36.172 --> 46:40.902
dividend--so the down state is
worth 3 fifths to you,

46:40.900 --> 46:41.810
right?

46:41.809 --> 46:43.289
And then what do you get?

46:43.289 --> 46:46.309
What's your dividend?

46:46.309 --> 46:52.329
1 half the price of the land
you can sell,

46:52.331 --> 46:56.151
P_land^(down).

46:56.150 --> 46:59.440
So that's what the price of
land is at 1.

46:59.440 --> 47:02.000
It depends, of course,
on what you can sell the price

47:02.001 --> 47:06.341
of land for in the future,
but we made a guess here that

47:06.338 --> 47:12.058
the price of land is just
proportional to the price of the

47:12.056 --> 47:13.256
dividend.

47:13.260 --> 47:16.200
So whatever the price of land
is here when the dividend is 1

47:16.204 --> 47:19.004
it should be twice as high here
and half as high here.

47:19.000 --> 47:21.760
So therefore this,
instead of looking at it as the

47:21.764 --> 47:25.324
price of land went up it's going
to be twice the price that land

47:25.317 --> 47:27.007
was at the very beginning.

47:27.010 --> 47:30.440
So it's just 2 times the price
of land at the very beginning

47:30.443 --> 47:31.843
times that same price.

47:31.840 --> 47:35.870
And this price of land at down,
the dividend is half,

47:35.869 --> 47:38.499
so the land is sort of half as
good from here on out as it was

47:38.498 --> 47:42.498
in the beginning,
so let's guess the price of

47:42.496 --> 47:47.836
land is half of what it was at
the beginning.

47:47.840 --> 47:50.890
But now you see we've just got
P_land in terms of

47:50.891 --> 47:53.051
other stuff and so we can solve
for it.

47:53.050 --> 47:57.250
So the price of land is going
to equal--well,

47:57.246 --> 47:59.436
now it's complicated.

47:59.440 --> 48:08.800
So 3 tenths 3 tenths times the
price of land 3 tenths 3 tenths

48:08.800 --> 48:17.090
times the price of land,
and so that means the price of

48:17.086 --> 48:20.766
land minus 6 tenths.

48:20.768 --> 48:30.838
So 4 tenths the price of land
is going to equal 6 tenths.

48:30.840 --> 48:38.200
So the price of land is 3
halves at the beginning.

48:38.199 --> 48:40.529
So we figured out the price of
land here.

48:40.530 --> 48:45.850
Price of land is 3 halves at
the very beginning.

48:45.849 --> 48:48.349
So we've solved for the whole
equilibrium.

48:48.349 --> 48:51.239
It took a long time,
but I'm at the end of this

48:51.244 --> 48:52.004
story now.

48:52.000 --> 48:54.710
So let's just review what we
did.

48:54.710 --> 48:58.810
And so I don't think it's that
complicated a story.

48:58.809 --> 49:03.279
The story is that you've got
land which has risky dividends.

49:03.280 --> 49:07.180
So instead of having one
straight line of what can happen

49:07.179 --> 49:11.149
in the future we've got this
infinitely expanding tree.

49:11.150 --> 49:14.780
So it's very hard to imagine
solving it, but then we've built

49:14.775 --> 49:16.825
in somewhat special assumptions.

49:16.829 --> 49:19.829
We've got all this homogeneity
and that allows us to solve it

49:19.833 --> 49:22.793
because it's the same problem
getting repeated over and over

49:22.789 --> 49:24.969
again,
just like we did before.

49:24.969 --> 49:27.679
So the price of land turns out
to be 3 halves.

49:27.679 --> 49:31.549
So what is this guy going to do?

49:31.550 --> 49:36.010
He's going to take his land,
his income which is 3,

49:36.010 --> 49:38.320
eat half of it,
which was 3 halves,

49:38.320 --> 49:40.360
that's what we said he always
does when he's young,

49:40.360 --> 49:43.910
spend half his income on
consumption,

49:43.909 --> 49:47.489
the rest of his income,
3 halves, he uses to buy all

49:47.487 --> 49:48.257
the land.

49:48.260 --> 49:52.510
Now, with the land he gets a
payoff of 2, but he gets to sell

49:52.507 --> 49:55.767
the land now for double the
price he bought it,

49:55.766 --> 49:56.966
namely for 3.

49:56.969 --> 50:01.879
So 2 3 is 5 and that,
by the way, the price of up was

50:01.880 --> 50:06.090
3 twentieths so this is 5,
right, because if I put in 3

50:06.094 --> 50:08.734
twentieths up here that's the
Arrow price of up,

50:08.730 --> 50:10.220
then Z_up is going to
be 5.

50:10.219 --> 50:11.769
And so that's exactly how we
got it.

50:11.768 --> 50:14.198
With the land he gets the
dividend of 2 plus he sells the

50:14.204 --> 50:14.774
land for 3.

50:14.769 --> 50:16.489
That's 5, so he does consume 5.

50:16.489 --> 50:18.519
Z_down,
incidentally,

50:18.523 --> 50:20.763
the price of down was 3 fifths.

50:20.760 --> 50:25.430
So the consumption of
down--what's consumption of down

50:25.427 --> 50:26.657
going to be?

50:26.659 --> 50:29.109
Student: 5 fourths.

50:29.110 --> 50:30.530
Prof: 5 fourths,
thank you.

50:30.530 --> 50:33.090
That'll be 5 fourths,
so let's see that that's going

50:33.094 --> 50:34.004
to work out too.

50:34.000 --> 50:38.930
So the guy buys the land,
he gets his dividend of 1 half,

50:38.929 --> 50:42.419
and then he sells the land for
half of this price which is 3

50:42.420 --> 50:44.770
quarters,
and 1 half plus 3 quarters is 5

50:44.769 --> 50:46.359
fourths,
exactly what he's supposed to

50:46.360 --> 50:46.580
have.

50:46.579 --> 50:49.269
So you see it works out that
everybody's doing exactly what

50:49.273 --> 50:51.833
they're supposed to and all the
markets are clearing.

50:51.829 --> 50:55.079
Anyhow, the point is not so
much the numbers,

50:55.077 --> 50:58.377
the point is the following;
that sure enough,

50:58.380 --> 51:01.530
just as we said before,
the price of Arrow securities

51:01.532 --> 51:04.572
are going to be expensive when
things are going down and cheap

51:04.567 --> 51:05.957
when things are going up.

51:05.960 --> 51:09.640
The upshot of that is the
return on stocks,

51:09.644 --> 51:12.984
like land, is going to be very
high.

51:12.980 --> 51:16.870
You put in 3 halves and what
happens with the 3 halves?

51:16.869 --> 51:21.219
With probability 1 half,
that's what you put in,

51:21.224 --> 51:26.974
with probability 1 half you get
2 plus you get to sell the land

51:26.971 --> 51:29.011
for 3, which is 5.

51:29.010 --> 51:33.440
And with the other probability
1 half you get--the dividend is

51:33.442 --> 51:36.932
1 half, plus you sell the land
for 3 quarters.

51:36.929 --> 51:39.159
That's what you're eating,
5 and 5 fourths.

51:39.159 --> 51:48.079
That's equal to 5 halves 5
fourths 5--I don't know what

51:48.077 --> 51:49.727
this is.

51:49.730 --> 51:51.120
What is this?

51:51.119 --> 51:54.619
1 half 3 quarters is 5 fourths
times 1 half...

51:54.619 --> 51:55.069
Student: 5 eighths.

51:55.070 --> 51:57.730
Prof: It's 5 eighths
divided by 3 halves.

51:57.730 --> 51:59.250
So this is a very high number.

51:59.250 --> 52:00.400
So what is this?

52:00.400 --> 52:06.410
4 times that,
that's 25 over 8 divided by 3

52:06.414 --> 52:09.284
over 2 which is...

52:09.280 --> 52:11.180
Student: 25 over 12.

52:11.179 --> 52:11.719
Prof: Is what?

52:11.719 --> 52:13.679
Student: 25 over 12.

52:13.679 --> 52:15.359
Prof: 25 over 12,
is that what you said?

52:15.360 --> 52:16.870
Student: 25 over 12.

52:16.869 --> 52:19.799
Prof: 25 over 12,
I'm just believing you now.

52:19.800 --> 52:23.080
So that is over 200%, right?

52:23.079 --> 52:25.099
So your return is 100%.

52:25.099 --> 52:28.509
Whatever you put in you've more
than doubled your money in

52:28.510 --> 52:30.780
expectation, whereas the
interest rate,

52:30.784 --> 52:33.184
we said, was 33 and 1 third
percent.

52:33.179 --> 52:35.889
So of course you're getting a
tremendous return by putting

52:35.891 --> 52:38.751
your money into capital because
that's the whole point of the

52:38.746 --> 52:39.266
theory.

52:39.269 --> 52:40.609
It's risky.

52:40.610 --> 52:43.430
The whole economy is going to
be rich or poor together,

52:43.429 --> 52:46.299
so the price of capital,
on the margin it's a very risky

52:46.304 --> 52:47.144
thing to do.

52:47.139 --> 52:50.259
It just adds to this inequality
in your consumption.

52:50.260 --> 52:51.620
So the price is going to be low.

52:51.619 --> 52:53.529
You're going to get a very high
return.

52:53.530 --> 52:54.920
That's all I wanted to do.

52:54.920 --> 52:58.460
I just solved it out concretely
so you can see very clearly that

52:58.458 --> 53:01.098
you get a high return in the
good state and--

53:01.099 --> 53:03.369
you get a high return on
capital, much higher than the

53:03.369 --> 53:04.569
riskless rate of interest.

53:04.570 --> 53:05.310
So there we are.

53:05.309 --> 53:08.429
We're back at the beginning now
where George Bush--we can see

53:08.434 --> 53:11.044
that somewhere in the middle
here things are really

53:11.038 --> 53:11.818
disastrous.

53:11.820 --> 53:14.150
These people who are getting
Social Security,

53:14.150 --> 53:18.050
which means they're getting a
fixed amount here and here are

53:18.045 --> 53:21.185
doing really badly,
at least in expected return,

53:21.190 --> 53:24.330
compared to what they would do
in the stock market.

53:24.329 --> 53:30.939
And so what should we do about
that, and is it true that just

53:30.940 --> 53:37.440
because stocks make a higher
return, we should privatize?

53:37.440 --> 53:38.410
So what do you think now?

53:38.409 --> 53:40.169
Where are we in this argument?

53:40.170 --> 53:47.110
Has anything materially changed?

53:47.110 --> 53:50.610
So George Bush is saying,
and many Republicans say,

53:50.614 --> 53:54.544
that we should let people,
you know, get them invested in

53:54.539 --> 53:55.309
stocks.

53:55.309 --> 53:57.659
There's a higher expected
return.

53:57.659 --> 54:10.479
So what do we think about that?

54:10.480 --> 54:23.820
What do you think about that?

54:23.820 --> 54:25.910
This is a real policy issue
here.

54:25.909 --> 54:27.239
We've got this problem in
America.

54:27.239 --> 54:31.429
Right now we've got this huge
deficit in Social Security.

54:31.429 --> 54:34.899
The rate of return has gotten
really poor for your generation.

54:34.900 --> 54:37.550
You're looking forward to not
making very much money,

54:37.550 --> 54:40.590
and now we know theoretically,
confirming what we've seen in

54:40.590 --> 54:42.910
the past,
stocks are making higher

54:42.905 --> 54:47.805
returns than bonds,
and Social Security is paying

54:47.811 --> 54:53.121
people a fraction of the wages
of the young.

54:53.119 --> 54:56.499
So let me remind you of the
arguments.

54:56.500 --> 55:00.140
So the issue has come up
because Social Security is

55:00.135 --> 55:01.805
running out of money.

55:01.809 --> 55:03.779
So it came up because of this
problem.

55:03.780 --> 55:05.240
There's going to be a deficit.

55:05.239 --> 55:08.269
If we continue to pay people at
the same rules that we've used

55:08.266 --> 55:11.336
up until now we're not going to
be able to afford to do it much

55:11.344 --> 55:13.744
longer,
so we're going to have to lower

55:13.742 --> 55:16.012
what we pay the people going
forward,

55:16.010 --> 55:19.960
lower it in some clever way
like they don't get money until

55:19.960 --> 55:21.050
they're older.

55:21.050 --> 55:24.360
Instead of 65 make them wait
until 70, or do something like

55:24.360 --> 55:25.730
that to pay them less.

55:25.730 --> 55:27.680
That's one way of balancing
things.

55:27.679 --> 55:30.439
And because we're going to have
to make changes like that,

55:30.440 --> 55:33.060
that's why the whole issue of
Social Security has come up,

55:33.059 --> 55:37.399
and now deeper thinkers are
questioning the whole idea of

55:37.402 --> 55:38.802
Social Security.

55:38.800 --> 55:42.220
So let me just remind you that
America was ahead of everyone in

55:42.215 --> 55:45.515
the world when we created Social
Security under Roosevelt.

55:45.519 --> 55:47.229
Nobody had anything like it.

55:47.230 --> 55:50.670
Then everybody in the rest of
the world gradually copied us,

55:50.670 --> 55:54.040
and now everybody's facing the
same problem we are,

55:54.039 --> 55:55.689
which we know why you have to
face it.

55:55.690 --> 55:59.280
You're giving away stuff to the
people at the beginning and so

55:59.284 --> 56:02.704
they're facing it by changing
Social Security in some crazy

56:02.701 --> 56:05.351
way or another,
and we haven't changed anything

56:05.351 --> 56:06.831
at all,
but obviously we have to,

56:06.829 --> 56:09.229
and the question is how should
we change it and what's the

56:09.226 --> 56:10.106
right thing to do.

56:10.110 --> 56:13.020
And just to remind you,
again, of the issues,

56:13.023 --> 56:16.873
the Democrats and Republicans
seem to be totally opposed to

56:16.865 --> 56:17.855
each other.

56:17.860 --> 56:21.950
The Democrats say, "Oh,
we want to continue to give

56:21.945 --> 56:27.025
people who have done poorly in
their lives a better deal on

56:27.030 --> 56:31.500
Social Security because we want
to redistribute.

56:31.500 --> 56:32.970
We want to help the poor."

56:32.969 --> 56:34.969
The Republicans,
actually some of them agree

56:34.965 --> 56:36.725
with that,
but some of them don't agree

56:36.731 --> 56:38.741
with that,
but anyway, even the ones who

56:38.737 --> 56:41.697
agree that's not the most
important thing they think of in

56:41.702 --> 56:42.692
Social Security.

56:42.690 --> 56:45.980
Then the Democrats say,
"Social Security is so

56:45.978 --> 56:49.858
important because we're sharing
risks across generations.

56:49.860 --> 56:55.830
If the next generation has poor
wages so they end up down here

56:55.827 --> 56:59.207
with bad wages,
you know, the economy takes a

56:59.206 --> 57:02.326
turn south with bad wages,
then the old people should

57:02.329 --> 57:03.769
suffer along with them.

57:03.768 --> 57:06.888
And if the young do better with
high wages because things went

57:06.889 --> 57:09.599
up then the old should also get
better Social Security

57:09.601 --> 57:11.801
dividends,"
and that's what the current

57:11.800 --> 57:13.080
situation promises.

57:13.079 --> 57:17.439
It's also indexed according to
inflation, all right,

57:17.440 --> 57:22.400
so once you retire then you're
protected against changes in

57:22.402 --> 57:23.602
inflation.

57:23.599 --> 57:25.309
And then another important
thing of Democrats,

57:25.313 --> 57:27.223
you don't have an opportunity
to make a mistake.

57:27.219 --> 57:29.949
If you invest in stocks and
stuff like that and the stock

57:29.945 --> 57:32.765
market suddenly collapses you're
not going to lose money in

57:32.766 --> 57:35.736
Social Security because Social
Security depends on the wage of

57:35.735 --> 57:38.955
the next generation,
and that moves much slower than

57:38.960 --> 57:39.640
the stock.

57:39.639 --> 57:41.329
The Republicans,
on the other hand,

57:41.329 --> 57:43.069
say, "This is just
terrible.

57:43.070 --> 57:45.630
Nobody knows what their
property rights are in Social

57:45.628 --> 57:46.168
Security.

57:46.170 --> 57:48.550
No one actually understands how
much money they're getting when

57:48.552 --> 57:49.092
they're old.

57:49.090 --> 57:52.170
They just know now it's going
to be bad compared to what

57:52.168 --> 57:55.248
they're paying in taxes,
but you don't even know what it

57:55.248 --> 57:57.038
is, so how can that be good?

57:57.039 --> 58:00.169
It's not transparent,
but not only that,

58:00.170 --> 58:02.720
whatever you think it is now
it's going to turn out to be

58:02.719 --> 58:05.179
worse because in ten years
somebody's going to say,

58:05.179 --> 58:06.489
'Oh, the system's not balanced.

58:06.489 --> 58:09.909
We have to delay benefits or
something to put it back into

58:09.909 --> 58:11.719
balance,
and we're going to take away

58:11.719 --> 58:13.689
what you thought you were going
to get.'"

58:13.690 --> 58:15.240
So Republicans say,
"That's horrible.

58:15.239 --> 58:18.279
Nobody knows really exactly
what it is, and they get an idea

58:18.280 --> 58:20.760
of what it might be,
but it could always be taken

58:20.755 --> 58:21.215
away.

58:21.219 --> 58:24.159
Really what they want to know
is, 'What's the value of my

58:24.159 --> 58:26.889
Social Security account,
and I want it to be mine.

58:26.889 --> 58:30.339
I can also then tell what the
redistribution is.

58:30.340 --> 58:33.460
If I know what I'm paying in
taxes and I know the value of

58:33.463 --> 58:36.813
the benefits I'm getting I can
see that my taxes are much more

58:36.807 --> 58:37.957
than my benefits.

58:37.960 --> 58:40.830
And if I happen to be a nice
guy and think it's a good idea

58:40.833 --> 58:42.373
to have redistribution,
fine.

58:42.369 --> 58:44.229
But if I'm a bad,
you know, not a bad guy,

58:44.230 --> 58:46.490
if I just don't believe in that
much redistribution I should be

58:46.492 --> 58:48.722
aware of it and have the chance
to vote against it.'"

58:48.719 --> 58:53.029
Also, a key thing is these
Republicans say,

58:53.030 --> 58:55.050
"People should get equity
like returns,

58:55.050 --> 58:57.360
not this wages of the next
generation,

58:57.360 --> 58:58.630
those grow slowly.

58:58.630 --> 59:01.530
Stocks might have a much higher
return on average.

59:01.530 --> 59:04.240
People should get equity like
return, so let's put them in the

59:04.244 --> 59:05.184
stock market."

59:05.179 --> 59:07.869
And then Republicans think
choice is always great.

59:07.869 --> 59:10.369
Even if people make mistakes
it's their own mistake,

59:10.367 --> 59:11.737
so let them make mistakes.

59:11.739 --> 59:14.449
So those are the opposite sides
of the argument.

59:14.449 --> 59:18.429
They seem totally at odds with
each other and impossible to

59:18.434 --> 59:19.264
reconcile.

59:19.260 --> 59:22.090
So I want to now tell you my
plan.

59:22.090 --> 59:24.660
So everyone's got the problem
straight.

59:24.659 --> 59:28.209
We're running out of money and
the philosophies of the two

59:28.208 --> 59:31.568
groups seem to be totally
opposed, so what should we do

59:31.570 --> 59:32.380
about it?

59:32.380 --> 59:36.820
All right, so my plan,
in five minutes because I want

59:36.818 --> 59:41.338
to end with Black-Scholes,
my plan in five minutes is,

59:41.340 --> 59:44.500
okay, to make a few
observations.

59:44.500 --> 59:47.460
First of all,
yes it's true that you get a

59:47.463 --> 59:50.723
higher return on stocks than you
get on bonds,

59:50.717 --> 59:52.957
but you face a higher risk.

59:52.960 --> 59:54.830
So it's not like you get it for
free.

59:54.829 --> 59:56.739
It's a bigger risk.

59:56.739 --> 59:59.679
So that's number one.

59:59.679 --> 1:00:02.719
So no, actually,
point zero is you've still got

1:00:02.721 --> 1:00:06.691
the problem because you gave
money to all those people in the

1:00:06.688 --> 1:00:08.048
'40s,
and the '50s,

1:00:08.052 --> 1:00:09.572
and the '60s,
and the '70s.

1:00:09.570 --> 1:00:10.600
That money is gone.

1:00:10.599 --> 1:00:13.859
We've essentially borrowed to
give them money and somebody's

1:00:13.860 --> 1:00:15.410
got to pay back that debt.

1:00:15.409 --> 1:00:17.229
And so there's no way around
that.

1:00:17.230 --> 1:00:20.550
There's this huge 17 trillion
dollar debt hanging out there

1:00:20.552 --> 1:00:23.822
that we have to pay back and you
can't get around that.

1:00:23.820 --> 1:00:26.010
So putting the money into
equities, or wherever you put

1:00:26.005 --> 1:00:27.905
the money there's still that
tremendous debt.

1:00:27.909 --> 1:00:30.509
Now the question is--so you
can't just make the problem go

1:00:30.514 --> 1:00:32.894
away by saying that equities
have a higher return.

1:00:32.889 --> 1:00:36.389
Bonds also have a higher return
than the return people are

1:00:36.387 --> 1:00:39.637
getting on Social Security
because the Social Security

1:00:39.641 --> 1:00:43.321
return includes the tax that
you're paying to make up for the

1:00:43.324 --> 1:00:44.924
original generation.

1:00:44.920 --> 1:00:47.520
So that's the first thing.

1:00:47.518 --> 1:00:53.368
So the next thing is maybe it's
not such a big difference,

1:00:53.369 --> 1:00:58.549
this equities and not equities,
because notice in this model

1:00:58.547 --> 1:01:02.697
when the stock is paying higher,
when the stock dividends are

1:01:02.702 --> 1:01:04.082
higher,
2 instead of 1,

1:01:04.079 --> 1:01:06.069
the price of stocks goes up.

1:01:06.070 --> 1:01:08.440
That's a great return from the
stock market,

1:01:08.436 --> 1:01:10.966
but the wages were also higher
here as well.

1:01:10.969 --> 1:01:14.549
So in fact I claim that in the
long run,

1:01:14.550 --> 1:01:17.040
and it's amazing that the
Republicans haven't noticed

1:01:17.036 --> 1:01:19.426
this,
in the long run over 30 or 40

1:01:19.434 --> 1:01:23.124
years it's obvious that the
stock market and wages are

1:01:23.117 --> 1:01:24.087
correlated.

1:01:24.090 --> 1:01:27.990
I mean, if the stock market
collapses that's disaster for

1:01:27.990 --> 1:01:32.520
America and you can be sure the
wages are going to go down too.

1:01:32.518 --> 1:01:35.388
If our stock market's booming
and America's incredibly

1:01:35.389 --> 1:01:38.479
successful it's a sure thing
that in 40 years if the stock

1:01:38.478 --> 1:01:41.668
market is just booming along
wages are going to be higher as

1:01:41.673 --> 1:01:42.273
well.

1:01:42.268 --> 1:01:46.768
So if you get the wages of the
generation 30 years from now in

1:01:46.773 --> 1:01:50.763
the Democratic plan you're
actually getting equity like

1:01:50.760 --> 1:01:53.870
returns,
but you're getting an advantage

1:01:53.867 --> 1:01:56.427
which is that the wages move
slowly.

1:01:56.429 --> 1:01:59.609
So although the stocks are
bouncing up and down,

1:01:59.610 --> 1:02:03.660
so somebody who retires in the
year 2007 if he held stock and

1:02:03.657 --> 1:02:07.367
sold it when he retired he could
get a huge pension,

1:02:07.369 --> 1:02:10.789
where someone who retired in
2008 and sold the stock just

1:02:10.788 --> 1:02:14.388
when he retired he would be
crushed because the stock market

1:02:14.389 --> 1:02:15.609
lost 50 percent.

1:02:15.610 --> 1:02:18.630
So that will never happen if
you just pay according to wages

1:02:18.628 --> 1:02:20.418
because they're much more
stable.

1:02:20.420 --> 1:02:23.730
But wages in the long run are
correlated with stocks in the

1:02:23.731 --> 1:02:24.361
long run.

1:02:24.360 --> 1:02:26.690
In the short run they just
don't fluctuate at much.

1:02:26.690 --> 1:02:29.340
So what is my plan?

1:02:29.340 --> 1:02:31.750
So those are just some
preliminary observations and

1:02:31.746 --> 1:02:32.946
I'll give you the plan.

1:02:32.949 --> 1:02:35.339
Then as I said this is
obviously controversial.

1:02:35.340 --> 1:02:39.240
I think I've identified the
problem in a scientific way.

1:02:39.239 --> 1:02:44.519
That is, everyone would agree
with me if they knew enough

1:02:44.523 --> 1:02:46.583
economics,
but now my plan,

1:02:46.581 --> 1:02:49.861
even people who do know as much
as me might disagree with me,

1:02:49.860 --> 1:02:55.000
but this is what I would--okay
so here's the plan.

1:02:55.000 --> 1:02:56.680
As I said, other plans just
say, "Well,

1:02:56.684 --> 1:02:57.354
things are bad.

1:02:57.349 --> 1:02:59.599
Let's just keep the same
system."

1:02:59.599 --> 1:03:01.239
So there are two basic ideas.

1:03:01.239 --> 1:03:04.049
The Democratic idea is,
"Let's just keep adjusting

1:03:04.054 --> 1:03:04.894
at the margin.

1:03:04.889 --> 1:03:07.669
We'll make up for it by giving
people money later.

1:03:07.670 --> 1:03:09.240
We'll do all kinds of things
like that.

1:03:09.239 --> 1:03:11.679
Maybe we'll raise some tax,
reduce some benefits,

1:03:11.677 --> 1:03:13.047
balance the system."

1:03:13.050 --> 1:03:16.040
The Republicans want to junk
the whole thing and privatize

1:03:16.043 --> 1:03:18.583
and let people,
you know, force them to save,

1:03:18.577 --> 1:03:21.477
but put it in the stock market
in their own account.

1:03:21.480 --> 1:03:26.260
Now, here's my plan.

1:03:26.260 --> 1:03:32.770
I don't have time to talk about
Bush's plan.

1:03:32.769 --> 1:03:33.569
So here's my plan.

1:03:33.570 --> 1:03:36.630
Number one, the fact that we
gave all this money away to

1:03:36.626 --> 1:03:40.386
people in the '40s,
and '50s, and '60s and '70s,

1:03:40.389 --> 1:03:45.009
why should that be the
responsibility of the workers

1:03:45.012 --> 1:03:45.832
today?

1:03:45.829 --> 1:03:48.429
I mean, our government decided
it was a good idea.

1:03:48.429 --> 1:03:51.849
Roosevelt and Frances Perkins
decided we had to rescue the old

1:03:51.849 --> 1:03:54.409
of the '40s,
and our Congresses kept that up

1:03:54.405 --> 1:03:57.835
for the next 20 or 30 years even
though the old weren't in such

1:03:57.838 --> 1:03:59.488
dire shape,
but they kept it up.

1:03:59.489 --> 1:04:00.799
Maybe that was a good idea.

1:04:00.800 --> 1:04:03.910
It's probably a very good idea,
but because we have that huge

1:04:03.909 --> 1:04:06.859
debt why should workers be the
only people responsible for

1:04:06.862 --> 1:04:08.212
paying back that debt?

1:04:08.210 --> 1:04:11.990
I would start by imposing a
legacy tax on everybody,

1:04:11.987 --> 1:04:15.247
not for Social Security,
just for the debt we

1:04:15.248 --> 1:04:19.248
accumulated by giving it to
those old generations.

1:04:19.250 --> 1:04:22.360
So I believe that would be
something like 1 percent.

1:04:22.360 --> 1:04:25.450
I wrote 2 to 3 percent,
but I think it's closer to 1

1:04:25.449 --> 1:04:27.569
percent, actually,
on all income.

1:04:27.570 --> 1:04:31.090
If I did it on all income it
would be like 1 percent and that

1:04:31.088 --> 1:04:34.138
fund would pay off for the
Social Security legacy.

1:04:34.139 --> 1:04:39.349
So then if we were starting the
system afresh how should we do

1:04:39.351 --> 1:04:39.781
it?

1:04:39.780 --> 1:04:42.770
And some countries like Chile
decided they're going to start

1:04:42.773 --> 1:04:43.233
afresh.

1:04:43.230 --> 1:04:46.420
So how should we start afresh
having gotten rid of this old

1:04:46.422 --> 1:04:48.572
debt that was hanging over our
heads?

1:04:48.570 --> 1:04:56.170
Well, what would I do?

1:04:56.170 --> 1:04:59.220
I would have what I call
Progressive Personal Accounts.

1:04:59.219 --> 1:05:02.939
So I like all the Republican
ideas of knowing what you've

1:05:02.938 --> 1:05:06.258
got, making it yours,
and making it transparent.

1:05:06.260 --> 1:05:09.710
I think that's all an extremely
good idea, but why should it be

1:05:09.706 --> 1:05:12.706
that that comes from putting
your money into stocks?

1:05:12.710 --> 1:05:14.360
I mean, stocks,
this is an old fashioned

1:05:14.362 --> 1:05:15.932
security and it's incredibly
risky.

1:05:15.929 --> 1:05:18.019
From one year to the next it
totally changes.

1:05:18.018 --> 1:05:23.318
I like the idea of indexing
something to wages.

1:05:23.320 --> 1:05:26.670
So I want to create a new
security that I called Personal

1:05:26.672 --> 1:05:28.772
Annuitized Average Wage
Security.

1:05:28.768 --> 1:05:31.668
So what this does,
this is a security that just

1:05:31.672 --> 1:05:35.522
pays proportional to the wage in
the whole country at the year

1:05:35.523 --> 1:05:36.473
you retire.

1:05:36.469 --> 1:05:40.099
So whenever you earn money on
Social Security--I'm running out

1:05:40.097 --> 1:05:43.427
of time so I'm going to skip
over this pretty quickly.

1:05:43.429 --> 1:05:46.139
So if you earn 1 dollar and you
pay,

1:05:46.139 --> 1:05:48.919
let's say, 12 percent in Social
Securities taxes,

1:05:48.920 --> 1:05:54.420
that income,
I'm going to say that's your

1:05:54.416 --> 1:05:57.216
income,
it's your 12 percent.

1:05:57.219 --> 1:06:00.899
You're going to be forced to
save it, and what you're forced

1:06:00.898 --> 1:06:03.078
to do is to buy these
securities.

1:06:03.079 --> 1:06:06.499
So it's a new kind of security
that pays proportional to the

1:06:06.503 --> 1:06:06.913
wage.

1:06:06.909 --> 1:06:10.219
So it might pay 1 percent of
the average wage.

1:06:10.219 --> 1:06:12.689
So it would pay 12 cents here,
3 cents here,

1:06:12.686 --> 1:06:14.576
and 3 quarters of a cent there.

1:06:14.579 --> 1:06:17.999
That's the wage in the economy
and it would pay 1 percent of

1:06:18.003 --> 1:06:18.413
that.

1:06:18.409 --> 1:06:21.699
And how much of it would you
get to buy, as much as you could

1:06:21.702 --> 1:06:24.232
afford to buy with your
security, with your tax

1:06:24.226 --> 1:06:25.156
contribution.

1:06:25.159 --> 1:06:29.489
Now, that almost replicates the
current system.

1:06:29.489 --> 1:06:32.919
The only difference is that it
doesn't replicate the current

1:06:32.922 --> 1:06:35.892
system, there's nothing
progressive about it yet.

1:06:35.889 --> 1:06:38.569
So what I would do is I would
make it a progressive tax.

1:06:38.570 --> 1:06:42.230
If you're making a hugely high
income I wouldn't give you the

1:06:42.230 --> 1:06:43.390
whole 12 percent.

1:06:43.389 --> 1:06:44.459
I would take part of it.

1:06:44.460 --> 1:06:47.340
And if you're making a really
low income I would have the

1:06:47.335 --> 1:06:49.335
government subsidize it a little
bit.

1:06:49.340 --> 1:06:51.910
So instead of getting 12
percent of your low income you'd

1:06:51.907 --> 1:06:53.557
get a little more than 12
percent.

1:06:53.559 --> 1:06:57.189
If you had a high income your
12 percent tax the government

1:06:57.192 --> 1:07:00.952
would take 1 of those 12 away
from you and you'd only have 11

1:07:00.949 --> 1:07:04.519
percent that you got to put in
your personal account.

1:07:04.518 --> 1:07:06.628
Now, but it has a tremendous
advantage,

1:07:06.630 --> 1:07:09.370
this system,
which is that if you can price

1:07:09.371 --> 1:07:11.741
the PAAWS,
if you know what the market

1:07:11.744 --> 1:07:14.744
price of PAAWS is then you're
balancing the system,

1:07:14.739 --> 1:07:17.499
because every time you hand
somebody money you don't make

1:07:17.503 --> 1:07:20.573
some crazy promise that when you
get to be old I'm going to pay

1:07:20.565 --> 1:07:23.375
you such and such dollars like
the current system is.

1:07:23.380 --> 1:07:26.050
You're letting the guy,
or the woman,

1:07:26.047 --> 1:07:29.797
let's say, who's working;
she is buying her own Social

1:07:29.795 --> 1:07:30.975
Security benefits.

1:07:30.980 --> 1:07:35.390
So the benefits have an equal
value to what she's paying for.

1:07:35.389 --> 1:07:38.879
So you've balanced the system.

1:07:38.880 --> 1:07:42.330
The legacy tax you got rid of
by having the tax on everybody

1:07:42.331 --> 1:07:45.261
of 1 or 2 percent,
and the balancing the system

1:07:45.262 --> 1:07:48.792
going forward is occurring
because you're forcing people to

1:07:48.789 --> 1:07:51.099
buy their Social Security
benefits.

1:07:51.099 --> 1:07:53.209
So anyway that's my,
in a nutshell,

1:07:53.206 --> 1:07:53.946
my system.

1:07:53.949 --> 1:07:56.849
And the last thing is how are
you going to get PAAWS priced by

1:07:56.851 --> 1:07:57.471
the market?

1:07:57.469 --> 1:07:59.959
Well, I'm going to get the
market to trade them,

1:07:59.956 --> 1:08:02.966
and I think that would be a
tremendous boon to the economy

1:08:02.974 --> 1:08:04.884
if we had these securities paid.

1:08:04.880 --> 1:08:06.930
Why is that?

1:08:06.929 --> 1:08:08.569
So how would I do that?

1:08:08.570 --> 1:08:12.130
I'd force everybody to invest
only in PAAWS,

1:08:12.130 --> 1:08:14.360
which I claim are like stocks
in the long run,

1:08:14.360 --> 1:08:15.890
but in the short run they're
less risky,

1:08:15.889 --> 1:08:17.569
so it's a better investment
vehicle,

1:08:17.569 --> 1:08:21.069
but they'd have to sell exactly
10 percent of their PAAWS into

1:08:21.074 --> 1:08:22.924
the market,
and with that 10 percent of

1:08:22.922 --> 1:08:25.362
money they could hold stocks or
whatever else they wanted to,

1:08:25.359 --> 1:08:29.069
and those 10 percent would all
be pooled together and traded in

1:08:29.070 --> 1:08:29.850
the market.

1:08:29.850 --> 1:08:33.380
And the market then would have
an idea of--a new instrument to

1:08:33.381 --> 1:08:36.451
price what they think future
wages are going to be.

1:08:36.448 --> 1:08:39.278
So anybody giving a pension
plan that's indexed to future

1:08:39.283 --> 1:08:42.423
wages would know what the market
price of those things are,

1:08:42.420 --> 1:08:44.470
so it would dramatically help
pension plans as well.

1:08:44.470 --> 1:08:49.240
Anyway, that's my idea for
Social Security.

1:08:49.238 --> 1:08:54.768
So I have four minutes left and
I want to end with one last

1:08:54.768 --> 1:08:59.438
thought, one last idea,
which is Black-Scholes.

1:08:59.439 --> 1:09:02.989
Now, we've already done
Black-Scholes in a few problem

1:09:02.989 --> 1:09:03.459
sets.

1:09:03.460 --> 1:09:06.890
So what is the idea of
Black-Scholes?

1:09:06.890 --> 1:09:09.940
It's just like the idea of the
example we gave.

1:09:09.939 --> 1:09:13.599
By the way, if you do come next
week and you want to question me

1:09:13.604 --> 1:09:17.154
about my Social Security plan
and criticize it I'd be thrilled

1:09:17.153 --> 1:09:20.353
to be criticized because you
can't learn anything unless

1:09:20.351 --> 1:09:23.611
you're criticized and I think I
can defend it too.

1:09:23.609 --> 1:09:26.679
But anyhow, this is an idea
which obviously hasn't caught on

1:09:26.684 --> 1:09:29.034
yet because Social Security
reform stopped.

1:09:29.029 --> 1:09:30.759
We've got worse problems to
worry about,

1:09:30.760 --> 1:09:33.660
but if we get through this
crisis the very next thing on

1:09:33.655 --> 1:09:36.705
Obama's agenda is going to be
reforming Social Security.

1:09:36.710 --> 1:09:39.730
So I'm ready.

1:09:39.729 --> 1:09:43.169
So let me just end with
Black-Scholes.

1:09:43.170 --> 1:09:48.420
So in 1972 Black and Scholes
wrote a famous paper.

1:09:48.420 --> 1:09:49.720
And what did they do?

1:09:49.720 --> 1:09:52.940
They started off by saying,
this model we had,

1:09:52.939 --> 1:09:56.909
you see, of the stock market
which follows a geometric random

1:09:56.909 --> 1:09:58.609
walk,
it can go up by a certain

1:09:58.609 --> 1:10:00.669
percentage or down by a certain
percentage.

1:10:00.670 --> 1:10:02.480
We've used that with interest
rates too.

1:10:02.479 --> 1:10:05.079
They can go up or down by a
certain percentage.

1:10:05.078 --> 1:10:08.108
Here the stocks can go up or
down by a certain percentage.

1:10:08.109 --> 1:10:11.739
We saw that you could solve
models like that very easily.

1:10:11.738 --> 1:10:14.588
So Black and Scholes,
Fischer Black who is a great

1:10:14.591 --> 1:10:17.621
economist, and Myron Scholes who
won the Nobel Prize,

1:10:17.618 --> 1:10:20.468
but was not as mathematical as
Fischer Black.

1:10:20.470 --> 1:10:23.100
Anyway, he started the hedge
fund Long Term Capital.

1:10:23.100 --> 1:10:25.540
Myron Scholes was one of the
people.

1:10:25.538 --> 1:10:30.508
They looked in 1972 at the
returns each day on the S&P

1:10:30.506 --> 1:10:34.076
500, and they binned them up
like this.

1:10:34.078 --> 1:10:37.898
So here are the number of times
the return was between .47

1:10:37.903 --> 1:10:40.053
percent and some other number.

1:10:40.050 --> 1:10:43.320
And then they compared that to
a normally distributed random

1:10:43.319 --> 1:10:46.699
variable, and look how close to
normally distributed it is.

1:10:46.699 --> 1:10:47.689
It's practically like that.

1:10:47.689 --> 1:10:51.219
So this thing over here is
exactly normally distributed,

1:10:51.220 --> 1:10:55.190
and this is the frequency graph
of what actually happened that

1:10:55.189 --> 1:10:57.119
year,
incredibly close to normally

1:10:57.122 --> 1:10:57.782
distributed.

1:10:57.779 --> 1:11:00.389
If you take the cumulative
occurrence of each thing and

1:11:00.386 --> 1:11:03.426
compare it to the normal it's
incredibly close to the normal.

1:11:03.430 --> 1:11:05.980
So they said, "Gosh,
isn't it great,

1:11:05.978 --> 1:11:09.208
this model of things going up
or down by a certain percentage

1:11:09.211 --> 1:11:11.001
every year,
maybe with a drift,

1:11:11.002 --> 1:11:14.112
that's exactly the model the
stock market seems to follow,

1:11:14.109 --> 1:11:17.439
and maybe interest rates follow
that sort of model too,"

1:11:17.442 --> 1:11:20.332
and that's why we've worked
with all those models.

1:11:20.328 --> 1:11:24.858
Well, it turns out if you make
those assumptions and then you

1:11:24.863 --> 1:11:29.103
try to solve for option prices
you can do it very quickly

1:11:29.095 --> 1:11:32.485
through some formula,
which I'm not going to have

1:11:32.488 --> 1:11:33.388
time to present.

1:11:33.390 --> 1:11:36.070
It'll only take one minute,
but I'm going to skip that.

1:11:36.069 --> 1:11:37.319
So what happened then?

1:11:37.319 --> 1:11:41.379
So this was the second high
point of, you know,

1:11:41.380 --> 1:11:46.500
there's the CAPM model and then
the Black-Scholes model.

1:11:46.500 --> 1:11:49.350
You've done problems with
Black-Scholes now in the problem

1:11:49.350 --> 1:11:51.700
set to figure out the value of a
call option.

1:11:51.698 --> 1:11:54.478
So I'm just pointing out that
you could put it in a spread

1:11:54.484 --> 1:11:56.884
sheet like I've done,
which will be on the web.

1:11:56.880 --> 1:12:01.100
And you can do daily returns,
and fix the standard deviation

1:12:01.100 --> 1:12:03.290
and stuff,
and do backward induction

1:12:03.289 --> 1:12:05.619
incredibly quickly,
and figure out the value of the

1:12:05.617 --> 1:12:07.817
call option,
even get a closed form formula

1:12:07.819 --> 1:12:10.229
for it,
and then explain why call

1:12:10.234 --> 1:12:13.474
option prices have the form that
they do.

1:12:13.470 --> 1:12:15.860
So it was a great triumph and
it relied on things being

1:12:15.860 --> 1:12:16.880
normally distributed.

1:12:16.880 --> 1:12:18.710
I'm down to 30 seconds.

1:12:18.710 --> 1:12:21.330
So what happened?

1:12:21.328 --> 1:12:25.708
If you do the same thing
recently--so you do exactly the

1:12:25.713 --> 1:12:30.103
same thing and bin everything up
like Fischer Black did,

1:12:30.097 --> 1:12:32.407
not in 1972--shit,
sorry.

1:12:32.408 --> 1:12:35.898
Not in 1972 but the last five
years, say, they only did one

1:12:35.902 --> 1:12:37.892
year, but you do the last five.

1:12:37.890 --> 1:12:40.750
Actually I did this a couple
years ago, so from seven years

1:12:40.753 --> 1:12:41.893
ago to two years ago.

1:12:41.890 --> 1:12:44.860
If the pink thing is normally
distributed and we do the same

1:12:44.863 --> 1:12:46.783
binning that Black and Scholes
did,

1:12:46.779 --> 1:12:50.069
look everyday at what the
return is and stick it in a bin

1:12:50.072 --> 1:12:53.352
and just do the frequency thing,
what do you see?

1:12:53.350 --> 1:12:57.380
You see that there are a lot
more times where in reality the

1:12:57.378 --> 1:13:00.768
move was very small,
but there are a lot more times

1:13:00.766 --> 1:13:03.186
in reality where the move was
very big.

1:13:03.189 --> 1:13:06.919
So this is precisely what you
call a fat tail,

1:13:06.920 --> 1:13:10.160
that you get smaller moves than
the normally distributed ones

1:13:10.162 --> 1:13:13.352
but also bigger moves than the
normally distributed ones.

1:13:13.350 --> 1:13:14.810
So you can have some big
negative moves.

1:13:14.810 --> 1:13:17.940
And so we know we've had some
huge negative shocks.

1:13:17.939 --> 1:13:22.699
So I'm ending now with this
thought that finance produced

1:13:22.703 --> 1:13:26.893
remarkable theories,
remarkably precise predictions,

1:13:26.894 --> 1:13:31.074
and for decades at a time it
seemed those were borne out in

1:13:31.074 --> 1:13:31.944
practice.

1:13:31.939 --> 1:13:35.509
But then looking back 50 years
later or 30 years later on these

1:13:35.505 --> 1:13:38.835
discoveries we see that they
don't do quite as well as they

1:13:38.841 --> 1:13:40.971
seem to be doing at first
glance.

1:13:40.970 --> 1:13:44.030
So something's missing in the
theory, and I think the subject

1:13:44.032 --> 1:13:46.892
is so exciting because it's so
connected to the world.

1:13:46.890 --> 1:13:50.850
Everybody talks about finance
nowadays.

1:13:50.850 --> 1:13:55.360
Anyone in the world is spending
half their time thinking about

1:13:55.359 --> 1:13:59.799
finance and the theory is still
up in the air because the old

1:13:59.795 --> 1:14:02.895
classics of the theory no longer
hold.

1:14:02.899 --> 1:14:05.599
And so it's an exciting time to
be developing a new theory and

1:14:05.595 --> 1:14:07.535
maybe you'll think about it in
the future.

1:14:07.538 --> 1:14:09.048
So I'll see you,
some of you,

1:14:09.051 --> 1:14:09.701
next week.

1:14:09.699 --> 1:14:14.999