WEBVTT

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So this class and the next
class and a half are going to be

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about Fisher's theory of present
value and the interest rate,

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and then we're going to move to
uncertainty.

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So up until now what we've done
is we found out first,

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if you know the whole economic
system, how to solve for

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equilibrium.

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To figure out from the
primitives of people's tastes,

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their impatience,
the technology,

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the economy,
how to figure out the real rate

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of interest if provided there is
no uncertainty in the world and

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people can forecast what is
going to happen later.

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We've found that once you've
done that,

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the price of every asset,
if people are rational and

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looking forward to the future,
the price of every asset is

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going to be the present value of
the future payments of the

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asset.

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So if you think of the payments
as real payments,

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which is what Fisher always
recommended, you discount by the

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real interest rate.

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If you think of them as cash
payments then you discount by

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the nominal interest rate.

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So every asset corresponds to
its present value of its

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dividends either discounted by
the real rate or the nominal

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rate.

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Now, this thinking is
surprisingly powerful and leads

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you to unexpected conclusions.

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So the next two classes is
about that.

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Mostly I'm going to talk about
Social Security,

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but I'm going to begin today by
finishing off a subject we

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didn't quite get through last
time.

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So you see, if you realize that
the price of every asset is just

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the present value of its
dividends,

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and you also suppose you know
what the dividends are going to

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be and what the future interest
rates are going to be,

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then it follows that you know
what the price of the asset is

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going to be,
not just today,

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but next year,
and the year after and the year

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after that.

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So your theory of asset pricing
today,

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which was based on the
assumption that you can forecast

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the future,
necessarily implies the theory

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of asset pricing in the future.

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So you can tell something about
how asset prices are going to

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change,
and of course you can also test

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the theory because the theory
implicitly is forecasting

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something about the future,
and therefore you can test the

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theory.

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So let's just take a couple
examples that are in the notes.

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So we said at the top,
if you can read it,

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I hope it's not too small--I
want to move a little quickly so

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I could be writing this on the
board,

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but if you can see it and you
look at the top line it says

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that the present value of the
assets is just the discount of

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future dividends.

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So maybe I'll start one line
up, actually,

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in these notes.

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So if you look in the middle
here the present value today,

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suppose you have an asset,
maybe I'm going to write on the

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board after all.

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Present value of an asset,
suppose you know the dividends

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are going to be paying C (1),
C (2), and maybe C (T) at the

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end.

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Those are the dividends that
are going to be paid,

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and you can ask what the
present value of the asset is

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today, PV_0 today,
0.

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Well, Fisher would say if you
think of these as nominal cash

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flows he would say what you need
to do is you need to find out

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the price of zeros.

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So you recall that Fisher said
that you could let

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pi_1 = the price today
of 1 dollar at time 1,

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and the price today
pi_T = the price today

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of 1 dollar time T.

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It's the price today of 1
dollar in the future.

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These were the crucial prices
that Fisher said that you should

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always look for.

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He said that you can always
find these prices,

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pi_1 through
pi_T by deriving them

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from the yield curve.

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So every morning everybody
looks at the yield curve,

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all financial analysts,
they look at the prices of

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bonds traded in the market.

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The simplest form is you get a
yield curve in the newspapers.

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You deduce from the yield curve
what these present values

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pi_1,
pi_T are,

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and that allows you to price
any asset like this one simply

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by multiplying by
pi_1,

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pi_2 and at the end
by pi_T.

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So that's step 1.

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But then step 2,
we said, was that once you've

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got these prices you can figure
out the forwards.

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So the forwards are going to be
1 i_t,

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so 1 i_t that's by
definition the interest from t

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to t 1 that would be agreed
today.

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It's not the interest rate
that's going to prevail from

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time t,
it's the interest rate that

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people today at time 0 would
agree to pay between time t and

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time t 1.

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So that, of course,
has to just equal

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pi_t over pi_t
1,

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because everybody today
recognizes that the cost of a

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dollar time t is pi_t,
and the cost of a dollar at

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time t 1 is pi_t 1.

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So the tradeoff between t and t
1 that's effectively what an

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interest rate does is it trades
off money at one time for

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another time.

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It has to be this ratio.

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So today people would agree on
1 i_t^(F),

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forward, as the forward rate.

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Now, you add to that the
assumption that everybody is

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certain about the future,
assume perfect forecasting.

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So I don't have to actually
assume people are right in their

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forecasting.

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I have to assume that they are
completely sure of their

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forecasting.

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So if they're completely sure
of their forecasting then

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everybody must foresee that they
think they're sure that the

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future interest rate that will
prevail at time t is also equal

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to this number.

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So we can then rewrite this
price.

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Hello.

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We can rewrite this price as 1
i_0^(F),

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forward;
instead of pi_2,

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pi_2 is just going to
be 1 over (1 i_0^(F))

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times (1 i_1^(F)),
and time pi_T is just

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going to be 1 over (1
i_0^(F)) times (1

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i_1^(F)) ...

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times (1 i_t 1^(F)).

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Because using the fact that (1
i_t) is pi_t

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divided by pi_t 1 I
just multiply pi_1

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divided by pi_2 times
pi_2 divided by

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pi_0 etcetera.

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If I take pi_1
divided by pi_0 times

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etcetera I'm going to get
exactly this formula.

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So pi_0 is always 1,
by the way.

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So if I want to take
pi_1 it's just going

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to be 1 over (1
i_0^(F)).

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If I want to take
pi_2 I can always do

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this,
pi_2,

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and so this is going to equal
pi_2,

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so pi_2 is going to
be 1 over (1 i^(F)_0)

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times 1 over (1
i^(F)_1) etcetera.

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And pi_3,
if I want to do pi_3,

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I just multiply by
pi_3 over

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pi_2 and so that's
equal to 1 over (1

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i^(F)_0) times 1 over
(1 i^(F)_1) times 1

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over (1 i^(F)_2).

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So instead of multiplying by
the pis I may as well take the

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product of the forwards.

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It's exactly the same thing.

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So the present value has this
simple formula,

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but this is a formula that
holds at every time t if you're

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totally confident of your
predictions of the Cs and of the

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future interest rates.

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This is where we ended last
time, basically with this

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formula.

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The key that you had to use in
the problem set was to realize

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if you're totally confident now
about the future you have to be

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totally confident about doing
this calculation in the future.

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So PV_1 is going to
be basically the same

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calculation.

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So what's going to happen at
time 1?

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After you've gone down 1 year
you've finished with this

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interest rate and you're looking
at everything 1 year later.

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So I may as well write the
PV_1 here and that's

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going to equal C (2)--
let's put it a little bit

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lower--PV_1 is going
to equal the same C (2) as

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before,
but now a year later.

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So it's just going to be 1
i^(F)_1 C (T),

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and I don't need the 1
i^(F)_0 anymore.

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(1 i^(F)_1) times ...

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(1 i^(F)_T-1).

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So it's exactly the same
formula 1 year later,

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and 1 year later you no longer
have to worry about the interest

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rate.

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That time already passed.

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So you just drop this at every
time and you write the same

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formula, and of course you drop
C (1) because that's all

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finished.

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So the price at time 1 is just
what's left except you've

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chopped off the 1
i^(F)_0 everywhere.

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So to write that the same way,
so PV_0 (I can write

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it the same way) =,
PV_0 = what?

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It's going to equal the
interest payment you get,

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C (1), not the interest,
the dividend you get,

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the cash flow you get plus
PV_1 divided by 1

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i^(F)_0.

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So this is a very important
formula.

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So why is that?

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Well, it's a proof by formula,
but another way of saying it is

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that PV_0,
when you get the asset at time

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0 it gives you a cash flow at
time 1,

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and then of course looked at
from the point of view of time 1

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you've got all the future cash
flows,

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but that's just what
PV_1 is.

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So basically the bond is going
to give you a cash flow at time

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1,
and then the right to cash

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flows in the future,
but this right to cash flows in

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the future at time 1 is worth
PV_1.

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So it's like you've got all
this money at time 1 and so to

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get the value at time 0 you have
to discount it back again.

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So this is a very famous and
important formula which I want

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to pause a second and think
about.

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So there's a controversy today
called marking to market.

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Does anybody know what that
controversy is about?

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What does marking to market
mean?

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Yep?

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Student: I believe that
it means that corporations and

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their accounting rules are
currently required to value

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their assets at what they would
fetch in the market if they were

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to sell them.

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Prof: Right,
but you know that they've been

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relieved of this responsibility
recently.

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Student: No,
I didn't know that.

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Prof: Well,
so they've been relieved of

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this responsibility lately.

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Now, why have they been
relieved of it?

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Because the thought was that
the market was so panicked in

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the crisis that the price that
they could fetch by selling

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their things really had nothing
to do with the value.

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So we're going to come back to
whether that was a good idea

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that Congress passed under
tremendous pressure.

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What is the point of marking to
market?

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So let's suppose that you
really could anticipate the

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future and everybody was right
about it.

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The market price then would
really be PV_0 today,

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and it really would be
PV_1 tomorrow,

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because if the interest rate's
do actually turn out to be what

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everybody expects,
and everybody's completely

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confident of their expectation,
then as we saw the prices would

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have to be this today and this
tomorrow,

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otherwise there'd be an
arbitrage.

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You could make money for sure,
or think you could make money

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for sure.

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So if you're marking to market
what are you going to mark as

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the profits?

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Are you going to say the profit
at time 1 is--so what is profit?

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If I had some room I'd put this
somewhere.

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How would you define profit?

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I'll get rid of this.

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I think we've got this straight.

13:38.870 --> 13:52.870


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So how would you define profit
at time 1?

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What would you write?

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So let's say that this isn't a
bond.

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It's an investment.

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You paid a bunch of money at
time 0, maybe PV_0 and

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in the future your investment is
going to pay off some money.

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Maybe it was a project you
invested in.

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Maybe you bought a bunch of
stuff and you're selling it in

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the future and getting this
money.

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Maybe you bought a bond which
is paying these coupons.

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Whatever it is these are the
cash flows of the project,

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and now of course your
investors are very curious.

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In year 1, they want to know
what profit have you made,

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how are you doing?

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So what's a number that you'd
think of giving?

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What's the first number you'd
think of telling them?

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Yep?

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Student: Maybe the first
cash flow payout.

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Prof: So you might think
of saying, C (1).

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That's the cash you've gotten.

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So all these people could see
you've gotten C (1).

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That's your revenue,
and I'm assuming this cash flow

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is net of expenses.

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So you could say here's your
revenue you got at time 1,

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C (1).

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Is that your profit?

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If it were, people would then
look and they'd say,

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"Well, we got profit of C
(1) and we put an investment in

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of PV_0 so is that the
rate of return?

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Is that my rate of return?"

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Yeah?

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Student: Can we do
PV_1 - PV_0

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and add it here?

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Prof: So he's exactly
right.

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I'm going to repeat what he
said, but I'm going to take

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longer to say it.

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This idea of writing C (1) over
PV_0 is actually what

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many people try to say is their
profit, but it's a bad number

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for profit.

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Now, if in period 1 you stopped
marking to market,

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and you had no idea,
you didn't have to report this

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number PV_1,
I mean, you didn't know what it

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was or you didn't have to report
it,

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what else could you report but
C (1) over PV_0 as the

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profit?

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So marking to market,
you see, is intimately

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connected to how you report
profit.

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So if you don't mark to market
you don't know,

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you don't have to declare what
the value of the assets are that

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are left.

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All you would do when you
describe your profits is you'd

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say C (1) and people would,
of course, in their heads,

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in fact they wouldn't do it in
their heads,

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you'd tell them,
"Our rate of return was C

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(1) over PV_0,"
but why might that be a very

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misleading number?

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Well, his point is it could
well be that C (1) is a very

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high number.

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You've got a lot of cash flow
this period, but he said it may

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turn out that PV_1 is
a terrible number.

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You may have gotten a lot of
cash flow, but there's nothing

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left going forward.

16:48.918 --> 16:53.548
So he doesn't think that's a
very good measure of profit.

16:53.548 --> 17:02.108
So he's suggesting why not
report profit as C (1)

17:02.107 --> 17:08.167
PV_1 - PV_0.

17:08.170 --> 17:11.710
Now, suppose you did that?

17:11.710 --> 17:13.810
So he's saying,
look, you've got a certain

17:13.814 --> 17:16.894
amount of cash but the assets
that you had also changed value

17:16.894 --> 17:19.414
and you ought to include that in
your profit.

17:19.410 --> 17:21.430
So what if you did that?

17:21.430 --> 17:25.270
What would your rate of return
be?

17:25.269 --> 17:28.419
And suppose PV_0 and
PV_1 were calculated

17:28.423 --> 17:28.953
as this?

17:28.950 --> 17:31.500
And so you divided this by
PV_0 what would that

17:31.496 --> 17:31.856
equal?

17:31.859 --> 17:52.069


17:52.068 --> 17:58.418
What number would I get if I
did that?

17:58.420 --> 17:59.130
I can't hear.

17:59.130 --> 18:00.890
What?

18:00.890 --> 18:03.190
Somebody speak up.

18:03.190 --> 18:05.640
Student:
i^(F)_0.

18:05.640 --> 18:06.960
Prof: Yes.

18:06.960 --> 18:09.800
This would just be
i^(F)_0,

18:09.798 --> 18:14.688
and you get the rate of return
that you're expecting to get.

18:14.690 --> 18:16.710
Now, how do I know that's
i^(F)_0?

18:16.710 --> 18:19.900
Because I multiplied by
PV_0 to this side,

18:19.896 --> 18:22.646
then I moved that
PV_0 to the other

18:22.646 --> 18:23.206
side.

18:23.210 --> 18:26.150
That gives me 1
i_0^(F)

18:26.146 --> 18:29.266
PV_0,
then I divide by that 1

18:29.272 --> 18:31.902
i^(F)_0 and put it
down here,

18:31.900 --> 18:34.960
and that's this formula.

18:34.960 --> 18:37.910
So that is what you would get,
i^(F)_0.

18:37.910 --> 18:40.160
And you see that's what you
should expect to get because you

18:40.156 --> 18:41.296
haven't done anything great.

18:41.299 --> 18:42.439
You've got a cash flow.

18:42.440 --> 18:45.100
You've got these cash flows at
the beginning.

18:45.098 --> 18:48.138
You paid a fair price for them
and next period everybody

18:48.143 --> 18:51.633
forecast that the values were
going to go to PV_1,

18:51.630 --> 18:53.560
and so it can't be that you're,
you know--

18:53.559 --> 18:54.889
this was an investment you made.

18:54.890 --> 18:55.780
You put your money in.

18:55.779 --> 18:57.239
You bought this bond.

18:57.240 --> 19:00.890
You could sell the bond now at
time 1 after having obtained the

19:00.893 --> 19:01.663
cash flows.

19:01.660 --> 19:04.750
It better be that your rate of
return is the market interest

19:04.753 --> 19:07.383
rate of return otherwise there'd
be some arbitrage,

19:07.375 --> 19:08.525
and in fact it is.

19:08.528 --> 19:12.128
So if you can compute all the
present values properly,

19:12.126 --> 19:16.196
the only fair thing to do--this
is not a great investment.

19:16.200 --> 19:19.490
Even if C (1) is a huge amount
of money it's only huge because

19:19.486 --> 19:21.746
PV_1 is a low amount
of money.

19:21.750 --> 19:24.080
Because it has to be that the
profit every period,

19:24.078 --> 19:26.388
the rate of profit,
is exactly equal to the

19:26.385 --> 19:29.765
interest rate,
because everything is always

19:29.766 --> 19:32.296
priced at its present value.

19:32.298 --> 19:40.848
So it's a simple concept which
somehow takes a long time to

19:40.849 --> 19:42.029
grasp.

19:42.029 --> 19:46.199
It just seems to people
that--here's the money that's

19:46.198 --> 19:46.998
come in.

19:47.000 --> 19:48.920
That's the cash you can count
in your hands.

19:48.920 --> 19:49.860
You've got it in your hands.

19:49.858 --> 19:52.238
That's the number you should
talk about as profit,

19:52.236 --> 19:54.996
but of course of the money
coming into your hands--there's

19:55.000 --> 19:56.360
this other hidden thing.

19:56.358 --> 19:58.938
The stuff that you own has
suddenly fallen in value

19:58.938 --> 20:00.638
compared to what it was before.

20:00.640 --> 20:03.370
You're really not putting the
firm in any better position than

20:03.365 --> 20:04.075
it was before.

20:04.078 --> 20:06.998
You just earned your normal
rate of return.

20:07.000 --> 20:13.480
So you can see why,
to give a fair description of

20:13.480 --> 20:17.950
how people are doing,
the law was written,

20:17.951 --> 20:21.401
evolved to the point where
people were forced not to just

20:21.397 --> 20:23.727
say C (1),
they were forced to

20:23.729 --> 20:27.309
declare--mark to market,
and add PV_1 -

20:27.305 --> 20:31.345
PV_0 to their profit
to get a real rate of return,

20:31.348 --> 20:37.238
to get a more revealing rate of
return.

20:37.240 --> 20:40.280
And so what happened in the
crisis is this PV_1

20:40.277 --> 20:43.207
became such a horribly low
number that if you plug that

20:43.205 --> 20:46.185
into this formula you get
PV_1 is a really low

20:46.190 --> 20:48.360
number compared to
PV_0.

20:48.359 --> 20:49.769
You get a giant negative here.

20:49.769 --> 20:53.769
It would look like the rate of
return was terrible.

20:53.769 --> 20:56.929
Everyone would panic and think
the firms had fallen apart.

20:56.930 --> 21:00.510
So especially the banks were
the ones who didn't want to do

21:00.506 --> 21:02.926
this,
and so Congress didn't want the

21:02.926 --> 21:05.536
public to be panicked so it
simply said,

21:05.539 --> 21:06.999
"Okay, forget about it.

21:07.000 --> 21:09.950
We're going to not hold you to
writing PV_1 anymore

21:09.953 --> 21:12.813
because we can't count anybody
figuring out what it is,

21:12.808 --> 21:15.298
and so you don't have to tell
us that.

21:15.298 --> 21:17.498
You just have to tell us
this," which happens to be

21:17.500 --> 21:20.210
a good number for the banks,
but that doesn't mean the banks

21:20.205 --> 21:23.085
are actually doing well because
the assets they hold have been

21:23.092 --> 21:24.182
collapsing in value.

21:24.180 --> 21:24.260
Yeah?

21:24.259 --> 21:26.779
Student: Does that
>

21:26.775 --> 21:29.735
say that assuming there's no
arbitrage opportunity if a firm

21:29.742 --> 21:32.462
pays out a high dividend its
stock should go down?

21:32.460 --> 21:34.510
Prof: Yes, right.

21:34.509 --> 21:36.929
That's exactly what it says and
that's what does happen.

21:36.930 --> 21:39.910
So you always talk about the
price, ex-dividend and stuff

21:39.910 --> 21:41.400
like that, precisely that.

21:41.400 --> 21:44.020
So if a firm pays a bigger than
usual dividend,

21:44.019 --> 21:47.849
if it suddenly decides it's
going to pay itself a gigantic

21:47.852 --> 21:51.822
dividend then the price of the
firm is going to go down,

21:51.818 --> 21:55.808
exactly, because there's less
value in the firm.

21:55.808 --> 21:58.448
You've paid it out here instead
of keeping it into the firm.

21:58.450 --> 22:00.910
So this is a very simple idea,
but it's very easy to get

22:00.909 --> 22:01.669
confused about.

22:01.670 --> 22:05.780
Are there any questions about
it?

22:05.779 --> 22:08.139
So let's do an example of it.

22:08.140 --> 22:14.090
The most basic example of it is
the premium bond.

22:14.088 --> 22:16.518
So we talked about this before,
the premium bond.

22:16.519 --> 22:21.649
So let's say you have
PV_0 = 5 divided by

22:21.650 --> 22:26.060
1.10 5 divided by 1.10
[correction: squared]

22:26.061 --> 22:30.681
(maybe this was exactly the
problem set,

22:30.680 --> 22:33.190
I can't remember) 105 divided
by 1.10 [correction:

22:33.193 --> 22:33.813
to the T].

22:33.808 --> 22:39.648
So in other words the interest
rate--I did that wrong--squared

22:39.653 --> 22:40.423
and T.

22:40.420 --> 22:43.120
So the forwards,
in other words,

22:43.118 --> 22:47.208
1 i^(F)_t (small t) =
1 .10 for all t,

22:47.212 --> 22:50.612
so all the forwards are 10
percent.

22:50.608 --> 22:54.578
The bond is paying--I can't
remember which one I did.

22:54.579 --> 22:57.209
Let's do 20 here.

22:57.210 --> 23:02.480
I'm going to make it a premium
bond, so it's paying 20.

23:02.480 --> 23:09.850
So what's going to be the price
of the bond?

23:09.848 --> 23:12.458
Well, in the first period it
looks like you get this

23:12.463 --> 23:13.493
incredible profit.

23:13.490 --> 23:15.040
The interest rate is 10 percent.

23:15.038 --> 23:19.278
You've paid some present value
and you've made 20.

23:19.278 --> 23:21.868
You've made a number much
bigger--so the price of this

23:21.867 --> 23:24.357
thing, by the way what was the
home work problem?

23:24.359 --> 23:26.659
What were the numbers?

23:26.660 --> 23:31.180
What was the interest rate?

23:31.180 --> 23:32.620
Did somebody do the homework?

23:32.618 --> 23:34.698
I did assign a homework on a
premium bond,

23:34.702 --> 23:35.112
right?

23:35.108 --> 23:38.458
The interest rate was 5 percent
and the coupon was 10,

23:38.457 --> 23:39.907
was that what it was?

23:39.910 --> 23:42.350
What?

23:42.349 --> 23:46.619
What was it?

23:46.619 --> 23:49.039
What was the homework problem?

23:49.039 --> 23:49.679
Student: 8 and 6.

23:49.680 --> 23:50.430
Prof: 8 and 6.

23:50.430 --> 23:51.950
So this was 8 percent.

23:51.950 --> 23:58.640
Might as well do this one,
6 here, yeah,

23:58.644 --> 24:04.144
6 percent, and this one was 8.

24:04.140 --> 24:08.860
So what was the price
PV_0?

24:08.859 --> 24:12.979
What was PV_0?

24:12.980 --> 24:16.890
You've done this homework
problem, right?

24:16.890 --> 24:27.020
Does anyone remember what
number they got?

24:27.019 --> 24:29.029
Ben, do you remember the number?

24:29.029 --> 24:31.359
No.

24:31.358 --> 24:39.178
I'm counting on my trusty class
here to provide me all the

24:39.178 --> 24:40.548
numbers.

24:40.549 --> 24:41.689
It was what?

24:41.690 --> 24:43.580
Student: 108.4.

24:43.578 --> 24:45.168
Prof: Was that what it
was, 108.4?

24:45.170 --> 24:47.760
That's all?

24:47.759 --> 24:57.739
This was the price just 108.4?

24:57.740 --> 24:58.980
So 108.4, right.

24:58.980 --> 25:00.240
That's a high price.

25:00.240 --> 25:02.240
So it's way above par.

25:02.240 --> 25:04.840
This is a bond that's worth
much more than 100.

25:04.839 --> 25:05.479
Why?

25:05.480 --> 25:08.690
Because the interest rate is 6
percent, but the coupon is 8 so

25:08.686 --> 25:10.366
this is called a premium bond.

25:10.368 --> 25:15.018
So if you look at the first
year the rate of return on the

25:15.016 --> 25:17.376
first year is 8 over 108.4.

25:17.380 --> 25:21.270
Now, is that more than 6
percent?

25:21.269 --> 25:25.399
It is way more than 6 percent,
8 over 108.4.

25:25.400 --> 25:34.660
It is way more than 6 percent
because 7 percent of this is

25:34.663 --> 25:38.893
going to be less than 8.

25:38.890 --> 25:42.980
So it's more than 7 percent,
so this is greater than 7

25:42.981 --> 25:47.231
percent, and so it's certainly
bigger than 6 percent.

25:47.230 --> 25:50.430
So it sure looks like at the
end of the first year like this

25:50.431 --> 25:51.681
bond was an ace bond.

25:51.680 --> 25:53.790
That's the kind of calls you
used to get.

25:53.788 --> 25:57.388
You still sometimes do get them
if you're a wealthy person and

25:57.387 --> 25:59.687
you actually answer calls like
this,

25:59.690 --> 26:02.230
which you don't of course,
but you can get some cold call

26:02.229 --> 26:04.789
from a sales person saying,
"We've got a fund and look

26:04.788 --> 26:05.598
how well it's doing.

26:05.598 --> 26:09.488
On this much investment last
year we got payments of 8

26:09.494 --> 26:10.234
dollars.

26:10.230 --> 26:12.720
That's more than 7 percent,
and look, everybody can see the

26:12.717 --> 26:15.077
interest rate is only 6 percent
and we did better than 7

26:15.075 --> 26:15.585
percent.

26:15.589 --> 26:16.599
We're doing great.

26:16.598 --> 26:18.308
Why don't you invest in our
fund?"

26:18.308 --> 26:21.448
But actually,
what the salesman hasn't told

26:21.451 --> 26:25.341
you is that the value of his
assets has gone down.

26:25.338 --> 26:29.388
So the present value
PV_1 must be less than

26:29.394 --> 26:33.374
PV_0,
because we know from this

26:33.372 --> 26:37.182
formula, the formula right up
here,

26:37.180 --> 26:39.810
that 6 percent is going to be
the cash flow over

26:39.810 --> 26:42.720
PV_0 which is more
than 7 percent plus this

26:42.722 --> 26:44.472
difference,
and this difference,

26:44.472 --> 26:46.352
therefore, is going to have to
be negative.

26:46.348 --> 26:50.408
So what he didn't tell you was
that the fund lost value even

26:50.407 --> 26:53.847
though the first payment was
better than 6 percent,

26:53.847 --> 26:56.047
the market rate of interest.

26:56.049 --> 27:00.899
So that's the first example.

27:00.900 --> 27:07.680
Now, let's do another example.

27:07.680 --> 27:15.320
Suppose you have a--let's see
if I can write on this board.

27:15.318 --> 27:26.528
There's a famous trade called
the carry trade.

27:26.528 --> 27:30.098
Now, suppose the
forwards--suppose 1

27:30.101 --> 27:34.691
i^(F)_0 is 2 percent,
sort of like now,

27:34.692 --> 27:41.052
the 1 year yield,
and 1 i^(F)_t is 5

27:41.048 --> 27:47.198
percent,
for t greater than 1?

27:47.200 --> 27:50.750
So if you have a 1 year bond
it's going to pay--well,

27:50.748 --> 27:54.838
let's say it's 2 percent and
this is equal to 1 --can you see

27:54.842 --> 27:56.892
this or it's disappearing.

27:56.890 --> 28:01.050
So let's make the first two of
them be 2 percent,

28:01.053 --> 28:05.133
and this is for t greater than
or equal to 3.

28:05.130 --> 28:09.200
So the interest rate is 2
percent and then it's going to

28:09.200 --> 28:10.680
jump to 5 percent.

28:10.680 --> 28:13.360
All right, so if you have a
2-year bond,

28:13.358 --> 28:22.178
a 2-year Treasury,
a 2-year bond might pay 2 and

28:22.181 --> 28:31.191
102 and the present value of
this equals 100,

28:31.190 --> 28:37.480
the present value of the 2-year
bond.

28:37.480 --> 28:44.040
But now maybe you've got a
longer bond that's a 5-year bond

28:44.042 --> 28:56.232
which pays coupons 4,
4,4, 104, so this is a 5-year

28:56.232 --> 29:00.972
bond,
and maybe its price is close to

29:00.973 --> 29:01.373
100.

29:01.368 --> 29:04.168
Actually, I haven't worked out
the number so you're going to

29:04.173 --> 29:06.173
have to do that in the next
problem set.

29:06.170 --> 29:09.340
So is it possible,
so I'll ask it this way,

29:09.338 --> 29:13.578
is it possible for this coupon
to be higher 4,

29:13.578 --> 29:18.598
4,4, 4,4 and yet still have a
present value of 100 than this

29:18.602 --> 29:20.732
one which is 2 and 102?

29:20.730 --> 29:27.020
Could you have a higher coupon
and yet the same present value

29:27.020 --> 29:32.160
of 100 on a longer bond than on
a shorter bond?

29:32.160 --> 29:38.660
How could this bond have a
higher coupon and sell for the

29:38.661 --> 29:41.681
same price as this bond?

29:41.680 --> 29:42.650
Yep?

29:42.650 --> 29:45.920
Student: You're losing
money on the assets you put on

29:45.924 --> 29:48.984
the principal value because you
get it in a later period

29:48.979 --> 29:50.589
>

29:50.588 --> 29:53.118
Prof: So the point is
you're discounting the first two

29:53.119 --> 29:56.089
payments by 2 percent a year,
but you're discounting these

29:56.086 --> 29:57.816
payments by 5 percent a year.

29:57.818 --> 30:00.188
So these things are going to be
much worse than they look.

30:00.190 --> 30:02.480
And so even though the 4s are
all better,

30:02.480 --> 30:04.740
this 100, you know,
it's 4,4, 4,4,

30:04.740 --> 30:08.480
4 100, that 100,
not to mention these three last

30:08.477 --> 30:11.417
4s are getting discounted by a
lot.

30:11.420 --> 30:15.080
So that 104 is going to be
worth less than 100 back,

30:15.078 --> 30:17.948
you know, it's going to be
worth less.

30:17.950 --> 30:20.790
So that's why these things are
going to go down a lot more than

30:20.789 --> 30:21.339
you think.

30:21.338 --> 30:22.968
They're going to be worth less
than 100.

30:22.970 --> 30:25.780
So even though these things are
better than the 2 percent rate

30:25.779 --> 30:27.579
of return--
this bond does great at the

30:27.577 --> 30:29.377
beginning,
but does poorly thereafter,

30:29.382 --> 30:31.932
because in the beginning it's
paying 4 percent when the

30:31.928 --> 30:34.768
interest rate is 2 percent,
but later it's paying 4 when

30:34.767 --> 30:38.397
the interest rate is 5 percent,
so clearly you could have some

30:38.401 --> 30:39.811
situation like that.

30:39.809 --> 30:41.579
So what's the carry trade?

30:41.578 --> 30:55.488
The carry trade is you buy the
long bond and sell short the

30:55.487 --> 31:08.427
short bond, so the lower
maturity--too many shorts--the

31:08.434 --> 31:14.194
lower maturity bond.

31:14.190 --> 31:18.160
So this is the,
let's say, 5 year and 2 year.

31:18.160 --> 31:28.530
Buy the 5-year bond and sell
short the 2-year.

31:28.528 --> 31:32.038
The word, sell short,
is different from the word,

31:32.038 --> 31:32.988
short bond.

31:32.990 --> 31:37.230
So you buy the 5-year bond and
you sell the 2-year bond.

31:37.230 --> 31:39.530
They both cost you 100,
so what's happening at the

31:39.527 --> 31:40.087
beginning?

31:40.088 --> 31:43.418
You're making 4 dollars and
you're only having to pay 2

31:43.422 --> 31:44.042
dollars.

31:44.038 --> 31:47.478
It looks like you're making a
profit for nothing,

31:47.477 --> 31:48.047
right?

31:48.049 --> 31:49.739
So that's the carry trade.

31:49.740 --> 31:51.710
You buy long bonds with a high
rate of interest.

31:51.710 --> 31:55.470
You sell short bonds with low
coupons and it looks like you're

31:55.470 --> 31:56.580
making a profit.

31:56.578 --> 31:58.678
But in fact,
what's really happening?

31:58.680 --> 32:00.730
So just repeat what you were
saying before,

32:00.730 --> 32:02.000
but now in this context.

32:02.000 --> 32:03.530
What's really happening?

32:03.528 --> 32:07.398
Student: You're paying
off that difference,

32:07.398 --> 32:10.478
the loss of the value of your
assets.

32:10.480 --> 32:18.820
You're not getting back as much
as you would if you had just

32:18.817 --> 32:22.347
bought the 2-year bond.

32:22.349 --> 32:23.009
Prof: Right.

32:23.009 --> 32:26.549
So the long bond you got a cash
flow of 4 the first year.

32:26.548 --> 32:30.748
You had to pay 2 because you
sold the 2-year short,

32:30.748 --> 32:31.418
right?

32:31.420 --> 32:34.650
So you're up 2 dollars,
but the thing that you owe now

32:34.648 --> 32:37.958
at the end of the first year,
since the interest rate is 2

32:37.962 --> 32:39.732
percent,
the next interest rate is 2

32:39.727 --> 32:41.847
percent,
the 2-year bond is still worth

32:41.845 --> 32:42.115
100.

32:42.118 --> 32:45.528
So your negative position is
still worth 100,

32:45.529 --> 32:47.989
but this positive position now,
these 4,

32:47.990 --> 32:50.830
4s and 4s it looks worse than
it did before because you've

32:50.833 --> 32:52.183
moved up the yield curve.

32:52.180 --> 32:56.000
Instead of having two 2 percent
years you only got one 2 percent

32:55.998 --> 32:59.568
year before you shift into the 5
percents which is worse and

32:59.573 --> 33:00.183
worse.

33:00.180 --> 33:03.480
So what's going to happen is
you're going to get a positive

33:03.480 --> 33:06.720
cash flow at the beginning,
it looks like positive profits

33:06.722 --> 33:08.262
right at the beginning.

33:08.259 --> 33:12.119
That C (1), the net C (1) looks
really good,

33:12.118 --> 33:15.688
but right after that,
the value of your assets is

33:15.692 --> 33:19.342
going to plummet compared to
your liabilities,

33:19.338 --> 33:21.758
because now all of a sudden
you're discounting this at 5

33:21.759 --> 33:25.499
percent and this thing is still,
you know, it's only got 1 year

33:25.498 --> 33:30.038
left where the interest rate is
still 2 percent and the rest of

33:30.041 --> 33:34.511
this is discounted at 5 percent
so it's starting to go down in

33:34.512 --> 33:35.322
value.

33:35.318 --> 33:46.078
So if you didn't have to mark
to market what would you do?

33:46.078 --> 33:49.438
If you didn't have to declare
to the world what your present

33:49.442 --> 33:51.612
value of your remaining assets
are,

33:51.608 --> 33:52.688
because you could say,
"Oh,

33:52.690 --> 33:54.050
it's so hard to figure out.

33:54.048 --> 33:56.168
I don't know what the stuff is
worth, the present value of

33:56.173 --> 33:57.033
what's going forward.

33:57.029 --> 33:58.819
I just know the cash that's
coming in."

33:58.818 --> 34:01.398
This carry trade would look
like a really good trade,

34:01.400 --> 34:03.480
wouldn't it,
and a lot of people would do it

34:03.480 --> 34:06.290
because then they would look--
the public would think that

34:06.292 --> 34:08.962
they're doing really well
because they're getting positive

34:08.960 --> 34:11.010
value,
but in the future that positive

34:11.007 --> 34:13.807
value they're getting is just
disguising losses that are

34:13.806 --> 34:16.196
happening in their portfolios
going forward.

34:16.199 --> 34:19.329
So any questions about that?

34:19.329 --> 34:20.389
Yeah?

34:20.389 --> 34:23.389
Student: Can you explain
where their losses

34:23.393 --> 34:25.113
>?

34:25.110 --> 34:26.320
Prof: I want you to
explain it.

34:26.320 --> 34:29.120
So I didn't calculate the
numbers.

34:29.119 --> 34:31.769
It would have been better to do
actual numbers.

34:31.768 --> 34:35.778
If we do 4,4,
4 at 5 percent interest,

34:35.780 --> 34:41.310
or maybe I can do a--let's just
do a real number.

34:41.309 --> 34:43.239
Well, let's just do the one
over here.

34:43.239 --> 34:45.949
So this one is--no,
I can't do it,

34:45.952 --> 34:49.982
because we've got 2 percent and
then 4 percent.

34:49.980 --> 34:53.070
So we take a minute to do it on
Excel and we've seen how great I

34:53.067 --> 34:54.437
am doing those on the fly.

34:54.440 --> 35:00.710
So the point is that you agree
that this payment 4 is bigger

35:00.713 --> 35:01.673
than 2.

35:01.670 --> 35:06.090
So the first year if you buy
this bond and you sell that bond

35:06.092 --> 35:09.632
you're going to have a positive
net 2 dollars.

35:09.630 --> 35:13.090
However, it's perfectly
possible for this whole bond at

35:13.094 --> 35:16.754
the beginning to be worth 100
the same as this bond at the

35:16.751 --> 35:17.651
beginning.

35:17.650 --> 35:19.230
Now, how could that be?

35:19.230 --> 35:23.640
Well, the payments--4 is bigger
than 2 so how could this whole

35:23.644 --> 35:27.414
thing have a higher present
value than this thing?

35:27.409 --> 35:32.839
It has to be that starting at
period 1 the present value of

35:32.840 --> 35:38.650
this 5 year bond (let's call it
this) in period 1 - the present

35:38.646 --> 35:44.636
value of the 2 year bond staring
in period 1 has to be what?

35:44.639 --> 35:48.749
If this present value of the 5
year bond,

35:48.750 --> 35:52.870
this is the 5 year bond at time
0, equals 100,

35:52.869 --> 35:58.219
and that's exactly the same as
this present value at time 0 of

35:58.215 --> 36:00.815
the 2 year bond,
if that equals 100,

36:00.815 --> 36:03.715
so the present value from the
beginning of this thing is the

36:03.717 --> 36:06.767
same as the present value of
this thing from the beginning.

36:06.768 --> 36:08.988
How could this thing have value
100?

36:08.989 --> 36:11.999
Well, it's because it makes
lots of high coupon payments,

36:12.000 --> 36:15.140
but the interest rate is going
to jump up in the future so

36:15.135 --> 36:18.105
you're discounting all these
future cash flows at a big

36:18.105 --> 36:18.705
number.

36:18.710 --> 36:23.170
So all these things
present-valued could well equal

36:23.173 --> 36:23.713
100.

36:23.710 --> 36:27.380
So this could be 100 and this
could be 100 even though this is

36:27.380 --> 36:30.630
paying off more at the beginning
than this thing is.

36:30.630 --> 36:34.700
But what does that formula that
we just wrote down over there,

36:34.697 --> 36:36.897
what does this formula tell us?

36:36.900 --> 36:41.710
Where was this formula that I
wrote down?

36:41.710 --> 36:45.790
This formula over here tells us
if the present values of two

36:45.791 --> 36:48.781
instruments--
I see I wrote it for 1 bond,

36:48.779 --> 36:52.539
but if you take 2 bonds with
the same present value,

36:52.539 --> 36:55.759
one of which has a higher cash
flow in the first period than

36:55.760 --> 36:58.180
the other,
then that formula tells you the

36:58.175 --> 37:01.465
bond with the higher cash flow
at the beginning has to have a

37:01.474 --> 37:04.614
bigger drop in the present value
than the other bond,

37:04.610 --> 37:07.390
otherwise you can't get them
both equal to the same 100.

37:07.389 --> 37:12.929
So this bond and this bond have
the same present value of 100.

37:12.929 --> 37:15.049
Because this payment is bigger
than this payment,

37:15.050 --> 37:16.670
but the present values are the
same,

37:16.670 --> 37:19.790
100, it has to be that starting
from this point on,

37:19.789 --> 37:22.549
this bond is worth less than
that bond.

37:22.550 --> 37:23.820
So what happens?

37:23.820 --> 37:25.980
You go long this bond,
you short that bond,

37:25.983 --> 37:27.843
you say to the world,
"Ah ha!

37:27.840 --> 37:28.920
I've made 2 dollars.

37:28.920 --> 37:32.080
I'm a genius,"
and then you hide from them,

37:32.079 --> 37:34.129
you might hide from them if you
didn't have to tell them,

37:34.130 --> 37:37.570
they wouldn't know that the
present value of the bond you're

37:37.574 --> 37:40.904
long going forward is actually
lower by 2 dollars than the

37:40.902 --> 37:44.322
present value going forward--
this is right after this

37:44.318 --> 37:47.728
period--the present value
starting at this point of this

37:47.728 --> 37:51.318
bond going forward has actually
dropped 2 dollars below the

37:51.324 --> 37:54.244
present value of this bond going
forward,

37:54.239 --> 37:57.669
and it has to have dropped
otherwise the present values

37:57.668 --> 37:59.128
wouldn't be the same.

37:59.130 --> 38:00.950
So to just say it much more
simply,

38:00.949 --> 38:04.079
if you take 2 bonds with the
same present value you could

38:04.076 --> 38:07.536
well have that situation where
they have the same present value

38:07.538 --> 38:10.998
because one of the bonds pays a
lot of stuff early and terrible

38:11.000 --> 38:11.950
stuff late.

38:11.949 --> 38:14.449
So in the beginning it looks
like this bond is paying you

38:14.445 --> 38:17.305
more money than the other bond,
but since they have the same

38:17.311 --> 38:20.211
present value it must mean that
this bond is going to pay you

38:20.206 --> 38:22.326
more money at the tail than this
bond is.

38:22.329 --> 38:24.229
That's why they had the same
present value.

38:24.230 --> 38:27.230
So if one of them gets ahead at
the beginning it has to be it's

38:27.230 --> 38:29.360
going to fall behind the rest of
the time.

38:29.360 --> 38:31.950
So this one got ahead at the
beginning, it has to fall behind

38:31.947 --> 38:32.937
the rest of the time.

38:32.940 --> 38:36.620
That's hard to see because it
looks like this bond it's paying

38:36.615 --> 38:39.445
a coupon that's always bigger
than that bond.

38:39.449 --> 38:42.639
So it's easy to lose track of
the fact that this bond,

38:42.639 --> 38:45.229
because its coupon is higher
than this bond,

38:45.228 --> 38:48.358
how could it possibly ever fall
below this bond?

38:48.360 --> 38:51.950
Well, it falls below because
it's longer and the cash flows

38:51.952 --> 38:56.042
towards the end of it are being
discounted by an interest rate--

38:56.039 --> 39:00.859
because everybody knows the
interest rate's going to go up.

39:00.860 --> 39:03.950
And remember we saw last time
the yield curve.

39:03.949 --> 39:07.029
The yield curve,
remember today's yield curve is

39:07.034 --> 39:10.844
practically 0 now because the
government's held it at 0 and

39:10.842 --> 39:14.782
it's going to go way up to 4
percent or something in a couple

39:14.782 --> 39:15.572
years.

39:15.570 --> 39:17.830
So that's the yield curve today.

39:17.829 --> 39:20.339
So everybody knows the interest
rates are really low now and

39:20.336 --> 39:22.076
they're going to get much higher
later.

39:22.079 --> 39:24.989
So what it means is that every
long bond that's being issued

39:24.989 --> 39:27.949
now is going to be issued with a
higher coupon than the short

39:27.947 --> 39:29.727
bonds,
and if you go long the long

39:29.726 --> 39:32.386
bond and short the short bond
you're going to make money at

39:32.385 --> 39:34.215
the beginning but lose it back
later.

39:34.219 --> 39:36.989
But if you don't have to report
mark to market,

39:36.989 --> 39:39.239
you don't have to say the value
of what's left over,

39:39.239 --> 39:43.179
the public's just going to see
that you're making money at the

39:43.175 --> 39:43.945
beginning.

39:43.949 --> 39:45.179
It's clear now?

39:45.179 --> 39:47.509
Any other questions about this?

39:47.510 --> 39:53.240
So a lot of this is going on
right now.

39:53.239 --> 39:56.349
So let's do one more
application of this.

39:56.349 --> 40:03.379
Let's explain how mortgages
work, one more idea.

40:03.380 --> 40:10.640
Since the present value is = to
the cash flow the present value

40:10.635 --> 40:14.005
at 1 times that,
given this formula,

40:14.007 --> 40:17.397
that tells you one more thing,
very important idea.

40:17.400 --> 40:20.470
How do you compute present
value 0?

40:20.469 --> 40:23.639
Well, the way we've always
computed present value at 0 is

40:23.644 --> 40:26.504
to do this calculation,
this long calculation

40:26.496 --> 40:29.116
discounting all the future cash
flows,

40:29.119 --> 40:32.539
but this formula tells you that
there's actually a more

40:32.536 --> 40:36.076
efficient way of calculating it
by backward induction.

40:36.079 --> 40:39.939
If I knew what the present
value was at time 1 then I could

40:39.943 --> 40:43.613
get the present value at time 0
just by this formula.

40:43.610 --> 40:46.590
I'd add the present value at
time 1 to the cash at time 1 and

40:46.585 --> 40:47.275
discount it.

40:47.280 --> 40:49.970
So in fact I don't have
to--now, I don't know the

40:49.967 --> 40:53.127
present value at time 1,
but if I go to the end,

40:53.126 --> 40:55.936
at the end of time,
I know the present value of the

40:55.943 --> 40:56.413
bond is 0.

40:56.409 --> 40:57.939
There's nothing coming up later.

40:57.940 --> 41:01.180
At time T - 1 I know the
present value's very easy to

41:01.181 --> 41:01.931
calculate.

41:01.929 --> 41:07.029
It's C (T) divided by 1
i^(F)_T - 1.

41:07.030 --> 41:12.180
So I can go backwards by
present value and compute.

41:12.179 --> 41:13.519
I can do backward induction.

41:13.518 --> 41:17.388
So that's the word I want to
describe which is going to play

41:17.394 --> 41:20.554
a very important role in the
future of the class,

41:20.548 --> 41:22.058
backward induction.

41:22.059 --> 41:25.839
It says if this formula is
correct then a good way to do

41:25.840 --> 41:29.620
the computation is by working
backwards from the end.

41:29.619 --> 41:31.949
Don't just blindly take the
present value.

41:31.949 --> 41:34.939
If you blindly take the present
value all you've got is

41:34.938 --> 41:35.878
PV_0.

41:35.880 --> 41:39.230
If I calculate by backward
induction I start to the end and

41:39.233 --> 41:41.433
say, what would PV_T-1
be?

41:41.429 --> 41:42.559
That's a really simple thing.

41:42.559 --> 41:45.529
Then I can very simply find out
what PV_T-2 is

41:45.527 --> 41:47.307
etcetera back to the beginning.

41:47.309 --> 41:51.399
I do basically the same
calculation without having to

41:51.402 --> 41:54.662
take powers of--
it's a shorter calculation

41:54.659 --> 41:58.909
because here I've got exponents
of interest rates multiplying

41:58.907 --> 41:59.897
each other.

41:59.900 --> 42:01.530
So it's actually a shorter
calculation,

42:01.530 --> 42:04.320
and on top of that I get much
more information because now

42:04.317 --> 42:07.147
I've calculated out what the
present value's going to be at

42:07.153 --> 42:08.233
every time period.

42:08.230 --> 42:11.220
So a much more efficient way of
calculating things is to do it

42:11.215 --> 42:13.855
by backward induction because it
also tells me more.

42:13.860 --> 42:19.050
It tells me what the future
path of the bond is going to be.

42:19.050 --> 42:23.060
So let's just see how that
works on an example that I hope

42:23.059 --> 42:25.239
I worked out properly before.

42:25.239 --> 42:27.679
Of course, I did it last year,
but let's assume I did it

42:27.684 --> 42:28.044
right.

42:28.039 --> 42:33.599
So let's take a mortgage,
if you can see this.

42:33.599 --> 42:35.169
So this is something you have
in your notes.

42:35.170 --> 42:37.060
So there's a mortgage.

42:37.059 --> 42:46.479
Now, how does a--all right,
well pay no attention to that.

42:46.480 --> 42:53.270
So let's just say that--oh no,
why did this happen?

42:53.269 --> 43:10.419
Let's say that the payment is 8.

43:10.420 --> 43:15.160
So I've made payments of 8
everywhere.

43:15.159 --> 43:16.079
I hope I haven't screwed this
up.

43:16.079 --> 43:16.989
So here's the mortgage.

43:16.989 --> 43:18.819
It's a 30-year mortgage.

43:18.820 --> 43:22.640
So these are the years 1,2,
3,4, 5,6, 7,

43:22.641 --> 43:27.641
blah, blah, blah,
blah, blah, blah up to year 30.

43:27.639 --> 43:32.439
Now, suppose I happen to have a
bond that pays a coupon of 8

43:32.442 --> 43:35.782
dollars every year,
and the interest rate,

43:35.780 --> 43:38.060
let's say, is 7 percent.

43:38.059 --> 43:39.469
So it would be the interest
rate on the mortgage,

43:39.469 --> 43:42.449
but let's say the interest rate
in the economy is 7 percent and

43:42.452 --> 43:44.942
the bond,
however, is a premium bond.

43:44.940 --> 43:48.830
The bond is paying 8 percent
every year.

43:48.829 --> 44:06.469
Now, this is a mortgage so what
does this mean?

44:06.469 --> 44:10.249
See the mortgage pays 8 every
year until the very last year

44:10.253 --> 44:12.083
where it's still paying 8.

44:12.079 --> 44:15.119
So it's not paying 108,
it's just paying 8 every year.

44:15.119 --> 44:16.449
So it's not a coupon bond.

44:16.449 --> 44:17.319
It's a mortgage.

44:17.320 --> 44:20.370
A mortgage pays the same amount
every year until the end.

44:20.369 --> 44:24.689
So if this were a coupon bond
the last payment would be 108

44:24.690 --> 44:28.340
and of course the thing would be
a tremendous--

44:28.340 --> 44:31.090
it would be a premium bond
because the interest rate's only

44:31.088 --> 44:34.168
7 because it would pay a higher
coupon of 8 and 108 at the end.

44:34.170 --> 44:36.980
But you see I'm not paying 108
at the end.

44:36.980 --> 44:38.680
I'm only paying 8 at the end.

44:38.679 --> 44:44.889
So the first question is,
what is the present value of

44:44.885 --> 44:46.285
this bond?

44:46.289 --> 44:50.529
So I could take 8 divided by
1.07 8 divided by 1.07 squared

44:50.529 --> 44:55.059
(all the way) 8 over 1.07 to the
thirtieth power and figure out

44:55.059 --> 44:56.229
that number.

44:56.230 --> 44:59.410
But a much better way of doing
it is by backward induction.

44:59.409 --> 45:00.409
So what do I do?

45:00.409 --> 45:05.289
I go to the end and I say this
line is the remaining balance.

45:05.289 --> 45:10.119
Well, at year 30 there'd be no
more payments of the bond so the

45:10.123 --> 45:13.713
present value of what's left is
obviously 0.

45:13.710 --> 45:18.640
Now, what is the present value
of what's left at time 29?

45:18.639 --> 45:22.409
Well, the only thing I'm going
to get is I'm going to get this

45:22.405 --> 45:24.685
payment at time 8 right over
there.

45:24.690 --> 45:26.170
Sorry.

45:26.170 --> 45:30.830
I'm going to get this 8 right
there and so the present value

45:30.831 --> 45:34.151
of 8 at 7 percent interest is
7.47, I mean,

45:34.152 --> 45:35.972
7 percent interest.

45:35.969 --> 45:39.579
So how did I figure that out?

45:39.579 --> 45:42.209
I just said,
take that payment on the right

45:42.210 --> 45:45.030
and discount it by 7 percent,
so it's 7.47.

45:45.030 --> 45:46.850
Now, what's the present value
here?

45:46.849 --> 45:50.039
Well, here you're going to get
two things.

45:50.039 --> 45:51.149
What are you going to get?

45:51.150 --> 45:53.600
You're going to get a coupon
payment.

45:53.599 --> 45:57.089
Just after the payment in year
28 what's the present value of

45:57.085 --> 45:57.895
what's left?

45:57.900 --> 46:03.090
You're going to get a payment
in year 29 of 8 dollars.

46:03.090 --> 46:06.070
You're also going to get one in
year 30, but you don't care

46:06.070 --> 46:06.740
about that.

46:06.739 --> 46:11.229
You just know that the value in
year 29 is the coupon you get in

46:11.226 --> 46:15.426
year 29 plus the present value
in year 29 of what's left.

46:15.429 --> 46:19.209
The PV at time t,
I can just put a t here,

46:19.210 --> 46:24.870
PV at time t is the coupon you
get at time t 1,

46:24.869 --> 46:32.999
the present value at time t 1
divided by the interest rate at

46:33.000 --> 46:34.220
time t.

46:34.219 --> 46:39.799
So all I have to do is take 8
7.47 and discount that by 7

46:39.800 --> 46:45.880
percent, and that gives me the
present value as of time 28.

46:45.880 --> 46:49.970
So if I go back to time 26 I
say, well, how do I figure out

46:49.972 --> 46:52.162
the present value at time 27?

46:52.159 --> 46:53.489
It's time 27.

46:53.489 --> 46:56.959
I say, well,
I'm going to get 8 at time 28,

46:56.960 --> 47:01.840
but the present value at that
time, just after that payment,

47:01.838 --> 47:02.828
is 14.4.

47:02.829 --> 47:07.789
So I take 22.4 and discount it
by 7 percent and I get about 21.

47:07.789 --> 47:10.939
So that's how I can work
backwards and figure out the

47:10.938 --> 47:12.268
present value today.

47:12.268 --> 47:15.408
Now, in mortgages this number
is very interesting.

47:15.409 --> 47:19.599
It's called the remaining
balance, which we'll see in a

47:19.601 --> 47:20.301
second.

47:20.300 --> 47:22.530
But anyway, that number you can
calculate it every t.

47:22.530 --> 47:25.180
It's just the PV_t
worked backward from the end.

47:25.179 --> 47:29.199
So it's a very simple
calculation and it tells you the

47:29.197 --> 47:33.057
present value of the bond,
of that 8 percent coupon,

47:33.063 --> 47:36.553
until year 30 and no principal
at the end.

47:36.550 --> 47:40.960
Well, a mortgage has to pay a
coupon of 8 percent that gives

47:40.961 --> 47:45.151
100 because if there were no
uncertainty and there are no

47:45.150 --> 47:48.270
prepayments or anything,
no uncertainty,

47:48.273 --> 47:51.833
the bank giving the coupon is
not going to give you money

47:51.833 --> 47:54.633
unless its present value is
equal to 100.

47:54.630 --> 47:58.540
So they're going to ask you to
pay a coupon.

47:58.539 --> 48:00.959
So now you see what have I done
over here?

48:00.960 --> 48:04.590
This is B 26 - B 30,
so the original face it was

48:04.590 --> 48:09.100
supposed to be 100,
but the present value of all

48:09.099 --> 48:13.719
those payments is only 99,
so there's a gap here of .72

48:13.717 --> 48:15.977
and the square of the gap is
that.

48:15.980 --> 48:20.480
The square of the gap is there,
and we want to minimize that.

48:20.480 --> 48:27.610
So we're going to find the
payment every period,

48:27.612 --> 48:28.982
Solver.

48:28.980 --> 48:33.700
So I want to minimize B 32,
minimize by choosing B 29 which

48:33.701 --> 48:34.761
looks good.

48:34.760 --> 48:41.070
That's the first payment,
and all the other payments are

48:41.074 --> 48:47.394
set to be equal to that,
to minimize that difference.

48:47.389 --> 48:52.279
B 29 is the first payment,
so why didn't this work?

48:52.280 --> 48:56.220
Student: You hardwired
in C 29 and D 29

48:56.222 --> 48:58.592
>

48:58.590 --> 48:59.680
Prof: Is that what I did?

48:59.679 --> 49:05.479
So here's 8 and then this over
here.

49:05.480 --> 49:08.560
I hardwired that in,
so I didn't want to do that.

49:08.559 --> 49:15.149
So that's got to be equal to
what's left, equal,

49:15.148 --> 49:16.128
left.

49:16.130 --> 49:18.430
So here I got--when I hardwire
this then, okay,

49:18.429 --> 49:19.279
so that's good.

49:19.280 --> 49:20.730
So let's try the same thing now.

49:20.730 --> 49:25.150
Tools, glad I have you guys,
Tools, so B 32 is what I'm

49:25.153 --> 49:26.223
minimizing.

49:26.219 --> 49:30.089
B 29 is the first payment and
all the others have been set

49:30.088 --> 49:32.258
equal to it, and if I solve...

49:32.260 --> 49:37.760
Student: C 29.

49:37.760 --> 49:38.150
Prof: All right,
let's try.

49:38.150 --> 49:43.670
The first payment is year 1,
right, so it should be--oh,

49:43.672 --> 49:45.482
C 29, thank you.

49:45.480 --> 49:50.140
Yeah, that's why I'm confused,
C 29, thanks.

49:50.139 --> 50:00.629
Tools, so let's just look at
this a second.

50:00.630 --> 50:03.070
So that's what I've hardwired
in.

50:03.070 --> 50:07.380
So Format, no Tools, Solver.

50:07.380 --> 50:15.590
Minimize B 32 subject to C 29
as you've told me 20 times,

50:15.590 --> 50:18.670
C 29 and now solve.

50:18.670 --> 50:20.650
So now we did it.

50:20.650 --> 50:23.600
So we got the right payment to
make the balance exactly equal

50:23.597 --> 50:24.037
to 100.

50:24.039 --> 50:25.969
So that's how a mortgage works.

50:25.969 --> 50:28.849
You have to find the coupon
payment such that if you take

50:28.847 --> 50:32.027
the present value of that same
coupon payment forever it's just

50:32.034 --> 50:34.454
going to be worth 100 which is
that number.

50:34.449 --> 50:36.509
And how do you figure out the
coupon payment?

50:36.510 --> 50:38.120
Well, you do it by backward
inductions.

50:38.119 --> 50:39.249
Figure out the present value.

50:39.250 --> 50:43.000
Do it by backward induction
just as we did.

50:43.000 --> 50:45.560
But we've gotten a lot of
information.

50:45.559 --> 50:47.499
We've gotten this number at
every period.

50:47.500 --> 50:50.960
So by doing it by backward
induction instead of just doing

50:50.956 --> 50:53.136
the long exponential
calculation,

50:53.139 --> 50:55.909
by doing it by backward
induction we've produced the

50:55.909 --> 50:58.299
present value at every time in
the future.

50:58.300 --> 51:00.850
Now, that's an incredibly
important number in mortgages.

51:00.849 --> 51:02.649
It's called the remaining
balance.

51:02.650 --> 51:06.160
Why is that such an important
number in mortgages?

51:06.159 --> 51:08.909
This will play a very key role
in the rest of the course.

51:08.909 --> 51:12.439
What is the remaining balance
and why is it so important?

51:12.440 --> 51:13.930
Does anyone know how a mortgage
works?

51:13.929 --> 51:14.779
Yep?

51:14.780 --> 51:17.990
Student: Is that the
mark to market value or just

51:17.989 --> 51:21.609
whatever you'd be able to sell
that mortgage for to someone?

51:21.610 --> 51:24.920
Prof: Not what you'd be
able to sell it for,

51:24.923 --> 51:25.723
but close.

51:25.719 --> 51:29.559
So when the bank gives you a
mortgage it says--so how did

51:29.563 --> 51:30.733
mortgages work?

51:30.730 --> 51:34.330
It used to be in the old days
that the mortgages were coupon

51:34.331 --> 51:34.821
bonds.

51:34.820 --> 51:38.470
They'd pay 8,8,
8,8, 8,108, and then what would

51:38.469 --> 51:43.469
happen is just before the 108
payment everyone would default.

51:43.469 --> 51:45.819
So in the Depression the people
who defaulted were people who

51:45.822 --> 51:47.902
defaulted just before their big
principal payment,

51:47.900 --> 51:50.360
so bankers got wise after the
Depression.

51:50.360 --> 51:52.290
They said, "Well,
that's a terrible thing to do.

51:52.289 --> 51:55.399
We should make the payment be
constant and that way there's no

51:55.400 --> 51:58.410
reason for the guy to default
right at the end and we're not

51:58.407 --> 52:01.567
going to get stuck with 100
dollars that's not paid."

52:01.570 --> 52:02.910
So it's constant.

52:02.909 --> 52:05.729
But of course if it's constant
that means the present value of

52:05.733 --> 52:07.683
what's left is going down all
the time,

52:07.679 --> 52:10.899
so that's why this number is
going down all the time.

52:10.900 --> 52:13.140
If it's 108 at the end,
that's why the present value

52:13.141 --> 52:14.111
would stay the same.

52:14.110 --> 52:18.680
So it's going down all the
time, so that's why it's called

52:18.682 --> 52:20.692
an amortizing mortgage.

52:20.690 --> 52:23.820
It's because what's left in the
mortgage is getting smaller all

52:23.822 --> 52:24.382
the time.

52:24.380 --> 52:30.050
So a fixed rate mortgage pays
the same coupon every year.

52:30.050 --> 52:32.040
The present value of what's
left, therefore,

52:32.036 --> 52:34.576
must be going down every year
and that's why it's called

52:34.577 --> 52:35.267
amortizing.

52:35.268 --> 52:38.588
And bankers wanted that to
happen because that way their

52:38.594 --> 52:40.534
risk is going down every year.

52:40.530 --> 52:43.560
Every year the house is
presumably still worth 120 or

52:43.556 --> 52:47.156
whatever it was at the beginning
and the amount owed is getting

52:47.164 --> 52:48.334
lower and lower.

52:48.329 --> 52:51.429
So the bankers are feeling more
and more secure every year

52:51.434 --> 52:54.654
because the house is backing a
smaller and smaller loan,

52:54.650 --> 52:56.930
or to put it another way,
if you're uncertain about what

52:56.934 --> 52:58.934
the price of the house will be
in the future,

52:58.929 --> 53:01.969
you want to make sure that what
is owed is going down in the

53:01.974 --> 53:02.444
future.

53:02.440 --> 53:05.640
If the price gradually goes
down of the house what's owed is

53:05.643 --> 53:07.223
gradually going to go down.

53:07.219 --> 53:10.329
But the main reason why the
number is so important is you

53:10.327 --> 53:13.817
have to realize the purpose of a
mortgage is you take out a loan

53:13.822 --> 53:15.712
using the house as collateral.

53:15.710 --> 53:17.350
If you don't make your payment
they can take your house.

53:17.349 --> 53:18.879
Well, what happens if you want
to move?

53:18.880 --> 53:22.090
If you want to move you're
going to sell the house.

53:22.090 --> 53:24.920
The house is no longer
collateral, so if you want to

53:24.918 --> 53:27.578
move you have to undo the
promise to the bank.

53:27.579 --> 53:30.949
So if in year 5 just after
you're making your payment of 8

53:30.947 --> 53:34.017
dollars and 5 cents in year 5
you decide to move,

53:34.018 --> 53:36.208
you say to the bank,
"I want to cancel the

53:36.210 --> 53:37.020
mortgage."

53:37.018 --> 53:38.718
How much will they ask you to
pay?

53:38.719 --> 53:42.159
Well, the remaining balance,
93.91.

53:42.159 --> 53:47.169
So that's why this remaining
balance is such an important

53:47.173 --> 53:47.983
number.

53:47.980 --> 53:51.600
So it allows people to leave
their house and pay off their

53:51.597 --> 53:54.577
mortgage by paying off the
remaining balance.

53:54.579 --> 53:57.189
You wouldn't want them to pay
100 if they left because they've

53:57.186 --> 53:57.866
made payments.

53:57.869 --> 54:00.939
You notice that the payment
here is 8 dollars.

54:00.940 --> 54:04.730
That's bigger than 7 percent,
right, because if it's a coupon

54:04.733 --> 54:08.153
bond you'd pay 7 all the way to
the end and pay 107.

54:08.150 --> 54:09.540
That would have a present value
of 100.

54:09.539 --> 54:11.319
If you're not paying the 100 at
the end,

54:11.320 --> 54:13.000
but just making a level payment
all the way through,

54:13.000 --> 54:15.380
the payment you have to make
every year better be more than

54:15.384 --> 54:16.764
7,
so it's 8.

54:16.760 --> 54:21.020
So this 8 - 7 is sort of what
you're paying down of your

54:21.016 --> 54:22.406
mortgage, right?

54:22.409 --> 54:23.779
The interest is only 7.

54:23.780 --> 54:24.670
You've paid 8.

54:24.670 --> 54:26.370
That's why you owe less than
100.

54:26.369 --> 54:29.359
You've paid 1 dollar 6 extra.

54:29.360 --> 54:33.270
That's why you only owe 98.94.

54:33.268 --> 54:35.958
So every year you're paying
part of your principal down.

54:35.960 --> 54:38.400
That means it's amortizing,
and that means if you want to

54:38.396 --> 54:41.136
get out of the mortgage you can
get out of it by paying less and

54:41.137 --> 54:41.527
less.

54:41.530 --> 54:43.440
It means the lender,
the mortgage lender,

54:43.438 --> 54:46.158
is more and more protected by
the house every year because

54:46.157 --> 54:47.777
what you owe is less and less.

54:47.780 --> 54:49.610
So that's how a mortgage works.

54:49.610 --> 54:52.740
Any questions about that?

54:52.739 --> 54:55.349
All right, so what's the point?

54:55.349 --> 54:58.779
The point is that by simple
present value thinking you can

54:58.779 --> 55:02.329
start to understand the main
instruments in the economy,

55:02.329 --> 55:05.579
how mortgages work,
why they're called amortizing,

55:05.579 --> 55:08.149
why the amount you have to pay
to get out of your mortgage goes

55:08.150 --> 55:11.050
down every year,
and exactly how much it goes

55:11.050 --> 55:13.010
down every year etcetera.

55:13.010 --> 55:15.660
So we can do a lot more
examples like that,

55:15.659 --> 55:20.519
but I want to change,
shift the discussion now to a

55:20.516 --> 55:25.616
much bigger subject,
a subject of tremendous policy

55:25.621 --> 55:29.631
interest in the country,
namely Social Security.

55:29.630 --> 55:32.630
What should we do about Social
Security?

55:32.630 --> 55:35.950
Now, it will turn out that you
can analyze the situation the

55:35.954 --> 55:38.384
same way we've just analyzed
these bonds.

55:38.380 --> 55:41.010
It's very simple to figure out
what the problem is and what

55:41.005 --> 55:43.475
went wrong,
yet very few people understand

55:43.483 --> 55:46.193
it, including most of our
politicians and,

55:46.190 --> 55:48.210
I'm sorry to say,
a lot of our economists.

55:48.210 --> 55:53.910
So I want to describe now in
the next class and a half the

55:53.914 --> 55:59.524
Social Security problem and how
to solve the problem,

55:59.518 --> 56:01.128
but also how to understand the
problem.

56:01.130 --> 56:04.020
You can't figure out the right
solution until you've understood

56:04.023 --> 56:05.053
what the problem is.

56:05.050 --> 56:07.810
So were there any questions?

56:07.809 --> 56:09.589
Before I start this,
were there any questions?

56:09.590 --> 56:10.210
I should have paused.

56:10.210 --> 56:13.610
Are there any questions about
the mortgage,

56:13.614 --> 56:17.264
or present value,
or how present value changes

56:17.262 --> 56:18.642
through time?

56:18.639 --> 56:20.769
So those ideas,
and marking to market,

56:20.773 --> 56:24.123
those are very important ideas
I think once you think about

56:24.117 --> 56:25.327
them not so hard.

56:25.329 --> 56:28.869
I'm now going to take exactly
those ideas and apply it to

56:28.865 --> 56:32.335
Social Security where the public
is totally baffled,

56:32.340 --> 56:34.610
but all you have to do is apply
the same thinking.

56:34.610 --> 56:37.520
So Social Security is supposed
to be in a terrible crisis.

56:37.518 --> 56:42.158
That's what they always tell
you.

56:42.159 --> 56:44.699
It was a big campaign issue in
2000,

56:44.699 --> 56:46.529
you probably were too young to
remember that,

56:46.530 --> 56:50.120
but there were three debates
between Gore and Bush in which

56:50.117 --> 56:53.767
Gore grimaced and everybody
thought he wasn't a good guy and

56:53.768 --> 56:55.438
so they voted for Bush.

56:55.440 --> 56:58.590
He was mostly grimacing about
Social Security.

56:58.590 --> 57:01.950
And then in 2000--well,
I'll get to the future.

57:01.949 --> 57:06.429
So anyway, in those debates
three mistakes were made.

57:06.429 --> 57:11.129
So Bush argued that the returns
on Social Security were

57:11.126 --> 57:12.776
disastrously low.

57:12.780 --> 57:20.430
He said the whole program is in
a terrible crisis and we've got

57:20.425 --> 57:24.615
to privatize to save the system.

57:24.619 --> 57:26.079
How did it get into the crisis?

57:26.079 --> 57:28.509
Well, it wasn't clear exactly
how it got into the crisis,

57:28.514 --> 57:31.034
but it seems like the baby
boomers had something to do with

57:31.034 --> 57:31.344
it.

57:31.340 --> 57:33.640
They're all getting old and
they're going to have to get

57:33.644 --> 57:35.284
these huge Social Security
payments,

57:35.280 --> 57:37.290
and that's why we're in the
crisis because the baby boomers

57:37.293 --> 57:37.923
are getting old.

57:37.920 --> 57:41.790
It's all my fault,
or my generation's fault.

57:41.789 --> 57:45.389
Then the third mistake was Gore
said, "Well,

57:45.387 --> 57:48.157
it's impossible to
privatize."

57:48.159 --> 57:51.499
Privatize means take the money
that your parents are paying in

57:51.498 --> 57:54.068
Social Security and that you'll
start to pay;

57:54.070 --> 57:57.670
instead of putting it into the
fund that's being used somehow,

57:57.670 --> 57:59.420
you don't probably know exactly
how,

57:59.420 --> 58:03.290
instead of doing that,
take that money and say it's

58:03.289 --> 58:05.069
the taxpayer's money.

58:05.070 --> 58:05.930
It's your money.

58:05.929 --> 58:08.089
You can put it in the stock
market if you want.

58:08.090 --> 58:11.450
So that's what Bush wanted to
do, privatize Social Security,

58:11.454 --> 58:14.594
say your tax contributions
should go into a stock market

58:14.590 --> 58:16.130
with your name on them.

58:16.130 --> 58:17.990
And Gore said,
"Well, that's impossible.

58:17.989 --> 58:20.369
If you privatize,
what are the old people today

58:20.373 --> 58:21.103
going to do?

58:21.099 --> 58:22.449
Where are they going to get the
payments?

58:22.449 --> 58:26.069
You can't privatize Social
Security and take today's young

58:26.072 --> 58:28.872
tax contributions to Social
Security and say,

58:28.867 --> 58:31.407
'You young guys,
there's your money.

58:31.409 --> 58:34.359
You can keep them in the stock
market,' and at the same time

58:34.360 --> 58:36.960
pay the old retirees,
so Bush must not know what he's

58:36.960 --> 58:38.160
talking about."

58:38.159 --> 58:40.459
So that also was wrong.

58:40.460 --> 58:44.310
So those three things,
that Social Security is going

58:44.313 --> 58:47.613
to give terrible returns,
it must be it's wasting money,

58:47.610 --> 58:50.010
something's horribly wrong with
it and the only way to save it

58:50.012 --> 58:50.882
is to privatize it.

58:50.880 --> 58:52.380
That's Bush's main claim.

58:52.380 --> 58:54.180
Blame it all on the baby
generation,

58:54.179 --> 58:56.389
that's everybody's claim,
and Gore saying you can't

58:56.385 --> 58:58.675
privatize without screwing
today's young [correction:

58:58.679 --> 58:59.649
today's retirees].

58:59.650 --> 59:02.970
All three of those things sound
pretty convincing and yet

59:02.969 --> 59:04.509
they're all three wrong.

59:04.510 --> 59:07.740
So I want to explain the system
to you and help you understand

59:07.742 --> 59:09.632
it,
and then I have a policy

59:09.626 --> 59:13.476
recommendation you'll get next
class which most people don't

59:13.480 --> 59:17.080
agree with,
so you probably won't either,

59:17.079 --> 59:22.769
but I'll warn you when we get
to a point that's controversial.

59:22.768 --> 59:26.428
So everything I'm going to say
in the first 90 minutes is going

59:26.425 --> 59:27.835
to be uncontroversial.

59:27.840 --> 59:30.170
Not everybody knows it,
but I think it's obviously just

59:30.166 --> 59:31.026
a matter of logic.

59:31.030 --> 59:34.320
And then my conclusion about
what to do, you can criticize

59:34.320 --> 59:34.610
it.

59:34.610 --> 59:37.130
I think it's a matter of logic
too, but I admit most people

59:37.125 --> 59:38.075
don't agree with it.

59:38.079 --> 59:42.779
So now, in 2005 if nothing else
Bush was tremendously

59:42.775 --> 59:43.945
consistent.

59:43.949 --> 59:46.999
So whatever he told you he was
going to do no matter how

59:47.003 --> 59:48.783
wrong-handed it was he did it.

59:48.780 --> 59:51.990
So he said in the debates that
he wanted to privatize Social

59:51.987 --> 59:54.377
Security and sure enough he kept
his word.

59:54.380 --> 59:56.230
He launched a huge program.

59:56.230 --> 59:58.950
That's how he started right
after the 2004 election.

59:58.949 --> 1:00:01.159
His first initiative,
you might remember,

1:00:01.157 --> 1:00:03.637
was we've got to privatize
Social Security.

1:00:03.639 --> 1:00:08.149
He went on a 60-day,
60-city tour to kick off his

1:00:08.152 --> 1:00:09.472
second term.

1:00:09.469 --> 1:00:12.759
So after the 2004 election
privatizing Social Security was

1:00:12.762 --> 1:00:13.632
a huge issue.

1:00:13.630 --> 1:00:16.710
In the 2008 election it was
still a big issue.

1:00:16.710 --> 1:00:19.220
McCain said sort of what Bush
said.

1:00:19.219 --> 1:00:22.029
"I want young workers to
be able to if they choose,

1:00:22.030 --> 1:00:24.420
to take part of their own money
which is their taxes,

1:00:24.420 --> 1:00:26.360
their money that's getting
taxed and getting put into

1:00:26.360 --> 1:00:28.180
Social Security,
I want them to have their own

1:00:28.182 --> 1:00:30.412
account and put it into the
stock market with their name on

1:00:30.409 --> 1:00:30.869
it."

1:00:30.869 --> 1:00:35.439
And Obama said he's totally
against that.

1:00:35.440 --> 1:00:36.670
That was 2008.

1:00:36.670 --> 1:00:40.680
Recently, of course,
the public has made another

1:00:40.677 --> 1:00:41.527
mistake.

1:00:41.530 --> 1:00:45.390
So everybody is saying now,
"Oh, the financial crisis.

1:00:45.389 --> 1:00:47.549
We better not talk about Social
Security anymore."

1:00:47.550 --> 1:00:49.990
Nobody's talking about Social
Security.

1:00:49.989 --> 1:00:53.369
They're saying, "Well,
could you have imagined what

1:00:53.365 --> 1:00:56.185
would have happened had we
privatized as Bush wanted us to

1:00:56.188 --> 1:00:58.018
do and the stock market
collapsed?

1:00:58.018 --> 1:00:59.528
Everybody would have lost all
their money.

1:00:59.530 --> 1:01:03.050
What a disaster that would have
been, and it would have ruined

1:01:03.054 --> 1:01:03.984
the old."

1:01:03.980 --> 1:01:05.490
This sounds pretty persuasive.

1:01:05.489 --> 1:01:08.829
So Krugman wrote a column
saying, "A bullet dodged.

1:01:08.829 --> 1:01:11.039
What would have happened if
Bush had succeeded?

1:01:11.039 --> 1:01:13.339
All the old people would be
broke now."

1:01:13.340 --> 1:01:17.410
And Robert Reich who was in the
Clinton Administration sort of

1:01:17.411 --> 1:01:21.351
more or less said the same thing
that it'd be a disaster.

1:01:21.349 --> 1:01:24.319
Now, the Obama Administration,
by the way, hasn't stopped

1:01:24.320 --> 1:01:26.020
talking about Social Security.

1:01:26.018 --> 1:01:28.668
So their director,
he's the Director of the White

1:01:28.670 --> 1:01:31.490
House Office of the Budget,
so this is an incredibly

1:01:31.485 --> 1:01:33.525
important position,
Peter Orszag.

1:01:33.530 --> 1:01:36.930
He's the son of--there's a math
professor here,

1:01:36.934 --> 1:01:38.494
Orszag, his father.

1:01:38.489 --> 1:01:41.719
So he's a friend of mine,
the son.

1:01:41.719 --> 1:01:45.859
He said once healthcare reform
is in place the U.S.

1:01:45.860 --> 1:01:48.280
can then focus on other
important things,

1:01:48.282 --> 1:01:50.042
especially Social Security.

1:01:50.039 --> 1:01:52.859
So Obama wants to do something
about it, but he just doesn't

1:01:52.855 --> 1:01:53.805
want to privatize.

1:01:53.809 --> 1:01:56.329
So it's a big problem and
everything everybody says about

1:01:56.333 --> 1:01:57.283
it seems plausible.

1:01:57.280 --> 1:02:00.820
Now, just to continue along the
plausibility of it,

1:02:00.820 --> 1:02:04.360
so Bush says what he really
wants to do is--

1:02:04.360 --> 1:02:07.220
why private accounts are a
better thing is that if you put

1:02:07.221 --> 1:02:09.431
the money in private accounts it
can grow.

1:02:09.429 --> 1:02:11.869
You can get a greater rate of
return than the current system

1:02:11.871 --> 1:02:12.701
which is terrible.

1:02:12.699 --> 1:02:16.839
If you were a young person by
putting your Social Security tax

1:02:16.835 --> 1:02:21.035
money aside in a private account
you'll be able to get a better

1:02:21.038 --> 1:02:24.898
rate of return on your money
than the government could get

1:02:24.902 --> 1:02:26.532
you on your money.

1:02:26.530 --> 1:02:28.410
So why would you just want to
give it to the government?

1:02:28.409 --> 1:02:31.889
It's for your retirement and
you'll be able to pass that

1:02:31.891 --> 1:02:35.941
money along to your children and
grandchildren if you want at the

1:02:35.943 --> 1:02:36.453
end.

1:02:36.449 --> 1:02:39.249
And best of all the money's
yours and the government can't

1:02:39.251 --> 1:02:39.991
take it away.

1:02:39.989 --> 1:02:43.889
So that's what Bush says and
he's said many times.

1:02:43.889 --> 1:02:46.849
So there's one sense in which
he's right.

1:02:46.849 --> 1:02:51.759
So let's look at the returns
people got on Social Security.

1:02:51.760 --> 1:02:53.280
Now, what is a return?

1:02:53.280 --> 1:02:54.810
We know what the rate of return
is.

1:02:54.809 --> 1:02:56.089
How do they calculate it?

1:02:56.090 --> 1:03:00.910
You can go back to people born
starting in 1878.

1:03:00.909 --> 1:03:03.049
Social Security,
as you'll see in a second,

1:03:03.047 --> 1:03:05.487
I'm going to give you the
history, began 1939.

1:03:05.489 --> 1:03:12.239
So these people in 1878 they're
60 when Social Security's

1:03:12.244 --> 1:03:16.954
beginning, if my arithmetic is
right.

1:03:16.949 --> 1:03:19.419
So they're 60 at that point.

1:03:19.420 --> 1:03:22.210
So you can look at all these
people and you can say,

1:03:22.210 --> 1:03:25.440
for every generation in the
past, you can say how much money

1:03:25.440 --> 1:03:27.520
did they pay when they were
young?

1:03:27.519 --> 1:03:28.579
They paid taxes.

1:03:28.579 --> 1:03:32.459
So they got negative 12.4,
that's the tax rate.

1:03:32.460 --> 1:03:34.650
Negative 12.4,
they did that a bunch of years

1:03:34.652 --> 1:03:37.542
when they were young and then
they started getting payments

1:03:37.543 --> 1:03:42.313
when they were old,
24,24, 20 something like that.

1:03:42.309 --> 1:03:45.619
Those are the payments when
they're old.

1:03:45.619 --> 1:03:47.969
So there are negative ones at
the beginning and positive ones

1:03:47.969 --> 1:03:48.479
at the end.

1:03:48.480 --> 1:03:51.480
You can calculate the internal
rate of return,

1:03:51.481 --> 1:03:55.151
the yield, the thing that makes
this present value 0.

1:03:55.150 --> 1:03:55.900
We know how to do that.

1:03:55.900 --> 1:03:57.070
We've done it.

1:03:57.070 --> 1:03:59.140
So people have done this.

1:03:59.139 --> 1:04:02.969
So there's a guy named Limmer,
Limmer or Leemer from the

1:04:02.967 --> 1:04:06.927
Social Security Administration
who did these calculations,

1:04:06.932 --> 1:04:09.162
prompted a little bit by me.

1:04:09.159 --> 1:04:12.649
So I should say that a lot of
the reason I got started

1:04:12.648 --> 1:04:16.858
thinking about this is I got put
on a Presidential Panel to study

1:04:16.862 --> 1:04:20.882
Social Security Reform in the
Clinton Administration and every

1:04:20.876 --> 1:04:23.836
Democrat was matched with a
Republican.

1:04:23.840 --> 1:04:25.530
So the two chairmen,
one Democrat,

1:04:25.534 --> 1:04:27.804
one Republican,
all the way along there was

1:04:27.798 --> 1:04:30.868
Democrat and Republican,
and after Bush got elected all

1:04:30.869 --> 1:04:33.479
the Democrats got kicked off the
committee.

1:04:33.480 --> 1:04:40.690
But anyway, so in any case here
are the rates of return.

1:04:40.690 --> 1:04:43.610
For people who are old when the
program began,

1:04:43.606 --> 1:04:46.776
they got sensational rates of
returns, 40 percent,

1:04:46.782 --> 1:04:49.572
30 percent, incredible rates of
return.

1:04:49.570 --> 1:04:54.040
As the generations get younger
and younger the returns go lower

1:04:54.036 --> 1:04:57.346
and lower and they're down now
to 2 percent.

1:04:57.349 --> 1:04:59.869
These are a forecast of these
rates of returns.

1:04:59.869 --> 1:05:02.459
And so let's see,
you're 20, say,

1:05:02.463 --> 1:05:04.333
something on average.

1:05:04.329 --> 1:05:08.829
You were born in 1990,
something like that or around

1:05:08.833 --> 1:05:09.543
there.

1:05:09.539 --> 1:05:11.529
So here's your rate of return.

1:05:11.530 --> 1:05:13.900
It's down here, right?

1:05:13.900 --> 1:05:16.720
It's 2 percent,
and there it is blown up.

1:05:16.719 --> 1:05:18.009
It's under 2 percent.

1:05:18.010 --> 1:05:20.160
So these are the people from
1924 to 2002,

1:05:20.163 --> 1:05:21.953
so you're right at the end
here.

1:05:21.949 --> 1:05:23.729
That's your rate of return
blown up.

1:05:23.730 --> 1:05:26.600
You can only expect 1 and a
half or 2 percent.

1:05:26.599 --> 1:05:27.929
So George Bush is right.

1:05:27.929 --> 1:05:30.709
The rate of return on Social
Security is terrible.

1:05:30.710 --> 1:05:34.570
If you look at the taxes that
you put in, and you look at the

1:05:34.568 --> 1:05:38.488
benefits that you can expect to
get your generation is getting

1:05:38.492 --> 1:05:39.782
totally screwed.

1:05:39.780 --> 1:05:43.050
So now if you look
historically--this was done in

1:05:43.045 --> 1:05:45.165
1994,
so the number's a little

1:05:45.166 --> 1:05:48.566
bit--it's not quite as dramatic,
but it hasn't changed as much

1:05:48.572 --> 1:05:49.142
as you think.

1:05:49.139 --> 1:05:52.559
From money put in the stock
market between '26 and 2004,

1:05:52.559 --> 1:05:56.159
that's before the crash of '29,
so I should have gotten the

1:05:56.164 --> 1:05:58.284
number after the recent crash.

1:05:58.280 --> 1:05:59.380
It doesn't change that much.

1:05:59.380 --> 1:06:02.420
Before the crash of '29 you
looked at keeping your money in

1:06:02.420 --> 1:06:04.990
the stock market,
just leaving it there for all

1:06:04.989 --> 1:06:07.899
that time,
after inflation you'd get 9.1

1:06:07.900 --> 1:06:09.160
percent return.

1:06:09.159 --> 1:06:13.839
On treasury bonds you get 2.7
percent return and yet on Social

1:06:13.835 --> 1:06:17.435
Security you're going to get
under 2 percent.

1:06:17.440 --> 1:06:20.040
So George Bush says,
"Look, put it in the stock

1:06:20.041 --> 1:06:20.501
market.

1:06:20.500 --> 1:06:21.550
Get 9 percent."

1:06:21.550 --> 1:06:24.830
We had a little disaster here,
so maybe it's 7 percent.

1:06:24.829 --> 1:06:26.709
"Put it in the stock
market and get 7 percent.

1:06:26.710 --> 1:06:28.750
Why be satisfied with 2 percent?

1:06:28.750 --> 1:06:29.540
There's something wrong.

1:06:29.539 --> 1:06:32.669
We've got to privatize,
put an end to this."

1:06:32.670 --> 1:06:36.100
So there seems to be something
to what he is saying.

1:06:36.099 --> 1:06:39.889
So now you look at what's going
on with Social Security.

1:06:39.889 --> 1:06:41.359
So what happens in Social
Security?

1:06:41.360 --> 1:06:43.980
I'm going to explain the whole
history and how it works here.

1:06:43.980 --> 1:06:50.210
What happens is you pay taxes,
12.4 percent tax.

1:06:50.210 --> 1:06:51.350
You probably know that.

1:06:51.349 --> 1:06:54.229
Everybody's paying taxes on the
money they make and then there

1:06:54.228 --> 1:06:55.878
are benefits that are being
paid.

1:06:55.880 --> 1:06:58.710
Now, the benefits are
not--there's a formula for

1:06:58.713 --> 1:07:02.153
benefits which doesn't have
anything to do with the amount

1:07:02.152 --> 1:07:05.192
of taxes being paid,
so at the present time the

1:07:05.186 --> 1:07:07.296
taxes are bigger than the
benefits.

1:07:07.300 --> 1:07:08.850
So where does the extra money
go?

1:07:08.849 --> 1:07:11.259
It goes into the Social
Security Trust Fund.

1:07:11.260 --> 1:07:14.890
So here's the Social Security
Trust Fund which is now around 2

1:07:14.885 --> 1:07:17.285
trillion,
which is going to keep growing

1:07:17.293 --> 1:07:20.853
because contributions are going
to be bigger than benefits until

1:07:20.851 --> 1:07:22.761
2020 or so,
and at that point

1:07:22.757 --> 1:07:25.807
contributions--that's the baby
boom generation,

1:07:25.809 --> 1:07:29.849
that's me retiring,
or a little later in my case,

1:07:29.849 --> 1:07:31.889
but anyway the baby boom
generation--

1:07:31.889 --> 1:07:33.649
in fact since I'm a Yale
professor it's out here

1:07:33.650 --> 1:07:34.100
somewhere.

1:07:34.099 --> 1:07:39.199
So anyway, my generation's
going to start retiring here and

1:07:39.202 --> 1:07:42.002
then the benefits--
so we're going to be not

1:07:41.998 --> 1:07:44.288
working, not paying taxes but
we're collecting benefits and

1:07:44.293 --> 1:07:46.713
there are so many of us that the
benefits are going to be less

1:07:46.706 --> 1:07:49.036
than the taxes and the trust
fund's going to go down,

1:07:49.039 --> 1:07:50.529
and down, and down.

1:07:50.530 --> 1:07:53.340
And then the year 2030,
at a little bit more than 2030,

1:07:53.340 --> 1:07:57.700
the trust fund's going to go to
0, and then after that the taxes

1:07:57.704 --> 1:08:01.174
are still going to be smaller
than the benefits.

1:08:01.170 --> 1:08:02.230
And so what's going to happen?

1:08:02.230 --> 1:08:04.370
They'll be no money to pay
these people and there's going

1:08:04.367 --> 1:08:06.427
to have to be a big drop in what
people are getting.

1:08:06.429 --> 1:08:10.049
So it looks like the system is
not only paying a horrible rate

1:08:10.052 --> 1:08:12.432
of return, it's not even going
to pay.

1:08:12.429 --> 1:08:15.469
It's going to run out of money
and go broke in 2040.

1:08:15.469 --> 1:08:18.769
So it seems like a total
disaster.

1:08:18.770 --> 1:08:21.060
So that's the setting of the
question.

1:08:21.060 --> 1:08:23.330
George Bush said it's a
disaster.

1:08:23.328 --> 1:08:25.198
It looks, at first glance,
like a disaster.

1:08:25.198 --> 1:08:27.878
The newspapers tell you all the
time it's a disaster.

1:08:27.880 --> 1:08:31.780
How did it get to be so bad and
what should we do about it?

1:08:31.779 --> 1:08:35.259
All right, now it's going to
turn out that by using the

1:08:35.257 --> 1:08:38.407
concept of present value it can
be very simple and

1:08:38.414 --> 1:08:42.314
straightforward to understand,
and it's going to be the exact

1:08:42.305 --> 1:08:44.865
opposite of what everybody seems
to be saying.

1:08:44.868 --> 1:08:48.558
So I'm going to play you a clip
next time of Roosevelt

1:08:48.564 --> 1:08:52.894
announcing the Social Security
program and this lady behind him

1:08:52.886 --> 1:08:57.536
is Frances Perkins,
the first woman to ever be in

1:08:57.539 --> 1:09:01.639
the Cabinet,
and she played a tremendous

1:09:01.639 --> 1:09:04.889
role in shaping Social Security.

1:09:04.890 --> 1:09:09.090
So after Roosevelt started
Social Security in 2004--I'm

1:09:09.090 --> 1:09:12.750
wondering whether I really have
time to do this,

1:09:12.747 --> 1:09:14.767
so I'll just say this.

1:09:14.770 --> 1:09:21.250
So Roosevelt started the
program in 1938-'39.

1:09:21.250 --> 1:09:23.950
He started the program in
'38-'39.

1:09:23.948 --> 1:09:28.138
It was one of the cornerstones
of the New Deal.

1:09:28.140 --> 1:09:31.000
It's an incredibly famous
program and it seems to be in

1:09:30.997 --> 1:09:32.107
incredible trouble.

1:09:32.109 --> 1:09:35.299
So we need to find out and get
to the bottom of why that is and

1:09:35.297 --> 1:09:37.147
we'll start doing that next
class.

1:09:37.149 --> 1:09:41.999