WEBVTT

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All right, so last time we
began, or maybe two times ago,

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we began a discussion of
various vocabulary and facts you

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have to know about the markets
if you want to think about

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finance.

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Today we're going to deal
mostly with the most important

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one, the most basic one,
the yield curve.

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And last time,
we introduced this word,

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"yield."

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Now, yield is an extremely
common expression in finance,

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and it turns out not to be that
well defined,

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often, or that useful.

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But the word is so important
and has been used so often that

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it still hangs around,
even when probably we should

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use different concepts.

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So remember the yield was an
attempt to look at an

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investment,
and without paying any

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attention to the market or
anything outside the investment,

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just looking at the investment
itself,

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try to assess,
give a number,

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quantifying how attractive the
investment was.

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So we said you could apply that
to a bond--it has cash flows.

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You could apply it to a hedge
fund that's taking in money and

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paying out money,
and the formula we came up with

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said that if the cash flows are
given by C(1),

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C(2), the net cash flows,
C(T) over the course of the

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period,
and its price is some P(0),

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maybe it's a negative cash
flow,

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so C(0).

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So some of these cash flows
might be negative and some of

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them might be positive,
then we should just look at the

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number Y,
such that discounting all these

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things at rate Y gives you 0.

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The Y that did that was what we
defined as the yield of the

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investment.

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So we saw that that had some
advantages.

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For example,
in a hedge fund,

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if you just look at the rate of
return it makes on its money

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every year,
that doesn't take into account

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that in some years,
it's got a lot more money.

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So if those were the years that
lost money,

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and the years when it hardly
had any money were the years it

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made money,
just taking the average,

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the multiplicative average,
the geometric average of all

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those yearly rates of returns,
would give a misleading figure.

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Well, the yield also gives a
somewhat misleading figure,

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and I don't want to spend too
much time on why it might be

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misleading,
but I'll give you just an

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example.

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Suppose that the cash flows
happen to be 1,

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-4, and 3.

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Now what's the yield to
maturity?

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Well, there are two of them.

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You could have Y = 0,
because 1 over (1 0),

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- 4 over (1 0),
3 over (1 0),

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is just 1 - 4 3.

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That equals 0,
so the yield to maturity of 0

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percent, the yield of 0 percent,
makes this have present value

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0.

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But also I could try Y = 200
percent,

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and then I'd have Y--I'd put a
2 and a 2 squared here,

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and I'd have 1 - 4 thirds 1
over 3 squared is 3 over 9,

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so it's 1 third.

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So it would be 1 minus 4
thirds, plus 1 third,

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which also equals 0.

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So is the yield to maturity,
the internal rate of return 0

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percent or 200 percent?

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It's ambiguous.

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So yield to maturity can't be
the right way of doing things.

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To go back to the hedge fund
example,

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you know, the hedge fund was
taking in money,

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paying out money,
taking in more money,

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paying out money,
and we calculated the yield to

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maturity.

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Well suppose that there was
some period,

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you know, here,
at which point everyone had

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taken all their money out,
so the hedge fund wasn't

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actually doing anything for a
bunch of years,

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maybe for a long time,
and then it started up and took

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money in and paid money out and
stuff.

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Well, because the gap in time
was very long with nothing

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happening,
if you take a positive Y,

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the stuff that happens in the
second incarnation of the fund

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is hardly going to be making any
difference,

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because by that time,
it will all be discounted a

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lot.

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So the yield will depend too
sensitively on stuff early

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rather than stuff late.

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And so again,
you get into troubles yielding

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just yield to maturity,
so that can't be the right

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thing to do,
even though people have done it

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for years.

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So the word,
however, lives on,

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and there's no getting rid of
the word because it's used in

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common vocabulary.

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Now what would Irving Fisher
say you should do,

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if you had to summarize how
good an investment was?

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What's his lesson?

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What do you do?

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An investment where there's no
doubt about what the cash flows

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are going to be,
what would he say you should

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do, to evaluate the
attractiveness of it?

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What's our lesson,
our main lesson from Irving

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Fisher?

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What would he say?

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Yes.

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Student:
>

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like to check?

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Prof: Well,
let's say they're cash flows,

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so it's money,
money that you're going to get

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coming in and out,
yeah, he'd say,

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deflate by inflation and turn
them into real flows and then do

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what?

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So just continue your answer.

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So turn them into actual
potatoes every time,

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apples each time.

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Deflate by inflation and then
do what with the numbers?

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This is a simple question.

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You're thinking too hard.

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Yes?

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Student:
Compare the present value.

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Prof: Okay,
he'd say, "Just look at

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the present value of all these
things."

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So of course,
to do that, you'd have to know,

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what is the market rate of
interest with which to compute

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the present value?

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So Fisher would say,
"It's ridiculous to

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evaluate how good an investment
opportunity is just by looking

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at the cash flows.

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You're throwing away too much
information."

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You know what the market is
doing, you know what the

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interest rates are.

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Use the market interest rates
and figure out what the present

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value of all the cash flows is.

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So we're going to now do that a
bunch of times,

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okay, for the rest of the
class, and see what that means.

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So we have to begin,
the two thirds of the class is

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going to be spent on the
question, how do you know what

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the market rates of interest
are?

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So how do you know what the
market rates of interest are?

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How could you find out what the
market rate of interest is?

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What would you do to find it
out?

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Yeah.

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Student:
You could go to a bank and see

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what they were estimating it to
be.

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Prof: And if you looked
in the newspaper,

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say, could you find it in the
newspapers?

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What would you find in the
newspapers?

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Yes?

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Student:
You'd want to find a riskless

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investment, say like a T-bill.

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Prof: Okay,
and so yes, you try and look at

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riskless investments like
government bonds,

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where there can't be any
default--at least,

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that's what they always used to
say--

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can't be any default on an
American promise.

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America's government never
broke a promise and they can

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always print the money,
so presumably they don't have

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to break a promise--
so they're just promising money

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which they can print,
so why should they ever break

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their promise--
so what would you find if you

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opened a newspaper?

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You would find,
for different maturities--

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it used to be up to 30
years--for different maturities,

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you would find the yield on the
various bonds,

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okay?

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So why would you find the yield?

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Well, the yield of various
government bonds,

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of gov.

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bonds.

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Why do they quote the yield?

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Well, that's just because,
you know,

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a hundred years ago,
people started using the idea

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of yield and so the vocabulary
has been kept,

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even though it's not the best
way of describing what's going

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on.

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So for instance,
let's just look at some of the

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yield curves you might have seen
over the last 9 years,

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almost 10 years,
since December 2000.

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You would see that in December
2000, the yield on the 1-year

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bonds, you know,
the short yields--this isn't a

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log scale, so this is 3,6,
12, okay.

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So the shortest bonds usually
have lower yields than the

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highest bonds,
but sometimes,

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like in December 2000,
the yields are almost all the

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same.

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It's called the flat yield
curve.

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Other times,
like now, we're in this light

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blue one here,
right now the short bonds have

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very small yields and the long
bonds have much higher yields,

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so the last one is the 30-year
bond.

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So you get the yield on every
single bond.

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Now what do you notice about
this picture,

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by the way?

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They can be very different at
different time periods,

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so in December 2000,
the interest rates were really

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high.

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The yields were 6 percent.

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I'm talking yields so far.

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We haven't talked about
interest rates.

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We have to figure out what the
interest rates are,

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but anyway, they're obviously
going to be connected.

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So the yields were very high in
December 2000,

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and they got much lower in
December 2008,

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and they've stayed very low.

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So why are they so low now?

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What got them to be so low now?

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Yeah?

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Student:
The Fed flooded the economy

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with money.

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Prof: The Fed flooded
the economy with money.

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It wanted to drive the interest
rates down to 0.

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So we're going to see very soon
why the Fed might have wanted to

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do that, but these money rates
don't move totally on their own.

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They have to do,
and we said that Irving

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Fisher--
we haven't described Irving

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Fisher's theory of money and
nominal interest rates--

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but somehow,
the Fed is controlling the

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nominal interest rates and it's
changed the yield curve.

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So you notice that the yield
curve now, December 2008,

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was this blue one.

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So the Fed, in the crisis of
2008, you know,

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was terrified,
and it dropped the interest

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rate almost to 0,
virtually 0,

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and it's kept it there,
because from December 2008 till

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now,
we're at October 2009,

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September 30^(th),
2009, a long time has passed

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from this dark blue to the light
blue line,

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and the rate has been kept
fixed there.

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But in the intervening time,
the long rates have started to

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go way up.

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Now why might that be the case?

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What does that suggest to
anybody?

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Does anybody know?

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Yeah?

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Student:
>

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Prof: That could be one
reason, and could there be

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another reason?

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Yeah?

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Student:
Future expected inflation.

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Prof: Okay,
so those are the two reasons.

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So they somehow know that,
and some of you have no idea

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how they could possibly be
thinking that.

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And so I'm going to explain,
what information is there in

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the different yield curves.

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Okay, so the point is that
every morning,

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every single financial analyst
wakes up and sees these yield

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curves,
you know, consults the market

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and sees where things are
trading,

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and can produce a yield curve
like that.

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Okay, so you've got a bunch of
yields.

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Now what are the yields?

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Well, let's just do an example
here.

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So I'm going to make up an
example, which is very easy to

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compute.

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So let's try this one.

11:47.038 --> 11:52.288
Okay, so I'm reading here at
the top, let's just say that

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you've got a bunch of different
bonds.

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A 1-year bond,
a 2-year bond,

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a 3-year bond,
a 4-year bond and a 5-year

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bond.

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Now each of the bonds was
issued--I'm assuming here that

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they were all issued on the same
day.

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So they're issued with
different coupons.

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Let's say they were all issued
today.

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We'll come back at the end.

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Obviously the Treasury doesn't
issue new bonds every single

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day, so how does this change
when you arrive on a day when

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they haven't issued things?

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But let's just keep it simple
and suppose that today,

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the Treasury has issued 5
different bonds over these 5

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different years.

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Now the Treasury has to set
what do they do?

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They decide how much of these
bonds they're going to sell and

12:40.480 --> 12:43.160
they decide what coupon they're
going to set.

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They set the coupon.

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So let's say the coupon they
set was 1 dollar for the 1-year

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bond,
2 dollars for the 2-year bond,

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3 dollars for 3 three-year
bond,

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4 for the 4-year bond,
5 for the 5-year bond.

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It's easy to remember,
that's why I chose those

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numbers.

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And the face value,
let's say, is always 100.

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So why did they set those
coupons?

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Well, because given how much
they want to sell,

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they're picking the coupon,
hoping that the price turns out

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to be close to the face value.

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So let's say,
when they actually market

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these,
and supply equals demand in

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equilibrium,
the prices turn out to be

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100.1,100.2,
100.3,100.4, and 100.5.

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So 100.5 is the price the
market's paying for the 5 year

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bond and if the coupon is 5,
and they pay coupons once a

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year--they may pay twice a year,
but let's say they pay once a

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year for simplicity,
you're going to get 5,5,

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5,5, and 105 the last year.

13:40.658 --> 13:44.528
If you bought the four-year
coupon bond, you get 4,4,

13:44.530 --> 13:46.690
4,104 the last year,
right?

13:46.690 --> 13:51.160
So those are the bonds.

13:51.158 --> 13:53.248
Now the newspaper's not telling
you any of that,

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so you're sort of losing that
information,

13:55.558 --> 13:59.428
so you don't actually know that
from reading the newspaper.

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So then, what do you know?

14:01.580 --> 14:10.200
You know that--you know the
yields on all these things,

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okay?

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So here, this tells you the
yield on each of these bonds.

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Going back to where I was.

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Okay, knowing the yield,
you could figure out what the

14:28.041 --> 14:31.551
price of each of the bonds is,
or in fact, the way that they

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calculated the yield that the
newspapers reported.

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How did the newspapers get the
yield?

14:36.320 --> 14:40.730
The newspapers said,
well, for the 4 year bond,

14:40.730 --> 14:53.080
we're going to say that 100.4 =
4 divided by (1 the 4 year

14:53.081 --> 15:02.681
coupon bond yield),
4 over (1 Y (4)) squared,

15:02.681 --> 15:13.381
plus 4 over (1 Y (4)) cubed,
plus 104 over (1 Y (4)) to the

15:13.381 --> 15:14.691
fourth.

15:14.690 --> 15:18.530
In this case,
because these numbers are all

15:18.532 --> 15:21.282
positive,
it's monotonic in Y (4),

15:21.275 --> 15:25.115
so there's a unique Y (4) which
you can use to solve this

15:25.118 --> 15:29.248
equation,
price = the discounted value at

15:29.245 --> 15:32.165
that yield of the payments.

15:32.168 --> 15:34.368
So that's how the newspapers,
the reporter,

15:34.365 --> 15:37.395
that's how he got all the
yields to show you that graph.

15:37.399 --> 15:39.849
He looked at the market,
or could call the bank or

15:39.852 --> 15:41.962
something like that,
had a computer screen,

15:41.956 --> 15:44.006
talked to his friends on Wall
Street.

15:44.009 --> 15:46.779
He knew the price of all the
bonds, he knew the coupons of

15:46.780 --> 15:48.920
all the bonds,
and then he produced the yield

15:48.919 --> 15:49.989
for all the bonds.

15:49.990 --> 15:52.720
So the yield,
as I say, that's the word that

15:52.717 --> 15:55.147
everybody uses,
but really, the information

15:55.147 --> 15:57.147
that you want to deal with is
the price,

15:57.149 --> 15:59.389
and what did the coupon
actually pay?

15:59.389 --> 16:00.499
Okay, so that's what you know.

16:00.500 --> 16:03.560
Everybody knows this every day,
the information I have given.

16:03.558 --> 16:05.768
Every morning,
maybe every few hours,

16:05.768 --> 16:07.238
people will update it.

16:07.240 --> 16:10.820
They'll look at what are the
coupon bonds paying and what are

16:10.815 --> 16:11.585
the prices?

16:11.590 --> 16:14.460
The thing that's changing from
hour to hour are the prices,

16:14.461 --> 16:17.331
but we're taking a snapshot at
the beginning of the day and

16:17.331 --> 16:18.621
looking at the prices.

16:18.620 --> 16:24.660
So now we've got prices of
bonds, which I'm going to call

16:24.655 --> 16:28.425
capital Pis, Pi (1),
Pi (2), Pi (3),

16:28.427 --> 16:30.797
Pi (4) and Pi (5).

16:30.798 --> 16:32.668
But now, what does Fisher say
you should do?

16:32.668 --> 16:34.698
What's the most important thing
to do?

16:34.700 --> 16:37.860
The most important thing to do
is find the interest rates.

16:37.860 --> 16:40.110
So what has this got to do with
interest rates?

16:40.110 --> 16:44.160
Well, if you modernize Fisher a
little bit,

16:44.158 --> 16:47.738
the most important thing--he
didn't put it this way,

16:47.740 --> 16:49.970
but this is really what he must
have meant--

16:49.970 --> 16:56.620
the most important thing to do
is find the prices of the zeros.

16:56.620 --> 17:02.550
So [little]
pi (1) is today's money price,

17:02.549 --> 17:09.059
today's money price for 1
dollar at time 1.

17:09.058 --> 17:14.868
pi (2) is today's money price
for 1 dollar at time 2.

17:14.868 --> 17:24.388
pi (3), today's money price at
time 3, and pi (5) is today's

17:24.394 --> 17:28.274
money price at time 5.

17:28.269 --> 17:31.429
Okay, now why do you want to
find these things?

17:31.430 --> 17:34.360
Because once you know these
things, you'd be able to value

17:34.356 --> 17:35.226
any investment.

17:35.230 --> 17:40.690
That original investment that
we talked about,

17:40.691 --> 17:45.061
which maybe disappeared,
this one.

17:45.059 --> 17:45.719
It disappeared.

17:45.720 --> 17:50.610
Anyway, once you have all the
pis, if anybody tells you,

17:50.608 --> 17:54.788
if a hedge fund tells you,
"This is the revenue I'm

17:54.787 --> 17:58.807
going to produce for you in the
next five years,"

17:58.813 --> 18:02.143
if a company says,
"This is our business plan.

18:02.140 --> 18:04.980
We're going to build a factory
today that's going come out a

18:04.983 --> 18:07.683
certain amount of money and
we're going to get profits in

18:07.683 --> 18:10.323
the next five years,
blah, blah, blah."

18:10.318 --> 18:13.868
If a new bond comes on the
market and you don't know how to

18:13.867 --> 18:16.557
price it, and somebody offers a
price for it,

18:16.559 --> 18:19.129
how do you figure out what it's
worth?

18:19.130 --> 18:22.980
All you do is you take the cash
flows, the Cs that I not very

18:22.983 --> 18:25.753
cleverly erased,
you take the cash flows and

18:25.746 --> 18:27.606
multiply them by the pis.

18:27.608 --> 18:33.698
So the correct price P is just
whatever the cash flows you're

18:33.698 --> 18:39.888
predicting times these pis that
Fisher says is what you should

18:39.886 --> 18:42.116
really be finding.

18:42.119 --> 18:43.559
So nothing could be simpler.

18:43.559 --> 18:45.529
Now why is this the right price?

18:45.529 --> 18:49.649
Because if you can go in the
market and buy 1 dollar at time

18:49.652 --> 18:52.362
1 for pi of 1,
and 1 dollar at time 2 for pi

18:52.362 --> 18:54.712
of 2,
etc., you can buy all the cash

18:54.708 --> 18:58.468
flows from this investment
project by spending this amount

18:58.468 --> 18:59.258
of money.

18:59.259 --> 19:02.589
So if the guy is offering you
the investment opportunity at a

19:02.590 --> 19:04.590
higher price,
it's crazy to do it.

19:04.588 --> 19:07.168
You could have bought those
cash flows yourself by paying

19:07.170 --> 19:07.770
this price.

19:07.769 --> 19:10.339
If he offers it to you at a
lower price than that,

19:10.338 --> 19:17.218
then definitely you should do
it, because it's a bargain,

19:17.220 --> 19:18.360
because if you had to buy it
yourself,

19:18.359 --> 19:19.309
it would be more expensive.

19:19.308 --> 19:21.508
In fact, you can make an
arbitrage profit.

19:21.509 --> 19:25.239
If he's offering it to you at a
lower price, you can buy it and

19:25.237 --> 19:26.437
how do you buy it?

19:26.440 --> 19:29.980
By selling these very promises,
C(1), C(2), C(T) on the market,

19:29.983 --> 19:33.473
and if people believe you that
you'll pay, you can sell it for

19:33.471 --> 19:34.331
this price.

19:34.328 --> 19:36.868
So you buy his project for a
lower price.

19:36.869 --> 19:39.009
You sell it for a higher price.

19:39.009 --> 19:41.519
You make the difference,
and when it comes time to keep

19:41.519 --> 19:43.619
your promises,
the project is giving you the

19:43.615 --> 19:46.175
cash to keep your promises,
so you lock in a profit for

19:46.180 --> 19:46.460
sure.

19:46.460 --> 19:49.170
So if you knew the pis,
you would know for sure how to

19:49.174 --> 19:52.254
value any project where you knew
for sure the cash flows,

19:52.250 --> 19:54.700
knowing the pis would tell you
how to value it,

19:54.700 --> 19:56.970
and would tell you whether it
was attractive or not

19:56.969 --> 19:57.559
attractive.

19:57.558 --> 20:00.428
You just look at how high the
present value is.

20:00.430 --> 20:04.090
Okay, any questions about that?

20:04.088 --> 20:08.748
So we just need to figure out
how to deduce what the little

20:08.750 --> 20:13.090
pis are from the data that we're
going to be given,

20:13.088 --> 20:19.418
and that we are given every day
by the market.

20:19.420 --> 20:25.160
Okay, so I said literally pi
(1) is the price you would pay

20:25.155 --> 20:28.415
today to buy 1 dollar tomorrow.

20:28.420 --> 20:31.900
Now how could you go about
buying 1 dollar tomorrow,

20:31.900 --> 20:34.950
given that the only things you
can trade on the market are

20:34.946 --> 20:37.776
these Treasury bonds,
these government bonds?

20:37.779 --> 20:40.659
And I've told you what they pay
off and I've told you what their

20:40.663 --> 20:41.263
prices are.

20:41.259 --> 20:45.959
So how would you go and buy 1
dollar tomorrow and how much

20:45.961 --> 20:49.261
would it cost you,
1 dollar next year?

20:49.259 --> 20:54.819
How would you do that?

20:54.818 --> 20:56.508
You can trade,
buy or sell any of these

20:56.505 --> 20:57.255
Treasury bonds.

20:57.259 --> 21:01.209
So in the background,
I keep saying that we're going

21:01.214 --> 21:04.554
to have to worry about people
defaulting.

21:04.549 --> 21:05.599
We're not quite doing it yet.

21:05.598 --> 21:08.478
So buying a Treasury bond,
you need the cash to buy it.

21:08.480 --> 21:12.030
Selling a Treasury bond means
you promise to deliver what the

21:12.029 --> 21:15.169
Treasury bond promises,
and your promise is as good as

21:15.166 --> 21:16.406
the government's.

21:16.410 --> 21:19.540
So if you sell it to somebody,
they'll pay you the same

21:19.535 --> 21:21.035
government price for it.

21:21.038 --> 21:23.168
So obviously in the background,
you're going to have to do

21:23.171 --> 21:25.301
something to convince the guy
you're making the promise to

21:25.301 --> 21:26.911
that you're going to keep your
promise.

21:26.910 --> 21:28.580
So we're going to worry about
that later.

21:28.578 --> 21:33.508
So for now, when I say that the
market for those Treasury bonds

21:33.510 --> 21:37.280
clears at those levels,
I mean that anybody who wants

21:37.276 --> 21:39.846
to can buy Treasury bonds at
those levels,

21:39.848 --> 21:42.848
or can sell them,
even if he doesn't have them,

21:42.848 --> 21:45.198
at those prices,
by making the promise of what

21:45.195 --> 21:46.495
the Treasury bond does.

21:46.500 --> 21:48.580
Because we're assuming that the
government and you,

21:48.576 --> 21:50.896
everybody is just as reliable,
everybody is going to keep

21:50.902 --> 21:51.652
their promise.

21:51.650 --> 21:53.470
So whether it's the Treasury
making the promise,

21:53.474 --> 21:55.034
or you making the promise,
same thing.

21:55.029 --> 21:59.609
Okay, so how do you buy 1
dollar next year?

21:59.608 --> 22:08.378
What would you do in the market
with the Treasury bonds to get 1

22:08.375 --> 22:11.015
dollar next year?

22:11.019 --> 22:13.779
Yeah?

22:13.778 --> 22:16.438
Student:
Can we just plug in 1 for our P

22:16.439 --> 22:19.729
in the bond prices and then
figure out which bond you want

22:19.733 --> 22:20.663
to purchase?

22:20.660 --> 22:22.540
Prof: Well,
you're supposed to be telling

22:22.538 --> 22:22.738
me.

22:22.740 --> 22:23.460
What do you want to do?

22:23.460 --> 22:25.160
I want to know exactly what to
do.

22:25.160 --> 22:26.340
You can look at these numbers.

22:26.338 --> 22:27.808
By the way, are you all
following these?

22:27.809 --> 22:29.819
Maybe this is mysterious.

22:29.818 --> 22:34.958
There's a 1-year Treasury bond
that pays 101 dollars next year.

22:34.960 --> 22:38.450
The 2-year Treasury bond pays 2
dollars next year,

22:38.454 --> 22:39.244
then 102.

22:39.240 --> 22:42.510
The 3-year Treasury bond pays 3
dollars at the end of the first

22:42.507 --> 22:45.617
year, 3 at the end of the second
year, 103 at the end of the

22:45.615 --> 22:46.665
third year, etc.

22:46.670 --> 22:49.460
And the 1 year Treasury bond
happens to be selling at this

22:49.463 --> 22:52.263
price, the 2-year happens to be
selling for that price.

22:52.259 --> 22:59.029
So what can I do with all these
bonds to buy 1 dollar next year?

22:59.029 --> 23:00.859
All right, go ahead,
you've started.

23:00.858 --> 23:02.058
Student:
Buy a 2-year bond.

23:02.059 --> 23:03.109
Prof: A 2-year bond?

23:03.108 --> 23:06.248
It's next year,
one year from now.

23:06.250 --> 23:09.400
Student:
You could just divide the price

23:09.402 --> 23:12.762
of the 1-year bond by
>

23:12.759 --> 23:14.449
Prof: You're a step
ahead of me.

23:14.450 --> 23:17.440
I'm saying, what do you
do--never mind how much does it

23:17.442 --> 23:17.832
cost?

23:17.828 --> 23:22.188
What do you do today to get 1
dollar next year?

23:22.190 --> 23:25.960
What transaction can you make
today, what purchase can you

23:25.961 --> 23:29.141
make today to get yourself 1
dollar next year?

23:29.140 --> 23:29.930
Yes?

23:29.930 --> 23:33.570
Student:
Just buy a 1-year bond.

23:33.569 --> 23:35.719
Prof: Buy a 1-year bond.

23:35.720 --> 23:39.060
Well, that will give me 101
dollars next year.

23:39.059 --> 23:41.379
I want 1 dollar next year.

23:41.380 --> 23:43.130
Student:
Take that fraction

23:43.134 --> 23:44.574
>

23:44.568 --> 23:47.558
Prof: Okay,
well, that's exactly the point.

23:47.559 --> 23:48.709
I take that fraction.

23:48.710 --> 23:51.380
That's what I wanted you to
tell me.

23:51.380 --> 24:03.230
So little pi (1) is going to be
(1 over 101) times the price of

24:03.231 --> 24:11.641
the one-year bond,
because the 1-year bond is

24:11.643 --> 24:16.043
paying 101 dollars.

24:16.038 --> 24:19.978
So you take 1/101 of it,
you'll get 1 dollar.

24:19.980 --> 24:22.090
And whatever the price of the
1-year bond is--actually,

24:22.089 --> 24:22.989
we know what that is.

24:22.990 --> 24:28.210
It's 100.1, that's how much it
costs.

24:28.210 --> 24:30.300
To buy 1 of them cost 100.1.

24:30.298 --> 24:35.848
To get 1 over 101 of them costs
pi (1).

24:35.848 --> 24:42.448
Okay, so this number,
by the way, is some number

24:42.450 --> 24:49.050
which, actually,
I of course worked out here.

24:49.048 --> 24:53.858
Happens to be .991,
but we'll come back to that.

24:53.859 --> 24:57.719
So it happens to be point 991.

24:57.720 --> 24:59.220
So now we know pi (1).

24:59.220 --> 25:12.100
Well, how would you buy 1
dollar in year 2?

25:12.098 --> 25:16.938
So there's a way of directly
buying 1 dollar in year 2,

25:16.936 --> 25:20.606
once you know how the
Treasuries trade.

25:20.608 --> 25:27.758
So what I'm doing is I'm
explaining the idea of

25:27.756 --> 25:31.326
replication, pricing.

25:31.328 --> 25:34.858
It's giving me pricing and it's
going to lead to arbitrage.

25:34.858 --> 25:38.428
They're all basically similar
ideas here.

25:38.430 --> 25:44.310
So what I want to do is
directly buy 1 dollar in year 2.

25:44.308 --> 25:47.128
So I could probably go to a
bank and they would actually

25:47.127 --> 25:48.407
make that trade for me.

25:48.410 --> 25:50.080
I could just call up the bank
and say,

25:50.078 --> 25:52.618
"I want 1 dollar in year
2," and they'd tell me,

25:52.618 --> 25:54.408
pi (2), how much I have to pay
for it.

25:54.410 --> 25:58.520
But how are they going to
figure out what it's worth?

25:58.519 --> 26:02.089
They're going to see
how--they're going to go out and

26:02.085 --> 26:04.275
have to buy the dollar for me.

26:04.278 --> 26:07.098
So they're going to go out and
go to the Treasury market.

26:07.098 --> 26:09.998
And what are they going to do
in the Treasury market to come

26:10.002 --> 26:11.482
up with my dollar in year 2?

26:11.480 --> 26:14.930
They're going to replicate my
purchase of 1 dollar with a more

26:14.932 --> 26:17.992
complicated portfolio that they
can actually trade,

26:17.990 --> 26:21.080
and that's how they're going to
figure out how to price my

26:21.079 --> 26:22.869
request for 1 dollar in year 2.

26:22.868 --> 26:29.328
So what is this bank going to
do in the Treasury market?

26:29.328 --> 26:38.678
What does it have to do to get
1 dollar for sure in year two,

26:38.679 --> 26:41.639
and nothing else?

26:41.640 --> 26:42.740
Okay?

26:42.740 --> 26:46.050
Student:
Do they buy a 2-year bond and

26:46.049 --> 26:47.629
sell a 1-year bond?

26:47.630 --> 26:49.490
Prof: Okay,
so what are they going to do?

26:49.490 --> 26:52.190
How much of the two-year bonds
should they buy?

26:52.190 --> 27:02.720
Student:
What they're going to sell is

27:02.722 --> 27:04.162
a...

27:04.160 --> 27:05.110
Prof: The 2 year bond.

27:05.108 --> 27:07.898
You're talking about the 2-year
bond, so how much of the 2-year

27:07.895 --> 27:09.195
bond are they going to buy?

27:09.200 --> 27:10.180
Student: 1/102.

27:10.180 --> 27:12.670
Prof: 1/102, right.

27:12.670 --> 27:13.420
That's very good.

27:13.420 --> 27:14.170
Why is that?

27:14.170 --> 27:17.200
Because in year 2,
we're talking about year 2 now,

27:17.202 --> 27:19.372
year 2, the 2-year bond pays
102.

27:19.368 --> 27:25.848
You get 1 over 102 of those,
you've got 1 dollar in year 2,

27:25.846 --> 27:28.076
so that's Pi of 2.

27:28.079 --> 27:33.219
Which happens to be 100.2.

27:33.220 --> 27:35.590
That's how much that costs.

27:35.588 --> 27:37.068
Okay, but is that all you need
to do?

27:37.069 --> 27:37.979
Is that it?

27:37.980 --> 27:42.710
Are you paying the right amount
or are you paying too much,

27:42.711 --> 27:44.671
or what are you doing?

27:44.670 --> 27:46.060
You've got to do more than just
that.

27:46.059 --> 27:47.729
Why is that?

27:47.730 --> 27:48.750
Yeah.

27:48.750 --> 27:55.010
Student:
When you subtract 2 times the

27:55.009 --> 27:58.849
>

27:58.848 --> 28:00.598
Prof: Close,
but not quite.

28:00.599 --> 28:04.289
Okay, so do your reasoning.

28:04.288 --> 28:08.508
You told me what else to do,
which you slightly mis-said.

28:08.509 --> 28:10.919
So why do you have to do
anything at all?

28:10.920 --> 28:13.820
Tell me the reason why you want
to do something else.

28:13.818 --> 28:16.458
You're on the right track,
you just slipped up a little

28:16.464 --> 28:16.764
bit.

28:16.759 --> 28:20.009
So why not just stop here?

28:20.009 --> 28:23.009
Student:
Because you're also getting 2

28:23.013 --> 28:24.383
dollars in year 1.

28:24.380 --> 28:26.820
Prof: Exactly,
that's exactly right.

28:26.818 --> 28:31.368
By buying the 2-year Treasury,
you got 102 in period--

28:31.368 --> 28:33.428
by buying this fraction of the
2 year,

28:33.430 --> 28:36.640
you got just what you want in
period 2,

28:36.640 --> 28:40.480
but you also purchased the
coupon in period 1,

28:40.480 --> 28:41.880
which you don't need.

28:41.880 --> 28:44.550
So that's giving you more than
you needed to buy.

28:44.548 --> 28:48.388
You've bought extra,
so you're going to actually be

28:48.394 --> 28:50.624
able--
the cost of getting the dollar

28:50.617 --> 28:54.047
at the end of year 2 is a little
bit less than what we've written

28:54.049 --> 28:55.739
so far,
because you bought more.

28:55.740 --> 28:57.430
So far, this is buying too much.

28:57.430 --> 28:58.800
You bought the dollar in year 2.

28:58.798 --> 29:00.948
You also bought a little bit in
year 1.

29:00.950 --> 29:04.540
You can now sell off the extra
stuff you've gotten in year one

29:04.540 --> 29:06.720
to reduce your cost of buying
that.

29:06.720 --> 29:08.500
So what should you do in year
one?

29:08.500 --> 29:11.290
That's exactly what you were
thinking.

29:11.288 --> 29:12.608
You just didn't quite say it
right.

29:12.609 --> 29:14.379
So what should you do in year 1?

29:14.380 --> 29:20.850
Student:
>

29:20.849 --> 29:23.079
Prof: I sell that.

29:23.079 --> 29:26.379
Okay, I sell.

29:26.380 --> 29:32.200
Okay, so I can get to sell 2 of
little pi of 1,

29:32.198 --> 29:33.208
right?

29:33.210 --> 29:36.830
Because I know how much it
costs me to buy 1 dollar at time

29:36.829 --> 29:37.329
1 now.

29:37.328 --> 29:40.088
It's that number,
so I'm getting-- so is that

29:40.094 --> 29:42.234
correct, what I've written here?

29:42.230 --> 29:42.930
That's what you said.

29:42.930 --> 29:43.880
That's not quite right.

29:43.880 --> 29:45.080
Yeah.

29:45.078 --> 29:48.888
Student:
If you didn't actually buy 2

29:48.887 --> 29:51.277
>

29:51.279 --> 29:54.229
Prof: Okay,
so this is what he meant to

29:54.234 --> 29:54.634
say.

29:54.630 --> 29:55.390
So that's fine.

29:55.390 --> 29:58.300
Okay, so that's what you do,
exactly.

29:58.299 --> 29:59.239
So everybody's following?

29:59.240 --> 30:01.720
You agree with me now, right?

30:01.720 --> 30:04.250
But, you know,
we could plug in for this too,

30:04.250 --> 30:05.000
by the way.

30:05.000 --> 30:07.570
So pi of 1, we know what that
is.

30:07.568 --> 30:09.898
Okay, so does everybody see
what's going on here?

30:09.900 --> 30:13.870
To buy 1 dollar at time 2,
you don't get the whole 2-year

30:13.865 --> 30:17.125
Treasury, you buy 1/102 of the 2
year Treasury,

30:17.125 --> 30:20.025
so it costs you that amount of
money.

30:20.028 --> 30:22.658
But that gives you a little bit
of extra at time 1.

30:22.660 --> 30:24.260
How much extra does it give you?

30:24.259 --> 30:28.139
Well, you've got 2 dollars
extra for every 2-year Treasury,

30:28.144 --> 30:31.164
but you didn't buy a whole
2-year Treasury.

30:31.160 --> 30:32.760
You bought that fraction of it.

30:32.759 --> 30:36.189
So it gives you this much extra
which you now get to sell off,

30:36.190 --> 30:38.720
so you're going to sell it off
for this price,

30:38.721 --> 30:39.341
pi (1).

30:39.338 --> 30:43.938
And of course,
we can plug in for pi (1),

30:43.942 --> 30:50.042
by putting 101 down here and
putting 100.1 up here.

30:50.038 --> 30:54.358
Okay, so that was pretty clear,
right?

30:54.359 --> 30:57.549
So now any questions about that?

30:57.548 --> 31:05.758
So that's going to be some
number, which I calculated

31:05.755 --> 31:11.905
again, which happens to be 962,
.962.

31:11.910 --> 31:14.870
So notice, of course,
it's getting cheaper to

31:14.872 --> 31:18.712
buy--how much does it cost to
buy 1 dollar in year one?

31:18.710 --> 31:19.380
It's that.

31:19.380 --> 31:21.390
To buy 1 dollar in year 2,
is less.

31:21.390 --> 31:23.120
Now what about pi (3)?

31:23.119 --> 31:27.369
How would we get pi (3)?

31:27.369 --> 31:28.809
We'll stop at pi (3).

31:28.809 --> 31:30.049
How would we get pi (3)?

31:30.048 --> 31:32.368
Then we're going to find a very
fast way of computing all these

31:32.365 --> 31:32.735
numbers.

31:32.740 --> 31:33.940
What's pi (3)?

31:33.940 --> 31:35.330
How would you get that?

31:35.328 --> 31:37.658
Student:
Buy the 3-year bond,

31:37.663 --> 31:40.203
divided by
>

31:40.200 --> 31:43.700
Prof: So the 3-year bond
costs 100.3 but we don't need

31:43.700 --> 31:44.400
all of it.

31:44.400 --> 31:53.210
We need 1 over 103 units times
that, okay.

31:53.210 --> 31:55.320
So that's our main cost.

31:55.319 --> 31:57.439
But then what else?

31:57.440 --> 32:01.770
Student:
We need to get - 3 times

32:01.765 --> 32:04.755
>

32:04.759 --> 32:10.609
Prof: - 3 over 103,
times little pi of 2.

32:10.608 --> 32:15.088
Right, because we got this
extra stuff that we didn't need.

32:15.088 --> 32:19.328
Student:
- 3 over 103 of little pi of 1,

32:19.329 --> 32:21.819
>

32:21.818 --> 32:25.728
Prof: Okay,
so he's saying - 3 times 103 of

32:25.729 --> 32:29.319
pi of 1, okay,
because we didn't need that.

32:29.319 --> 32:35.869
So is that the right answer?

32:35.869 --> 32:36.929
It's not the right answer.

32:36.930 --> 32:38.460
It's close.

32:38.460 --> 32:39.910
What did he overlook?

32:39.910 --> 32:42.550
So he said, you buy the
three-year bond.

32:42.548 --> 32:45.508
So by buying the three-year
bond, you're getting--if you

32:45.509 --> 32:48.039
bought the whole three-year
bond, you'd get 3,3,

32:48.038 --> 32:48.468
103.

32:48.470 --> 32:51.700
You only want 1 at the end,
so you have to divide by 103.

32:51.700 --> 32:56.800
Now we get 3 over 103,3 over
103,1, and so he's saying we've

32:56.798 --> 32:58.958
got two extra payments.

32:58.960 --> 33:02.450
Let's sell them off.

33:02.450 --> 33:04.820
And so he sold them off like
that.

33:04.819 --> 33:05.789
That's correct.

33:05.788 --> 33:08.498
So he sold them off,
so this one he sold off at pi

33:08.498 --> 33:10.818
(2) and this one he sold off at
pi (1),

33:10.818 --> 33:14.138
so he's making use of the fact
that we've already found out

33:14.144 --> 33:15.754
this price and this price.

33:15.750 --> 33:17.900
But actually,
that's slightly--okay,

33:17.900 --> 33:21.520
but we're talking about not
what you would do talking to the

33:21.523 --> 33:22.203
banker.

33:22.200 --> 33:23.660
We're talking about what the
banker would do,

33:23.660 --> 33:25.220
and he's got to trade in the
Treasury market.

33:25.220 --> 33:27.260
So how's this guy going to do
this?

33:27.259 --> 33:31.789
The banker and the Treasury
market now, this Pi over 2

33:31.786 --> 33:36.136
dollars, he's going to have to
hold this complicated

33:36.142 --> 33:39.732
portfolio--what's he going to do
to--?

33:39.730 --> 33:43.430
He's going to have to combine
the 1 and the 2-year to do this

33:43.430 --> 33:46.330
thing and then the 1-year to
undo that thing.

33:46.328 --> 33:50.048
So it's actually going to
be--so in terms of trading,

33:50.046 --> 33:54.116
if you just had to trade
Treasuries, what would you do?

33:54.119 --> 33:55.529
So this is the correct formula.

33:55.529 --> 33:58.619
That's correct and we can
figure out what that is,

33:58.617 --> 33:59.057
okay.

33:59.058 --> 34:04.118
And so the correct formula is
91.68.

34:04.119 --> 34:08.779
That's .917.

34:08.780 --> 34:12.390
Okay, but you see what you've
done is, these are the kind of

34:12.391 --> 34:15.881
fictitious things that Irving
Fisher has told us to do.

34:15.880 --> 34:17.970
What you're really doing in the
market is trading the

34:17.967 --> 34:18.487
Treasuries.

34:18.489 --> 34:20.359
So here, you've traded a
Treasury.

34:20.360 --> 34:24.250
You've bought 1 over 103 units
of a 3-year Treasury.

34:24.250 --> 34:27.510
Now what else should you do?

34:27.510 --> 34:28.810
You've got to trade Treasuries.

34:28.809 --> 34:33.529
How can you sell off this
amount of money in year 2?

34:33.530 --> 34:36.260
You have to sell some
Treasuries to do that,

34:36.255 --> 34:37.835
so what would you sell?

34:37.840 --> 34:40.240
Student:
The 2-year coupon.

34:40.239 --> 34:48.619
Prof: The 2 year coupon
bond, and so how much of that

34:48.623 --> 34:51.043
would you sell?

34:51.039 --> 34:57.919
Well, this is the amount of
money you have to get.

34:57.920 --> 35:04.520
The 2-year coupon bond delivers
how much money?

35:04.518 --> 35:08.008
It delivers 102,
so if you did 1 over 102,

35:08.005 --> 35:11.995
you would get one,
so you have to divide this by

35:12.000 --> 35:12.680
102.

35:12.679 --> 35:24.939
Okay, and that you multiply by
the price, which is 100.2.

35:24.940 --> 35:28.890
Okay, so there's that term,
right?

35:28.889 --> 35:30.469
So what have we done here?

35:30.469 --> 35:33.139
We've had to sell off this
amount of money.

35:33.139 --> 35:35.259
So how can you sell off this
amount of money?

35:35.260 --> 35:39.120
Well, by selling 1 over 102 2
year Treasuries,

35:39.119 --> 35:40.979
you're selling off 1 dollar,
but you don't want to sell off

35:40.983 --> 35:42.313
1 dollar,
you want to sell off something

35:42.313 --> 35:44.043
smaller than 1 dollar,
so it's that amount.

35:44.039 --> 35:46.469
So you're selling that amount
of 2 year Treasuries.

35:46.469 --> 35:50.709
But now what do you have to do?

35:50.710 --> 35:54.380
Now, you see,
you've bought some 1-year

35:54.384 --> 35:58.644
dollars by getting the 3-year
coupon bond.

35:58.639 --> 36:01.119
But by selling the 2-year
coupon bond,

36:01.119 --> 36:03.349
you've made some promises in
year one,

36:03.349 --> 36:05.639
so you've got to net out all
those things and do the right

36:05.635 --> 36:07.115
thing on the one-year coupon
bond,

36:07.119 --> 36:08.109
right?

36:08.110 --> 36:10.980
So that looks a little
complicated, but you can

36:10.980 --> 36:12.790
obviously do it by algebra.

36:12.789 --> 36:14.959
So everybody following?

36:14.960 --> 36:17.160
You're not following what the
right thing to do is,

36:17.157 --> 36:19.177
but let's just say in words
what we've done.

36:19.179 --> 36:22.149
In words, what we've done is
we've said, there are things you

36:22.148 --> 36:23.878
can actually trade on the
market.

36:23.880 --> 36:24.870
Those are the Treasuries.

36:24.869 --> 36:27.769
Those are our benchmark
securities.

36:27.769 --> 36:32.029
Let's call them benchmarks.

36:32.030 --> 36:35.850
Now what we're interested in is
some other maybe fictitious

36:35.847 --> 36:37.887
securities or new securities.

36:37.889 --> 36:40.779
The price of the zeros,
those are the basic building

36:40.784 --> 36:43.794
blocks that will help us
evaluate the present value of

36:43.791 --> 36:44.871
any investment.

36:44.869 --> 36:48.509
So the reason why we know these
prices is because we can

36:48.514 --> 36:51.504
replicate them by trading only
the benchmarks,

36:51.498 --> 36:53.088
only the Treasuries.

36:53.090 --> 36:56.470
So to get the 1-year zero,
we just buy us the correct

36:56.469 --> 36:58.549
fraction of 1 year Treasuries.

36:58.550 --> 37:01.870
To get the 2-year zero,
we have to buy the correct

37:01.873 --> 37:06.013
fraction of 2 year Treasuries
and sell the correct fraction of

37:06.010 --> 37:09.090
1 year Treasuries,
and that gets us that thing.

37:09.090 --> 37:13.300
So we've replicated the 2-year
zero by a portfolio consisting

37:13.298 --> 37:17.018
of being long the 2 year
Treasury and short the 1-year

37:17.016 --> 37:17.926
Treasury.

37:17.929 --> 37:19.919
Right?

37:19.920 --> 37:24.540
To get the 3-year zero coupon,
we have to buy the 3-year

37:24.541 --> 37:27.431
Treasury,
sell the 2-year Treasury and do

37:27.425 --> 37:30.925
something complicated that we
haven't quite figured out yet

37:30.934 --> 37:34.644
with the 1-year Treasury,
and that will duplicate the 3

37:34.639 --> 37:35.379
year zero.

37:35.380 --> 37:38.420
And then we'll just add up the
cost of that portfolio that

37:38.420 --> 37:40.820
replicates this,
and that must be the price of

37:40.820 --> 37:41.940
that thing, okay?

37:41.940 --> 37:43.170
So that's what we're doing.

37:43.170 --> 37:46.530
Any questions about that?

37:46.530 --> 37:49.100
Are you following this?

37:49.099 --> 37:50.469
Yes?

37:50.469 --> 37:53.079
Student:
Just to clarify,

37:53.079 --> 37:58.049
so pi of 1 is today's price for
1 dollar at time 2 or...?

37:58.050 --> 37:59.650
Prof: Time 1.

37:59.650 --> 38:04.100
Today is 0, so pi of 1 is what
you pay at time 0 to get 1

38:04.099 --> 38:05.609
dollar at time 1.

38:05.610 --> 38:10.290
pi of 2 is what you pay today
at time 0 to get 1 dollar at

38:10.288 --> 38:11.518
time 2, okay?

38:11.518 --> 38:15.798
So knowing those little pis,
you can evaluate the price of

38:15.802 --> 38:20.392
anything, just by multiplying
the little pis by the cash flows

38:20.387 --> 38:21.737
in the future.

38:21.739 --> 38:24.259
And now the trick--this is the
trick we're going to see over

38:24.264 --> 38:26.744
and over and over again--
the subtlety in finance is that

38:26.739 --> 38:28.869
they don't just tell you what
the little pis are.

38:28.869 --> 38:31.569
You have to figure that out
yourself, okay?

38:31.570 --> 38:33.830
And so how are you going to
figure out the little pis?

38:33.829 --> 38:36.639
Well, you know the Treasuries.

38:36.639 --> 38:38.619
You can trade the Treasuries,
and you know what those prices

38:38.617 --> 38:38.817
are.

38:38.820 --> 38:40.160
You can see it on the market.

38:40.159 --> 38:43.299
So by combining the Treasuries
in a very clever way,

38:43.300 --> 38:48.280
you can end up getting the
prices of all the zero coupon

38:48.275 --> 38:50.395
bonds,
the things that pay just 1

38:50.400 --> 38:51.360
dollar at the end.

38:51.360 --> 38:53.380
Why are they called zero coupon
bonds?

38:53.380 --> 38:56.490
Because it's like--you just get
principal at the end,

38:56.494 --> 38:58.774
of 1 dollar,
without any coupons in the

38:58.771 --> 38:59.431
middle.

38:59.429 --> 39:02.649
So the little pis are called
the zero coupon prices,

39:02.648 --> 39:05.678
because the payments are just 1
dollar--you know,

39:05.677 --> 39:08.577
pi (3) is the price of 1 dollar
at time 3.

39:08.579 --> 39:11.549
It's as if there was a bond
that paid no coupons and paid 1

39:11.550 --> 39:13.190
dollar of principal at time 3.

39:13.190 --> 39:17.410
So the little pis are the
prices of zero coupon bonds of

39:17.405 --> 39:21.155
various maturities,
and those aren't really traded

39:21.159 --> 39:23.229
directly in the market.

39:23.230 --> 39:26.850
What's traded directly in the
market, where pieces of paper

39:26.847 --> 39:29.277
change hands,
are the Treasury bonds.

39:29.280 --> 39:32.310
But everybody,
every day is calculating these

39:32.306 --> 39:35.556
zero coupon prices,
because that's what they need

39:35.556 --> 39:38.726
to do to evaluate every single
project that they might

39:38.731 --> 39:41.551
conceivably do that day,
and decide whether it's a good

39:41.545 --> 39:42.525
project or a bad project.

39:42.530 --> 39:44.780
Is it worth the price or not
worth the price?

39:44.780 --> 39:48.140
And it's done by the principle
of replication,

39:48.143 --> 39:49.493
just as we said.

39:49.489 --> 39:52.869
So this formula is going to be
slightly complicated.

39:52.869 --> 39:55.349
I don't know whether it's worth
writing down.

39:55.349 --> 39:57.939
So we've got,
buying the 3-year Treasury,

39:57.940 --> 39:59.690
the right amount of that.

39:59.690 --> 40:03.570
Then we have to sell a certain
amount of the 2-year Treasury,

40:03.568 --> 40:06.088
because we accumulated extra
coupons.

40:06.090 --> 40:10.020
But now we're also going to be
able to sell a certain amount of

40:10.021 --> 40:13.261
the 1-year Treasuries,
and so how much is that going

40:13.255 --> 40:13.885
to be?

40:13.889 --> 40:15.979
It's going to be some formula,
okay.

40:15.980 --> 40:18.530
So it's going to keep track of
everything we did and get a

40:18.528 --> 40:19.198
formula here.

40:19.199 --> 40:22.189
So I'm actually not going to
bother,

40:22.190 --> 40:24.110
I think--I was going to write
down the formula,

40:24.110 --> 40:28.010
but it'll take 3 minutes to
work it out--

40:28.010 --> 40:31.440
because there's a much faster
way of getting all these

40:31.442 --> 40:32.092
numbers.

40:32.090 --> 40:34.630
But is everybody with me here?

40:34.630 --> 40:37.520
You all understand how I could
get this number if I wanted to

40:37.521 --> 40:38.681
do the work to get it?

40:38.679 --> 40:42.379
I'd figure out I had to
sell--I'd sell some of the 1

40:42.378 --> 40:45.858
year and buy some of the 2
year--I'd do something

40:45.860 --> 40:47.820
complicated here,
okay?

40:47.820 --> 40:51.610
Sorry, I would do something
with the 1 year Treasury here to

40:51.612 --> 40:55.662
compensate for the fact that the
3-year thing I bought is paying

40:55.664 --> 40:56.954
me coupons here.

40:56.949 --> 41:00.689
The 2-year thing I sold is
reducing some of those coupons,

41:00.690 --> 41:02.880
and so it's only the net coupon
that I can sell,

41:02.880 --> 41:06.820
and I'm going to sell that by
selling the 1 year Treasury,

41:06.820 --> 41:07.350
okay?

41:07.349 --> 41:09.879
So that's how I would get the
number there,

41:09.884 --> 41:13.204
and I added the cost of doing
all these things together,

41:13.202 --> 41:14.352
and I get .917.

41:14.349 --> 41:19.609
So you're silent,
but are you following it?

41:19.610 --> 41:21.220
Who can I--okay.

41:21.219 --> 41:25.259
So it's too complicated to just
figure this stuff out all the

41:25.257 --> 41:25.727
time.

41:25.730 --> 41:29.940
So instead, there's a very fast
algorithm that you can do almost

41:29.942 --> 41:33.952
instantly, and that's why it's
such a triviality to calculate

41:33.954 --> 41:35.764
these numbers ever day.

41:35.760 --> 41:39.060
So it's called the principle of
duality.

41:39.059 --> 41:42.319
You go backwards,
and you say to yourself,

41:42.320 --> 41:47.390
"What I want is pi (1),
pi (2), pi (3),

41:47.385 --> 41:51.665
pi (4), and pi (5),
and I've started to figure out

41:51.670 --> 41:54.660
what the replicating--
" so these are the prices

41:54.664 --> 41:55.214
of zeros.

41:55.210 --> 42:03.420
Prices of zero coupon bonds.

42:03.420 --> 42:09.690
That's what I want--want prices
of zero coupon bonds.

42:09.690 --> 42:12.580
I have the prices of the
Treasuries and the way I'm

42:12.583 --> 42:15.653
figuring out the prices of the
zero coupon bonds is by

42:15.652 --> 42:16.582
replication.

42:16.579 --> 42:21.139
Now if somebody stupidly,
as happened 50 and 60 years

42:21.135 --> 42:24.175
ago,
fairly routinely,

42:24.175 --> 42:32.875
if somebody was willing to give
me 1 dollar in year 3 and only

42:32.876 --> 42:38.856
ask 90 cents for it,
then I would be able to lock in

42:38.862 --> 42:39.692
a profit.

42:39.690 --> 42:41.650
How could I lock in a profit?

42:41.650 --> 42:46.180
Because I would just--he's
willing to give this to me for a

42:46.175 --> 42:49.605
low price of 90 cents instead of
91 cents.

42:49.610 --> 42:51.590
So what can I do?

42:51.590 --> 42:55.860
Let's say he's willing--he'd
pay me, let's say more

42:55.858 --> 42:59.358
likely--let's say he'd pay me 93
cents.

42:59.360 --> 43:01.160
Say some guy came to me,
I'm the banker,

43:01.159 --> 43:03.829
and he says,
"I'll pay you 93 cents

43:03.829 --> 43:07.729
today to get 1 dollar in year
3," in other words,

43:07.730 --> 43:09.450
for a 3 year zero.

43:09.449 --> 43:12.699
Well, I'd say,
"That's wonderful."

43:12.699 --> 43:17.349
I'll sell them this promise in
year 3, of 1 dollar for 93

43:17.346 --> 43:18.006
cents.

43:18.010 --> 43:22.150
Then with that 93 cents,
I'll only use 91.7 of those

43:22.148 --> 43:26.368
cents and I'll go out and buy
the 3-year Treasury.

43:26.369 --> 43:29.629
I'll sell some of the 2 year
Treasury and I'll sell a little

43:29.630 --> 43:31.510
bit more of the 1 year Treasury.

43:31.510 --> 43:35.670
And that portfolio which I've
done by doing that will pay me

43:35.666 --> 43:39.526
exactly 1 dollar in year 3,
enabling me to keep my promise

43:39.525 --> 43:42.095
to him,
but it will only have cost me

43:42.101 --> 43:42.951
91.7 cents.

43:42.949 --> 43:45.629
So I'll have made a 1.3-cent
profit for sure,

43:45.630 --> 43:48.070
with no chance--it's a pure
arbitrage.

43:48.070 --> 43:51.230
I made a profit of 1.3 cents
with no chance of losing any

43:51.231 --> 43:53.271
money,
okay, because I've done all the

43:53.271 --> 43:55.661
transactions today,
and the government's going to

43:55.663 --> 43:56.553
keep its promises.

43:56.550 --> 43:59.760
I don't have to worry about the
government giving me the money,

43:59.764 --> 44:02.934
and so I'll be able to turn the
money over to that guy in year

44:02.927 --> 44:03.237
3.

44:03.239 --> 44:05.809
Meanwhile, he's given me his 93
cents.

44:05.809 --> 44:08.779
So if you want to do an
arbitrage and make your profit,

44:08.780 --> 44:11.540
you have to figure out what the
replicating portfolio is,

44:11.539 --> 44:14.159
and the replicating portfolio
also tells you the price.

44:14.159 --> 44:17.549
But it takes a long time to
figure out what all these

44:17.554 --> 44:20.104
arbitrage-replicating portfolios
are.

44:20.099 --> 44:22.849
And maybe nobody's coming to
you and offering a stupid deal

44:22.849 --> 44:23.419
like that.

44:23.420 --> 44:27.590
So you don't need to figure
out--so the principle of duality

44:27.594 --> 44:29.754
is,
you don't need to figure out

44:29.751 --> 44:33.341
the replicating portfolio to
figure out what the pi (1),

44:33.340 --> 44:36.060
pi (2), pi (3),
pi (4), and pi (5) are.

44:36.059 --> 44:39.699
I can find those numbers now
just by clicking a button in

44:39.702 --> 44:42.692
Excel, trivially,
without bothering to find the

44:42.693 --> 44:44.453
replicating portfolios.

44:44.449 --> 44:47.889
Then if some,
you know, bad trader comes to

44:47.894 --> 44:52.494
me and offers me 93 cents for
the 3 year zero coupon,

44:52.489 --> 44:55.179
then I'll figure out the
replicating portfolio and take

44:55.184 --> 44:58.034
advantage of that offer to make
a pure profit for sure.

44:58.030 --> 45:01.500
So what I want to show you know
is how to get pi (1) through pi

45:01.503 --> 45:05.093
(5) without having to go through
this complicated calculation.

45:05.090 --> 45:08.320
And it just reasons backwards,
okay.

45:08.320 --> 45:13.240
So please interrupt if you're
not following this logic.

45:13.239 --> 45:17.589
So you reason like this:
we don't know what pi (1)

45:17.594 --> 45:21.174
through pi (5) are,
but if you did know them,

45:21.170 --> 45:24.740
you'd be able to price the very
bonds that the market is

45:24.735 --> 45:25.445
trading.

45:25.449 --> 45:32.159
So you'd know that 100.1 had to
equal 101 times pi of (1).

45:32.159 --> 45:34.939
And you'd know that 100.2,
the 2 year zero coupon

45:34.942 --> 45:36.742
[correction: Treasury]
bond,

45:36.739 --> 45:46.859
whose price is 100.2,
would have to be 2 times pi of

45:46.864 --> 45:51.934
1 102 times pi of 2,
right?

45:51.929 --> 45:54.699
Because pi of 1,
remember, is the price you pay

45:54.701 --> 45:56.931
today for 1 dollar 1 year from
now.

45:56.929 --> 45:59.369
101 dollars,
1 year from now,

45:59.373 --> 46:04.353
costs 101--if you knew pi (1),
this would be the price.

46:04.349 --> 46:08.069
If you knew pi (1) and pi (2),
you could figure out the price

46:08.074 --> 46:11.124
of the zero coupon bond--
I mean, of the 2 year Treasury

46:11.119 --> 46:13.309
bond,
because 2 dollars at time 1

46:13.309 --> 46:17.259
cost 2 pi (1) and 102 dollars at
time 2 cost 102 pi (2).

46:17.260 --> 46:26.410
And then the 3 year is 100.3 =
3 times pi (1) 3 times pi (2)

46:26.414 --> 46:31.074
plus 103 times pi of 3,
etc.

46:31.070 --> 46:33.350
Then we can go down to the
last--well, I'll just write them

46:33.353 --> 46:33.593
all.

46:33.590 --> 46:46.860
It doesn't take a second.

46:46.860 --> 46:55.170
Okay, and the last one is,
100.5 = 5 times pi (1) plus 5

46:55.166 --> 47:02.716
pi (2) plus 5 pi (3) plus 5 pi
(4) plus 105 pi (5),

47:02.719 --> 47:04.079
okay?

47:04.079 --> 47:07.539
So you don't know the little
pis, but you do know these

47:07.539 --> 47:09.999
prices,
because the market tells you,

47:09.998 --> 47:12.758
and you know the payoffs of all
the bonds,

47:12.760 --> 47:15.830
because that's just written on
them,

47:15.829 --> 47:17.939
literally, so you can just read
what the payoffs are.

47:17.940 --> 47:19.640
You know the government's going
to keep its promise.

47:19.639 --> 47:22.759
So rather than doing this
complicated stuff,

47:22.764 --> 47:26.764
trying to figure out the pis,
assume you had the pis.

47:26.760 --> 47:28.990
And then if you had the pis,
it would tell you what the

47:28.985 --> 47:30.135
prices of everything were.

47:30.139 --> 47:33.589
So if you guessed the wrong
pis, you'd get the wrong prices.

47:33.590 --> 47:36.190
But basically,
you're solving 5 equations and

47:36.186 --> 47:39.136
5 unknowns, and that's what
Excel is so good at.

47:39.139 --> 47:41.649
It's going to start with a wild
guess of the pis,

47:41.650 --> 47:44.630
and then it's going to move
around the pis until you match

47:44.630 --> 47:45.730
all these prices.

47:45.730 --> 47:48.520
And since it's 5 equations and
5 unknowns, and they're all

47:48.518 --> 47:50.918
linearly independent,
it'll be a unique set of pis

47:50.918 --> 47:52.238
that it will calculate.

47:52.239 --> 47:57.409
But that 1 set of pis has to be
the replicating portfolio

47:57.407 --> 48:00.157
prices,
because there's only 1 set of

48:00.163 --> 48:03.643
pis that are going to work and
solve these equations,

48:03.639 --> 48:06.419
namely the ones you got by the
replicating argument.

48:06.420 --> 48:11.080
So we can figure out the pis by
solving 5 equations and 5

48:11.083 --> 48:13.753
unknowns, so that's what I do.

48:13.750 --> 48:18.790
So if you guess the pis,
1,1, 1,1, 1,

48:18.789 --> 48:23.969
any questions about what I'm
doing?

48:23.969 --> 48:27.729
If you write 1,1,
1,1, 1, you're going to get

48:27.726 --> 48:29.346
prices, you know.

48:29.349 --> 48:32.299
For the first one,
it will just be 101,

48:32.302 --> 48:36.112
and for the 2 year,
it will be 2 times 1 102 times

48:36.110 --> 48:37.200
1, is 104.

48:37.199 --> 48:38.959
For the third one,
with all the pis 1,

48:38.958 --> 48:41.808
which is obviously not the
right thing, it would be 3 3 3.

48:41.809 --> 48:45.709
That's 109, so those are bad
prices.

48:45.710 --> 48:49.000
We're trying to match what the
market says the prices are.

48:49.000 --> 48:51.400
So all I do is,
I subtract the market prices

48:51.398 --> 48:54.018
we're trying to match from the
actual prices.

48:54.018 --> 48:57.308
I look at what the error is,
which we're trying make 0,

48:57.306 --> 48:58.886
then I square the error.

48:58.889 --> 49:03.219
And then presumably this was
adding the error,

49:03.215 --> 49:04.845
sum C16 to G16.

49:04.849 --> 49:08.519
I added the error,
and so I now want to do my

49:08.521 --> 49:09.691
Excel thing.

49:09.690 --> 49:15.710
Hopefully--I haven't done this,
but let's--it's got to work.

49:15.710 --> 49:21.260
Okay, so minimize, good, that.

49:21.260 --> 49:25.630
Such that by changing
cells--which are the cells I

49:25.625 --> 49:27.135
want to change.

49:27.139 --> 49:28.719
I want to change the pis.

49:28.719 --> 49:32.389
Those are the ones that are
wrong, so I do that.

49:32.389 --> 49:38.919
So I'm minimizing the squared
error by changing the pis,

49:38.920 --> 49:41.890
B18, okay, and I solve.

49:41.889 --> 49:42.949
Okay, and I've done it.

49:42.949 --> 49:44.529
And there is the answer.

49:44.530 --> 49:52.440
So you notice that I got the
same prices that I told you

49:52.436 --> 49:59.476
about before by replication,
.991, .962, and .917,

49:59.480 --> 50:00.630
etc.

50:00.630 --> 50:02.410
So we got the pis.

50:02.409 --> 50:04.419
So that's step 1.

50:04.420 --> 50:08.970
All right, so that's what every
single financial firm in the

50:08.965 --> 50:13.435
entire world does every single
morning, and sometimes every

50:13.436 --> 50:14.666
single hour.

50:14.670 --> 50:24.190
So are there any questions
about what we just did?

50:24.190 --> 50:26.260
You have to do this in the
problem set.

50:26.260 --> 50:32.300
Is there anything puzzling you
about this?

50:32.300 --> 50:36.740
Okay, now I'm going to start
deducing all kinds of surprising

50:36.735 --> 50:38.135
things from this.

50:38.139 --> 50:41.329
I hope that you'll be
surprised, but I want to make

50:41.333 --> 50:44.723
sure you've got the concept of
what we've done now.

50:44.719 --> 50:48.109
Anybody puzzled by it?

50:48.110 --> 50:51.720
Okay, so somehow,
Fisher's pi (1),

50:51.722 --> 50:56.652
pi (2), pi (3),
pi (4), pi (5) are going to be

50:56.650 --> 51:01.580
deducible from what's going on
in the markets,

51:01.577 --> 51:03.327
every day.

51:03.329 --> 51:06.449
All right, so let's ask one
more thing that's deducible.

51:06.449 --> 51:13.539
Suppose I go to a bank and say,
"I promise to give you 1

51:13.536 --> 51:15.776
dollar in year 2.

51:15.780 --> 51:21.240
How many dollars will you give
me in year 3?"

51:21.239 --> 51:25.449
What do you think the bank's
going to tell me?

51:25.449 --> 51:27.649
Every bank will give me the
same answer,

51:27.650 --> 51:31.880
if that yield curve--given this
morning,

51:31.880 --> 51:33.760
and that was this morning's
yield curve,

51:33.760 --> 51:36.420
if I ask every bank in the
world, "I'll give you 1

51:36.422 --> 51:39.902
dollar in year 2,
you tell me how many dollars

51:39.896 --> 51:43.666
you'll be willing to give me--
" So what am I doing?

51:43.670 --> 51:46.830
I'm saying, "I promise
today to hand over to you 1

51:46.829 --> 51:49.579
dollar in year 2,
and you know I'm going to keep

51:49.581 --> 51:50.461
my promise.

51:50.460 --> 51:53.200
And in exchange,
I want a promise from you to

51:53.197 --> 51:56.557
give me a certain number of
dollars in year 3."

51:56.559 --> 52:00.839
How many dollars is the bank
going to offer to give me in

52:00.840 --> 52:01.530
year 3?

52:01.530 --> 52:04.810
Every bank will give the same
answer, and what will that be?

52:04.809 --> 52:12.289
So the thing I'm asking,
is, I'm asking for what's

52:12.293 --> 52:17.643
called the forward interest
rate.

52:17.639 --> 52:20.249
So we've got these things,
which are obviously very

52:20.246 --> 52:21.286
important numbers.

52:21.289 --> 52:22.619
Those are the most important
things.

52:22.619 --> 52:24.999
Fisher would say those are the
prices you use to get

52:25.001 --> 52:25.611
everything.

52:25.610 --> 52:28.840
But now I want to say
something, I'm going to ask

52:28.842 --> 52:32.012
another important thing,
almost as important.

52:32.010 --> 52:33.960
I want the forward rate.

52:33.960 --> 52:40.390
So 1 i_1--
Student:

52:40.391 --> 52:40.851
We can't see that.

52:40.849 --> 52:41.589
Prof: You can't see that.

52:41.590 --> 52:43.150
I'm glad you pointed that--can
you see this?

52:43.150 --> 52:43.800
Student: Yes.

52:43.800 --> 52:46.450
Prof: Okay.

52:46.449 --> 52:48.649
The cameraman told me this
board was great.

52:48.650 --> 52:58.160
But anyway, so how about,
I'll write 1 i_1^(f),

52:58.157 --> 53:05.457
forward, is--by the way,
am I calling that 1

53:05.458 --> 53:11.738
i_0 or 1
i_1?

53:11.739 --> 53:18.359
Sorry, just want to get my
notation straight.

53:18.360 --> 53:29.070
Okay, so let's call 1
i_0 is the--1

53:29.067 --> 53:44.157
i_t is the number of
dollars at t 1 in exchange for 1

53:44.155 --> 53:48.045
dollar at t.

53:48.050 --> 54:03.480
So this is the number of
dollars at t 1 agreed today.

54:03.480 --> 54:08.380
So we agreed today that you're
going to pay this many dollars

54:08.378 --> 54:12.378
at time t 1 in exchange for 1
dollar at time t.

54:12.380 --> 54:15.840
So this is like the interest
rate that you might pay at time

54:15.835 --> 54:16.065
t.

54:16.070 --> 54:18.290
You give up a dollar at time t,
how much do you get at time t

54:18.286 --> 54:18.616
plus 1?

54:18.619 --> 54:19.839
The interest rate.

54:19.840 --> 54:21.510
But we're not there yet.

54:21.510 --> 54:23.940
We're agreeing to it today.

54:23.940 --> 54:26.840
So today we're agreeing to this
interest rate.

54:26.840 --> 54:29.370
So what is the interest rate
we'd agree to today,

54:29.369 --> 54:30.949
so we've locked in the rate?

54:30.949 --> 54:33.739
When it comes to time t,
one guy's going to hand over

54:33.739 --> 54:35.999
the dollar,
and when it comes to time t 1,

54:36.003 --> 54:38.783
the other guy is going to give
back this many dollars.

54:38.780 --> 54:41.010
So what is the rate we would
lock in today?

54:41.010 --> 54:43.670
It's called the period t
interest rate forward,

54:43.670 --> 54:46.620
because we're locking it in
today for a forward period of

54:46.617 --> 54:48.607
time,
but it's really just the normal

54:48.612 --> 54:50.442
time t interest rate for one
year,

54:50.440 --> 54:52.010
but we're locking it in today.

54:52.010 --> 54:55.990
So what would we lock in today?

54:55.989 --> 54:57.519
How do we compute that?

54:57.518 --> 54:58.908
We already know what that
number is.

54:58.909 --> 55:00.499
What is it?

55:00.500 --> 55:01.430
Yes?

55:01.429 --> 55:03.609
Student:
It's the ratio of pi (2) over

55:03.612 --> 55:04.062
pi (3).

55:04.059 --> 55:06.299
Prof: Well,
I put t here,

55:06.300 --> 55:08.110
so something like that.

55:08.110 --> 55:10.280
Student: pi t over t 1.

55:10.280 --> 55:11.360
Prof: Okay, exactly.

55:11.360 --> 55:16.410
That's pi (t) over pi (t 1).

55:16.409 --> 55:17.229
That's it exactly.

55:17.230 --> 55:19.000
So why is that?

55:19.000 --> 55:21.440
Student:
It's a tradeoff between the

55:21.440 --> 55:22.370
dollar t, t 1.

55:22.369 --> 55:24.369
Prof: Right,
so all we're doing is this

55:24.371 --> 55:25.041
forward rate.

55:25.039 --> 55:29.859
We're exchanging time t dollars
for time t 1 dollars at this

55:29.864 --> 55:30.524
ratio.

55:30.518 --> 55:33.798
But we're committing to do it
today.

55:33.800 --> 55:37.410
But today we already know what
the ratio is of time t dollars

55:37.407 --> 55:38.727
to time t 1 dollars.

55:38.730 --> 55:43.050
We know that pi (2)--in fact,
we know what it is.

55:43.050 --> 55:48.750
pi (2) happens to be .962.

55:48.750 --> 55:50.980
That's a bigger number than pi
(3).

55:50.980 --> 55:54.110
From today's point of view,
1 dollar at time 2 is worth

55:54.105 --> 55:55.895
more than 1 dollar at time 3.

55:55.900 --> 55:59.780
We already know how much more 1
dollar at time 2 is worth than 1

55:59.779 --> 56:00.949
dollar at time 3.

56:00.949 --> 56:04.039
It's the ratio pi (2) over pi
(3).

56:04.039 --> 56:06.829
So that ratio,
as he says, pi (2) over pi (3),

56:06.831 --> 56:10.181
has to be exactly the exchange
rate that the people are

56:10.184 --> 56:11.554
agreeing to today.

56:11.550 --> 56:13.730
That's what pi (2) and pi (3)
mean.

56:13.730 --> 56:16.290
If you express it as an
interest rate,

56:16.289 --> 56:18.709
it's 1 the forward interest
rate.

56:18.710 --> 56:22.120
That ratio is 1
i^(f)_t.

56:22.119 --> 56:26.539
Okay, any questions about that?

56:26.539 --> 56:28.119
Yes?

56:28.119 --> 56:31.299
Student:
What happens if your yield

56:31.304 --> 56:33.484
curve is downward sloping?

56:33.480 --> 56:37.030
Prof: If the yield curve
is downward sloping,

56:37.032 --> 56:37.452
yes.

56:37.449 --> 56:40.209
Student:
Do you agree to give them 1

56:40.213 --> 56:42.983
dollar in year 2,
they give you less than 1

56:42.978 --> 56:44.358
dollar in year 3?

56:44.360 --> 56:48.680
Prof: Okay,
so you've made a little mistake

56:48.681 --> 56:50.271
in your premise.

56:50.268 --> 56:52.258
Good question,
but let me phrase your question

56:52.260 --> 56:54.560
a little differently,
so you see the answer to it.

56:54.559 --> 57:06.569
The yield curve was almost flat
in year 2000.

57:06.570 --> 57:08.830
So in the year 2000,
the yield curve was almost

57:08.826 --> 57:09.166
flat.

57:09.170 --> 57:14.010
In fact, there are moments
where the yield curve seems to

57:14.005 --> 57:14.865
go down.

57:14.869 --> 57:22.949
So if the yield curve goes
down, what does that mean?

57:22.949 --> 57:28.409
Does that mean--between year 6
and year 7, the yield curve went

57:28.409 --> 57:30.169
down a little bit.

57:30.170 --> 57:39.670
Does that mean that pi (7) is
less than pi (6)?

57:39.670 --> 57:43.300
Maybe, but it couldn't really
be that way.

57:43.300 --> 57:45.020
Okay, so let me translate his
question.

57:45.018 --> 57:48.328
He's saying,
look, yield curves very often

57:48.331 --> 57:49.221
are flat.

57:49.219 --> 57:51.799
Mostly they go up,
very often they're flat.

57:51.800 --> 57:54.230
Sometimes they even start to go
down.

57:54.230 --> 57:59.350
He said, "That worries me
that maybe pi (7) is less than

57:59.349 --> 58:00.629
pi (6)."

58:00.630 --> 58:03.360
But that could never happen.

58:03.360 --> 58:04.920
That would be crazy,
because that would mean that

58:04.916 --> 58:06.636
there would be a negative
interest rate in the future,

58:06.637 --> 58:07.997
and with money,
that can never happen.

58:08.000 --> 58:09.280
You can store the money.

58:09.280 --> 58:12.000
No one's ever going to ask for
a negative interest rate.

58:12.000 --> 58:14.520
He could just keep the dollar
and keep it in his pocket.

58:14.519 --> 58:15.639
Why is that?

58:15.639 --> 58:23.959
Remember, pi (6) = 1 over (1
the 6 year yield) to the 6^(th)

58:23.960 --> 58:25.090
power.

58:25.090 --> 58:33.840
And pi (7) = 1 over (1 the 7
year yield) to the 7^(th) power.

58:33.840 --> 58:38.960
So it could be that Y(7) is
less than Y(6) as it is there,

58:38.956 --> 58:41.826
and yet pi (7) is still small.

58:41.829 --> 58:45.109
Could be that Y(7) is less than
Y(6),

58:45.110 --> 58:47.380
as it is over there,
but because you're taking this

58:47.378 --> 58:49.738
to the 7^(th) power and this to
the 6^(th) power,

58:49.739 --> 58:52.559
you still have pi (7) less than
pi (6).

58:52.559 --> 58:54.809
So just because the yield curve
is downward sloping,

58:54.811 --> 58:56.711
doesn't mean that the pis are
going down.

58:56.710 --> 58:57.630
The pis could never go down.

58:57.630 --> 59:00.510
The pis are always going to go
up.

59:00.510 --> 59:03.170
So excellent question.

59:03.170 --> 59:06.360
Any other questions?

59:06.360 --> 59:08.390
Okay, so we could get the i's.

59:08.389 --> 59:11.959
The i's will typically be going
up.

59:11.960 --> 59:14.700
Suppose the yield curve is
going up, by the way.

59:14.699 --> 59:26.759
Will the i's be going up faster
or slower than the yields?

59:26.760 --> 59:31.040
Yeah, if this is the yield
curve and I calculate the

59:31.041 --> 59:35.911
forwards, do you think the
forwards will be going up faster

59:35.909 --> 59:38.679
or less fast than the yields?

59:38.679 --> 59:41.769
All right, well let's do it in
the example.

59:41.768 --> 59:47.448
Let's just go back to our
example that we were doing.

59:47.449 --> 59:50.679
Yield curve spreadsheet, okay.

59:50.679 --> 59:52.029
So maybe I did it here.

59:52.030 --> 59:53.230
Hopefully I solved it all.

59:53.230 --> 59:56.880
Okay, so here we got the actual
pis.

59:56.880 --> 1:00:00.070
You see the pis are always
declining.

1:00:00.070 --> 1:00:07.600
And if we now look at the yield
curve, you can figure out the

1:00:07.596 --> 1:00:08.596
yield.

1:00:08.599 --> 1:00:10.579
How can you figure out the
yield?

1:00:10.579 --> 1:00:13.299
Because you solve that formula
we gave at the very beginning.

1:00:13.300 --> 1:00:18.470
You take the price of the--I
guess I've erased it now.

1:00:18.469 --> 1:00:20.779
Okay, you know what the price
is.

1:00:20.780 --> 1:00:22.730
To figure out the yield on the
3 year,

1:00:22.730 --> 1:00:28.680
we just plug in 1 Y of 3,1 Y of
3 squared,

1:00:28.679 --> 1:00:31.919
1 over 1 Y of 3 squared,
1 over 1 Y of 3 cubed,

1:00:31.920 --> 1:00:32.920
and that gives us the yield.

1:00:32.920 --> 1:00:35.540
Remember, that's how the
newspaper reporter figured out

1:00:35.539 --> 1:00:36.169
the yields.

1:00:36.170 --> 1:00:40.000
So I figured out the yields in
the spreadsheet down here,

1:00:40.001 --> 1:00:41.851
and these are the yields.

1:00:41.849 --> 1:00:43.959
So this is what would appear in
the newspaper.

1:00:43.960 --> 1:00:46.350
The 1-year yield is a little
under 1 percent.

1:00:46.349 --> 1:00:48.419
The 2-year yield is a little
under 2 percent.

1:00:48.420 --> 1:00:50.180
The 3-year is a little under 3
percent.

1:00:50.179 --> 1:00:53.369
The 4-year is a little under 4
percent, and the 5-year is a

1:00:53.373 --> 1:00:54.753
little under 5 percent.

1:00:54.750 --> 1:00:56.150
Those are the yields.

1:00:56.150 --> 1:00:57.870
So what if we did the forwards?

1:00:57.869 --> 1:01:00.629
The forwards,
remember, are just the ratios

1:01:00.625 --> 1:01:01.605
of these pis.

1:01:01.610 --> 1:01:02.530
What are the forwards?

1:01:02.530 --> 1:01:04.550
They're down here.

1:01:04.550 --> 1:01:07.060
So what do they do?

1:01:07.059 --> 1:01:11.839
Sorry, I don't know how I did
that, but here are the forwards,

1:01:11.838 --> 1:01:12.778
over here.

1:01:12.780 --> 1:01:18.110
So the forwards have gone up
much faster than the yields.

1:01:18.110 --> 1:01:22.150
They went from .008 percent,
which is the same as that one,

1:01:22.150 --> 1:01:25.750
to 2.9, which is bigger than
2.8, to 5,

1:01:25.750 --> 1:01:28.590
which is way more than 3.8,
to 7.2,

1:01:28.590 --> 1:01:31.070
which is way more than that,
to 9.6,

1:01:31.070 --> 1:01:32.450
which is way more than that.

1:01:32.449 --> 1:01:35.869
So the forwards went up much
faster than the yields.

1:01:35.869 --> 1:01:39.059
So why is that obviously going
to be the case whenever the

1:01:39.059 --> 1:01:40.849
yield curve is upward sloping?

1:01:40.849 --> 1:01:46.969
So if we go back to our picture
here.

1:01:46.969 --> 1:01:50.189
We go back to our picture.

1:01:50.190 --> 1:01:52.070
If the yield curve were
completely flat,

1:01:52.068 --> 1:01:54.378
what do you think the forward
yields would be?

1:01:54.380 --> 1:01:57.310
This is just common sense to
see if you have any idea what's

1:01:57.313 --> 1:01:57.863
going on.

1:01:57.860 --> 1:02:00.290
If you think about batting
averages and how somebody's

1:02:00.286 --> 1:02:01.976
average changes each time he
bats--

1:02:01.980 --> 1:02:05.010
if the yield curve is flat,
like in 2006,

1:02:05.010 --> 1:02:08.240
the forwards are going to
basically be flat.

1:02:08.239 --> 1:02:11.159
But if the yield curve is
upward sloping,

1:02:11.163 --> 1:02:15.333
then the forward yields are
going to go up much faster.

1:02:15.329 --> 1:02:20.839
So why is that?

1:02:20.840 --> 1:02:35.420
Okay, well, remember,
the yields, you know--

1:02:35.420 --> 1:02:38.990
when you do a 5 year coupon
bond, you're discounting all the

1:02:38.992 --> 1:02:41.322
cash flows,
the previous 4 cash flows,

1:02:41.320 --> 1:02:43.770
using the same yield to
discount them all.

1:02:43.768 --> 1:02:47.888
So if you go from year 4 to
year 5, and you have to raise

1:02:47.889 --> 1:02:50.469
the yield a lot,
it means, you know,

1:02:50.465 --> 1:02:54.435
like if you're a batter,
and your average goes up.

1:02:54.440 --> 1:02:57.050
It means the last thing you did
was better than the average of

1:02:57.052 --> 1:02:59.112
what you've done before,
so it's going to be even

1:02:59.108 --> 1:02:59.578
higher.

1:02:59.579 --> 1:03:02.569
If your average was .300,
and then you played a series

1:03:02.568 --> 1:03:06.068
against the Red Sox in which you
did very well and your average

1:03:06.065 --> 1:03:08.615
went up to .320,
in that series against the Red

1:03:08.615 --> 1:03:10.295
Sox,
you obviously did even better

1:03:10.297 --> 1:03:11.797
than .320,
because you have to average

1:03:11.797 --> 1:03:14.607
what you did then with what,
your previous .300 to get .320.

1:03:14.610 --> 1:03:17.650
So if the average sort of is
going up, remember the yield is

1:03:17.648 --> 1:03:19.708
the same thing over the whole
history.

1:03:19.710 --> 1:03:22.390
If, when you take a longer
history, the average has gone

1:03:22.385 --> 1:03:25.395
up, it must mean that the most
recent thing went up really much

1:03:25.400 --> 1:03:26.130
more, okay?

1:03:26.130 --> 1:03:29.410
So the 4-year yield is sort of
averaging the payoffs of the

1:03:29.414 --> 1:03:30.324
first 4 years.

1:03:30.320 --> 1:03:32.670
The 5-year yield's averaging it
over 5 years.

1:03:32.670 --> 1:03:34.630
So if that yield,
the 5-year yield,

1:03:34.630 --> 1:03:36.780
has gone up,
what happened in the 5^(th)

1:03:36.782 --> 1:03:40.152
year must have gone up a lot to
bring the long run average up,

1:03:40.152 --> 1:03:40.652
okay?

1:03:40.650 --> 1:03:41.820
So that's why the yield curve's
going to go up much faster

1:03:41.817 --> 1:03:43.027
[correction: the forward rates,
compared to the yield curve,

1:03:43.025 --> 1:03:43.655
are going to go up faster].

1:03:43.659 --> 1:03:47.299
Okay, so we know now to
summarize, everybody can look at

1:03:47.298 --> 1:03:49.548
these pictures every single day.

1:03:49.550 --> 1:03:52.020
From these pictures,
they can deduce the pis.

1:03:52.018 --> 1:03:54.438
That's the crucial variable in
the whole economy,

1:03:54.443 --> 1:03:54.953
the pis.

1:03:54.949 --> 1:03:58.929
But a second crucial variable
is the forward yields,

1:03:58.929 --> 1:04:02.199
the 1 i^(f)s,
which you can just get by the

1:04:02.204 --> 1:04:02.834
pis.

1:04:02.829 --> 1:04:05.869
Now why are the 1 i^(f)s so
important?

1:04:05.869 --> 1:04:08.549
We know that the pis are
critical, because they evaluate

1:04:08.550 --> 1:04:11.330
every project by multiplying the
cash flows by the pis.

1:04:11.329 --> 1:04:14.259
Why are the forwards so
important?

1:04:14.260 --> 1:04:19.430
The forwards are so important
because, suppose you believed

1:04:19.427 --> 1:04:24.237
that--so the forwards,
let's go back to what we got.

1:04:24.239 --> 1:04:27.799
Let's just look at the numbers
here.

1:04:27.800 --> 1:04:31.390
Here are the forwards,
remember, down here.

1:04:31.389 --> 1:04:34.519
Okay, suppose I said to you,
"You tell me."

1:04:34.518 --> 1:04:37.298
You don't know anything about
the economy, maybe,

1:04:37.302 --> 1:04:40.782
but you can read the newspapers
and do mathematics like we've

1:04:40.780 --> 1:04:41.940
just been doing.

1:04:41.940 --> 1:04:48.980
What do you guess the interest
rate's going to be in year 2?

1:04:48.980 --> 1:04:51.530
So this is the 0 year forward,
the 1 year forward,

1:04:51.529 --> 1:04:53.969
the 2 year forward,
the 3 year forward and the 4

1:04:53.974 --> 1:04:54.864
year forward.

1:04:54.860 --> 1:04:57.000
If I say in year 2,
"What do you think the

1:04:56.998 --> 1:04:59.938
interest rate--
guess what the interest rate's

1:04:59.943 --> 1:05:02.893
going to be,"
what would you guess?

1:05:02.889 --> 1:05:03.489
Yeah.

1:05:03.489 --> 1:05:05.149
Student:
I have a question.

1:05:05.150 --> 1:05:09.020
Could you make this all real
interest rates by doing this for

1:05:09.018 --> 1:05:09.468
TIPS?

1:05:09.469 --> 1:05:10.729
Prof: Yes.

1:05:10.730 --> 1:05:13.970
Right, I could do this real
interest rate by doing it for

1:05:13.974 --> 1:05:14.384
TIPS.

1:05:14.380 --> 1:05:16.650
Fisher would say do that.

1:05:16.650 --> 1:05:20.490
Trouble is, that TIPS are not
traded--they're becoming more

1:05:20.494 --> 1:05:23.084
and more freely traded in the
market.

1:05:23.079 --> 1:05:26.229
They used to be traded
very--people didn't want to

1:05:26.233 --> 1:05:27.073
trade them.

1:05:27.070 --> 1:05:30.050
So my classmate,
Larry Summers,

1:05:30.045 --> 1:05:35.555
introduced TIPS,
Treasury Inflation Protected

1:05:35.556 --> 1:05:38.106
Securities,
and he, you know,

1:05:38.108 --> 1:05:41.068
announced this was a fantastic
idea and was going to change

1:05:41.074 --> 1:05:42.664
radically the whole markets.

1:05:42.659 --> 1:05:46.659
And then nobody traded them,
and they offered astronomical

1:05:46.664 --> 1:05:49.124
interest rates,
real interest rates,

1:05:49.121 --> 1:05:51.231
to get anyone to buy them.

1:05:51.230 --> 1:05:55.650
And so they were
nicknamed--it's really bad on

1:05:55.648 --> 1:06:01.148
camera--but their nickname
became totally illiquid pieces

1:06:01.146 --> 1:06:02.026
of...

1:06:02.030 --> 1:06:05.410
and so the market has not used
the TIPS to do most of its

1:06:05.405 --> 1:06:06.005
pricing.

1:06:06.010 --> 1:06:08.610
It uses the Treasury bonds,
but yes,

1:06:08.610 --> 1:06:11.070
Fisher would say,
if the TIPS were a reliable

1:06:11.070 --> 1:06:13.220
market,
you would use the TIPS to get

1:06:13.219 --> 1:06:15.349
the real interest rate,
and that's really what you

1:06:15.353 --> 1:06:17.073
should care about,
is the real interest rate,

1:06:17.065 --> 1:06:18.405
not the nominal interest rate.

1:06:18.409 --> 1:06:21.469
But we're using the Treasuries
here to get the nominal interest

1:06:21.474 --> 1:06:21.824
rate.

1:06:21.820 --> 1:06:23.980
However, you've now just dodged
my question.

1:06:23.980 --> 1:06:27.550
My question was,
if I asked you to predict,

1:06:27.550 --> 1:06:30.320
on the basis of the yield curve
in this example,

1:06:30.320 --> 1:06:31.660
and what we've been able to
deduce,

1:06:31.659 --> 1:06:34.419
what would you predict the
interest rate was going to turn

1:06:34.423 --> 1:06:36.783
out to be 2 years from now,
the 1-year interest rate?

1:06:36.780 --> 1:06:37.650
What would you predict?

1:06:37.650 --> 1:07:06.920


1:07:06.920 --> 1:07:09.030
Yeah?

1:07:09.030 --> 1:07:09.970
Student:
The market predicts

1:07:09.971 --> 1:07:10.721
>

1:07:10.719 --> 1:07:12.439
Prof: Which forward rate?

1:07:12.440 --> 1:07:13.730
Student:
Sorry, which years were you

1:07:13.730 --> 1:07:14.590
>?

1:07:14.590 --> 1:07:15.360
Prof: Year 2.

1:07:15.360 --> 1:07:18.250
In year 2, what do you think
the interest rate will be

1:07:18.251 --> 1:07:19.781
between year 2 and year 3?

1:07:19.780 --> 1:07:20.310
Student:
Year 2

1:07:20.309 --> 1:07:20.989
>

1:07:20.989 --> 1:07:22.829
Prof: It's today,
and we're asking,

1:07:22.831 --> 1:07:26.011
what do you predict the market
rate of interest will be in year

1:07:26.012 --> 1:07:28.112
2,
between year 2 and year 3?

1:07:28.110 --> 1:07:32.570
Student:
The forward rate,

1:07:32.565 --> 1:07:37.295
it would be 1
i_2^(f).

1:07:37.300 --> 1:07:39.660
Prof: Okay,
and I_2^(f) happens

1:07:39.661 --> 1:07:41.171
to be right here,
5 percent.

1:07:41.170 --> 1:07:43.450
Okay, so that's the forward.

1:07:43.449 --> 1:07:44.859
Student:
>

1:07:44.860 --> 1:07:46.420
Prof: So 5 percent you'd
predict.

1:07:46.420 --> 1:07:48.660
Student:
>

1:07:48.664 --> 1:07:50.914
position, but not the best
prediction.

1:07:50.909 --> 1:07:53.179
Prof: Okay,
so let me refine that a little

1:07:53.184 --> 1:07:53.474
bit.

1:07:53.469 --> 1:07:56.419
If the world were one of total
certainty,

1:07:56.420 --> 1:08:00.060
so everybody trading today had
a perfect forecast of what was

1:08:00.057 --> 1:08:02.917
going to happen in the future,
then of course,

1:08:02.920 --> 1:08:06.430
the forward rates in the market
today would have to be exactly

1:08:06.425 --> 1:08:08.605
equal to the forward interest
rate.

1:08:08.610 --> 1:08:12.300
Because suppose that you knew
for sure the interest rate was

1:08:12.295 --> 1:08:14.415
going to be 4 percent in year 2.

1:08:14.420 --> 1:08:17.610
How could the market get to a 5
percent forward?

1:08:17.609 --> 1:08:20.839
That means that some guy is
promising today,

1:08:20.836 --> 1:08:24.956
"You give me 1 dollar in
year 2 and I'll give you 1

1:08:24.962 --> 1:08:27.142
dollar 5 in year 3."

1:08:27.140 --> 1:08:28.620
And we're agreeing to that deal.

1:08:28.618 --> 1:08:30.488
But that's a ludicrous thing
for him to do,

1:08:30.488 --> 1:08:36.588
because when he got to year 2,
he could simply--

1:08:36.590 --> 1:08:38.890
if he knew for sure what was
going to happen in the future,

1:08:38.890 --> 1:08:42.660
and that the rate was going to
be 4 percent,

1:08:42.658 --> 1:08:46.238
he would just--I said it
backwards.

1:08:46.239 --> 1:08:46.849
What an idiot.

1:08:46.850 --> 1:08:49.560
Suppose he knew for sure the
rate was going to be 6 percent,

1:08:49.560 --> 1:08:55.110
he would be--oh yeah,
if he knew for sure the rate

1:08:55.109 --> 1:09:01.079
was only going to be 4 percent,
he'd be a fool for promising to

1:09:01.078 --> 1:09:04.388
give the guy 5 percent today,
because in the future,

1:09:04.393 --> 1:09:06.783
when he got the dollar,
what would he do with it?

1:09:06.779 --> 1:09:08.849
Put it in the bank and get 1
dollar 4 next year?

1:09:08.850 --> 1:09:10.120
That wouldn't cover his promise.

1:09:10.119 --> 1:09:11.619
He'd be screwed, okay.

1:09:11.618 --> 1:09:15.368
So if he knows for sure that
the rate 2 years from now is

1:09:15.367 --> 1:09:18.647
going to be 4 percent,
the forward rate would also

1:09:18.645 --> 1:09:20.315
have to be 4 percent.

1:09:20.319 --> 1:09:22.669
So to say it backwards,
if you assume everybody knows

1:09:22.671 --> 1:09:24.891
for sure what's going to happen
in the future,

1:09:24.890 --> 1:09:29.060
then the forward rates would be
exactly equal to what everyone

1:09:29.055 --> 1:09:31.715
is expecting to happen in the
future.

1:09:31.720 --> 1:09:34.310
To say it slightly differently,
if you happen to be the one

1:09:34.306 --> 1:09:36.756
ignoramus in the world who
didn't know what was going to

1:09:36.760 --> 1:09:39.180
happen in the future,
but you knew that everybody

1:09:39.182 --> 1:09:41.852
else who was trading in the
market did know what was going

1:09:41.850 --> 1:09:45.350
to happen in the future,
and you saw a forward rate of 5

1:09:45.345 --> 1:09:47.005
percent,
then you could deduce,

1:09:47.009 --> 1:09:48.579
even though you were an
ignoramus,

1:09:48.578 --> 1:09:51.518
that actually 2 years from now,
the interest rate was going to

1:09:51.524 --> 1:09:52.254
be 5 percent.

1:09:52.250 --> 1:09:55.550
Okay, so just what you said,
but just said a little bit more

1:09:55.548 --> 1:09:56.218
precisely.

1:09:56.220 --> 1:09:59.770
We're assuming here perfect
certainty about what's going--

1:09:59.770 --> 1:10:02.530
we're assuming the traders who
trade today all are completely

1:10:02.528 --> 1:10:04.918
convinced of what's going to
happen in the future.

1:10:04.920 --> 1:10:11.060
Okay, so let's go back to our
picture now.

1:10:11.060 --> 1:10:13.250
The picture of the zero yield
curve.

1:10:13.250 --> 1:10:18.940
So what do you think this blue
curve means?

1:10:18.939 --> 1:10:21.579
What are the traders convinced
is going to happen in the

1:10:21.578 --> 1:10:22.008
future?

1:10:22.010 --> 1:10:25.990
The second half of the course
is going to be dealing with

1:10:25.993 --> 1:10:26.993
uncertainty.

1:10:26.988 --> 1:10:28.778
We're now assuming,
like Irving Fisher,

1:10:28.777 --> 1:10:31.547
that everybody trading today
has no doubt about what's going

1:10:31.551 --> 1:10:32.871
to happen in the future.

1:10:32.868 --> 1:10:38.428
So what do you think these
traders think about these

1:10:38.431 --> 1:10:42.251
prices, about the interest
rates?

1:10:42.250 --> 1:10:44.660
We're now in the world today,
this is September 30^(th),

1:10:44.659 --> 1:10:45.229
it's today.

1:10:45.229 --> 1:10:47.319
That's this curve.

1:10:47.319 --> 1:10:49.839
What does this curve mean?

1:10:49.840 --> 1:10:51.770
Making the assumption that
traders today are convinced

1:10:51.765 --> 1:10:53.105
about what's going to happen
next,

1:10:53.109 --> 1:10:55.549
you know, in the future 10
years and 30 years,

1:10:55.550 --> 1:10:57.860
what do we know that they are
convinced of?

1:10:57.859 --> 1:10:58.009
Yes?

1:10:58.007 --> 1:10:59.647
Student:
That interest rates are going

1:10:59.645 --> 1:11:00.385
to keep going up.

1:11:00.390 --> 1:11:02.810
Prof: That interest
rates are going to go up and go

1:11:02.811 --> 1:11:03.281
up a lot.

1:11:03.279 --> 1:11:06.359
They're not just going to go up
to 4 percent,

1:11:06.364 --> 1:11:08.824
because that's the 30-year
yield.

1:11:08.819 --> 1:11:11.589
They're going to go up--the
forward rates are going up much

1:11:11.594 --> 1:11:13.844
faster than that,
so we could have computed what

1:11:13.841 --> 1:11:14.561
they think.

1:11:14.560 --> 1:11:17.310
So they think rates are going
to go way up in the future,

1:11:17.313 --> 1:11:20.213
okay, much higher than that,
because you're starting so low,

1:11:20.212 --> 1:11:21.592
staying low for a while.

1:11:21.590 --> 1:11:23.590
So the rates have to go up,
the forward rates,

1:11:23.590 --> 1:11:25.680
really sharply to pull the
average that high.

1:11:25.680 --> 1:11:28.030
So people are convinced that
rates are going to go up in the

1:11:28.030 --> 1:11:28.390
future.

1:11:28.390 --> 1:11:29.590
That's what that tells you.

1:11:29.590 --> 1:11:31.860
And why would they be convinced
of that?

1:11:31.859 --> 1:11:34.219
Well, for the two reasons that
you gave at the beginning.

1:11:34.220 --> 1:11:36.320
One of you said,
"The market is going to

1:11:36.322 --> 1:11:37.662
get more productive."

1:11:37.658 --> 1:11:40.468
Irving Fisher has already told
us that when the market gets

1:11:40.469 --> 1:11:42.189
more productive,
you know, you're more

1:11:42.189 --> 1:11:44.019
optimistic about what's going to
happen later,

1:11:44.020 --> 1:11:45.520
the real interest rate goes up.

1:11:45.520 --> 1:11:48.420
And if inflation's constant,
and the real interest rate goes

1:11:48.421 --> 1:11:50.391
up, the nominal interest rate
goes up.

1:11:50.390 --> 1:11:53.540
The other possibility is that
the real interest rate stays the

1:11:53.543 --> 1:11:55.823
same, but there's inflation in
the future.

1:11:55.819 --> 1:11:57.969
The real interest rate the
inflation is the nominal

1:11:57.970 --> 1:11:58.660
interest rate.

1:11:58.658 --> 1:12:01.838
That's another explanation for
why people might expect the

1:12:01.841 --> 1:12:04.021
nominal interest rate to go up,
okay?

1:12:04.020 --> 1:12:07.590
So you know that the market is
predicting rates going up,

1:12:07.590 --> 1:12:09.860
and the two obvious
explanations according to Fisher

1:12:09.863 --> 1:12:12.453
is that either inflation is
going to go up or the real rate

1:12:12.448 --> 1:12:13.428
is going to go up.

1:12:13.430 --> 1:12:14.690
And why might the real rate go
up?

1:12:14.689 --> 1:12:16.719
Well, there are a bunch of
reasons, but most likely because

1:12:16.716 --> 1:12:17.656
productivity is going up.

1:12:17.658 --> 1:12:23.188
Okay, so I've got one more
surprising conclusion to end

1:12:23.192 --> 1:12:23.912
this.

1:12:23.908 --> 1:12:33.518
So if you were certain about
the future and you took the

1:12:33.516 --> 1:12:39.636
5-year coupon bond,
could you tell me what the

1:12:39.637 --> 1:12:44.807
price of the 5-year coupon bond
was going to be next year?

1:12:44.810 --> 1:12:46.830
How would you figure that out?

1:12:46.828 --> 1:12:50.438
Assume that everybody is
convinced that the 5 year coupon

1:12:50.438 --> 1:12:53.208
bond--that they know the future
for sure.

1:12:53.210 --> 1:12:55.440
So therefore,
from the zero curve--I erased

1:12:55.435 --> 1:12:57.445
my graph--this is the last
question.

1:12:57.448 --> 1:12:59.068
I'll let you go as soon as you
answer this.

1:12:59.069 --> 1:13:06.009
You need to answer this to do
the problem set.

1:13:06.010 --> 1:13:07.330
Wrong graph, shit.

1:13:07.329 --> 1:13:08.239
Sorry.

1:13:08.238 --> 1:13:10.578
Okay, it'll only take 1 second
to answer this.

1:13:10.578 --> 1:13:14.678
Okay, I'm telling you now that
this is what everybody's looking

1:13:14.679 --> 1:13:17.389
at in the morning,
okay, these numbers.

1:13:17.390 --> 1:13:19.510
They're getting all the forward
rates and stuff like that.

1:13:19.510 --> 1:13:21.530
They're making all the
deductions that we made.

1:13:21.529 --> 1:13:23.809
Now if you suppose that those
people are convinced,

1:13:23.814 --> 1:13:26.564
they don't have any doubt about
what's going to happen in the

1:13:26.556 --> 1:13:27.056
future.

1:13:27.060 --> 1:13:29.290
Because they don't have any
doubt about what's going to

1:13:29.287 --> 1:13:31.427
happen in the future,
you can infer from these prices

1:13:31.432 --> 1:13:32.962
what they think about the
future.

1:13:32.960 --> 1:13:36.710
So the question is,
can you infer what the price of

1:13:36.712 --> 1:13:40.022
the 5-year Treasury,
which is now 100.5,

1:13:40.020 --> 1:13:44.020
that 5-year bond is 100.5,
next year it will only be a

1:13:44.024 --> 1:13:44.834
4-year bond.

1:13:44.828 --> 1:13:48.328
Do we know what its price is
going to be next year?

1:13:48.329 --> 1:13:50.009
Yes.

1:13:50.010 --> 1:13:51.780
Student:
Yes, you can stick the cash

1:13:51.783 --> 1:13:53.183
flows in
>

1:13:53.176 --> 1:13:54.946
year 2,3, 4 and 5,
and multiply them by the

1:13:54.949 --> 1:13:56.259
>

1:13:56.260 --> 1:13:58.070
Prof: By what pis?

1:13:58.069 --> 1:13:59.719
Student:
The big pi, the price of the

1:13:59.716 --> 1:14:00.746
>

1:14:00.750 --> 1:14:01.610
Prof: Those pis.

1:14:01.609 --> 1:14:04.519
Those pis or something slightly
different from those pis?

1:14:04.520 --> 1:14:06.980
It's going to be a year later,
remember.

1:14:06.979 --> 1:14:10.999
Student:
Oh, by the equivalent of those

1:14:10.997 --> 1:14:12.067
in year 2.

1:14:12.069 --> 1:14:16.009
Prof: How would you get
that?

1:14:16.010 --> 1:14:17.320
Yeah?

1:14:17.319 --> 1:14:20.879
Student:
Discount by forward rates,

1:14:20.882 --> 1:14:24.362
so it's like
>

1:14:24.359 --> 1:14:27.749
4 and 5, forward rate in 3,4,
>

1:14:27.747 --> 1:14:29.437
year forward,
add a discount

1:14:29.439 --> 1:14:31.259
>

1:14:31.260 --> 1:14:32.400
Each >

1:14:32.404 --> 1:14:33.744
would have one less forward in
it.

1:14:33.738 --> 1:14:35.518
Prof: Okay,
so what you both said is

1:14:35.520 --> 1:14:36.410
absolutely correct.

1:14:36.408 --> 1:14:39.178
Unfortunately,
we're 2 minutes--we're ending

1:14:39.182 --> 1:14:39.572
now.

1:14:39.569 --> 1:14:42.179
So let me just end by saying,
in the problem set,

1:14:42.179 --> 1:14:43.809
that's exactly the question.

1:14:43.810 --> 1:14:47.040
What is the 5-year coupon going
to be priced next year?

1:14:47.038 --> 1:14:49.688
If there's a world of
certainty, you're going to know

1:14:49.692 --> 1:14:52.142
what all the interest rates are
in the future.

1:14:52.140 --> 1:14:54.220
And if you know what all the
interest rates are in the

1:14:54.220 --> 1:14:56.460
future, obviously Fisher tells
you, you can figure out the

1:14:56.458 --> 1:14:56.968
price is.

1:14:56.970 --> 1:14:59.360
However, to get the exact
formula would take a few minutes

1:14:59.364 --> 1:15:01.344
and I unfortunately am a few
minutes behind,

1:15:01.340 --> 1:15:03.090
so you're going to have to
figure out what the right

1:15:03.088 --> 1:15:05.368
formula is,
but it's what he said and what

1:15:05.368 --> 1:15:06.628
you were getting to.

1:15:06.630 --> 1:15:12.000