WEBVTT

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Prof: So we're spending
a couple classes these days

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learning basic facts and
vocabulary about finance,

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and along the way we're trying
to apply the simple lessons that

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Irving Fisher taught about
turning a financial problem into

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a general equilibrium problem
and making use in particular of

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the budget set.

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That very simple budget set we
wrote down at the very beginning

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turns out to be quite useful and
people often can get quite

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confused.

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So the last issue we ended
with, I'm going to take up

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again.

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Suppose that you've got a very
long-lived institution like

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Yale.

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How should Yale think of how
much to spend every year?

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What is Yale's budget set?

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Almost every big institution
like Yale creates a fiction of

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an annual budget and they talk
about the deficit and having to

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bring the deficit under control
and making cuts to close the

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deficit gap,
but really there is no such

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thing as a one-year budget set.

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I mean, why one year?

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Why not one month?

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Why not one day?

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Nobody expects Yale to balance
its budget every day.

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Some expenditure comes in one
day.

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They have to hire an
electrician to fix something

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unexpected.

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They're going to spend more
money than they take in student

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tuition that day.

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So the fact that they're
supposed to budget the balance

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every year is just a fiction.

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Irving Fisher taught us that
Yale really has--

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if you can borrow and lend and
you don't have to worry about

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risk there's one infinite-lived
budget set.

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It's an infinite horizon budget
set where you just take the

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present value of all the
expenditures,

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that's the left hand side,
and the present value of all

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the revenue,
that's the right hand side,

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and make sure that the left
hand side is smaller than the

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right hand side over the whole
course of Yale's life.

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So that simple principle has a
tremendous implication which was

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overlooked, to the chagrin of
the last Yale president.

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So as I said,
the issue was in 1997,

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I believe, it could have been
'96 something like that,

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1997, Benno Schmidt,
who was then the Yale

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president,
released a white paper,

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he called it,
documenting the fact that Yale

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had deferred maintenance in the
buildings,

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he called it,
and a study that he

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commissioned,
a very good study that he

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commissioned,
argued that the deferred

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maintenance--
Yale could be brought up to

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snuff and then go on afterwards
as a normal running institution

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provided it spent 100 million
dollars a year for ten years,

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and that included fixing every
college--

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they're going to do more than
one a year over a 10 year

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period.

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So Yale's total budget,
as I told you,

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was about 1 billion dollars at
the time,

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and then here all of a sudden
was this 100 million dollar a

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year expense for 10 years.

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That's 10 percent of the Yale
budget.

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And a lot of the costs you
can't change.

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You have to have the lights on.

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You have to heat the buildings.

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You can't really reduce those
costs.

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So Benno Schmidt came to the
conclusion that he'd have to

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reduce the costs he could change
by 15 percent in order to

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balance the budget,
to cut about 100 million

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dollars a year out of the
budget.

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So he announced one day that he
was going to fire 15 percent of

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the faculty by attrition.

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If they were junior faculty he
wouldn't promote them,

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and if they were senior
faculty, wait until they retired

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and not replace them.

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So this, needless to say,
caused a tremendous commotion

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among the faculty,
and as I told you a committee

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was formed and I had to present
the report.

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So actually the report went
pretty carefully through all the

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calculations made in the white
paper,

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but the heart of the report was
simply to apply the lesson of

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Irving Fisher.

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So what is the lesson of Irving
Fisher?

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Let's suppose that there's no
inflation so that when they say

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100 million dollars a year they
mean 100 million real dollars a

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year.

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So Irving Fisher would say
Yale's going to live forever.

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Let's suppose that Yale wants
the same quality of education

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every year forever,
so it should have the same real

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spending every year forever
after it compensates for

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inflation.

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So at the moment we're assuming
there's no inflation.

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So what does that mean?

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That means that you just look
at the right hand side and you

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say, what's Yale's revenue?

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Well, whatever it was before we
were told by this report of the

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president that as long as you
did the deferred maintenance

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Yale would be back in balance.

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So what's the loss of revenue
on the right hand side?

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It's 10 years of 100 million
dollars a year as you can see.

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Now, you need an interest rate.

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What should the interest rate
be?

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Well, should it be the nominal
interest rate or the real

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interest rate?

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Well, we're supposing now
there's no inflation so it

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should be the real interest rate
because all the hundreds have no

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inflation in them.

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So what real interest rate
shall we use?

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Well, the white paper used 5
percent because they thought

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that was the number that Yale
could earn after inflation

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pretty reliably every year.

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They think that's the real rate
of return Yale gets,

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and so they discounted it 5
percent.

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Now the real rate of interest
typically in the economy is 3

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percent, but let's suppose that
we calculated this at 5 percent.

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The present value of 100 for 10
years is 772.

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Now, how could you do that in
your head?

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Well, we know that 5 percent is
going to double every 14 years,

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5 into 72 is about 14.

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If it doubles every 14 years 10
years is going to be less than

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half the value of the bond.

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So if you got 100 forever at 5
percent interest that would be 2

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billion,
and we know for only 10 years

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it's less than half the value,
so considerably less than half

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the value,
so it's not one billion it's

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something less than that.

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It's 772.

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So I just did that in Excel and
I calculated 772,

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but in your head you know that
if it had gone on for 14 years

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then the present value,
our formula,

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our famous formula is that you
would take the coupon 100

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divided by the interest rate .05
times (1 - 1 over (1 R) to the

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10th).

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And so we know that if this
were 14 instead of 10 you'd get

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a half here.

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So this is 20 times 100 which
is 2 billion times 1 half would

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be 1 billion,
but since it's only 10 years

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and not 14 years it's less than
a billion,

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so 772.

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So in your head you could have
probably figured that out

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approximately.

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So you could be sitting there
in the audience hearing Benno

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Schmidt talk and be computing in
your head that we're talking

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about something under 1 billion,
like 3 quarters of 1 billion.

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So now, how much does that mean
reduction in every year?

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Well, if Yale's going to spend
the same amount every year that

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means it should be spending 5
percent of 772 less every year.

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That's 38.6 million dollars
less every year.

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So that's a drastically smaller
number than 100 million dollars

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a year.

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It's crazy just to think that
because you've got these

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expenditures for 10 years and
then no expenditures after that,

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that you should cut the budget
by a 100 million and then let it

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go up after 10 years.

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So you'd only need to cut it by
38 million.

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Now, by the way,
5 percent is a pretty arbitrary

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number.

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Suppose you put 3 percent here?

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Well, 3 percent would give you
a much higher present value,

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but then when you multiply it
by 3 percent at the end for the

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annual reduction it will give
you a much smaller number.

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Anyway, this number,
which I computed in Excel,

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but again you can do it sort of
in your head,

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is 853 million,
but you multiply that by 3

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percent and you get 26 million a
year.

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So now the reduction is
starting to sound like it's not

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such a frightening thing.

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So let's stick with the 5
percent which is what the white

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paper,
take all the assumptions of the

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white paper and take it
literally,

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and then notice that they never
said anything about inflation.

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So actually,
this calculation of present

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value loss--there's inflation,
and say the inflation at that

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time is around 4 percent.

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In fact all the Yale contracts
that are still in place assume a

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4 percent inflation even though
inflation's less than that now.

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But anyway, so that 100 million
a year of dollars is actually

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less in present value terms
because what should you discount

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by?

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If you look at the present
value of 100 million dollars

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over 10 years and you take into
account its dollars you should

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be discounting by the real
interest rate times the

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inflation,
so by 9 percent,

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a tiny bit over 9 percent.

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So if you discount that by 9
percent you get 641 million as

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the present value loss to Yale.

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Now, given that there's
inflation how much should you be

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spending every year?

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You should be spending in real
dollars, reducing your

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expenditure how much in real
dollars?

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Well, by 5 percent of the 641
million.

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So if you have 641,
that's today's present value.

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There hasn't been any inflation
yet.

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So that's the real loss in
dollars.

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So if you ask,
what's the real expenditure

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reduction every year,
it's 5 percent of 641 and

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that's 32 million.

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So 32 million is a far smaller
number than 100 million and

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requires a far smaller drop in
expenses,

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so our committee recommended
that we cut the faculty by 6

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percent instead of by 15
percent,

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and 6 percent--there are a lot
of people leaving every year.

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You can do 6 percent pretty
quickly.

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So the upshot of this is that
it is a simple application of

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present value,
a very elementary calculation.

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It came as somewhat of a
revelation to our

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administrators,
I'm afraid, and the day after

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the report the provost of the
university resigned.

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Two weeks later the dean of the
university resigned and two

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months later the president of
the university resigned.

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And Rick Levin,
the current president,

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took over and he cut the
faculty by 6 percent,

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but by no more than that.

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And then, of course,
the finances of Yale got much

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better and he's since added back
that 6 percent plus a little bit

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more than that.

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So just to tell you,
though, something good about

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the Yale administration,
the provost who resigned that

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next day happens to be a friend
of mine.

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I've had dinner with him every
month for the last 12 years

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since this happened and he's
never once criticized me or

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shown the slightest discomfort
about the report that basically

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ended his administrative career.

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He cares so much about Yale and
was so determined to do the

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right thing.

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He just thought he made a
miscalculation and stepped

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aside.

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So I believe that he wanted to
do the right thing for Yale and

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just made the wrong calculation,
not that he had some political

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agenda or something to cut such
a huge part of the faculty.

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So it's the most honest and
most Yale-loving administrator

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that you could imagine.

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And I didn't know what the
reaction would be of someone

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like him after giving the
report.

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I was quite terrified,
actually, that they'd be--

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they were still the president,
the provost and the dean,

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that they would be quite angry
at our committee,

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but they responded with
tremendous integrity.

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Yes?

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Student: Why did you
multiply the present value by

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the interest rate to find the
>?

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Prof: You tell me.

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Why did I do that?

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So someone else tell me.

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So that's a good question.

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Why is that?

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Yes?

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Student: It's like
finding the coupon of the

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perpetuity with a 5 percent
interest rate,

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because it's like you're
rearranging C over r equals the

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present value,
so it'd make it present value

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times the interest rate equals
C.

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Prof: Right.

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So the question was why,
after I figured out the present

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value loss like 772 million,
why did I multiply that by 5

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percent to figure out how much
Yale should reduce its spending

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every year.

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And the answer that was given
down here is that I'm assuming

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that Yale is going to go on
forever.

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So Yale can reduce its
expenditures every year forever

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and by doing that make up for
the same present value loss,

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so forever means perpetually,
so it's a perpetuity.

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So how much do you have to
reduce--

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what is the coupon reduction,
the expenditure reduction every

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year at 5 percent interest that
just makes a present value

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decline of 772 million?

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Well, it's 5 percent of the
principal.

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If you have 772 million in the
bank and every year 5 percent of

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that you throw away,
you've thrown away the whole

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value,
at 5 percent interest,

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of the 772 million.

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So by reducing your
expenditures by 5 percent every

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year you defray the 772 million
dollar loss.

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So the critical thing,
the critical mistake that the

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administration made is they had
a short run problem with a bunch

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of short run costs,
but Yale's going to live

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forever and Yale should share
the cost and the loss over all

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future generations,
not just make the current

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faculty, and the current
students,

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and the current city bear all
the costs of this one shot loss,

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one shot problem that Yale
faced.

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So they weren't thinking in
Fisher's terms of taking the

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present value over the whole
course of the lifetime of the

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institution.

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They were thinking,
well, we've got to spend 100

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million dollars this year we
better cut costs by 100 million

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dollars.

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But that's obviously crazy.

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Like suppose you had to spend
an extra 100,000 dollars in one

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day.

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Does that mean you should lay
off your faculty for one day so

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you can find the money to pay
that?

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And of course not,
so you have to spread the loss

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over the lifetime of the
university.

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Are there any other questions
about this principle?

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Yes?

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Student: If you wanted
to return to say spending 100

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million dollars a year again
after 10 years would you spend

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77 million a year for those just
10 years if you wanted to incur

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the whole cost over a fixed
period of time?

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Prof: If I wanted to
incur the whole cost over 10

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years?

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Student: Yes.

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Prof: Then I would have
to reduce my expenditures by 100

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million dollars a year.

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If at the end of 10 years I
wanted to be back even then I

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would have to spend less.

15:29.519 --> 15:31.919
I would have to cut my
expenditures by exactly the

15:31.921 --> 15:33.931
money I was pouring into the
buildings.

15:33.928 --> 15:37.238
So if I wanted to reduce my
expenditures by an equal amount

15:37.236 --> 15:40.426
every year it would have to be
100 million dollars for 10

15:40.429 --> 15:41.399
years, right?

15:41.399 --> 15:47.359
If the maintenance costs go
over a 10-year period and I want

15:47.361 --> 15:51.811
the expenditures to go over a
10-year period,

15:51.808 --> 15:52.818
right?

15:52.820 --> 15:56.230
So if I want the expenditures
to be reduced evenly over a

15:56.227 --> 15:59.817
10-year period I'd have to do
100 million dollars a year.

15:59.820 --> 16:02.300
If I wanted to eat away the
costs all in 1 year--I guess I

16:02.302 --> 16:03.872
didn't understand you're
question.

16:03.870 --> 16:07.760
You're saying if I wanted to
reduce expenditures entirely in

16:07.764 --> 16:11.334
1 year and then return next year
to my usual pattern of

16:11.328 --> 16:15.418
expenditure then I'd have to cut
the 1 billion dollar budget by

16:15.421 --> 16:16.611
772 million.

16:16.610 --> 16:20.300
So that would involve basically
firing the whole faculty and

16:20.296 --> 16:24.166
saying take a year off you're on
furlough, sort of what they're

16:24.169 --> 16:25.669
doing in California.

16:25.669 --> 16:26.529
Yes?

16:26.528 --> 16:29.638
Student: Can you also
spread the present value cost

16:29.639 --> 16:32.799
evenly over 10 years and not
like 100 million dollars every

16:32.803 --> 16:35.183
year,
but 100 million in present

16:35.182 --> 16:36.102
value terms.

16:36.100 --> 16:37.170
Prof: I could do that if
I wanted.

16:37.168 --> 16:40.558
I could rearrange the 100
million any way I wanted to.

16:40.558 --> 16:43.898
So you would cut less than 100
million dollars this year out of

16:43.904 --> 16:46.984
the budget and a little bit more
every year after that?

16:46.980 --> 16:50.320
Student: Assuming you
wanted to get these costs over

16:50.315 --> 16:52.035
with in a 10-year timeframe.

16:52.038 --> 16:54.638
Prof: Well,
one way to do the costs over

16:54.635 --> 16:57.285
with in a 10-year timeframe is
reduce costs,

16:57.288 --> 17:00.568
reduce paying the faculty by
100 million dollars every year

17:00.573 --> 17:01.873
for 10 years,
right?

17:01.870 --> 17:04.410
That would obviously do it,
because that's the money I need

17:04.405 --> 17:04.795
to get.

17:04.798 --> 17:07.548
You could now rearrange that by
reducing costs a little less at

17:07.545 --> 17:10.285
the beginning and a little more
at the end of the 10 years,

17:10.288 --> 17:13.208
but I would say that doesn't
sound--

17:13.210 --> 17:14.060
why do that?

17:14.058 --> 17:17.918
That's kind of what bad
politicians do.

17:17.920 --> 17:20.950
They say, "It's not our
fault.

17:20.950 --> 17:24.230
We'll just make those guys in
year 10 get totally

17:24.227 --> 17:27.027
crushed,"
and pretty soon they are in

17:27.026 --> 17:31.666
year 10 and then they've got 200
million they have to cut costs.

17:31.670 --> 17:32.680
Yes?

17:32.680 --> 17:36.020
Student: So say in 25
years Yale wants to do another

17:36.016 --> 17:39.236
round of rebuilding all of the
buildings they'll still be

17:39.238 --> 17:42.688
paying for the buildings that
they built 25 years prior?

17:42.690 --> 17:43.050
Prof: Right.

17:43.049 --> 17:44.539
So there's a good question.

17:44.538 --> 17:48.608
So actually some people,
the administration,

17:48.608 --> 17:50.768
that was their best response,
they said,

17:50.769 --> 17:53.859
"Well even though the
white paper said this was a one

17:53.859 --> 17:57.049
shot thing,
and after we do this 10 year

17:57.054 --> 18:01.904
plan Yale is back in good shape,
and of course every year Yale

18:01.901 --> 18:04.121
has allowed maintenance
expenses.

18:04.118 --> 18:05.778
That's part of the budget is
maintenance.

18:05.778 --> 18:08.968
So after we get the buildings
back in tip top shape we're

18:08.973 --> 18:12.173
going to keep them in tip top
shape by doing these normal

18:12.169 --> 18:15.649
expenditures every year so we
should never have another period

18:15.648 --> 18:19.128
where you have to do something
drastic like that."

18:19.130 --> 18:22.240
That's what the white paper
said, but after the report they

18:22.244 --> 18:23.914
responded just like you said.

18:23.910 --> 18:26.020
They said, "Well,
we didn't really mean that.

18:26.019 --> 18:30.009
Maybe in 25 years we're going
to have to do another remodeling

18:30.009 --> 18:30.989
effort."

18:30.990 --> 18:34.040
And so well,
if you need to that then it

18:34.040 --> 18:37.640
wasn't just a one-time deferred
maintenance.

18:37.640 --> 18:40.910
It means that you've
drastically underestimated the

18:40.913 --> 18:44.913
cost of keeping up the buildings
over Yale's whole future,

18:44.910 --> 18:49.520
so then you would have these
reductions in expenditures for

18:49.523 --> 18:54.383
the first 10 years and then in
year 35 you'd have to have more

18:54.376 --> 18:57.156
reductions,
and then in year 70 you'd have

18:57.164 --> 18:58.534
more reductions like that.

18:58.529 --> 19:01.729
So you have to take the present
value of all those things and

19:01.731 --> 19:04.771
then figure out how much to
reduce expenditures on an even

19:04.773 --> 19:07.713
basis and so it would be much
more than 32 million.

19:07.710 --> 19:11.820
It would be 60 or something
million or 50 million.

19:11.818 --> 19:13.618
So you're exactly right,
but that's not what they said

19:13.616 --> 19:14.326
in the white paper.

19:14.328 --> 19:20.228
So I took them literally what
they meant.

19:20.230 --> 19:21.390
So what happened after that?

19:21.390 --> 19:24.640
Yale has done much more
building expenditures than that,

19:24.642 --> 19:28.192
but that's because Yale's
endowment went up to 23 billion.

19:28.190 --> 19:31.340
So from 3 billion which it was
at the time it's now 23 billion

19:31.344 --> 19:33.984
so Yale's launched an incredible
program of building

19:33.980 --> 19:34.860
construction.

19:34.858 --> 19:36.108
Basically they've done two
things.

19:36.108 --> 19:40.668
They've built a huge number of
construction jobs and they've

19:40.665 --> 19:43.905
hired a lot of administrators
and stuff.

19:43.910 --> 19:47.990
So the faculty is still not
that much bigger.

19:47.990 --> 19:49.580
It went down 6 percent.

19:49.578 --> 19:51.908
It's now back a little bigger
than it was before.

19:51.910 --> 19:55.240
So the plan to expand the
college and expand the faculty

19:55.244 --> 19:56.584
hasn't happened yet.

19:56.578 --> 19:59.538
So Yale faces another choice
now.

19:59.538 --> 20:03.778
You know the endowment went to
23 billion and then this past

20:03.780 --> 20:06.940
year they managed to lose down
to 17 billion,

20:06.943 --> 20:08.673
30 percent got lost.

20:08.670 --> 20:11.190
So we're down to 17 billion now.

20:11.190 --> 20:12.500
So again we have the same
question.

20:12.500 --> 20:14.050
We just lost 6 billion dollars.

20:14.048 --> 20:20.628
How much should we reduce
expenditures every year?

20:20.630 --> 20:23.800
So what's your answer to that?

20:23.798 --> 20:28.338
Student: About 30
percent?

20:28.339 --> 20:32.489
Prof: Not 30 percent.

20:32.490 --> 20:36.540
So how much would you reduce
expenditures?

20:36.539 --> 20:38.009
Why wouldn't it be 30 percent?

20:38.009 --> 20:41.179
Because Yale spends a lot of
money it doesn't get from the

20:41.182 --> 20:42.242
endowment, right?

20:42.240 --> 20:47.620
It gets money from tuition,
for example.

20:47.619 --> 20:48.369
So what should Yale do?

20:48.368 --> 20:50.708
What do you think Yale's going
to have to take out of the

20:50.707 --> 20:51.247
budget now?

20:51.250 --> 20:56.270
Student:
>

20:56.271 --> 20:58.031
calculation.

20:58.029 --> 20:59.949
Prof: Yeah,
and let's say it's still 5

20:59.953 --> 21:02.013
percent real interest then what
would you do?

21:02.009 --> 21:07.269
Student: Present value's
6 billion dollars and we assume

21:07.266 --> 21:09.806
we're at 5 percent interest.

21:09.808 --> 21:10.438
Prof: Yeah,
so what's that?

21:10.440 --> 21:12.800
Student: 6 over .05?

21:12.798 --> 21:17.328
Prof: 6 times .05,
so what's that?

21:17.328 --> 21:20.088
Hard to do these things in your
head, right, but what is it?

21:20.089 --> 21:21.849
Student: 300 million.

21:21.849 --> 21:25.429
Prof: 300 million,
so Yale's got to somehow cut

21:25.430 --> 21:30.210
300 million out of its budget so
it's not going to do it in one

21:30.214 --> 21:32.154
year,
but over the course of the next

21:32.153 --> 21:34.123
few years it's going to have to
cut 300 million.

21:34.118 --> 21:37.878
Now the budget is well over 2
billion so that's 15 percent of

21:37.883 --> 21:41.023
the budget, though,
Yale's going to have to cut.

21:41.019 --> 21:42.139
So this is a serious thing.

21:42.140 --> 21:45.510
How do you cut 15 percent of
the Yale budget?

21:45.509 --> 21:46.639
Student: Firing faculty.

21:46.640 --> 21:48.960
Prof: Firing faculty,
well, I hope they don't do

21:48.959 --> 21:49.259
that.

21:49.259 --> 21:54.289
I think they learned their
lesson so I doubt if they'll do

21:54.291 --> 21:54.911
that.

21:54.910 --> 21:56.270
Things are already changing.

21:56.269 --> 22:00.589
They're charging for long
distance telephone calls and all

22:00.592 --> 22:02.642
kinds of stuff like that.

22:02.640 --> 22:04.940
That doesn't get you quite 300
million, but there's going to be

22:04.942 --> 22:06.022
a bunch of stuff like that.

22:06.019 --> 22:07.609
So anyway, we have another
budget problem,

22:07.605 --> 22:08.105
by the way.

22:08.108 --> 22:10.478
So these kinds of budget
problems are happening all over

22:10.477 --> 22:11.077
the country.

22:11.078 --> 22:15.268
I gave a talk at Albany
University and they're going to

22:15.267 --> 22:19.607
abolish their graduate economics
program, SUNY Albany.

22:19.608 --> 22:23.638
These are serious problems
losing that much money.

22:23.640 --> 22:26.670
But in any case 6 billion
translates to,

22:26.670 --> 22:30.700
right, the difference here is 6
billion and you multiply that by

22:30.702 --> 22:34.352
.05 just as we said and that
equals 300 million a year.

22:34.348 --> 22:38.108
So Yale won't do it right away,
but over the course of a few

22:38.111 --> 22:41.491
years Yale's going to have to
reduce its budget by 300

22:41.490 --> 22:44.230
million,
so they're going to obviously

22:44.234 --> 22:48.334
choose to do a lot less building
and presumably some of the new

22:48.330 --> 22:51.700
people that got hired they're
going to not keep.

22:51.700 --> 22:54.370
So any other questions?

22:54.369 --> 22:54.899
Yep?

22:54.900 --> 22:57.920
Student: Doesn't that
presume that the endowment stays

22:57.924 --> 22:58.484
that way?

22:58.480 --> 23:00.050
Prof: Yes.

23:00.048 --> 23:03.718
Student: Could you also,
once the stock market and the

23:03.718 --> 23:07.448
real estate goes back up,
can you have some assumption

23:07.450 --> 23:10.120
that they don't need to cut as
much?

23:10.118 --> 23:11.688
Prof: Right,
very good question.

23:11.690 --> 23:15.580
So in the front he's saying
this presumes that we know for

23:15.575 --> 23:18.365
sure that the endowment lost 6
billion.

23:18.369 --> 23:20.119
It'll never recover it.

23:20.118 --> 23:23.778
Maybe that's a temporary drop
in the stock market and it'll go

23:23.778 --> 23:26.048
back up,
and basically the principle

23:26.048 --> 23:29.378
he's applying is he's saying you
can't make these drastic

23:29.384 --> 23:31.654
reductions in annual
expenditures,

23:31.650 --> 23:34.210
firing people and then two
years later realizing you've got

23:34.211 --> 23:36.821
a lot of money trying to hire
them back because you won't be

23:36.817 --> 23:38.007
able to hire them back.

23:38.009 --> 23:41.369
So clearly Yale has to have a
more complicated rule about how

23:41.374 --> 23:44.404
it gradually adjusts its
spending when there's a change

23:44.402 --> 23:45.582
in the endowment.

23:45.578 --> 23:47.498
And so we're going to talk
about that later because it

23:47.503 --> 23:49.613
involves uncertainty and how to
think about uncertainty.

23:49.609 --> 23:52.949
But you're absolutely right.

23:52.950 --> 23:56.210
So Levin did not announce a 300
million dollar reduction

23:56.210 --> 23:58.100
immediately,
but he announced a big

23:58.098 --> 24:00.618
reduction immediately,
and you're going to expect next

24:00.622 --> 24:03.582
year if the stock market doesn't
drastically improve for there to

24:03.579 --> 24:04.689
be another reduction.

24:04.690 --> 24:07.360
And, by the way,
this number could go down as

24:07.356 --> 24:08.626
well as it goes up.

24:08.630 --> 24:11.730
So we're going to come back to
Yale's investments and what

24:11.732 --> 24:12.552
they're like.

24:12.548 --> 24:15.108
A lot of Yale's investments are
called private equity

24:15.105 --> 24:17.165
investments that are very hard
to value.

24:17.170 --> 24:20.540
So for all we know this 17 is a
lot worse than that,

24:20.535 --> 24:23.895
but we'll be finding out in the
next year or two.

24:23.900 --> 24:27.400
It's not like a hedge fund
where you have to value all your

24:27.401 --> 24:30.481
assets by what the market will
be willing to pay.

24:30.480 --> 24:33.550
A lot of these assets there is
no market so they just sort of

24:33.547 --> 24:35.027
make up what the number is.

24:35.029 --> 24:37.709
Anyway, we're going to come
back and discuss this.

24:37.710 --> 24:41.990
It's a very interesting
question.

24:41.990 --> 24:44.920
So one last thing about this
present value calculation,

24:44.920 --> 24:49.220
one last obvious thing,
it's hard to keep in your mind

24:49.221 --> 24:52.631
the difference between real and
nominal.

24:52.630 --> 24:55.510
So let's just do a very simple
thing.

24:55.509 --> 25:03.489
The mortgage,
mortgages are traditionally

25:03.490 --> 25:08.480
nominal fixed payments.

25:08.480 --> 25:16.720
So for example,
a 100,000 dollar 30 year

25:16.718 --> 25:28.968
mortgage at 2.3 percent is about
4,600 dollars per year.

25:28.970 --> 25:31.190
How did I do that so quickly in
my head?

25:31.190 --> 25:35.220
Well, because I know if the
interest rate is 2.3 percent and

25:35.221 --> 25:39.051
you're going to pay it forever
you'd pay 2,300 a year.

25:39.048 --> 25:43.128
We know at 30 years at 2.3
percent, 2.3 percent doubles

25:43.125 --> 25:44.705
almost in 30 years.

25:44.710 --> 25:46.320
That's 69.

25:46.318 --> 25:49.018
That's getting pretty close to
72, so maybe it takes 31 years

25:49.016 --> 25:50.136
or something to double.

25:50.140 --> 25:58.420
So after 30 years the remainder
is worth half the mortgage.

25:58.420 --> 26:01.310
So you've lost half of the
value by only getting it for 30

26:01.313 --> 26:01.723
years.

26:01.720 --> 26:05.800
So instead of paying 2,300 you
have to pay 4,600.

26:05.798 --> 26:12.588
So the coupon over .023 times
(1 - 1 over 1.023 to the

26:12.586 --> 26:17.136
thirtieth),
that's 1 - 1 half about,

26:17.140 --> 26:23.460
so if this coupon equals
100,000 the payment is going to

26:23.463 --> 26:25.913
be--
since this is 1 half the

26:25.906 --> 26:28.156
payment isn't going to be 2,300.

26:28.160 --> 26:30.500
It has to be twice that, 4,600.

26:30.500 --> 26:32.940
So it's 4,600 per year.

26:32.940 --> 26:35.590
So if there's no inflation that
means you're making the same

26:35.590 --> 26:36.760
real payment every year.

26:36.759 --> 26:38.759
Now what happens if there's
inflation?

26:38.759 --> 26:47.309
What if inflation goes up?

26:47.308 --> 26:54.798
Now what's going to happen to
what you have to pay?

26:54.799 --> 27:00.129
How would you figure that out?

27:00.130 --> 27:04.580
Well, if inflation is another
2.3 percent or something,

27:04.578 --> 27:10.868
then the nominal interest rate
1 i is going to equal the real

27:10.874 --> 27:15.494
interest rate times the rate of
inflation.

27:15.490 --> 27:19.790
So let's say this is 1.023 and
this is also 1.023,

27:19.794 --> 27:23.574
so that's 1.046,
a little bit more than 4 6,

27:23.570 --> 27:26.910
almost a little bit more than 4
6.

27:26.910 --> 27:31.700
So you know that the interest
rate the mortgage companies are

27:31.703 --> 27:35.143
now going to charge is going to
be 1.046.

27:35.140 --> 27:40.800
So the 4.6 is going to be the
mortgage interest rate and so

27:40.799 --> 27:46.559
you can figure out by the same
calculation what the coupon's

27:46.557 --> 27:48.117
going to be.

27:48.118 --> 27:52.358
So what's the coupon going to
be?

27:52.358 --> 27:56.838
Well, instead of doubling every
30 years at 4.6 percent it's

27:56.835 --> 28:00.395
going to double approximately
every 15 years.

28:00.400 --> 28:03.510
So this is going to be doubling
twice.

28:03.509 --> 28:06.929
This is 1 quarter,
so this'll be 3 quarters here.

28:06.930 --> 28:19.840
And so if you multiply
everything, 2,300 a year times 4

28:19.842 --> 28:31.322
thirds--am I doing the right
calculation here?

28:31.318 --> 28:39.018
I'm telling you it's so easy to
compute in your head and

28:39.019 --> 28:40.699
meanwhile.

28:40.700 --> 28:44.940
Oh, I forgot to change this to
4 6, so the interest rate is 4

28:44.936 --> 28:45.216
6.

28:45.220 --> 28:54.290
So this to the other side is
4,600 times 4 thirds and that's

28:54.288 --> 28:56.438
6,000 about.

28:56.440 --> 29:02.400
So the annual payment is going
to go up to 6,000 instead of

29:02.397 --> 29:03.217
4,600.

29:03.220 --> 29:04.880
It was 4,600.

29:04.880 --> 29:07.690
The interest rate went up
because there was inflation,

29:07.690 --> 29:11.420
so of course they're going to
ask you for more money every

29:11.415 --> 29:14.545
year,
because if you pay the same

29:14.554 --> 29:19.304
amount every year and this is
the real payment--

29:19.298 --> 29:22.438
if you make the same amount and
this is time in terms of

29:22.443 --> 29:25.533
inflation corrected dollars
you're paying less and less

29:25.531 --> 29:26.391
every year.

29:26.390 --> 29:29.950
So clearly if you started with
no inflation and a number like

29:29.953 --> 29:33.483
this,
so no inflation and now you've

29:33.480 --> 29:38.360
got inflation but the same real
interest rate,

29:38.358 --> 29:40.658
and the present value of your
expenditures,

29:40.660 --> 29:43.420
the real present value,
right--the mortgage company's

29:43.417 --> 29:45.897
going to want,
the lender's going to want to

29:45.895 --> 29:49.265
get the same amount back in real
terms as it got before because

29:49.265 --> 29:51.815
the inflation hasn't changed the
real world.

29:51.818 --> 29:55.368
So Irving Fisher would say the
inflation is just a veil.

29:55.368 --> 29:58.238
Everybody's going to want the
same real interest rate and so

29:58.236 --> 30:01.196
the mortgage is going to have to
return the same real thing it

30:01.201 --> 30:01.931
did before.

30:01.930 --> 30:04.510
The present value in real
terms, or the real payments is

30:04.513 --> 30:05.833
still going to be 100,000.

30:05.828 --> 30:08.898
So if the real payments go down
over time and have the same

30:08.903 --> 30:11.873
present value they had before
it's got to be that they're

30:11.871 --> 30:15.211
higher at the beginning and in
real terms lower at the end.

30:15.210 --> 30:21.560
So sure enough 6,000 is a much
higher number at the beginning

30:21.555 --> 30:22.925
than 4,600.

30:22.930 --> 30:26.480
So of course when inflation
went up and everybody knows it's

30:26.482 --> 30:30.042
up the mortgage companies are
going to ask for higher annual

30:30.036 --> 30:33.706
payments so it'd be 6,000 a year
instead of 4,600 a year.

30:33.710 --> 30:36.230
But now if you inflation
correct that,

30:36.230 --> 30:38.430
the 6,000 every year is going
to be less,

30:38.430 --> 30:41.610
in terms of real goods,
less and less every year,

30:41.608 --> 30:44.488
but the present discounted
value of this thing has to be

30:44.486 --> 30:46.156
the same as where you started.

30:46.160 --> 30:49.240
So the effect is the young
borrowers are going to be

30:49.238 --> 30:52.678
spending a lot more in real
goods when they're young and a

30:52.679 --> 30:54.489
lot less when they're old.

30:54.490 --> 30:58.950
So inflation has an unfortunate
impact on mortgages quoted in

30:58.950 --> 31:03.560
nominal dollars that it makes
the repayments happen earlier.

31:03.558 --> 31:06.398
So the young who have less
money are having to pay a huge

31:06.402 --> 31:08.202
amount,
and when they get old the

31:08.198 --> 31:10.768
inflation's so high that that
same 6,000 dollars is

31:10.773 --> 31:11.963
practically nothing.

31:11.960 --> 31:13.800
So when they're 50 and 60
they're paying

31:13.804 --> 31:16.694
practically--they're peanuts to
them, but when they were young

31:16.688 --> 31:18.058
it was really a hardship.

31:18.058 --> 31:20.758
So there's a big problem with
nominal mortgages,

31:20.759 --> 31:23.919
which is that in inflationary
times it kills the housing

31:23.917 --> 31:24.547
market.

31:24.548 --> 31:28.448
Fortunately we're not in
inflationary times.

31:28.450 --> 31:31.160
Any questions about that?

31:31.160 --> 31:35.330
All right, so that's the basic
lesson of taking the present

31:35.334 --> 31:35.914
value.

31:35.910 --> 31:39.390
And again, you've always got to
sort out the nominal from the

31:39.385 --> 31:41.105
real,
and look though the veil,

31:41.105 --> 31:44.265
and don't get all mixed up by
the fact that there's inflation.

31:44.269 --> 31:47.619
It's the real thing that you
want to concentrate on as much

31:47.618 --> 31:48.368
as you can.

31:48.368 --> 31:51.718
So that's it for the obvious
lesson of present value.

31:51.720 --> 31:55.190
Now I want to introduce another
word which is very famous in

31:55.191 --> 31:55.781
finance.

31:55.779 --> 31:58.429
It's called the yield or yield
to maturity.

31:58.430 --> 32:02.510
And I'm going to do it,
unlike the way I've presented

32:02.509 --> 32:05.879
in the notes,
I'm going to do it in terms of

32:05.883 --> 32:09.103
a hedge fund,
so if you can see this?

32:09.098 --> 32:14.768
So yield, the next topic,
or yield to maturity is a way

32:14.769 --> 32:21.279
of trying to compute one number
that summarizes how good a bond

32:21.278 --> 32:23.118
is,
or how good,

32:23.119 --> 32:25.789
how well a hedge fund has done.

32:25.788 --> 32:30.428
So I think the more interesting
case, and the less obvious one,

32:30.432 --> 32:32.832
is to start with a hedge fund.

32:32.828 --> 32:36.118
How do you measure how well a
hedge fund's doing or how well

32:36.121 --> 32:37.461
it's done in the past?

32:37.460 --> 32:39.560
Yeah, how well it's done in the
past.

32:39.558 --> 32:43.358
We're going to spend a lot of
the course talking about this in

32:43.355 --> 32:45.775
various ways,
but the first way to do it

32:45.780 --> 32:47.710
involves yield to maturity.

32:47.710 --> 32:51.350
So let's see why the problem is
a little complicated.

32:51.348 --> 32:54.528
So I imagine that there are
three investors in this hedge

32:54.531 --> 32:54.931
fund.

32:54.930 --> 32:58.600
So every year some of the
investors are going to decide

32:58.603 --> 33:02.553
what to do, and they're going to
decide whether to withdraw

33:02.548 --> 33:03.228
money.

33:03.230 --> 33:04.310
Here's investor one.

33:04.308 --> 33:05.758
Maybe he's going to withdraw
money.

33:05.759 --> 33:07.069
The hedge fund's just beginning.

33:07.068 --> 33:09.058
He's going to put in 100
dollars.

33:09.058 --> 33:11.418
The other two guys haven't done
anything.

33:11.420 --> 33:16.490
So now the hedge fund before
this guy put in his money had

33:16.490 --> 33:17.380
nothing.

33:17.380 --> 33:18.390
It's just beginning.

33:18.390 --> 33:22.310
He's put in his 100 dollars,
so the hedge fund's got 100

33:22.307 --> 33:23.017
dollars.

33:23.019 --> 33:24.229
So that's it.

33:24.230 --> 33:27.180
So I'm imagining these all
happen, they usually happen

33:27.180 --> 33:29.240
quarterly or annually or
something.

33:29.240 --> 33:30.550
They don't happen every day.

33:30.548 --> 33:33.128
There's a fixed moment at which
everyone deposits their money.

33:33.130 --> 33:35.160
So let's say they happen
annually.

33:35.160 --> 33:38.080
The guy puts in 100 dollars at
the beginning of the year.

33:38.078 --> 33:39.968
For the rest of the year nobody
can do anything.

33:39.970 --> 33:41.090
They can't take money out.

33:41.089 --> 33:42.629
They can't put money in.

33:42.630 --> 33:46.870
So the hedge fund,
let's say, manages to put the

33:46.874 --> 33:51.484
100 dollars to work and finds a
7 percent return.

33:51.480 --> 33:56.680
So it's now got,
the hedge fund all together has

33:56.678 --> 33:58.668
got 107 dollars.

33:58.670 --> 34:03.560
So let's just go to the hedge
fund all together.

34:03.558 --> 34:08.098
The hedge fund had 100 after
these guys, because only one guy

34:08.096 --> 34:12.326
put in money and now the hedge
fund's got 107 dollars.

34:12.329 --> 34:14.889
Well, that 107 dollars is all
the first guy's money,

34:14.889 --> 34:16.999
because nobody else has put
anything in.

34:17.000 --> 34:18.210
He still owns it.

34:18.210 --> 34:21.670
So, so far the hedge fund got a
7 percent return.

34:21.670 --> 34:25.220
Well, now the next year,
we're now at the beginning of

34:25.219 --> 34:28.119
year 2,
our first investor thinks to

34:28.121 --> 34:30.011
himself,
"Well, they did fine,

34:30.010 --> 34:33.930
7 percent, not great,
but I'm okay.

34:33.929 --> 34:36.699
I'm not going to do anything,
won't take any money out or put

34:36.695 --> 34:37.105
any in.

34:37.110 --> 34:42.520
A rich second investor puts in
1,000 and another guy puts in

34:42.518 --> 34:43.068
200.

34:43.070 --> 34:48.310
So now what's happened to the
NAV of the fund?

34:48.309 --> 34:52.859
Well, the first guy,
at the moment they put in the

34:52.864 --> 34:57.794
money, the first guy still owns
107 of the dollars.

34:57.789 --> 35:03.249
The second guy's now got 1,000
in the fund and the third guy's

35:03.251 --> 35:08.261
got 200 in the fund and the
hedge fund now has 1,200 plus

35:08.264 --> 35:09.344
the 107.

35:09.340 --> 35:10.380
That's 1,307.

35:10.380 --> 35:12.140
That's how much money is in the
fund.

35:12.139 --> 35:15.459
So that's at the beginning of
year 2 if you're still following

35:15.458 --> 35:15.838
this.

35:15.840 --> 35:17.570
If you're not following it
interrupt me.

35:17.570 --> 35:18.250
Sorry.

35:18.250 --> 35:23.170
So what happens in the
beginning of the next year,

35:23.170 --> 35:27.970
year 3, well let's say our
guy--so the hedge fund makes

35:27.972 --> 35:31.622
money and this time it made 3
percent,

35:31.619 --> 35:34.499
a crappier, sorry,
a less good return,

35:34.500 --> 35:35.630
only 3 percent.

35:35.630 --> 35:37.120
God, it's on film.

35:37.119 --> 35:38.949
I'm glad that's going to live
for posterity.

35:38.949 --> 35:44.929
Only a 3 percent return,
and so the hedge fund which

35:44.929 --> 35:52.079
ended the year at 1,307 now by
the next of this next year it's

35:52.081 --> 35:57.711
made 3 percent on that so it's
up to 1,346,

35:57.710 --> 36:03.930
so 39 dollars,
3 percent on 1,300 so 1,346.

36:03.929 --> 36:06.139
Now of that who's got the money?

36:06.139 --> 36:13.529
Well, our original guy he's now
made--everyone made 3 percent so

36:13.530 --> 36:16.580
his 107 turned into 110.

36:16.579 --> 36:19.229
The second guy's got 1,030 in
the fund,

36:19.230 --> 36:24.860
and the third guy's got 206 in
the fund and the total fund is

36:24.856 --> 36:28.166
1,346,
Now let's suppose that our guy,

36:28.170 --> 36:30.880
this is the beginning of year
3,

36:30.880 --> 36:32.670
our first guy says,
"3 percent,

36:32.670 --> 36:34.360
that's a terrible return.

36:34.360 --> 36:35.760
I'm taking my money out.

36:35.760 --> 36:36.680
I've had it.

36:36.679 --> 36:38.369
It's 110 dollars.

36:38.369 --> 36:39.349
That's what I have.

36:39.349 --> 36:42.339
I'm taking it out,"
and no one else does anything.

36:42.340 --> 36:45.420
So at the end of the year now
he's down to zero and everybody

36:45.422 --> 36:48.662
else is where they were and the
hedge fund thing has gone down a

36:48.659 --> 36:49.429
little bit.

36:49.429 --> 36:51.809
Well now next year the thing
does even worse.

36:51.809 --> 36:53.909
It makes a 0 percent return.

36:53.909 --> 36:57.789
So everybody's money is just
the same except that the second

36:57.789 --> 37:01.539
guy decides this is really
getting lousy and he takes half

37:01.536 --> 37:02.716
his money out.

37:02.719 --> 37:04.349
So this is taking half his
money out.

37:04.349 --> 37:05.619
What was his money?

37:05.619 --> 37:09.419
He was 1,112 and half of that
is 556.

37:09.420 --> 37:12.280
So he takes half of it out
leaving half behind,

37:12.275 --> 37:15.745
and the column on the right
reduces what the hedge fund's

37:15.751 --> 37:16.871
total cash is.

37:16.869 --> 37:20.659
But now the hedge fund has a
great year and it makes 50

37:20.657 --> 37:21.357
percent.

37:21.360 --> 37:35.200
Having made 50 percent--sorry,
so this guy takes half his

37:35.202 --> 37:38.172
money out.

37:38.170 --> 37:41.700
At the beginning of the year
the fund does badly then the

37:41.701 --> 37:43.721
fund--I skipped the 8 percent.

37:43.719 --> 37:45.909
There was an 8 percent return,
sorry.

37:45.909 --> 37:47.179
Oh, what an idiot.

37:47.179 --> 37:51.679
Anyway, so the next year the
fund returned not 0 percent it

37:51.679 --> 37:53.309
returned 8 percent.

37:53.309 --> 37:56.729
So the first guy after the 3
percent return this guy took his

37:56.726 --> 37:57.406
money out.

37:57.409 --> 38:00.889
The other guys left it in and
then the fund had an 8 percent

38:00.889 --> 38:01.419
return.

38:01.420 --> 38:04.830
So it's a little bit better,
but this guy decides to take

38:04.829 --> 38:06.109
half his money out.

38:06.110 --> 38:11.030
Then the fund has a 0 percent
return and after that this guy

38:11.034 --> 38:15.004
decides to take his money out,
half his money out,

38:15.001 --> 38:18.641
but then finally the last year
the fund gives a 50 percent

38:18.637 --> 38:20.797
return,
which is fantastic,

38:20.797 --> 38:22.637
so everybody does well.

38:22.639 --> 38:25.879
And now let's say they all
decide to take their money out.

38:25.880 --> 38:31.800
So now there's nothing left in
the fund, and they withdrew the

38:31.795 --> 38:32.955
total 934.

38:32.960 --> 38:35.130
So what I've done here,
just to summarize it,

38:35.126 --> 38:37.786
is every year people are
putting in money or taking out

38:37.788 --> 38:39.708
money at the beginning of the
year.

38:39.710 --> 38:41.790
You can never take out more
than you have or you can put

38:41.793 --> 38:42.213
money in.

38:42.210 --> 38:45.410
The fund earns returns over the
whole year and then people,

38:45.409 --> 38:48.079
again, decide to take money out
or put money in and then the

38:48.081 --> 38:50.211
fund earns a different return
the next year,

38:50.210 --> 38:53.640
and eventually the fund returns
all the money or people withdraw

38:53.637 --> 38:54.287
the money.

38:54.289 --> 38:58.479
So the question is how has the
fund done?

38:58.480 --> 39:03.100
How would you summarize in one
number how the fund has done

39:03.103 --> 39:05.973
over its 1,2,
3,4, 5 years of earning

39:05.972 --> 39:06.932
returns?

39:06.929 --> 39:08.389
That's the question.

39:08.389 --> 39:14.319
So this is a standard--this is
obviously what happens every day

39:14.322 --> 39:16.142
with hedge funds.

39:16.139 --> 39:20.189
So how do hedge funds report
how they've done historically?

39:20.190 --> 39:21.460
So do you have any suggestions?

39:21.460 --> 39:26.210
What would you do to summarize
how the hedge fund has done?

39:26.210 --> 39:32.950
If you had to pick one number
what would it be?

39:32.949 --> 39:36.749
How good an investor is the
fund?

39:36.750 --> 39:37.700
Yeah?

39:37.699 --> 39:38.859
Student: Just multiply
the return.

39:38.860 --> 39:40.980
Take a geometric average.

39:40.980 --> 39:45.930
Prof: So one thing you
could do is you could say--he

39:45.934 --> 39:49.954
said literally multiply all of
these returns.

39:49.949 --> 39:50.989
What does that mean?

39:50.989 --> 39:54.019
That means if you put 1 dollar
in the fund at the beginning

39:54.018 --> 39:55.218
you'd earn 7 percent.

39:55.219 --> 39:57.939
If you left it there and never
took it out you get another 3

39:57.938 --> 39:58.398
percent.

39:58.400 --> 40:01.380
Then you'd get 8 percent on top
of that, then 0 percent,

40:01.376 --> 40:02.346
then 50 percent.

40:02.349 --> 40:05.399
Of course this is a
multiplicative thing,

40:05.400 --> 40:09.980
so he says you'd get 1.07 times
1.03 times 1.08 times 1 times

40:09.978 --> 40:10.588
1.5.

40:10.590 --> 40:13.570
Multiplying all that would give
you the number of dollars you'd

40:13.570 --> 40:16.600
have at the end of 5 years given
that you put 1 dollar in at the

40:16.599 --> 40:18.329
beginning and never took it out.

40:18.329 --> 40:22.269
And if you wanted to annualize
that he said take the geometric

40:22.268 --> 40:24.478
average,
the fifth root of that and

40:24.480 --> 40:27.880
that's the constant rate of
return that would have given you

40:27.882 --> 40:31.522
the same amount of money at the
end that you would get by having

40:31.518 --> 40:35.088
left 1 dollar from the beginning
in the fund all the way to the

40:35.094 --> 40:35.734
end.

40:35.730 --> 40:37.120
Is that clear to everybody?

40:37.119 --> 40:39.509
That seems like a logical thing
to do.

40:39.510 --> 40:41.970
That's what money hedge funds
do do, in fact.

40:41.969 --> 40:44.049
That's the number they tell you.

40:44.050 --> 40:49.080
Now, why might not that be a
great number?

40:49.079 --> 40:51.509
Did everyone follow what his
suggestion was?

40:51.510 --> 40:54.530
So by the way,
his number's going to come out

40:54.534 --> 40:56.464
to be--well, I don't know.

40:56.460 --> 40:57.640
Anyway it's going to be some
number.

40:57.639 --> 40:59.709
We could do that.

40:59.710 --> 41:01.340
In fact it wouldn't be that
hard to do.

41:01.340 --> 41:07.520
Let's just do it.

41:07.519 --> 41:19.489
Sum, oh this wasn't a very--ah!

41:19.489 --> 41:21.189
How about equals?

41:21.190 --> 41:37.960


41:37.960 --> 41:49.980
Oh, dear, all right,
circular reference.

41:49.980 --> 42:00.600
Equals sum.

42:00.599 --> 42:03.139
Oh, why did I get zero here?

42:03.139 --> 42:04.489
Oh, because I'm trying to
multiply these.

42:04.489 --> 42:06.829
I'm adding instead, so equals.

42:06.829 --> 42:08.909
I'll just have to do it one by
one.

42:08.909 --> 42:14.769
That times the next one,
times the next one.

42:14.768 --> 42:16.538
There's obviously a much faster
way of doing this.

42:16.539 --> 42:21.819
Times the next one,
times that one and zero,

42:21.820 --> 42:24.000
that's what 1 dollar would have
gotten you if you had put it in

42:24.000 --> 42:26.930
and kept it until the end,
and now he's saying take this

42:26.931 --> 42:28.251
to the fifth power.

42:28.250 --> 42:36.320
So I'll take up this .2 enter.

42:36.320 --> 42:42.830
So 12.2 percent,
now why isn't that the right

42:42.827 --> 42:44.157
number?

42:44.159 --> 42:49.739
Why might you think there
should be another number?

42:49.739 --> 42:50.369
What's another number?

42:50.369 --> 42:53.209
What's the matter with
that--way back there?

42:53.210 --> 42:58.290
Student: It's grossly
inflated by that last year's 50

42:58.286 --> 42:59.746
percent return.

42:59.750 --> 43:01.440
Prof: Well,
is it grossly inflated,

43:01.440 --> 43:03.130
but why is it grossly inflated
by that?

43:03.130 --> 43:06.120
Student: There are going
to be lots of years where it

43:06.117 --> 43:07.027
doesn't do that.

43:07.030 --> 43:08.600
Prof: That's true,
but you've taken that into

43:08.601 --> 43:08.911
account.

43:08.909 --> 43:13.479
So the years we didn't do that
well like the 0 percent return

43:13.476 --> 43:17.586
that brought the average down,
so why is that a problem

43:17.585 --> 43:18.495
exactly?

43:18.500 --> 43:22.840
Yeah, it's averaging the good
years with the bad years,

43:22.838 --> 43:23.238
so.

43:23.239 --> 43:23.929
Yeah?

43:23.929 --> 43:26.439
Student: As far as a
measure of past performance it

43:26.440 --> 43:29.170
doesn't take into account that
after three mediocre years a lot

43:29.172 --> 43:30.892
of money was removed from the
fund.

43:30.889 --> 43:33.239
Prof: That's the crucial
thing.

43:33.239 --> 43:39.269
So I didn't do extreme enough
numbers.

43:39.268 --> 43:44.718
The crucial thing to take into
account is that suppose you have

43:44.722 --> 43:48.952
a fund that starts off,
many funds like my fund started

43:48.947 --> 43:52.497
off with very little money,
but we did it at the right time

43:52.498 --> 43:54.628
because we knew that was a good
time.

43:54.630 --> 43:55.950
You're going to see when the
leverage cycle,

43:55.947 --> 43:56.527
we talk about it.

43:56.530 --> 43:58.830
It was at the bottom of the
leverage cycle just like this

43:58.827 --> 43:59.317
past year.

43:59.320 --> 44:01.930
We're up 30 percent this year.

44:01.929 --> 44:03.849
So at the bottom of the
leverage cycle you're going to

44:03.853 --> 44:04.583
have a great year.

44:04.579 --> 44:08.109
Of course we hardly had any
money because the fund was just

44:08.112 --> 44:11.342
starting, and so we made 50
percent the first year.

44:11.340 --> 44:13.030
But then everybody said,
"Oh,

44:13.030 --> 44:14.770
these guys must be
geniuses,"

44:14.768 --> 44:17.718
and they poured a huge amount
of money into our fund,

44:17.719 --> 44:22.079
and let's say the next year we
did 10 percent.

44:22.079 --> 44:24.519
Actually we had another great
year the second year,

44:24.518 --> 44:27.198
but let's say that we did 10
percent the second year.

44:27.199 --> 44:31.489
So the young man in the front
is saying you made 50 percent on

44:31.487 --> 44:35.637
pennies and then you made 10
percent on a gigantic amount of

44:35.635 --> 44:36.335
money.

44:36.340 --> 44:38.960
It isn't right to take the
average of 50 percent and 10

44:38.956 --> 44:41.906
percent because almost all the
money that you managed you made

44:41.914 --> 44:43.664
10 percent on not 50 percent on.

44:43.659 --> 44:44.639
That's his point.

44:44.639 --> 44:47.449
So how would you deal with his
point?

44:47.449 --> 44:51.089
How could you figure out a way
of computing the right return to

44:51.094 --> 44:54.504
compensate for the fact that
some years you have a lot more

44:54.503 --> 44:57.153
money at stake than you have
other years?

44:57.150 --> 44:57.770
Yes?

44:57.768 --> 44:58.908
Student: Take a weighted
average?

44:58.909 --> 44:59.909
Prof: Take a weighted
average.

44:59.909 --> 45:03.559
Well, how would you take the
weighted average?

45:03.559 --> 45:06.469
Sounds a little complicated.

45:06.469 --> 45:08.569
That's what I'm going to do,
but it's not immediately

45:08.570 --> 45:09.500
obvious how to do it.

45:09.500 --> 45:12.570
So I wouldn't have expected you
to be able to answer that.

45:12.570 --> 45:14.300
You're right on the right track.

45:14.300 --> 45:16.580
So does anyone have anything
else to say?

45:16.579 --> 45:17.999
Yep?

45:18.000 --> 45:21.070
Student: I guess you
multiply each

45:21.074 --> 45:22.994
>

45:22.994 --> 45:26.684
, and then you add it all up
and divide it by the

45:26.684 --> 45:28.994
>

45:28.989 --> 45:33.549
Prof: All right,
so I'm going to now give you

45:33.552 --> 45:37.582
the answer which is a little bit
like that.

45:37.579 --> 45:40.859
She's saying do some dollar
weighted thing,

45:40.860 --> 45:45.550
and so you somehow weight the
numbers by how much money there

45:45.547 --> 45:47.967
was invested for that year.

45:47.969 --> 45:51.259
So because there was a lot more
money invested in year 3 than

45:51.255 --> 45:54.485
there was in year 1 that number
should somehow have a bigger

45:54.487 --> 45:55.087
weight.

45:55.090 --> 45:59.310
And it's not exactly clear how
the weights are going to get in

45:59.309 --> 46:03.319
there, but it's obvious that
that's something like that you

46:03.322 --> 46:04.432
ought to do.

46:04.429 --> 46:10.539
So here's the mathematical
solution that the internal rate

46:10.536 --> 46:13.426
of return or yield gives.

46:13.429 --> 46:23.479
So it says every year let's
look at what happened in the

46:23.480 --> 46:24.760
fund.

46:24.760 --> 46:28.220
We shouldn't care about which
investor put in which dollar.

46:28.219 --> 46:30.229
We care about how the fund
managed dollars.

46:30.230 --> 46:32.590
The names of the investors
don't make any difference.

46:32.590 --> 46:35.040
It's how did the fund manage
its money.

46:35.039 --> 46:38.789
So in the first year the fund
got 100 dollars.

46:38.789 --> 46:42.969
So as for producing money it
produced a negative 100.

46:42.969 --> 46:44.729
Money went into the fund.

46:44.730 --> 46:46.240
That was the one guy invested.

46:46.239 --> 46:47.229
We don't care who it was.

46:47.230 --> 46:49.010
The total that went into the
fund was 100.

46:49.010 --> 46:51.840
The second year 1,200 went into
the fund.

46:51.840 --> 46:53.460
Those are the second two guys.

46:53.460 --> 46:56.080
The third year 110 came out.

46:56.079 --> 46:57.749
That was the first guy.

46:57.750 --> 47:01.360
The fourth year 556 came out.

47:01.360 --> 47:02.810
That was the second guy.

47:02.809 --> 47:06.699
This is beginning of the fifth
year.

47:06.699 --> 47:10.079
The third guy took out 155
dollars, and then the last year

47:10.081 --> 47:13.761
the second and third guys took
out everything that was left.

47:13.760 --> 47:17.930
So from the point of view of
money creation and use this is

47:17.931 --> 47:22.101
every year what went into the
fund and what came out of the

47:22.103 --> 47:24.193
fund, the net inflow out.

47:24.190 --> 47:28.250
So there are a bunch of numbers.

47:28.250 --> 47:32.320
So the question is,
so the one number summary is

47:32.318 --> 47:35.838
what rate of return,
it's called the internal rate

47:35.840 --> 47:38.480
of return which if you
discounted all these numbers

47:38.480 --> 47:41.700
what would Fisher say if you
discounted all these numbers?

47:41.699 --> 47:44.239
If you had to use just one
interest rate,

47:44.237 --> 47:47.027
Fisher would say,
what's the present value of

47:47.027 --> 47:48.357
these cash flows?

47:48.360 --> 47:50.740
Well, if the interest rate was
0 you just add up all the

47:50.739 --> 47:52.859
numbers and you're going to get
a big positive.

47:52.860 --> 47:55.860
If the interest rate is
infinity then that means that

47:55.858 --> 47:59.198
after the first year you're
discounting everything to 0 and

47:59.204 --> 48:01.344
you're going to get negative
100.

48:01.340 --> 48:05.320
So you could say,
what interest rate could you

48:05.320 --> 48:09.390
discount all the cash flows at
to produce 0?

48:09.389 --> 48:12.689
That would be like saying at
that interest rate,

48:12.688 --> 48:16.058
all the fund has done is
rearranged its money.

48:16.059 --> 48:18.929
It's taken money in and put
money out, but at that same

48:18.934 --> 48:21.494
constant interest rate the
present value is 0.

48:21.489 --> 48:27.219
So it's allowed you to trade
money across periods at this

48:27.217 --> 48:32.637
internal rate of return,
the interest rate which makes

48:32.637 --> 48:35.397
the present value zero.

48:35.400 --> 48:38.030
So 10 percent turns out to be
the right number.

48:38.030 --> 48:40.380
So if you discounted things by
10 percent,

48:40.380 --> 48:44.090
you see what the formula is,
you take the inflow and you

48:44.094 --> 48:48.284
discount it by 1.10 to the first
power and this you discount by

48:48.282 --> 48:53.392
1.10 to the second power,
the inflow, the net outflow,

48:53.389 --> 48:57.209
I guess,
which is 110 you discount by

48:57.208 --> 49:00.508
1.10 to the third power
etcetera.

49:00.510 --> 49:03.810
You keep discounting by that
and you get all the discounted

49:03.806 --> 49:04.486
net flows.

49:04.489 --> 49:07.429
You add them all up and you get
practically nothing.

49:07.429 --> 49:10.429
That's adding them up and this
is taking the square,

49:10.434 --> 49:14.154
and I used Solver to figure out
what the right discount rate was

49:14.146 --> 49:15.676
to make all this zero.

49:15.679 --> 49:20.549
So that's the simple way of
averaging, dollar weighting

49:20.547 --> 49:21.717
everything.

49:21.719 --> 49:24.519
You don't care about who the
people are.

49:24.518 --> 49:27.278
You don't care about whether
one guy's putting money in,

49:27.280 --> 49:29.640
another guy's taking it out at
the same time.

49:29.639 --> 49:32.159
You just care about the net,
and if you've got a bunch of

49:32.163 --> 49:34.053
net numbers,
that's the net outflow,

49:34.048 --> 49:37.438
and you're trying to say,
what's the single rate of

49:37.438 --> 49:38.068
return?

49:38.070 --> 49:42.440
The idea is to say at what
interest rate?

49:42.440 --> 49:45.480
If there were a bank paying an
interest rate and all those

49:45.483 --> 49:48.693
things discounted gave you zero
that would be like saying the

49:48.688 --> 49:50.878
fund is functioning just like a
bank.

49:50.880 --> 49:54.100
No matter when people put the
money in or take it out they're

49:54.099 --> 49:57.159
always getting this rate of
return which is 10 percent.

49:57.159 --> 50:00.139
So they're getting a constant
10 percent rate of return no

50:00.139 --> 50:03.489
matter when the money goes in or
out and that kind of gives you a

50:03.485 --> 50:05.625
measure of how well the fund's
doing.

50:05.630 --> 50:09.260
So that's the internal rate of
return, or the yield to

50:09.264 --> 50:10.024
maturity.

50:10.018 --> 50:12.328
It says take the net cash flows
every year.

50:12.329 --> 50:18.199
Find the number which when you
discount at that number you get

50:18.195 --> 50:21.075
present value equal to zero.

50:21.079 --> 50:25.649
So it's 10 percent which is a
different number from 12

50:25.648 --> 50:26.508
percent.

50:26.510 --> 50:30.140
Now before we got the geometric
average of 12 percent.

50:30.139 --> 50:34.409
Now very typically this is the
case that this internal rate of

50:34.414 --> 50:38.834
return is lower than the dollar
return from putting the money in

50:38.827 --> 50:41.817
at the beginning,
assuming the fund doesn't just

50:41.824 --> 50:43.574
collapse and go to zero at the
end.

50:43.570 --> 50:44.380
So why is that?

50:44.380 --> 50:47.310
For funds that have survived
typically that number,

50:47.306 --> 50:49.646
12 percent, is higher than 10
percent.

50:49.650 --> 50:51.970
Why would that be?

50:51.969 --> 50:55.839
What does that tell you about
the world?

50:55.840 --> 50:58.340
Someone who hasn't--well,
go ahead.

50:58.340 --> 51:00.610
Student: That it's
easier to make money with a

51:00.606 --> 51:01.736
smaller amount of money?

51:01.739 --> 51:04.799
Prof: It tells you that,
and how is it that the hedge

51:04.800 --> 51:06.410
fund--it could tell you that.

51:06.409 --> 51:08.409
It tells you that the hedge
funds are doing better when they

51:08.409 --> 51:10.379
have a smaller amount of money
than when they have a larger

51:10.376 --> 51:11.356
amount of money,
exactly.

51:11.360 --> 51:14.070
You've concluded that it's
easier to make money when you

51:14.067 --> 51:15.147
have a small amount.

51:15.150 --> 51:18.540
What's another possible
explanation?

51:18.539 --> 51:20.929
Student: People normally
invest a lot after a big year

51:20.932 --> 51:22.012
>

51:22.010 --> 51:22.500
Prof: Right.

51:22.500 --> 51:23.510
I think that's the reason.

51:23.510 --> 51:26.970
The reason is that people pour
money into hedge funds just

51:26.965 --> 51:29.265
after they've done incredibly
well,

51:29.268 --> 51:31.668
and they keep pouring money in,
then eventually there's a blow

51:31.672 --> 51:31.872
up.

51:31.869 --> 51:36.079
And so when the blow up comes
the hedge funds have zillions of

51:36.076 --> 51:39.106
dollars and they're losing a lot
of money.

51:39.110 --> 51:41.410
Then everybody pulls their
money out and that's when the

51:41.407 --> 51:43.997
cycle is going up and then all
of a sudden the hedge funds have

51:43.996 --> 51:46.876
these huge returns again,
but they hardly have any money.

51:46.880 --> 51:52.630
So, any other questions about
this?

51:52.630 --> 51:58.840
All right, so internal rate of
return is a way--

51:58.840 --> 52:00.910
we are going to see that it has
many shortcomings,

52:00.909 --> 52:03.499
but it's a way at getting at
the idea,

52:03.500 --> 52:06.250
as several of you have said,
that you can't just take the

52:06.248 --> 52:09.198
geometric average,
which is what every hedge fund

52:09.201 --> 52:10.931
like ours always produces.

52:10.929 --> 52:13.079
That's the number we tell
everybody because it's a better

52:13.076 --> 52:14.146
number than the other one.

52:14.150 --> 52:18.740
So the geometric average of the
returns are,

52:18.739 --> 52:23.129
if you're an investor who puts
1 dollar in at the beginning and

52:23.128 --> 52:27.308
leaves it there forever what's
your geometric average of all

52:27.306 --> 52:28.506
your returns.

52:28.510 --> 52:31.080
That's not a good reflection of
how the hedge fund's done

52:31.081 --> 52:33.841
necessarily because some years
the fund had a lot of money to

52:33.836 --> 52:34.476
work with.

52:34.480 --> 52:37.750
And so the average dollar
didn't do that well,

52:37.750 --> 52:40.120
and now there's a question
about how should you measure the

52:40.123 --> 52:42.143
average dollar,
and I've given the internal

52:42.139 --> 52:42.899
rate of return.

52:42.900 --> 52:44.560
There are actually other
formulas you could give.

52:44.559 --> 52:50.889
This is the most famous one.

52:50.889 --> 52:57.319
Now let's see how this internal
rate of return is used all the

52:57.320 --> 52:59.640
time on Wall Street.

52:59.639 --> 53:03.129
By the way, if you're not
following what I'm saying you

53:03.132 --> 53:05.012
should please interrupt me.

53:05.010 --> 53:11.840
So what if you took a bond,
a simple coupon bond?

53:11.840 --> 53:13.600
What is a simple coupon bond?

53:13.599 --> 53:16.499
The yield to maturity of a
simple coupon bond,

53:16.501 --> 53:20.371
I'm now on this lecture called
yield, what is a simple coupon

53:20.369 --> 53:20.949
bond?

53:20.949 --> 53:24.739
A simple coupon bond pays the
same coupon every year and then

53:24.742 --> 53:28.032
pays the principal and the
coupon at its maturity.

53:28.030 --> 53:34.060
So the yield to maturity is
going to be the price,

53:34.057 --> 53:40.577
which is like a negative
payment--suppose you knew the

53:40.579 --> 53:43.409
price of this bond.

53:43.409 --> 53:46.459
If you knew the price of the
bond, and so the bond is

53:46.456 --> 53:49.736
promising all these payments,
how good a deal is that?

53:49.739 --> 53:53.139
Well, how good a deal it is
they would say is you simply

53:53.135 --> 53:57.025
take this first negative payment
and all these positive payments

53:57.027 --> 54:00.667
and find the unique interest
rate which when you discount it

54:00.670 --> 54:03.080
will give you present value of
0.

54:03.079 --> 54:07.929
And so if this is a coupon
bond, say paying 7 percent,

54:07.929 --> 54:10.829
say the face is 100,
it pays 7 dollars forever,

54:10.829 --> 54:14.989
and 107 at the end,
and the price is 105,

54:14.989 --> 54:21.479
what do you think the yield to
maturity is going to be?

54:21.480 --> 54:23.240
Can you say anything
qualitative about it?

54:23.239 --> 54:28.229
Suppose it's a 7 percent coupon
bond, face of 100,10-year bond,

54:28.226 --> 54:32.806
no one thinks that it'll
default, but its price is 105.

54:32.809 --> 54:38.259
What is the yield to maturity
in that case do you suppose?

54:38.260 --> 54:41.450
Just a vague guess,
I just want a qualitative

54:41.447 --> 54:42.097
number.

54:42.099 --> 54:44.909
Student: 6.7?

54:44.909 --> 54:53.019
Prof: 6.7,
that's qualitatively wrong.

54:53.018 --> 54:54.448
Well, I mean it's not
qualitatively wrong.

54:54.449 --> 54:55.539
No, it's qualitatively right.

54:55.539 --> 54:57.099
It could have been better.

54:57.099 --> 54:57.909
So he's right.

54:57.909 --> 55:03.239
So what if the price were 100
what would the yield to maturity

55:03.242 --> 55:03.682
be?

55:03.679 --> 55:05.779
Student: 7 percent.

55:05.780 --> 55:07.620
Prof: 7 percent,
that's obvious,

55:07.621 --> 55:08.011
right?

55:08.010 --> 55:13.830
If it's a 7 percent coupon bond
on face of 100 and its price is

55:13.831 --> 55:15.581
100,
price = to the face,

55:15.581 --> 55:18.691
then obviously the thing that
discounts you back to 100 is

55:18.693 --> 55:20.553
going to be 7 percent interest.

55:20.550 --> 55:23.920
So if the price were 100 the
yield to maturity would just be

55:23.922 --> 55:24.612
7 percent.

55:24.610 --> 55:27.500
But I told you the price was
105, which is a lot more

55:27.501 --> 55:28.171
expensive.

55:28.170 --> 55:29.450
So it's a bad deal.

55:29.449 --> 55:31.589
So it's not going to be as good
as 107.

55:31.590 --> 55:36.130
So it's not going to be 7
percent and he said 6.7.

55:36.130 --> 55:39.030
So I think it would be a little
worse than that,

55:39.030 --> 55:41.870
but that's qualitatively just
what I asked for,

55:41.869 --> 55:44.029
something worse than 7 percent.

55:44.030 --> 55:45.980
So who said 6.7 percent?

55:45.980 --> 55:47.620
You did.

55:47.619 --> 55:53.659
Student: I just took the
price of the bond over the

55:53.657 --> 55:59.057
coupon payment and that's 6.7,
but it's not the only

55:59.057 --> 56:02.127
>

56:02.130 --> 56:04.820
Prof: So that's another
number.

56:04.820 --> 56:10.430
So I'm going to come back to
your question.

56:10.429 --> 56:11.269
It's a good question.

56:11.268 --> 56:23.658
So do you all see that if you
measured the yield to maturity

56:23.664 --> 56:33.124
on this bond--so the bond,
remember, pays 7,7,

56:33.117 --> 56:39.627
7,107 and its price is 105.

56:39.630 --> 56:46.000
So the yield to maturity is
going to be that number such

56:45.998 --> 56:53.058
that 105 = 7 over (1 the yield)
7 over (1 the yield) squared 7

56:53.063 --> 56:56.773
over (1 the yield) cubed ...

56:56.768 --> 57:03.348
107 over (1 yield) to the
tenth, that's 105.

57:03.349 --> 57:09.269
So what we observed is that Y
has to be less than 7 percent

57:09.266 --> 57:15.586
because if Y were exactly equal
to 7 percent this would give us

57:15.592 --> 57:16.412
100.

57:16.409 --> 57:19.839
But this bond is more
expensive, so you're paying more

57:19.842 --> 57:23.212
to get the same payments you
would--than the face.

57:23.210 --> 57:25.420
You're paying more than the
face to get the same payment.

57:25.420 --> 57:27.630
If the price were equal to the
face it would be a 7 percent

57:27.634 --> 57:27.944
yield.

57:27.940 --> 57:30.740
So since you're paying more
you're getting a worse deal,

57:30.739 --> 57:34.259
so it's pretty obvious that if
you want to discount this number

57:34.255 --> 57:37.745
to more than 100,
namely 105, Y is going to have

57:37.753 --> 57:39.883
to be less than 7 percent.

57:39.880 --> 57:41.420
So that's the first thing we
said.

57:41.420 --> 57:42.860
Now what did he do?

57:42.860 --> 57:55.900
He gave a number and he said 7
over 105 which he said was about

57:55.896 --> 57:58.836
6.7 percent.

57:58.840 --> 58:11.270
So that number that he gave is
called the current yield.

58:11.268 --> 58:15.998
It's another number people
give, and he figured that was

58:15.996 --> 58:17.196
6.7 percent.

58:17.199 --> 58:25.999
So let's believe him that's 6.7
percent.

58:26.000 --> 58:41.450
How does that number compare to
the yield to maturity,

58:41.449 --> 58:43.489
to Y?

58:43.489 --> 58:51.149
Well, we could compute this out
on Excel since I'm doing so

58:51.150 --> 58:54.320
brilliantly at it now.

58:54.320 --> 59:02.180
So we could go 7,7,
7,7, 7,7, 7,7,

59:02.181 --> 59:05.281
7, and 107.

59:05.280 --> 59:13.350
Those are our payments and then
we could try some yield to

59:13.353 --> 59:21.573
maturity, internal rate of
return and let's guess 1.067.

59:21.570 --> 59:28.960
And now we'd say the cash flow
is going to be this,

59:28.958 --> 59:32.798
is going to be the left.

59:32.800 --> 59:34.630
Oh dear, I have to number
things.

59:34.630 --> 59:37.010
So again, there's probably some
clever way of doing this.

59:37.010 --> 59:46.160
So this'll be--I forgot to
write the year.

59:46.159 --> 59:52.209
Let's just add this.

59:52.210 --> 59:56.690
Equals up 1 enter.

59:56.690 --> 59:57.980
So I'm just going to copy this.

59:57.980 --> 1:00:05.740
All right, so now I've numbered
all the years.

1:00:05.739 --> 1:00:14.609
Equals up 1 enter and now
control copy.

1:00:14.610 --> 1:00:16.970
So I've numbered all the years
here and here are the payments.

1:00:16.969 --> 1:00:24.129
And now at this yield to
maturity I'm going to go equal

1:00:24.132 --> 1:00:32.622
the thing on the left divided by
the yield to maturity that we're

1:00:32.619 --> 1:00:37.129
guessing raised to this power.

1:00:37.130 --> 1:00:43.800
Now I can just copy that and
I've got all these cash flows.

1:00:43.800 --> 1:00:45.790
Oh, what did I do that time?

1:00:45.789 --> 1:00:47.049
Student:
<<overlapping

1:00:47.052 --> 1:00:47.872
conversation>>

1:00:47.869 --> 1:00:48.729
Prof: What?

1:00:48.730 --> 1:00:52.290
Student:
<<overlapping

1:00:52.293 --> 1:00:54.603
conversation>>

1:00:54.599 --> 1:00:55.589
Prof: Control copy,
sorry.

1:00:55.590 --> 1:00:59.420
Student:
<<overlapping

1:00:59.420 --> 1:01:01.900
conversation>>

1:01:01.900 --> 1:01:02.920
Prof: Control copy,
right?

1:01:02.920 --> 1:01:04.280
So I just want to copy this?

1:01:04.280 --> 1:01:05.430
Student:
<<overlapping

1:01:05.432 --> 1:01:06.182
conversation>>

1:01:06.179 --> 1:01:06.929
Prof: Oh, I see.

1:01:06.929 --> 1:01:09.309
Yeah, yeah, yeah,
right, right,

1:01:09.313 --> 1:01:12.893
right, so here I've got
the--you are right.

1:01:12.889 --> 1:01:17.029
So there's a trick here which I
forgot which is the discount

1:01:17.027 --> 1:01:19.607
rate,
the internal rate of return E

1:01:19.605 --> 1:01:26.285
I've got to put a dollar sign,
dollar E, dollar 1 so that way

1:01:26.289 --> 1:01:29.709
it remembers the spot.

1:01:29.710 --> 1:01:35.350
So now when I copy it it's
going to remember that.

1:01:35.349 --> 1:01:36.779
Student: B1.

1:01:36.780 --> 1:01:37.660
Prof: What's B1?

1:01:37.659 --> 1:01:40.089
Student:
<<overlapping

1:01:40.088 --> 1:01:41.658
conversation>>

1:01:41.659 --> 1:01:42.819
Prof: Oh, B1.

1:01:42.820 --> 1:01:52.230
Thank you, so there are two
mistakes, B1.

1:01:52.230 --> 1:01:55.990
Now, control copy.

1:01:55.989 --> 1:01:58.899
So I'm supposed to be showing
you how easy it is to do this,

1:01:58.902 --> 1:02:00.782
but--all right,
so anyway that's it.

1:02:00.780 --> 1:02:03.890
So if you see for each number
here I've got the payments for

1:02:03.885 --> 1:02:06.935
every year and I've discounted
them by taking this internal

1:02:06.936 --> 1:02:11.146
rate of return,
and now I just have to sum all

1:02:11.148 --> 1:02:11.778
this.

1:02:11.780 --> 1:02:23.690
Equals sum parenthesis.

1:02:23.690 --> 1:02:24.810
Oh shit.

1:02:24.809 --> 1:02:27.779
Student:
<<overlapping

1:02:27.777 --> 1:02:29.697
conversation>>

1:02:29.699 --> 1:02:31.269
Prof: I'm trying to sum
it, you're right.

1:02:31.268 --> 1:02:37.588
So here equals,
I want to sum all these.

1:02:37.590 --> 1:02:39.760
So what did I do wrong?

1:02:39.760 --> 1:02:42.880
Student: C1 colon C10.

1:02:42.880 --> 1:02:48.010
Prof: C1 colon C10,
that's what I thought I did,

1:02:48.005 --> 1:02:50.375
but obviously I didn't.

1:02:50.380 --> 1:02:56.490
Good, and now we can do this
and square it.

1:02:56.489 --> 1:03:05.849
So that's the thing I want to
minimize, and so now I'm going

1:03:05.847 --> 1:03:12.987
to Tools, Solver,
Min, C12 by concentrating on

1:03:12.987 --> 1:03:17.267
this number, and solve.

1:03:17.268 --> 1:03:22.618
Student:
<<overlapping

1:03:22.617 --> 1:03:26.077
conversation>>

1:03:26.079 --> 1:03:26.939
Prof: All right,
what did I do?

1:03:26.940 --> 1:03:31.610
Student:
<<overlapping

1:03:31.614 --> 1:03:34.644
conversation>>

1:03:34.639 --> 1:03:36.319
Prof: Here's the sum,
here's the...

1:03:36.320 --> 1:03:40.110
Student: The original
price.

1:03:40.110 --> 1:03:41.340
Prof: Oh,
the original price.

1:03:41.340 --> 1:03:42.140
Ah ha!

1:03:42.139 --> 1:03:43.889
Thank you very much.

1:03:43.889 --> 1:03:47.199
So we need the original price
of 105.

1:03:47.199 --> 1:03:49.779
Very good, so I see that
preparing this would have

1:03:49.784 --> 1:03:50.264
helped.

1:03:50.260 --> 1:03:51.860
So here's the sum.

1:03:51.860 --> 1:03:59.660
So we just summed all these
things, and here we're going

1:03:59.661 --> 1:04:04.771
to--so we're summing those,
right?

1:04:04.768 --> 1:04:12.888
So I summed all these and then
I've got the original price 105

1:04:12.885 --> 1:04:13.945
enter.

1:04:13.949 --> 1:04:29.309
Now we'll add equals this plus
this.

1:04:29.309 --> 1:04:32.589
Student:
<<overlapping

1:04:32.588 --> 1:04:34.708
conversation>>

1:04:34.710 --> 1:04:46.570
Prof: You're right,
this minus that.

1:04:46.570 --> 1:04:52.440
And now we want to square this,
equals up squared enter and now

1:04:52.443 --> 1:04:54.153
we'll do Solver.

1:04:54.150 --> 1:04:56.880
Hopefully there isn't another
mistake.

1:04:56.880 --> 1:05:15.620
So Tools, Solver,
so I want that times E1.

1:05:15.619 --> 1:05:17.789
Oh, that's very bad.

1:05:17.789 --> 1:05:23.029
Anyway, you can solve it using
Solver and it's extremely simple

1:05:23.030 --> 1:05:26.920
to do, and a child could learn
how to do it.

1:05:26.920 --> 1:05:31.490
So we get Solver and we solve
all this, and you should be able

1:05:31.490 --> 1:05:34.340
to use Excel with no problem at
all.

1:05:34.340 --> 1:05:38.170
So the question is what are the
relationships between the

1:05:38.170 --> 1:05:42.210
current yield and the yield to
maturity, and suppose there's

1:05:42.206 --> 1:05:44.256
some actual interest rate.

1:05:44.260 --> 1:05:51.390
So there's an actual market
interest rate of,

1:05:51.389 --> 1:05:56.249
say, 6 percent or something.

1:05:56.250 --> 1:05:59.860
So those are the things that we
want to sort out now in the next

1:05:59.860 --> 1:06:00.720
five minutes.

1:06:00.719 --> 1:06:09.779
So let me go back to the notes
and we'll re-ask all the

1:06:09.777 --> 1:06:12.627
questions here.

1:06:12.630 --> 1:06:13.260
You can see that's Solver.

1:06:13.260 --> 1:06:25.890
I've broken Solver.

1:06:25.889 --> 1:06:31.889
Suppose that there were an
actual interest rate in the

1:06:31.891 --> 1:06:36.801
economy and our bond,
the bond that was 7,7,

1:06:36.795 --> 1:06:40.865
7,107, if the actual interest
rate was,

1:06:40.869 --> 1:06:47.009
say, 6 percent the price of the
bond would be more than 100.

1:06:47.010 --> 1:06:50.140
So some price which will be the
present value will be greater

1:06:50.143 --> 1:06:52.343
than 100,
obviously, because it's

1:06:52.338 --> 1:06:56.368
paying--if the interest rate's
only 6 percent this is giving

1:06:56.365 --> 1:06:57.795
you more than 100.

1:06:57.800 --> 1:07:05.830
Now, the current yield is 7
over the present value,

1:07:05.829 --> 1:07:11.609
exactly analogous to what he
said.

1:07:11.610 --> 1:07:14.120
So if someone calls you on the
phone,

1:07:14.119 --> 1:07:15.689
you haven't gotten these calls
yet,

1:07:15.690 --> 1:07:19.550
but when you get older you'll
get--they're screened now,

1:07:19.550 --> 1:07:22.410
so it's harder to get these,
but it used to be a few years

1:07:22.414 --> 1:07:25.284
ago you'd get called on the
phone quite often and somebody

1:07:25.278 --> 1:07:27.288
would say he's running a bond
fund,

1:07:27.289 --> 1:07:30.369
and the bond fund is really
doing great,

1:07:30.369 --> 1:07:34.519
and he wants to tell you that
the bonds they have in the fund

1:07:34.518 --> 1:07:38.458
last year paid a current yield
of 7 over the present value

1:07:38.460 --> 1:07:42.750
which is much bigger than the
interest rate of 6 percent,

1:07:42.750 --> 1:07:46.490
and therefore you should buy
his bonds.

1:07:46.489 --> 1:07:52.469
Now, what can you say about
that?

1:07:52.469 --> 1:07:55.749
Suppose somebody tells you
there's a market price for the

1:07:55.751 --> 1:07:58.061
bonds,
which we know is the present

1:07:58.056 --> 1:08:00.716
value at the interest rate of 6
percent,

1:08:00.719 --> 1:08:02.789
and he tells you that,
"Look,

1:08:02.789 --> 1:08:05.139
look at the market value I got
last year,

1:08:05.139 --> 1:08:08.519
the yield I got;
the current yield I got on

1:08:08.518 --> 1:08:09.218
these bonds.

1:08:09.219 --> 1:08:12.369
The present value was some
number bigger than 100,

1:08:12.367 --> 1:08:16.287
but I take 7 over the present
value and I get something bigger

1:08:16.287 --> 1:08:17.507
than 6 percent.

1:08:17.510 --> 1:08:20.750
At your bank you're only
getting 6 percent,

1:08:20.751 --> 1:08:24.611
so therefore you should invest
in my fund."

1:08:24.609 --> 1:08:31.219
Is that a good argument to
invest in his fund?

1:08:31.220 --> 1:08:32.280
Why not?

1:08:32.279 --> 1:08:45.679


1:08:45.680 --> 1:08:55.830
Now, this bond is called a
premium bond because the price

1:08:55.827 --> 1:09:05.237
is bigger than the face,
and a discount bond means the

1:09:05.242 --> 1:09:13.192
price is less than the face,
and a par bond,

1:09:13.194 --> 1:09:19.094
the price equals the face.

1:09:19.090 --> 1:09:25.290
So just because a bond pays a
coupon of 7--

1:09:25.288 --> 1:09:27.518
it may be when the bond was
issued everybody thought the

1:09:27.520 --> 1:09:29.590
interest rate was going to be 7
percent forever,

1:09:29.590 --> 1:09:33.100
so that's why they picked a
coupon of 7 so that the price

1:09:33.103 --> 1:09:36.933
when they first issued it would
be equal to its face value.

1:09:36.930 --> 1:09:40.240
But maybe the next day,
so it's still a 10-year bond,

1:09:40.240 --> 1:09:43.550
practically no time has
changed, but unexpectedly the

1:09:43.552 --> 1:09:45.912
interest rates fell to 6
percent.

1:09:45.908 --> 1:09:49.798
If you take the same coupon
bond paying 7 all the time at 6

1:09:49.795 --> 1:09:53.805
percent interest its price is
obviously going to go up in the

1:09:53.814 --> 1:09:57.704
market because everybody is
going to discount the 7s,

1:09:57.698 --> 1:10:00.438
not at 7 percent,
but at 6 percent and get a

1:10:00.439 --> 1:10:02.479
number that's bigger than 100.

1:10:02.479 --> 1:10:06.999
So you're going to have to pay
more for the bond because the

1:10:06.996 --> 1:10:08.906
present value's higher.

1:10:08.908 --> 1:10:13.268
However, people who now will
try and market the bond they're

1:10:13.268 --> 1:10:16.048
going to tell you,
"Well, look at the market

1:10:16.047 --> 1:10:17.807
price," whatever the market
price is.

1:10:17.810 --> 1:10:20.760
So the current yield is the
market price.

1:10:20.760 --> 1:10:23.410
They'll say,
"Look at the market price.

1:10:23.408 --> 1:10:25.148
This is what we bought the
bonds for.

1:10:25.149 --> 1:10:25.989
I'm a fund.

1:10:25.988 --> 1:10:31.078
I went out and bought these
bonds.

1:10:31.078 --> 1:10:34.938
Look at the price I paid and I
got 7 dollars for these bonds

1:10:34.940 --> 1:10:38.930
this year in income and 7 over
the market price of the bond is

1:10:38.932 --> 1:10:43.042
bigger than 6 percent,
so I was doing a great job.

1:10:43.038 --> 1:10:45.328
You should invest in my
fund."

1:10:45.328 --> 1:10:49.278
So, that can't be a correct
thing to say or a persuasive

1:10:49.279 --> 1:10:51.919
thing to say,
because the market price

1:10:51.916 --> 1:10:55.566
reflected the fact that the
interest rates were 6 percent.

1:10:55.569 --> 1:10:59.289
Everybody was properly
computing the present value,

1:10:59.288 --> 1:11:01.858
and let's say the market price
was equal to the present value,

1:11:01.859 --> 1:11:07.199
the present value would indeed
be greater than 100 and in fact

1:11:07.199 --> 1:11:12.279
the current yield would be more
than the interest rate of 6

1:11:12.279 --> 1:11:13.329
percent.

1:11:13.329 --> 1:11:20.649
So why is that?

1:11:20.649 --> 1:11:35.339
So, theorem,
if market price equals present

1:11:35.344 --> 1:11:55.294
value at a going interest rate
then the current yield on a

1:11:55.287 --> 1:12:15.577
premium bond is always greater
than the interest rate.

1:12:15.579 --> 1:12:19.629
So why is that?

1:12:19.630 --> 1:12:22.390
So in this case,
if I hadn't screwed up the

1:12:22.389 --> 1:12:25.739
Excel we would have calculated
the present value.

1:12:25.738 --> 1:12:30.278
So 7,7, 7,107 there's only a 6
percent interest.

1:12:30.279 --> 1:12:33.789
So everybody taught by Irving
Fisher computes the new present

1:12:33.792 --> 1:12:37.362
value which of course is bigger
than 100 and that's the market

1:12:37.363 --> 1:12:37.953
price.

1:12:37.948 --> 1:12:43.708
Some unscrupulous salesman
starts a fund,

1:12:43.710 --> 1:12:46.240
buys the bond for whatever this
present value,

1:12:46.238 --> 1:12:49.158
the market price is,
then goes out to a bunch of

1:12:49.164 --> 1:12:50.764
clients,
potential clients,

1:12:50.759 --> 1:12:53.839
investors, and says,
"Look, my very first year

1:12:53.837 --> 1:12:57.707
in business I spent a little
more than 100 dollars and I got

1:12:57.706 --> 1:13:01.636
7 dollars as a coupon and 7 over
this little more than 100 is

1:13:01.640 --> 1:13:05.510
giving me at current yield
that's more than 6 percent.

1:13:05.510 --> 1:13:06.980
I beat the interest rate.

1:13:06.979 --> 1:13:08.859
You should invest in me,
and by the way,

1:13:08.858 --> 1:13:11.698
I'll charge you a little fee to
do that because I'm doing so

1:13:11.698 --> 1:13:12.468
great."

1:13:12.470 --> 1:13:15.700
Now, that's always going to be
the case so it has to be that he

1:13:15.697 --> 1:13:18.037
really hasn't accomplished
anything at all.

1:13:18.038 --> 1:13:23.178
So why is it easy to see that
whenever I computed the present

1:13:23.179 --> 1:13:27.119
value it was going to have to be
more than--

1:13:27.118 --> 1:13:30.208
this current yield would always
be more than 6 percent.

1:13:30.210 --> 1:13:31.180
How do I know that?

1:13:31.180 --> 1:13:33.280
Yep?

1:13:33.279 --> 1:13:37.389
Student: Because of the
face value that's going to be at

1:13:37.391 --> 1:13:41.111
the end at maturity isn't going
to reflect that increased

1:13:41.106 --> 1:13:43.956
interest or relatively higher
interest.

1:13:43.960 --> 1:13:45.910
It's going to be the original
face value.

1:13:45.909 --> 1:13:48.319
Prof: Exactly.

1:13:48.319 --> 1:13:52.989
So let's say,
to keep this simpler,

1:13:52.993 --> 1:14:00.693
let's suppose these were 10s
everywhere, and the interest

1:14:00.690 --> 1:14:05.090
rate went down to 5 percent.

1:14:05.090 --> 1:14:09.710
Now, what's going to be the
present value of this bond?

1:14:09.710 --> 1:14:12.150
It's not going to be 200, right?

1:14:12.149 --> 1:14:20.229
If the bond paid 10,10,
210, suppose I have something

1:14:20.230 --> 1:14:28.780
paying 10-10-10 and 110,
and the coupon is 5 percent.

1:14:28.779 --> 1:14:36.209
The present value is going to
be less than 200.

1:14:36.210 --> 1:14:40.280
The coupon is always double the
interest rate,

1:14:40.279 --> 1:14:43.009
so it looks like that's what
you'd get if you had 200

1:14:43.011 --> 1:14:44.661
dollars,
but at the end,

1:14:44.658 --> 1:14:47.718
as he's saying,
you're only going to get 110

1:14:47.720 --> 1:14:48.790
and not 210.

1:14:48.788 --> 1:14:52.818
So this present value of this
thing has to be less than 200.

1:14:52.819 --> 1:14:57.409
So if you double the coupon--if
you halve the interest rate,

1:14:57.408 --> 1:14:59.268
the interest rate was
originally 10 percent,

1:14:59.270 --> 1:15:02.870
if you cut the interest rate in
half to 5 percent it looks like

1:15:02.868 --> 1:15:05.768
your annual coupon is double the
interest rate,

1:15:05.770 --> 1:15:09.320
but at the end you don't get
principal that's double the

1:15:09.315 --> 1:15:10.665
original principal.

1:15:10.670 --> 1:15:12.980
All you did was
double--relative to the interest

1:15:12.978 --> 1:15:15.238
rate of 5 percent,
the coupon's twice as big as

1:15:15.238 --> 1:15:17.398
you normally expect,
but the face isn't.

1:15:17.399 --> 1:15:20.669
So therefore,
this has to be worth less than

1:15:20.672 --> 1:15:21.132
200.

1:15:21.130 --> 1:15:25.650
If it were 200 at 5 percent it
would give you 10,

1:15:25.649 --> 1:15:28.719
10,10, 10,10,
210, but this gives you 10,

1:15:28.720 --> 1:15:33.740
10,10, 110, so obviously the
present value is less than 200,

1:15:33.738 --> 1:15:37.528
but therefore 10 over something
less than 200 is going to be

1:15:37.527 --> 1:15:38.937
more than 5 percent.

1:15:38.939 --> 1:15:42.939
So that's his intuitive proof,
which is the essence of the

1:15:42.938 --> 1:15:46.738
thing,
that if ever you have a coupon

1:15:46.743 --> 1:15:52.883
bond that's a premium bond then
the current yield is always

1:15:52.881 --> 1:15:55.741
above the interest rate.

1:15:55.738 --> 1:16:00.268
So you can always advertise it
as having a spectacular current

1:16:00.266 --> 1:16:04.346
yield when in fact it's just
priced perfectly fairly.

1:16:04.350 --> 1:16:07.240
So I'm going to just continue
this story of what's the right

1:16:07.239 --> 1:16:09.789
way to measure things and how
you can get confused by

1:16:09.787 --> 1:16:11.697
measuring the wrong way next
class.

1:16:11.699 --> 1:16:16.999