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50:54
Transcript
0:17
Okay, so let me let me continue with the
0:20
the topic of the previous lecture, which
0:21
is asset pricing.
0:23
And we said the the tricky thing with
0:25
asset pricing is that
0:27
the payoff
0:28
of having an asset comes in the future.
0:31
And that that that implies
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0:35
at least two things.
0:36
The first one is that
0:38
we need to have a method to value
0:41
returns in the future
0:43
as of today.
0:44
Okay? So, what is the equivalent to?
0:46
After all, if you want to buy a
0:47
financial asset, you need to pay for it
0:49
today with dollars of today, and you are
0:52
expected to receive some payoff in the
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0:54
future. You need to be able to compare
0:56
these two things.
0:58
And the second is that is related is
1:00
that because this payoff is in the
1:02
future, you need to have expectations
1:05
about it. Okay? So, those are the two
1:07
concepts
1:08
we play with.
1:09
Um
1:10
and and the and and there's a third
1:12
related concept, which is because it
1:15
comes in the future, many things can
1:17
happen in between, and so there's also a
1:19
concept of risk. Okay? Those are the
1:21
three
1:22
elements we discuss.
1:24
And
1:25
remember we did I'm going to go very
1:27
quickly over what we did in the previous
1:28
lecture because I could see some faces.
1:31
Uh so so let me go quickly over that and
1:34
then then continue with equity, uh which
1:36
was the next step. Um
1:40
So, the first step was says, "Okay,
1:42
ignore the expectations part for now and
1:44
risk and so on. Assume that you know the
1:46
future." And we ask the question,
1:49
uh well, how do we value a dollar next
1:51
year?
1:52
Uh and in particular, do we want the
1:54
question, is it equivalent to having a
1:56
dollar today?
1:57
And the answer quickly became no because
2:00
imagine that you had the dollar today,
2:01
then you can invest it for a year and
2:05
you get the return of the
2:06
the one-year interest rate return.
2:08
So, with $1 today, you can do more than
2:11
with $1 in the future.
2:13
In fact, that calculation
2:16
gave us the exact recipe to
2:19
valuing a dollar in the future because
2:22
in order to get a dollar in the future,
2:24
I don't need a dollar today. I need one
2:25
over one plus the interest rate.
2:28
Uh I invest this in in the one-year
2:31
bond, uh and and I get a return of that
2:35
over that amount, that gives you exactly
2:37
a dollar in the future. Okay? So, that
2:39
gives us a very natural way of valuing a
2:42
dollar next year, it's just one over one
2:44
plus the interest rate. And by the same
2:46
logic, if I have a dollar today and I
2:48
want to invest it for two years, well,
2:51
I'm going to earn that interest rate for
2:53
the first year, and then I'm going to
2:55
learn that earn that interest rate on
2:57
the full product, not not on the
2:59
original dollar, in the on the one plus
3:02
IT dollars, I'm going to
3:04
earn one plus IT plus one.
3:07
And and and so I can generate sort of a
3:10
lot of
3:11
you know, if the interest rate is 10% on
3:13
average, a dollar today generates 1.21
3:17
uh dollars two years from now. So, that
3:19
tells you by the same logic that one
3:22
over 1.21 dollars
3:24
uh
3:25
today is equivalent to $1 in the future.
3:28
Okay?
3:29
So, then we said, "Let's pick a very
3:32
general asset, an asset that has you
3:34
know, that pays
3:35
ZT dollars
3:37
uh this year, then ZT plus one dollars
3:41
one year from now, ZT plus two dollars
3:43
two years from now, and so on and so
3:45
forth up to n years ahead. Uh well, what
3:49
is the value of that asset today? Well,
3:51
you apply exactly the same logic that we
3:52
apply here for every single uh year in
3:56
the future,
3:57
and you get that's that's the the Let's
4:00
call the present present discounted
4:01
value
4:02
uh
4:03
of those cash flows, that gives you the
4:06
value today. Okay? Present discounted,
4:08
those are the discount factors, one over
4:11
and then that's the value that you get
4:12
out of that. So, that asset
4:15
has that present discounted value of uh
4:18
future cash flows,
4:20
and uh
4:21
and uh
4:23
that should be more or less the price
4:24
that you are willing to pay for that
4:26
asset. Okay?
4:29
Uh and then we introduce expectations
4:32
and okay, well, but we're talking about
4:33
cash flows in the future, in many cases,
4:35
we don't know. Well, we don't know two
4:37
things. First, we don't know
4:39
what the cash flows may be.
4:41
In a very safe bond, you do know the
4:43
cash flow, but but but almost any other
4:47
asset, you don't know exactly the cash
4:50
flows you receive, and you don't know
4:52
what the future interest rates, one-year
4:55
interest rate will be.
4:56
Okay?
4:57
So, that took us to the concept of
4:59
expected present discounted value, in
5:01
which you just replace all the things we
5:04
don't know today for the expectations of
5:06
those things. Okay? So, we don't know
5:08
the cash flows in the future, that's the
5:09
reason
5:10
but we have an expectation,
5:12
that's that's what you put there, and uh
5:25
we don't know the future we know the
5:26
current interest rate, but we don't know
5:27
the less
5:28
than it was when the interest rate was a
5:30
little lower. Okay?
5:32
Okay, and then we look at a two-year
5:34
bond, a bond that pays nothing up to two
5:36
years from now, and we said, "Well, two
5:38
years from now pays 100 and then
5:40
matures." Well, the price of that bond
5:42
will be
5:44
you know, this. Okay? And notice that in
5:47
this case, the price of a two-year bond
5:49
at time t goes down if the either of the
5:52
one-year rates goes up. Okay? It can be
5:55
the first this year's one-year rate, or
5:59
then maybe that's the expectation that
6:00
the one-year rate uh
6:03
next year will go up. Okay?
6:07
Good.
6:08
Then I introduce an important concept,
6:10
which is this concept of arbitrage
6:12
pricing.
6:13
Okay? Which is
6:16
uh two instruments
6:18
uh
6:19
um
6:21
should give you sort of the same
6:22
interest rate. We're leaving risk
6:23
considerations aside. It should give you
6:25
the same return
6:27
when you compare them
6:29
uh um
6:31
uh over the same maturity. Okay? So,
6:35
in this particular example, I said,
6:37
"Look,
6:38
a one-year bond
6:40
and a two-year bond that you invest you
6:42
hold for only one year should give you
6:45
more or less the same return."
6:47
Okay?
6:48
So so
6:49
so that means
6:52
that
6:53
this is the return you get from a dollar
6:55
invested in a one-year bond,
6:58
okay? Should be equal to the return you
7:01
get
7:02
by investing in a in a two-year bond and
7:04
selling that bond after one year.
7:07
And that's the expression we had here.
7:10
Okay?
7:11
If you this is what you pay for a for a
7:13
for a two-year bond, and this is what
7:16
you expect uh uh
7:19
to to be paid for that bond when you
7:21
sell it one year from now. Notice that
7:24
one year from now, the two-year bond
7:26
will
9:55
when you sell it 1 year from now. Notice
9:57
that 1 year from now the 2-year bond
9:59
will be a 1-year bond because 1 year
10:02
will have expired and that point it will
10:03
be a 1-year bond. That's the reason we
10:05
have a subscript P1T here.
10:08
So, that means that we can solve from
10:09
here that P2T is simply that.
10:13
But there's an expression like the one
10:15
we had for the 1-year bond at time T,
10:17
there is 1 over T plus 1. We put
10:19
expectations because we don't know the
10:21
actual interest rate in the future.
10:25
And then I stuck this into there and I
10:29
we got exactly the same price that we
10:32
got with the net present expected
10:34
present discounted value approach, okay?
10:36
And so, this asset pricing this
10:38
arbitrage way of pricing things is an
10:40
incredibly powerful tool
10:42
that is used very extensively in
10:43
finance. This These are simple
10:45
calculation, but when assets gets to be
10:47
tricky, much more complicated,
10:50
this is is very useful.
10:54
Then we talk about bond yields.
10:57
And bond yields are defined
11:00
as the constant interest rate
11:03
that
11:06
that is consistent with the current
11:08
price of that particular bond.
11:11
Okay? So, in the case of the 2-year bond
11:14
we call the 2-year rate.
11:16
That interest rate that is constant over
11:19
the two periods.
11:21
That's Okay, that's the reason I have
11:22
squared it. It's not I1T * 1 I1T + 1.
11:27
I squared it.
11:29
It's not constant over time. This The
11:31
2-year interest rate may be moving a
11:32
lot. I mean, the the Fed just hiked by
11:34
25 basis points. I'm sure all rates are
11:36
moving at this moment. So, the rates can
11:38
be moving at all points in time, but
11:41
they But we define as the yield is at
11:42
one point in time. You tell me the price
11:44
of the bond. You tell me the payoff of
11:46
the bond, then what is the the the
11:49
constant interest rate that makes this
11:52
price this expression equal to the
11:54
actual price? That's the way we define
11:57
the 2-year rate. That's the 2-year rate.
12:00
And if you have a bond that pays 100 n
12:03
years from now, then there would be a
12:05
constant interest rate In n, you know,
12:08
that that gives you 100 divided by 1
12:11
plus InT
12:13
uh
12:14
to the n
12:15
to the n power
12:17
that will give you
12:19
that you set that equal to the price the
12:22
actual price of the bond, the one you
12:24
get out of expected present discounted
12:26
value or out of arbitrage, then you have
12:29
found the yield or the yield to
12:31
maturity.
12:34
You know, we know what the We already
12:36
got the price from the previous slide.
12:38
We know that the price of this bond is
12:39
going to be 100 as a 2-year bond
12:42
divided by this product of 1 plus
12:44
interest rate 1-year interest rate. So,
12:47
this has to be equal to that. That's the
12:48
way actually you calculate the 2-year
12:50
yield.
12:52
Uh
12:52
and numerators are the same, that means
12:54
the denominators have to be the same.
12:56
And this implies approximately that the
12:59
2-year rate is a sort of average of the
13:02
expected 1-year rate, okay?
13:05
So, in this case the 2-year rate is a
13:08
sort of average of the 1-year rate. That
13:10
means that when the
13:12
when you expect the interest rate to be
13:15
the 1-year rate to be rising over time
13:17
then the 2-year rate will be above the
13:19
1-year rate today.
13:21
That's when the curve is We say the
13:23
curve the yield curve is steep. Let me
13:25
show you something.
13:31
There.
13:33
When the curve looks like that, so steep
13:36
means that
13:38
the the the later the 2-year rate the
13:41
3-year Well, here in particular the
13:43
3-year rate is the 2-year rate is higher
13:45
than the 1-year rate. The 3-year rate is
13:48
higher than the 2-year rate and so on
13:49
and so forth.
13:50
That happens when when you expect the
13:54
market expects the interest rate to be
13:55
rising
13:56
over time. The 1-year rate to be rising,
13:59
okay? Because Remember the 2-year rate
14:02
is the average of the existing the
14:04
current 1-year rate plus the expected
14:06
1-year rate 1 year from now.
14:08
For that average to be higher than the
14:10
1-year rate now, it has to be the case
14:13
that the one expected 1-year rate 1 year
14:15
from now has to be higher than the
14:17
current 1-year rate. Okay? So, that's
14:20
what you tend to get uh
14:22
that's when you get to the upward
14:23
sloping term structure. And when you get
14:25
a downward sloping term structure, which
14:27
is the way it looks right now, actually
14:29
right now looks very downward sloping.
14:31
There you are. You know, it looks very
14:32
downward sloping. Is people expect that
14:35
we're getting to the peak of current
14:38
policy rate of short-term interest rate.
14:40
And so, people expect now for the
14:42
interest rate to decline going forward.
14:45
And that's the reason
14:46
the the the 2-year rate now is lower
14:50
than the 1-year rate.
14:53
And the 5-year rate is lower than the
14:55
2-year rate and so on.
14:59
Uh as you can see here, it's very steep.
15:02
Okay. Then we said, "Well, let's add
15:05
risk because here Sure, here we assume
15:08
that you were indifferent between
15:10
investing in a completely safe 1-year
15:12
bond
15:13
and a and a 2-year bond in which you
15:15
have to make an expectation about the
15:17
price, but that price could move around.
15:18
So, there's risk on that price or the on
15:20
the price of 1-year
15:22
bond the 1-year bond
15:25
uh
15:25
as of today.
15:27
And then and so
15:31
So, we added risk. And there are two
15:33
type of risk in bonds. One is default
15:35
risk that, you know, that that they had
15:37
promised they would pay you 100, but it
15:39
may it may be happen that they cannot
15:41
pay you the 100. The corporation or the
15:43
government or so on. Argentina defaults
15:45
in its bonds regularly, okay?
15:48
Uh for example. Uh
15:50
many of the of the of the
15:53
regional banks that had gone under will
15:54
default on their bonds as well, okay?
15:57
So, that kind of risk. But we remove
15:59
that risk and we'll focus for now on the
16:01
I'm going to focus mostly on the price
16:02
risk because I'm going to be talking
16:04
mostly about US Treasury bonds. US
16:06
Treasury bonds have no default risk, we
16:08
think. I mean, there could be an event
16:10
in a few weeks from now, but no one
16:13
expects that to be a lasting event. I
16:15
mean, if it is, there's a real mess, but
16:18
But anyway, but there is also price risk
16:20
because you have to hold this and then
16:22
sell it at the end of 1 year and you
16:24
don't know exactly the price what the
16:25
price will be. Okay? There's a risk
16:27
associated to that.
16:29
So, so that means that really you
16:32
shouldn't equalize the return on the
16:34
1-year bond to the return you expect to
16:37
get in in the 2-year bond. You should
16:40
add a little compensation for holding
16:42
the 2-year bond, for going the 2-year
16:44
bond route, okay? And so, rather than
16:47
expect to make 1 plus I1T
16:50
uh
16:51
with with the 2-year bond after 1 year,
16:54
you should expect to earn a little more,
16:56
okay?
16:57
And that's what this XB being positive
17:00
reflects. And so, in that case the price
17:03
the price of the 2-year bond is a little
17:05
different from what we had. In fact,
17:07
it's a little lower than what we had
17:09
because that's the way you compensate
17:10
for risk. I sell you an instrument a
17:12
little cheaper than it would have been
17:14
in the absence of risk,
17:16
so you you expect to get a little a
17:18
slightly higher return out of that,
17:20
okay? So, this price is lower than the
17:23
price without the risk premium here.
17:26
No? That means but it's still is
17:28
promising you 100, so that's exactly how
17:30
you get more return out of it because
17:32
you were buying something at a lower
17:33
price.
17:34
Okay?
17:43
So, I can do the same logic now and see
17:46
what the 2-year rate is, but now that I
17:49
have this
17:50
taking to account this risk and you have
17:52
that the 2-year rate now is the average
17:55
not only of the expected 1-year rate,
17:57
but also includes a risk premium.
18:00
Okay?
18:01
And so, and that tends to be the case
18:03
that the the further out in the curve
18:05
you are, the larger is that risk
18:06
premium. It's called term premium
18:09
because term is the same as maturity,
18:11
okay?
18:13
Um
18:16
Actually
18:18
sometimes that that is negative,
18:20
actually.
18:21
May and and recently up to very
18:23
recently. Now it's positive. But until
18:25
very recently that XB was negative.
18:28
And the reason for that, you don't need
18:29
to understand that now, is because
18:32
long-term bonds were great hedges.
18:35
Uh meaning meaning, you know, if there
18:37
is a for any major event, for a
18:39
financial crisis or something like that,
18:42
because in a financial crisis or a major
18:44
disaster
18:46
interest rates tend to fall.
18:49
And when interest rates fall, the price
18:50
of bonds go up.
18:52
Okay? And and so so that was a good
18:55
hedge. If you wanted to to protect your
18:57
your portfolio of equities and so on
18:58
against a major catastrophic major event
19:02
like a financial crisis or, you know, a
19:04
war or something like that, it was not a
19:06
bad idea to have some long-term US
19:08
Treasury bonds in your portfolio because
19:12
they would tend to go up precisely when
19:14
everything else was going to be losing
19:16
money, okay? And so, that's the reason
19:17
tend to be negative. Now that's not the
19:19
case because now one of the biggest risk
19:21
is inflation.
19:23
And so so uh if there's an inflationary
19:26
spike,
19:27
then interest rate will go down up, not
19:29
down. And that means the price of bonds
19:31
will decline. So, they will decline at
19:33
the wrong time,
19:35
So, the price of bonds of long-term
19:36
bonds now will tend to decline
19:38
uh when everything else is also
19:40
plummeting. I mean, if we get a negative
19:42
if we get an inflation surprise that
19:43
inflation is a lot higher than people
19:45
expected, asset prices are going to
19:47
decline, all of them, including
19:49
long-term bonds. And that's the reason
19:51
now this XB is positive.
19:56
Okay, so that's I think that's where we
19:58
were at in the previous lecture.
20:01
Any questions about that? Then I'm going
20:02
to Next step is to talk about equity.
20:06
No?
20:07
Yeah.
20:08
Why don't we add the interest the risk
20:10
to the interest rate for the one year
20:12
now?
20:15
Well, because next year that one for
20:17
this particular bond
20:19
that that bond will have no risk because
20:23
it will be one year to go
20:25
and at the end of that year you're going
20:26
to get the 100.
20:28
So, there's no risk that added. If it
20:30
was a three-year bond, then you would
20:32
have in two of those you would have risk
20:35
premium.
20:36
And but you wouldn't have it in the last
20:37
one because in the last one you don't
20:38
have the you're going to receive the
20:40
100.
20:42
If the bond could could could default
20:45
so because I'm only looking at price
20:47
risk in the bond.
20:48
Uh uh
20:49
if the bond could could default, then I
20:52
would add an extra
20:54
term there because it's the fall risk.
20:56
But but here I'm just looking at price
20:58
risk and I'm assuming the the unit of
21:00
time is one year. So, just one year
21:03
before it expires there's no more risk
21:05
because there's no price in between
21:07
and and you're going to receive a 100
21:10
uh uh
21:11
at the end of the year. In reality
21:14
time is continuous. So, so every second
21:16
there's a little bit of a risk. So, you
21:17
have a little bit of that risk all the
21:19
time except for the last second.
21:21
Uh but but
21:23
I'm looking at a simple example where
21:24
you know
21:26
things happen every one year. And
21:31
In the book I think they mess up
21:33
actually. They put the risk premium in
21:35
the wrong place. But
21:37
there was another question.
21:40
No?
21:41
Okay.
21:44
So
21:44
let's look at the stock prices now.
21:47
Uh
21:49
So, a stock price has two key
21:50
differences with respect to
21:53
um
21:56
Well, certainly there were but two that
21:57
I want to highlight.
21:59
The first is that they don't pay
22:01
coupons, fixed amount. They don't
22:02
promise you to pay, you know, $100 two
22:05
years from now or anything like that.
22:07
They pay dividends.
22:09
Okay?
22:10
They tell you we have a policy of paying
22:12
dividends and even different companies
22:14
differentiate themselves by how much
22:16
they promise to give you on average in
22:18
dividends, but it's a promise that if
22:20
everything goes as planned, they'll pay
22:22
you those dividends.
22:24
It's not a commitment to pay you a
22:26
dividend. When it's very different from
22:28
a bond. A bond says, "I'll pay you a
22:30
coupon of this amount every six months."
22:33
And if you don't pay that coupon, that's
22:35
a default.
22:37
There's nothing like that in equity.
22:38
Equity you buy shares of Apple and you
22:41
sort of look at the history of dividend,
22:43
what what the CEO told you the last time
22:45
the in the last release uh and and and
22:49
you know, you you can you you think,
22:50
"Okay, these are more or less going to
22:51
be my dividends." But there's no
22:52
commitment.
22:55
They will always tell you
22:57
what's their plan
22:58
but it's a plan. It's not a commitment.
23:00
So, that's the first thing. It doesn't
23:01
have fixed coupons or anything like
23:03
that. There's no commitment. And in that
23:05
sense there's no sense of default
23:07
because there was no commitment, so
23:08
there's no default.
23:10
Uh if if a company has to cut dividends
23:13
to zero, that's not a default.
23:15
That's
23:16
conditions change. That's it. There was
23:17
no commitment to that.
23:20
The second
23:21
feature is that they don't have a fixed
23:23
terminal date.
23:25
99.9999999%
23:28
of the bonds do have a terminal date.
23:29
They have a maturity. I mean, there's a
23:31
few exceptions which are called
23:32
perpetuities.
23:34
That I think the US has none for
23:36
example. But but but but most bonds have
23:39
a
23:40
uh uh a a maturity.
23:42
Okay?
23:44
Equity doesn't come that way. Nobody
23:46
tells you buy a share of Apple you don't
23:47
buy shares of Apple that
23:50
they will that will be retired 30 years
23:52
from now. Okay?
23:54
They will be there as long as Apple's
23:56
exist.
23:57
Okay?
23:58
Uh
24:00
Now, of course, you know, if you had
24:02
shares of First Republic Bank, you have
24:04
nothing now.
24:05
And because of that but but that was not
24:07
the original plan. If First Republic
24:09
Bank had been successful, you would have
24:12
the the shares would have survived for a
24:13
very long period of time. Okay?
24:15
So so there's no sense of maturity. In
24:18
principle
24:19
equity can last forever.
24:22
Okay?
24:27
So, I'm going to use arbitrage to to to
24:30
price equity.
24:33
So
24:34
uh
24:35
let me So, let's we have the following
24:37
uh
24:38
portfolio of options here.
24:40
Uh
24:41
one is our old one-year bond.
24:44
Okay? So, you can invest your dollar
24:45
today in a one-year bond.
24:48
The alternative I'm going to say there
24:49
is some equity out there. And I'm going
24:51
to call the price of that equity Q
24:55
and the dividend of that e- e-
24:57
equity D. Okay?
25:01
So
25:03
so let's price this stock by by
25:06
arbitrage. So
25:07
equity is risky.
25:09
I mean, that is much riskier than than
25:12
than than bonds unless you are into
25:14
Argentinian bonds or things like that.
25:16
But I mean, it's much riskier than
25:17
bonds.
25:18
So, there's always a risk premium and
25:20
actually that itself is a trade. You
25:22
trade the risk premium of equity market.
25:25
So, I'm going to put an XS here. So what
25:28
do you what do you expect to get from
25:30
from holding
25:31
Remember, arbitrage means the same
25:33
holding period. So, I'm going to compare
25:35
investing in a one-year safe bond
25:39
versus
25:41
buying equity today, buying a stock
25:44
holding it for a year
25:46
and then selling it there.
25:48
Okay? That because that's That's I
25:50
cannot do arbitrage for paying different
25:52
holding periods. That's a one-year
25:54
holding period.
25:55
So, I'm saying this is what I'm going to
25:57
get from the bond. I'm going to require
25:59
some risk compensation for that because
26:01
risk equity is risky. So, I'm going to
26:03
want that. And this is what I'm going to
26:05
get That's my return on equity I get.
26:07
This is what I'm going to pay today for
26:09
the stock
26:10
say for a share of Apple
26:12
and I'm going to get this. This is the
26:13
dividend I expect to get
26:16
at the end of the year
26:18
and then I this is the price at which I
26:19
expect to sell
26:21
that share
26:23
one year from now.
26:24
Okay?
26:25
So, that's the return I'm expecting to
26:27
get from holding the share of Apple for
26:30
one period.
26:31
Okay?
26:32
And that's what I need to compare with
26:33
holding for one year
26:35
one-year bond. But I want also to be
26:38
compensated uh
26:40
for uh
26:42
risk. Okay?
26:44
Good.
26:47
Is this clear?
26:51
Okay,
26:51
good.
26:53
I don't know whether silence means yes
26:54
or no. But this is
26:56
No, we did something like this with the
26:57
two-year bond except that we didn't have
26:59
a a dividend there, you know,
27:02
because there was no coupon at day one.
27:04
We only had a final payment of 100. But
27:07
we did this already when we compare the
27:09
one-year bond with holding the two-year
27:11
bond for one period. We had exactly that
27:14
except that there was the expected
27:15
dividend there was zero because there
27:17
was no payment at the intermediate date.
27:20
Okay?
27:22
Good. So, we we know this concept
27:23
already. The only difference here is
27:25
again that there is expected dividend
27:27
and second that we have a risk premium
27:31
here which we added for bonds, but for
27:32
equity as I said it's typically much
27:34
larger than for bonds, especially if
27:36
you're talking about treasury bonds.
27:41
So, I'm going to reorganize this to
27:43
solve out for the price, this QT here.
27:45
That's what I want to figure out. What
27:46
is the price of the share of Apple?
27:48
Okay?
27:49
Well
27:50
I can reorganize this which means, you
27:53
know, move
27:54
dollar QT to the left, divide these two
27:57
guys here by 1 + I1T + XS and I get
28:00
this. Okay?
28:02
So, the price is equal to
28:05
the discounted
28:07
expected dividend. I have to discount it
28:09
because I expect to receive it one year
28:11
from now and I want I also compensation
28:13
for risk
28:15
plus the discounted value of the
28:19
money I'm going to get from from selling
28:20
the share of Apple one year from now.
28:23
Okay? Which I also discount
28:25
by the interest rate, but also with a
28:27
risk premium because that's a risky
28:28
investment.
28:30
Okay?
28:31
So, that's what we have.
28:34
Now
28:36
notice that
28:39
at T + 1
28:42
I will have an expression like that as
28:44
well.
28:46
Okay, again.
28:48
When we did the two-year bond
28:50
we didn't have an expression like that
28:52
because
28:54
after after one year the two-year bond
28:56
was going to be a one-year bond.
28:58
And so, we didn't need to think of put a
28:59
price there. We just put the 100. Okay?
29:02
Here is different because we said this
29:04
equity never expires unless the company
29:06
goes bankrupt, it's there.
29:09
So, in the next date I'm going to have
29:11
an expression exactly like that. I'm
29:14
just going to have an expected T +
29:16
dividend at T + 2 and expected price at
29:19
T + 2. Okay? And so on and so forth.
29:22
That means
29:24
I can replace this expression here
29:27
by an expression like this shifted all
29:30
by one year.
29:33
Okay? And I keep can keep doing that.
29:36
Then if I do that, I'm going to get then
29:39
two expected dividends here and then I'm
29:41
going to get a
29:42
uh So, I'm going to get
29:44
something like this but shifted by one
29:46
year and discounted by two terms in the
29:49
denominator, and then I'm going to get a
29:51
expected Q QT + 2.
29:54
Around here, okay?
29:56
Well, I can do a substitution of that as
29:57
well. Again,
29:59
okay? By everything shifted by two
30:01
years, and so on.
30:03
So, I can keep going.
30:05
And I can keep going, and going, and
30:06
going, and going on forever.
30:08
Okay?
30:09
So, if you keep doing it,
30:11
you're going to end up with an
30:12
expression that gives you the price of
30:15
the asset as expected this
30:18
present discounted value of all the
30:19
future dividends you expect.
30:22
Okay?
30:24
You see? I I'm summing
30:26
the T + 2, 3, 4, 5, and doesn't stop
30:30
here.
30:31
If I stop here, I'm going to have here a
30:34
you know, a Q
30:36
E T + N
30:38
+ 1.
30:40
Well, I can replace that thing again,
30:41
and I can keep going, keep going
30:42
forever.
30:43
Okay? So, you're going to integrate the
30:45
expected dividends, discounted dividends
30:48
to infinity.
30:51
Now, each future dividend is discounted
30:53
more and more heavily because the
30:55
denominator is growing, and growing, and
30:57
growing, because it's further out in the
30:58
future, it's worth less and less. Okay?
31:00
But, still it can go on forever.
31:03
And in fact, even if you if you
31:05
substitute this stuff a million times,
31:07
there's going to still be a little price
31:09
at the very end floating around.
31:12
Discounted, but it will never go away.
31:16
Okay? So, it never ends. There's no
31:18
maturity.
31:19
They keep going.
31:22
Now, I did everything up to now for
31:24
nominal in nominal terms. You can do
31:28
And that's the reason I
31:29
didn't want to spend much time with
31:30
this. You can do everything in real
31:31
terms as well.
31:33
Uh
31:34
and and and all all that happens here is
31:35
just remove the dollars, and just be
31:37
careful to replace uh
31:41
the nominal interest rate by the real
31:42
interest rate, but nothing deep there.
31:44
Okay? I can you can go to real pricing,
31:47
nominal pricing, and so on.
31:50
Okay? But, the the important concept is
31:52
not that. It is is the fact that
31:55
this that the the in principle we call
31:58
that, by the way, the fundamental value
32:01
of a of a of a of equity or of stock is
32:04
the expected present discounted value of
32:06
all the dividends. And you have to
32:08
discount it by the proper discounting
32:09
factor, which includes interest rate and
32:11
risk premium. But, that's what we call
32:13
typically fundamentals. We differentiate
32:15
that from what we call sometimes, I'm
32:17
going to show you an example later on,
32:18
bubbles.
32:20
When when the price seems to exceed
32:23
any reasonable sense of fundamentals.
32:26
Okay?
32:32
Okay, good.
32:34
Okay, let me sort of start
32:36
going back to to things that that um
32:40
we worry about in this course, and in
32:41
fact is a big issue. I don't know what
32:43
is happening to markets now. The what
32:45
the Fed did was very anticipated, but
32:47
but
32:48
um
32:50
but markets of often find a way to react
32:53
to things even if things were
32:54
anticipated, but
32:57
What happens? So, let me ask you a
32:59
following question.
33:01
What is the effect What do you think is
33:03
the effect
33:05
of an expansionary monetary policy
33:08
on the asset prices we have discussed?
33:09
So, bonds and equity.
33:13
Let's start with bonds
33:15
first.
33:16
What do you think is the effect of an
33:18
expansionary monetary policy? That means
33:20
a reduction in the interest rate on the
33:21
price of your 1-year bond, 2-year bond,
33:24
any any year you pick.
33:30
We already talked about that earlier.
33:35
Goes up.
33:36
The price of a bond is inversely related
33:39
to
33:41
the interest rate because if I cut an
33:43
interest rate,
33:44
means
33:45
a bond is something that pays the payoff
33:47
is in the future.
33:49
That thing in the future is worth more
33:52
if the interest rate goes down.
33:54
There's less discounting of it.
33:56
So, the price of the bond, any bond
33:58
here, will go up. The 1-year, 2-year,
33:59
3-year, 5-year, all of them.
34:02
They'll go up. Okay?
34:04
Assuming that nothing changes as a
34:06
result of the monetary policy. Look,
34:07
what happens is sometimes,
34:09
you know, markets think, "Oops, the Fed
34:11
messed up." And that leads to lots of
34:13
changes in all the term structure and
34:14
things like that because
34:16
they expect the market to react in a
34:18
strange ways to to this mistake made by
34:20
the Fed. But, here I'm saying suppose
34:22
that the Fed just cuts the interest rate
34:24
once, and everyone believes that the Fed
34:25
will continue to do so, and so on.
34:27
Well, then you're going to get uh that
34:31
that the price of bonds will go up.
34:34
What will happen to the price of stocks?
34:38
You want to answer.
34:41
Up.
34:43
But, it's
34:45
Well, but it's important to see that it
34:46
will go up probably for two reasons.
34:49
The first one
34:50
is that that
34:52
um
34:54
is that
34:55
it's also the case that a lot of the
34:58
price of an equity, actually even more
35:00
so than a bond,
35:01
has to do with expected payoffs in the
35:04
future.
35:05
So, if I lower interest rate, just the
35:06
effect of discounting will tend to raise
35:09
the price of So, even if I don't change
35:11
the expected dividends at all,
35:13
the fact that the interest rate goes
35:14
down,
35:15
for the same reason that the price of a
35:17
bond went up, the price of equity will
35:19
tend to go up. Okay? So, that's exactly
35:21
is the same logic.
35:23
But, there's an extra kick here for
35:25
equity, which is what?
35:27
That bonds did not have,
35:29
but equity does.
35:31
At least if it is an equity that is
35:33
positively related to aggregate
35:35
activity, but that's what I'm assuming
35:36
here.
35:53
Well,
35:55
yeah, that's the logic, no? Here, the
35:57
expansionary monetary policy is cutting
35:59
interest rate, but as a result of that,
36:00
output is going up.
36:02
When output is going up, sales will go
36:04
up, revenues will go up, dividends will
36:06
probably go up as well.
36:08
So, monetary policy can have very large
36:10
effect. I mean,
36:12
people in financial markets are looking
36:13
at the Fed all the time because it can
36:15
have a big impact on the price of those
36:18
assets.
36:19
An equity in particular can can be very
36:21
strong. And in fact, that's one of the
36:23
ways monetary policy works.
36:25
You know, when when when
36:28
the Fed cuts interest rates,
36:31
inflate it inflates the value of asset
36:32
prices, and that creates more wealth,
36:35
people feel richer, consume more, blah
36:37
blah blah. Firms feel also richer, they
36:40
invest more, and so on. That's That's it
36:42
That's
36:43
That's deliberate in a sense. Okay?
36:45
Uh that's one of the main mechanisms
36:47
through which monetary policy affects
36:49
aggregate demand. Just creates wealth.
36:52
And when there's too much demand too
36:54
much aggregate demand, like last like is
36:56
going on now, that's the reason we have
36:57
inflation, and so on.
36:59
You know, in 2022, the Fed went out and
37:02
deliberately destroyed wealth.
37:05
Because that's what that's what needed
37:06
to. Raise interest rate a lot, the price
37:08
of equity came down, even houses began
37:10
to bubble. Okay? The price of
37:13
uh of of treasury bonds also collapsed,
37:16
and so on and so forth. Okay?
37:19
Good.
37:21
Another experiment that we did sort of
37:22
early on, lecture three, four, but
37:25
around there,
37:26
is
37:27
What happens What do you think happens
37:29
when there's an increase in consumer
37:30
spending?
37:32
So, suppose that now, remember we had a
37:34
a C 0 floating around, an autonomous
37:36
consumption component, and so suppose
37:39
that that goes up.
37:43
What do you think happens to asset
37:44
prices?
37:47
And this is a big issue these days,
37:48
actually.
37:54
Exactly. That's right. That's That's
37:56
That's very good. It depends a lot. I
37:58
mean, when financial markets receive
38:00
news every day, there are releases of
38:02
news and of all sort of things. Okay?
38:05
And and
38:06
in financial markets, they people always
38:08
think, "Okay, this is the news.
38:10
The obvious thing for this is
38:13
you know, good news, because this will
38:14
tend to increase output. Output will
38:16
increase dividends. That's a good good
38:17
thing for
38:19
for stocks."
38:20
Uh
38:21
But, the immediate reaction is, "Whoa,
38:24
but what will the Fed do about this?
38:26
Does the Fed like
38:27
that we have more aggregate demand or
38:29
not?"
38:30
Okay?
38:31
And so so so that's that's
38:34
key here.
38:35
And and uh so suppose that in this case,
38:39
the Fed did not like
38:41
the Fed like today to the Fed doesn't
38:43
want more aggregate demand today.
38:45
There's no central bank around the
38:46
world, maybe in China, but but there's
38:48
no other central bank around the world
38:50
that wants more aggregate demand.
38:53
Okay?
38:54
So, so if if it's if if you the release
38:57
is consumer
39:00
are very bullish now,
39:02
uh
39:03
that's not good news. I mean, financial
39:06
markets immediately say, "Uh-oh, we have
39:08
a Fed that is watching for inflation.
39:10
This means they're going to hike
39:11
interest rates."
39:12
Okay?
39:13
So, what happens to the price of bonds
39:15
then in this environment when C 0 goes
39:19
up, and the Fed doesn't like it? And and
39:21
the markets know that the Fed doesn't
39:22
like it. The Fed may take a month to
39:24
react to it, but markets react
39:26
immediately, say, "Whoa, this is what
39:28
the Fed will do 1 month from now."
39:30
Okay?
39:32
So, what do you think happens to the
39:33
price of bonds
39:35
if we get news that, you know, consumers
39:37
are
39:38
very bullish, and and and and it turns
39:41
out that we also have
39:42
of you know 4% or so, so we know that
39:45
the Fed doesn't like more aggregate
39:46
demand.
39:48
What do you think will happen to the
39:49
price of bonds?
39:56
Well,
39:58
again,
39:59
the news happens say
40:02
uh
40:03
a week ago
40:05
and the Fed moves one week later.
40:07
So so markets are going to anticipate
40:10
that in this case the Fed will hike
40:11
interest rates.
40:14
If the Fed is the markets anticipate
40:15
that the Fed will hike interest rate,
40:17
interest rate will go up immediately.
40:19
Not the not the rate that the Fed
40:21
controls, but the one-year rate, the
40:22
two-year rate, the three-month rate, all
40:24
those rates are going to go up
40:25
immediately as a result of that.
40:28
Okay? And that
40:30
we know
40:31
reduces the price of bonds. Bonds and
40:33
interest rates are The price of a bond
40:35
and the interest rates are inversely
40:36
related. So the anticipation that the
40:38
Fed will hike rate will lead to higher
40:41
interest rates at all horizons and and
40:43
and that will reduce the price of bonds.
40:46
Okay? So this thing that and for equity,
40:50
well, look what happened for equity
40:52
here. Well, for equity you say, "Okay,
40:54
well, I get the same discounting effect
40:56
of the bond, which is bad news, goes
40:58
down."
40:59
And
41:00
and what about The good news is the
41:01
dividend, no? Because now I have more
41:03
consumers.
41:05
Well, that depends on how much the Fed
41:07
dislikes this stuff because if the Fed
41:09
does this, that mean it offsets it fully
41:11
offsets
41:13
the the effect on aggregate demand.
41:16
Increasing this zero shift IS to the
41:17
right, that would have increased output
41:19
to here. The Fed doesn't want more
41:21
output, so we will hike interest rate up
41:23
to the point in which output doesn't go
41:24
up.
41:25
That means dividends are not going to go
41:27
up either.
41:28
So we get just a negative effect of the
41:30
discounting and we don't get the benefit
41:33
of the extra activity that would have
41:34
come from having consumers that are more
41:36
optimistic and so on. Okay?
41:39
So this is actually this has happened a
41:41
lot
41:42
uh
41:43
over the last few months.
41:45
This is an environment people call it's
41:47
an environment where good news is bad
41:49
news.
41:50
Okay?
41:51
Good news about aggregate demand,
41:52
consumers are happy, blah blah blah, is
41:54
bad news or labor markets are very
41:56
tight, wages are going up.
41:58
All things that sound wonderful in other
42:00
environments
42:01
sound terrible news for the financial
42:03
markets. Okay?
42:06
For most, I mean there's difference in
42:08
different sectors and so on, but but for
42:10
the aggregate, for the average,
42:12
it's bad news. So this is an environment
42:14
where good news is bad news. Good news
42:16
about aggregate demand, you have to be
42:17
specific about what. Good news about
42:19
aggregate demand is bad news
42:21
for asset markets.
42:23
It's not always like that.
42:24
If you're in a recession,
42:27
the Fed doesn't want to fight that. It
42:28
wants to have more aggregate demand. So
42:30
if you get good news about aggregate
42:31
demand, that's very good news for asset
42:33
prices
42:34
because the Fed will not offset that and
42:36
you get the positive effect of the extra
42:38
dividends and things like that. Okay?
42:41
So
42:43
Okay.
42:45
Another component that is that moves
42:47
asset prices a lot. So monetary policy
42:49
moves asset prices a lot. Okay? And and
42:52
monetary but monetary policy doesn't
42:54
happen in
42:55
some separate isolated space. It it it
42:58
reacts to news about the economy, about
43:00
consumers, about firms, about regional
43:03
banks, all sort of things. Okay?
43:07
Uh another big driver of asset prices is
43:11
this guy here
43:13
of of equity in particular
43:15
is this risk premium.
43:17
Okay?
43:18
So that risk premium can move a lot
43:21
and and it's an important driver of
43:23
asset prices.
43:25
This index, this is the it's called VIX.
43:28
VIX is I'm not going to explain what it
43:30
is, but
43:32
people call it so you get a the picture,
43:34
an index of fear in an equity market. It
43:37
it it's it's done
43:38
Well, I'm not going to tell you what it
43:39
is. It's it's based on option prices and
43:42
so on.
43:43
Uh so this is
43:45
this is, you know, when people realize
43:47
that COVID
43:48
was coming and so what you see is that
43:51
this thing exploded up.
43:54
Big big risk off.
43:56
That's a massive spike in the little
43:58
excess.
44:00
Well, not surprisingly look what
44:01
happened to equity.
44:03
You know, collapsed by 35% or so.
44:06
Part of that was expected dividends,
44:07
blah blah blah,
44:09
but a lot of it was the risk off.
44:11
And it's called risk off when
44:14
markets are very fearful. They don't
44:16
want to take risks, risk off. Okay? Uh
44:20
the recovery actually also had a lot to
44:22
do with
44:24
the recovery on the risk environment.
44:26
People were sort of
44:27
getting used to the thing.
44:29
But that recovery also was a result of
44:31
very aggressive monetary policy. The Fed
44:33
tried to offset this by it cutting
44:35
interest rates very aggressively and
44:38
that also gave a boost to asset prices.
44:40
In fact, they did so much that we ended
44:42
up with a big
44:43
lots of overvaluation in asset prices
44:46
and then that's the reason when they
44:47
hiked rates, so we had big a big decline
44:49
in asset prices
44:50
as a result. Okay?
44:54
What is this? Ah, look, this is
44:57
you know
44:58
over the weekend
45:00
over the weekend the
45:02
I I
45:03
we talked about this in the previous
45:04
lecture
45:06
um essentially the First Republic Bank
45:09
went under
45:11
uh and JP Morgan absorbed it.
45:14
Uh so people thought that um
45:18
that on Monday was was good because you
45:20
know, people thought that
45:22
this mini crisis was over.
45:26
Well, yesterday
45:28
uh it turns out that that
45:31
two other regional banks, their shares
45:33
began to collapse in the same way as the
45:36
First Republic Bank shares
45:38
collapsed the week before. Okay? So
45:41
panic immediately set in. So the VIX,
45:43
the fear index
45:45
This is intraday. So markets open here
45:49
and and the shares of this this this two
45:51
banks began to decline very rapidly
45:54
and so
45:56
VIX went up a lot.
45:58
And what you do This is SP This is the
46:00
main This is the SPX, the the main SP
46:04
S&P 500. It's the main price index
46:07
equity price index in the US
46:09
immediately declined.
46:11
Okay? So it's a That's the excess
46:13
moving.
46:14
Here excess move up
46:16
little X
46:18
and then it began to come down and the
46:20
markets began to recover.
46:21
So this risk on and off is a is a very
46:25
big driver
46:26
of equity prices.
46:32
This is one of the banks actually
46:34
that was in trouble.
46:36
Uh
46:37
You you see that
46:39
but by the end of the day this this this
46:42
this is
46:44
PacWest. PacWest had the decline by 28%
46:48
by the end of the day. But you see
46:49
things look very weird here. They don't
46:51
look like normal prices.
46:53
Okay? Here they look like normal prices.
46:55
They're moving all the time.
46:57
Here they don't.
46:59
What happens is that these prices
47:00
decline so rapidly that they they
47:02
trigger what is called circuit breakers.
47:04
So the
47:06
you cannot trade those those shares when
47:08
they decline too rapidly. And that's
47:09
done deliberately so this little X
47:12
doesn't get completely out of control.
47:14
People to calm down. Okay?
47:17
And so it triggered several times.
47:19
Just as
47:21
the the whole idea is that people calm
47:23
down.
47:26
Is there a question? Yeah, there's some
47:28
of us like
47:29
The previous or this one? Yeah, the
47:30
previous one.
47:32
Is
47:33
Are either of them dependent on the
47:35
other or are they more just showing the
47:37
same sort of trend? No, no. Okay, it it
47:40
doesn't a good question. Uh uh
47:43
This is the risk component only. So this
47:46
is more independent what I'm saying.
47:49
When this guy goes up, if nothing else
47:50
happens,
47:51
uh this will decline because you're
47:53
discounting things more heavily.
47:55
But it is true that there were some
47:57
common elements. Like there there are
47:58
also common elements, which is people
48:00
got very worried about having another
48:02
regional bank collapsing and so on. And
48:04
so that that also created fear about the
48:07
economy, which is an independent reason
48:09
for this to decline. And normally in
48:11
recessions as well, this risk in
48:14
appetite is is is is lower. So so you're
48:17
right that it's a common component. But
48:19
the point I was highlighting is that
48:21
is that this VIX sort of is a big
48:23
driver. It has a big impact on asset
48:26
prices.
48:28
But it's not the cause.
48:29
It was an event that caused both, but
48:32
the fact that this event came with this
48:34
biggest spike in in the VIX meant that
48:37
that the impact on the equity index was
48:39
was larger than if it had been only news
48:41
about the economy, meaning that there
48:43
was a recession ahead or something like
48:45
that.
48:46
And let me just finish with a with with
48:48
the opposite phenomenon.
48:51
You know,
48:52
I was talking in episodes of fear, but
48:54
sometimes markets get very carried away
48:56
in the opposite direction. Okay? And
48:58
here I'm showing you you know, examples.
49:01
I put together this picture many years
49:03
back and now Deutsche Bank keeps
49:05
updating it, which is it shows you some
49:08
some It seems that the world needs a
49:10
bubble somewhere.
49:11
And then here it shows you several sort
49:13
of big asset valuations, you know, look
49:16
500%.
49:18
This here is the Nikkei. I mean, it was
49:20
enormous appreciation of the Nikkei.
49:22
Here was Bitcoin. Then it collapsed.
49:24
Okay? They always end up bad. When you
49:26
never you see this big sort of a spiking
49:28
up, they almost always end up quite
49:31
poorly. Now, this is
49:34
is much more likely that it happens in
49:36
equity than in bonds. In bonds, it
49:37
cannot happen because there is a
49:38
terminal date,
49:40
a terminal value. So, so what happens
49:43
with these kind of things, people dream
49:44
that the value go will go to infinity.
49:47
No, and it could because the thing will
49:48
last to infinity and and you know, the
49:50
price could go to infinity. For a bond,
49:51
that cannot happen because it has a
49:52
terminal date and at that date they're
49:54
going to pay you 100, so it can't
49:55
happen.
49:56
But for equity, people's imagination can
49:59
run very wild. In fact, there is a
50:01
famous bubble, the South Sea Bubble.
50:04
It's a company in the UK.
50:06
It is a famous for many reasons, but but
50:08
one of them is that Isaac Newton got
50:10
involved in in this one. And and you
50:13
know,
50:14
he got carried away. He he sold, he made
50:16
a profit, you know, he sold the shares
50:18
at 7,000. He profited 3,500 pounds,
50:21
which must have been an enormous amount
50:22
of money at the time.
50:24
Prices kept going up,
50:26
couldn't resist, went back in, ended up
50:29
losing 20,000 pounds, which must have
50:31
been a lot of money. So, he famously
50:33
said, "I can calculate the motions of
50:34
the heavenly bodies, but not the madness
50:36
of people." It's all about expectations,
50:38
okay?
50:39
Let me stop here.
— end of transcript —
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