Ses 4: Present Value Relations III & Fixed-Income Securities I

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visit MIT OpenCourseWare at ANDREW LO: These are the
financial highlights of Lehman Brothers as of the end of 2007. Now, you can get more
recent highlights from looking at
their SEC filings, their 10-K and 10-Qs
which are accounting reports that they provide to
the SEC on a quarterly basis.

But I just thought we'd take a
look at the annual financials of this business. At the end of 2007, the net
revenues for Lehman Brothers was $19 billion. This is a firm that earned $19
billion in revenues in 2007. We're not talking about
a small little shop here. This is a major
financial institution. And if you look at their
profits, their net income, $4 billion of net
income in 2007. And 2007 was not a great
year, so $4 billion of income is a pretty impressive number. And if you look at their
long-term capital, the capital base, we're looking
at $145 billion. And if you take a look at
their assets under management, the assets under management,
in billions, is $282 billion of assets under management. Now, at the end of
2007, would anybody have forecasted that
a company like this could be gone nine months later? Gone– I mean, just obliterated. 28,500 employees, so we're
talking about major disruption to the New York workforce. A number of people are going
to be looking for jobs. Now, a number of
jobs are going to be created as a consequence
of these dislocations. I'll come to that in a minute.

But this is an
extraordinary set of events. And one key to what's
going on and why this might have happened
is this number right here, the net leverage ratio. That net leverage
ratio tells you something about how much
exposure Lehman Brothers had relative to how much capital
they're actually managing. And let me give you an example
of what I mean by that. And I'm going to give you a
personal example that we're going to come back to. We talked about
mortgages last time, and I told you all that
you now have the power to compute mortgage payments.

Well, you know that a
mortgage is a loan, right? You're borrowing
money from the bank to buy this beautiful home
that you want to live in. Does anybody know how
much money you typically have to put down
when you buy a home? Yeah. AUDIENCE: [INAUDIBLE] ANDREW LO: 20% is
the typical number, although in recent years,
it's much less than that. For example, when I first
bought my home way back in 1988, my first home, when I
moved here to Boston, I actually only
had to put 5% down because I was able to get a
jumbo loan and, in addition, purchase mortgage insurance
so that the bank was willing to lend me quite a bit
more than they usually would. Now, let's take the 20%
down as the standard number because that is absolutely
industry standard. If you put down 20% for,
let's say, a $500,000 home– which in the Boston area
is a little starter home, I'm afraid– a half a million dollar
home you put down $100,000.

And the bank lends you $400,000. The value of your total assets
is, of course, 500,000, right? You've got 100,000 of your own
money, 400,000 of the bank's money, and with that 500,000,
you give it to the other party to buy the home. And now you are the happy
owners of a $500,000 home. What kind of leverage ratio do
you have in that circumstance? Anybody calculate that quickly? AUDIENCE: It's 4 to 1? ANDREW LO: Close, but no cigar. 5 to 1, right? 5 to 1 in the sense that you
have five times leverage.

Your total exposure is 500. You've got 100. It's 5 to 1. Now, what does that
mean, 5 to 1 leverage? That sounds scary. That sounds like you
are really levered up. Well, it's only scary if
the value of the assets swings around a lot. For example, let's do a
simple back-of-the-envelope calculation. Suppose house
prices fall by 10%. That's only 10%, right? That's not a huge number. It's significant,
but it's not huge.

What's the return
on your investment? How much have you
invested in the home? AUDIENCE: 100,000. ANDREW LO: $100,000. If the value of the
home falls by 10%, how much has the value
of your assets fallen by? 50,000, right? Of that 50,000, how
much does the bank lose? AUDIENCE: None. ANDREW LO: None, right,
because they've lent you money, and they expect
you to pay it back. They're not equity holders. They're not looking to
take on any downside risk. They just want their
money back with interest. So the bank doesn't
care what the value is.

They still expect you to pay
back the $400,000 that they lent you with interest. So that $50,000
loss, it's all yours. And you've put down 100,000,
and you've lost 50– half of your assets
just got wiped out with only a 10% move in
the value of the home. Now, instead of putting 20%
down as a standard, what if you did what I did,
which is you put down 5%? So 5% of $500,000
is $25,000, right? The bank lends you $475,000. So this is not a
conforming loan. You've got to buy insurance,
and it's subprime, so on and so forth. 5% is your investment, $25,000. Now, suppose housing
prices go down by 10%. What's the return
on your capital? AUDIENCE: Negative. ANDREW LO: Well, you've
lost everything, right? The $50,000 loss is still
there, but you only put in 25. So you've now lost all of your
capital, and on top of that, you're in the hole
for another 25. So you've actually lost not
only all of your wealth, but actually, you've
lost more than all of it. You've lost minus 100% of your
wealth or your total return. Your net return is minus 200%. So, if you're a major
financial institution, and you're leveraged 16 to 1,
and the value of that portfolio declines by 10% or 20%, you
can go through capital very, very quickly.

Now let's do a back
of the envelope. The amount of capital
that they have– let's go up and take a look at this. The amount of capital that
Lehman had is something like– total long-term capital
$145 billion, OK? If you leverage that 16 to 1,
and then you ask the question, with that leverage
amount of capital, if it drops by, I
don't know, 10%, 5%, 7% of that total
asset base, you can see how you can go through
$145 billion of capital pretty quickly with leverage. Now, you might ask, why on
earth would anybody do this? Why would you leverage 16 to 1? Well, why would anybody
buy a house in New England with 5% down? That's just as crazy. What's the leverage
ratio if you put 5% down? AUDIENCE: 20 to 1. ANDREW LO: 20 to
1, exactly, so I was a proud leveraged investor
that had 20 to 1 leverage.

I beat Lehman Brothers. Why would I do that? Is that insane? Well, yeah. AUDIENCE: So you don't
[? tie ?] up too much capital. ANDREW LO: Well, yes. That's a very polite
way of saying it. Yes, I would tie up too much
capital if I didn't do that. The fact is, I didn't
have the capital. So thank you for being kind. But why wasn't it nuts? Yeah. AUDIENCE: [INAUDIBLE] ANDREW LO: Exactly. If the value goes
up, then I earn that kind of money,
the same kind of money. So if housing prices go up by
10%, then at 20 to 1 leverage, I look like a hedge
fund manager, right? Make a ton of money, but
that's not the only reason that I'm willing to do
that because you're saying that I want to take that risk.

Why would I do that? Yeah, Michael. AUDIENCE: Well, your
risk seems very low. ANDREW LO: Why? AUDIENCE: Well, in
the past, there's nothing to indicate that
prices would go down. ANDREW LO: Exactly. The risk of 20 to 1
leverage is only a risk if the amount of housing
price fluctuation is such that it could
actually wipe me out. But up until very
recently, housing prices have done nothing but this. They've gone up. And not only have
they gone up, they've gone up in a very smooth
and orderly fashion. You know, if house prices went
up by 15% a year every year, you might be thrilled,
but also a bit scared. That's not what happened. Housing prices have gone
up, maybe, I don't know– 8%, 10%, 7%, 5%, 6%. It's been relatively smooth.

And so the volatility,
the volatility of those kinds of
investments were low enough that the leverage
didn't scare me at all. And in fact, I
didn't lose money. I held that house for
about five or six years and bought another
one, and it was fine. It was fine because
that kind of leverage is not a problem as
long as the volatility of the overall investment
wasn't out of hand. What happened over the
last two or three years is that the volatility
has gotten out of hand. And we're going to talk
about that Wednesday at that pro seminar. I'm going to give you a concrete
illustration not only of how it got out of hand, but
how financial engineering and the design of
derivative securities to expand the housing market and
provide people with these loans exacerbated the problem
on the downside.

But of course, the
purpose of it was to help people on the upside. It's exactly looking
at the investments going up and thinking that,
gee, they could never come down. Yeah, question. AUDIENCE: What about the fact
that at the end of the day, you can live in your house? And the total valuation
of your house, if it goes down $100,000,
it's still a [INAUDIBLE].. ANDREW LO: Right. AUDIENCE: So you only
have to deal with the mark to market [? up and down. ?] ANDREW LO: That's a
very important point. The mark to market.

What does mark to market mean? Anybody know? We've never used that
term in class so far. Yeah. AUDIENCE: It's something that
book value gets [? matched ?] [? together with ?] reality. ANDREW LO: That's right. When something that may
have a book value gets marked to a reality check
in terms of market price. So for example,
the first lecture, where I auctioned off
that little tiny box that you had no idea
what was in there, it had no market
value beforehand, at least not to any of you. But we marked it to market. We marked it to
market at 45 bucks. And so it established
a market price. Now, the question is, who cares
what the value of the house is? You're living in it,
you're enjoying it, so what's the big deal? Well, that's right. It's not a big deal if you
enjoy living in the house, and you can afford to pay
the mortgage, and you're OK. And millions of homeowners
are exactly in that situation. So we can't forget that. That the subprime mortgage
has enabled literally millions of homeowners
to become homeowners who never could have.

But what if there's a problem
in terms of interest rates going up and your mortgage
payment going up because you ended up
getting a very low teaser rate for your mortgage? You've got an
adjustable rate mortgage because they said, gee,
you could buy this house with virtually no money down. And you've got
plenty of resources to be able to pay for it because
your payment is only $300 a month. And then, a year later,
that mortgage payment is $1,000 a month. Then it's a real problem. OK, then you've got a decision. The decision is, are
you going to keep paying all of your income
and have a hard time making ends meet for a house
that you'll never get the money back? It's literally taking
your money and burning it because you've lost your equity.

And you've lost so much
more beyond your equity that in order to
make money you'd have to hold onto the
house for 20 years, and you can't afford
the house anyway. Do you do that? Or do you put the
key in the front door and move out and say, you know
what, bank, it's all yours. I'm moving on. That's what's happened
across the country. It's the fact that people
can't afford these mortgages because they got in
at low teaser rates, and now the rates have come
up because the interest rates have been going up. Now, something very significant
is going to happen tomorrow. Tomorrow, the Fed
is almost surely going to cut rates
because they want to reduce the pressure
on the system for exactly these kinds of issues. They want to reduce the
kind of default rates. And by keeping
interest rates low, they actually are going
to be able to encourage liquidity and reduce
the kind of pressure that we've been seeing.

Yeah, question. AUDIENCE: I was
going to ask what happens if you put your 5%
down, and the value of the house goes down, say, 25%,
it's been only a year. You feel like you're not
going to get– it's never going to come back up. Can you literally just go to
the bank and say it's yours? ANDREW LO: Well, that depends
on what you signed when you got your mortgage from the bank. Most mortgage contracts are
known as non-recourse loans, meaning that they've got
your house as collateral, but that's all they've got. They don't have
your firstborn, they don't have your pinky finger.

And depending on where
you borrow, in some cases, you may have to give that up. But no, the fact of the
matter is the most they can do is take your house
away and sell it. And a lot of homeowners are
saying, great, it's all yours. I'm moving out of
Stockton, California. I don't need the house. I don't need to have
these mortgage payments where I'm throwing in
good money after bad. That's their perspective. AUDIENCE: What about
your credit score? ANDREW LO: Yes, so your
credit score will go to hell. So you wait. So you'll wait five
years or seven years, and then you'll be back again.

There's a finite
limit on how long they can keep those
kind of credit scores. And beyond a certain point,
you will have a clean record. But even with that
bad credit score– I mean, don't forget, that's
how the subprime mortgage market got created. You saw the TV ads, right? Doesn't matter if
you're in default, doesn't matter if
you have no credit, doesn't matter if
you don't have a job, we'll still give you a loan. Now, that's not true today,
or not as true today, but at some point when
the market recovers, we're going to see
that come back again.

And so you will be
able to borrow again. Yeah. AUDIENCE: Given that the
interest rates are now going up, does that mean
the [INAUDIBLE]—- ANDREW LO: Going down. AUDIENCE: Despite the fact that
the financial cut [INAUDIBLE],, the actual interest rate
that homeowners are paying hasn't changed. ANDREW LO: Right. AUDIENCE: So does that mean
that those with good credit are effectively subsidizing
those with bad credit? ANDREW LO: Well, yes and no. I mean, I think that
the subsidization that you're talking about really
happens very, very indirectly. The fact that there are
large numbers of defaults ultimately may mean that it's
harder to get a subprime loan. So the folks that
are actually good credits, but don't meet the
prime borrowing rate criteria, yes, they will suffer. But at equilibrium– by
equilibrium I mean when supply equals demand– the price is the
price is the price. So it depends on what kind
of a borrower you are, but whatever type
of borrower you are, if you can signal that
that's the type you are, you will be able to get that
appropriate kind of credit.

All right, so in
that sense, it's not as if taxpayers
are footing the bill for the particular interest
rate shifts that are going on. Taxpayers may end up
footing the bill for what happened with Bear Stearns,
what happened with Fannie Mae and Freddie Mac. And that's one of the reasons
why, over the weekend, when the Fed was approached
by Lehman Brothers and said, hey, you've got to
help us out here, the Fed said, you know what? We're done with that.

You know, sorry, but we can't
ask the American taxpayer to foot this bill either. Otherwise there's going
to be tremendous backlash. And so when Lehman
Brothers was left without backing
from the Fed, they went to a number of private
organizations like Barclays. Barclays said that they
would be willing to do it if the Fed was able to
provide some kind of backstop.

The Fed was not willing
to provide a backstop, so Barclays said
thanks, but no thanks. And at that point, Lehman said,
we have no choice because we cannot close a sale within a
matter of 24 to 48 hours from this point on. And we've got some
notes coming up. We've got to do something,
so they filed for Chapter 11. Yeah. AUDIENCE: If they cut the
rates [? as far as ?] they do, what's the negative part? Inflation? ANDREW LO: Yes. We're actually going
to talk about that in this next segment– inflation. If the Fed cuts
rates, one could argue that the reason we're
in the mess that we are is because the Fed
had kept the Fed funds rate so low for so long
that even after the stock market crashed with the
internet bubble bursting, the housing market
continued on with its bubble because it was still
so cheap to borrow.

And I'm sure I've
mentioned before that when I was an assistant
professor at the Wharton School back in 1986 looking
to buy a house, the 30-year fixed was at 18%. 18% for a 30-year
fixed mortgage. I didn't do it because I
couldn't afford it at the time, but think about
that versus today. Mortgage rates are maybe at
a recent high of 6%, 7%, 8%. That's not bad, relative
to historical standards. OK, so yes, I mean, I
think that's the concern that if we keep
interest rates too low, that's going to
encourage inflation. And inflation will
have its own costs. Anybody who's from any
Latin American country will know the ghost of inflation
is tremendously frightening. And we don't want to let
that get out of hand.

If you remember
back to the 1970s, we had some inflation in the
US that was a real problem. So we're going to talk about
that in just a couple minutes. Any other? Yes. AUDIENCE: I mean, is one
thing to do [INAUDIBLE].. You said that when
the market comes back, we will still have
another bubble. ANDREW LO: Absolutely, yes. AUDIENCE: And do you
think this is reasonable? ANDREW LO: Do I think
it's reasonable? You're not allowed to ask
that question to an economist. Or rather, an economist is
not allowed to answer that. Reasonable is relative. And there are moral
and ethical overtones that economists don't
like to get involved in.

It's human nature. Is it human to suffer
from fear and greed? Well, yes, and I
don't think I'm going to change that any
time soon, nor are you going to be able to
change that any time soon. So that's one of
the reasons why we study finance is to develop an
intellectual and disciplined framework for thinking
about these issues. Because if you
don't, if you don't have a framework for
thinking about this, then you're left responding
to fear and greed. Right now, we are in the
absolute grips of fear. Those of you who aren't
in financial markets, if you read the papers,
my guess is you'll start getting scared anyway. And if you're in
financial markets, I promise you this
is the scariest time that we've been in, including
August of '98, October '87, '94, 2001.

All of the kind of periods
of market dislocation is trumped by what's been going
on over the last few weeks. And it's exciting from the
point of view of being a finance student because you actually
have the opportunity to understand and do
something about this. But it requires a certain
discipline to do that. Yeah, Ingrid. AUDIENCE: What does it exactly
mean that Lehman Brothers are bankrupt? Because everybody, I guess
it's not a written one, but if I have some
money deposited there, will they give it back to
me because I am a liability? ANDREW LO: Well, that's
exactly the problem. The answer is I don't know. And that's one of the reasons
why there is this dislocation. Nobody knows
because nobody knows how large the losses could be. And part of the thing
is that the losses at Lehman and other
financial institutions, including Merrill Lynch– Merrill Lynch in some ways has
bigger exposure than Lehman. The difference is
that Merrill Lynch has other sources
of revenue that are able to let it get
through this situation a bit more gracefully.

But the problem is we
don't know because we don't know how the value
of these large assets are going to be valued. If you value them at zero,
then they're in deep trouble. And not only are
the shareholders going to get wiped out,
but a lot of the creditors are going to get wiped out. If you value them at
what they're valued now, well, then there are going to
be some hiccups along the way, but a number of
people should get out without outrageous losses.

AUDIENCE: And can't you sort
of declare default, stop paying now, until thing get better? I'm sort of applying my Latin
American experience here. ANDREW LO: Yes, yes. I mean that's exactly what
filing for bankruptcy does. When you file for bankruptcy,
you basically go to the courts and say, I cannot
make good on my IOUs. And I recognize that
this is a problem. So I'm going to ask the court
to appoint a conservator or supervisor to
oversee the disposition and dissolution of
my assets in order to make an orderly transition
to pay off all of the creditors.

And you know who's last in line? Shareholders. That's right. So most people think
the shareholders are going to get
nothing, which is kind of astonishing because
take a look at their closing price in 2007. The closing price of Lehman
Brothers stock, $62 a share at the end of 2007. Nine months later,
it's worth zero. Zero, from $62 a share. That's a huge
destruction of value.

And you know what? Part of that loss in value is
really due to the loss of brand and the loss of
business viability. It's intangible assets. It's not like all of a sudden,
the Lehman investment bankers and proprietary traders
and asset managers, they had brain damage and
they're a lot stupider than they used to be. They're just as smart, just
as savvy, just as experienced, just as knowledgeable
as ever were. The problem is that
because of the magnitude of their exposures,
there is general concern about their viability
as a business. And when you don't want to
do business with them, when everybody doesn't want
to do business with them, when nobody wants to
do business with them, they're not a business. And the value of their
business goes to zero. And so there's a
chicken and egg problem and you know the bottom
line is that irrespective of whether it's the chicken or
the egg, when the egg breaks, you're done. Yeah? AUDIENCE: [INAUDIBLE]
Bear Stearns [INAUDIBLE] extremely high? ANDREW LO: Yes, what
happened with Lehman is quite similar to
what happened with Bear.

Except that with Bear,
there was a panic that was triggered by what seems
to be some kind of a rumor, not necessarily large
exposures coming due. Bear Stearns
actually hedge funds that were engaged in these kinds
of subprime mortgages, CDOs and CDSs. Those funds went under
during the summer. But Bear Stearns as a business
collapsed because individuals really didn't want to
do business with it because of this kind of a risk. And the same thing
happened at Lehman. Except Lehman's exposure
was much larger. They have much larger
exposure to these markets. They're one of the
biggest players in these particular
kinds of securities. OK, because we're
running short on time, I'd like to just take
one more question and then let me go
on with our lecture. And believe it or
not, we are going to cover material
exactly related to this when we start talking
about fixed income securities. So this is very much apropos. Yeah, [INAUDIBLE]. AUDIENCE: How do you
think this affects us in terms of the people
that want to [? be bias? ?] ANDREW LO: Yeah, great question. AUDIENCE: [? 25,000 ?] people
from Lehman [INAUDIBLE] jobs [INAUDIBLE].

ANDREW LO: Absolutely. So this is a great question. I'm actually talk about that
specifically Wednesday evening. But let me let me give
you the short answer now. The short answer is that within
the next two or three months, Wall Street will be frozen. They're going to be a deer
caught in the headlights. They won't know what's going on. They won't know what
their hiring plans are. They won't know the
number of slots. There's resumes
flying back and forth. So it's going to be a bit of
chaos for the next two or three months. It's not clear that that's
going to affect you. Because internships
still have to be filled. Entry level positions are
actually of least concern to businesses because
those are the ones that they want to fill
because the new generation are hungry and smart.

Ready to do anything, take
on anything, and cheap. That's right. I didn't want to say
that but you said that. Good value. Let me put it that way. You're a good value. So what's going to
happen is it will be virtually impossible
for a senior managing director from one
firm to easily get a job at another firm
within the next two or three months until
things settle down. At the entry level job
market, I suspect that there will be some disruption. For example, just
a simple indication of that today after
my 4 o'clock session, I was supposed to meet with
the CFO of Bank of America, Joe Price. As many of you
know, we established a relationship with
Bank of America just recently– the Laboratory
for Financial Engineering to work with B of A to do
some interesting research and to get access to
their tremendous database.

And we were going to launch
that set of discussions today with Joe Price. Not surprisingly, at
3:00 in the morning, I got an email from
a B of A employee saying that he will not be
coming to MIT today after all. He was a little bit tied up. By the way, B of A also looked
at Lehman over the weekend. So over the weekend, B of A
folks wee pretty busy shopping. They looked at Lehman. But again, when the
Fed wouldn't guarantee any kind of a backstop for
Lehman, B of A passed as well. So that's an example of
the kind of dislocation I'm talking about. There will be scheduling
glitches and things like that. Going forward though, after
the two or three months, I actually think this
is a fantastic time to get into the industry.

Because when you have
these kind of dislocations, opportunities get created. And opportunities for
people that are smart, that are hungry, that are
willing to work hard– I mean, that's exactly
the kind of situation that you want to be in. When things are going
well, they don't need you. They're going to hire
people just to be clerks and to get people lunch. But now is the time where you
can actually have a big impact. So rather than be discouraged,
I think all of you have perfect timing in terms
of being in school now. In two years time,
you'll get out. That's when all
of the businesses are going to be recovering and
certainly doing quite well, I suspect. And even within the
next six months, you're going to see
that a number of firms are going to be hiring.

And by the way, the
dislocation we're talking about is on the broker-dealer side. On the asset management side,
hedge funds, pension funds, asset management companies,
foundations, endowments, non-financial corporations–
they're hiring and they need people
with financial expertise to deal with these kind
of market dislocations. So I think that the job
prospects are actually quite bright for this
class and the class after. The folks that are going to be
in a little bit of a tough bind are the second years who will
be interviewing for their jobs in the next two or three months.

They may end up having to
wait a little bit longer. And I suspect that they
will take a little bit longer to settle on their jobs. But even then, MIT
students end up having a bit of an advantage
over other MBAs simply because of the expertise
that we bring to the table. OK. So sorry about taking
them so much of your time, but I think this is relevant and
will be useful for what we're going to be talking about next. Let me turn to what we ended
with in the last class, which is the inflation topic. Last class, you'll recall, we
talked about the two formulas that you're going
to know very well by the end of this
course, perpetuities and annuities and compounding. And where we ended with was
this notion of inflation. How many of you already know
what inflation is and you've talked about it in macro? OK, some of you.

So let me go over it briefly. And I think you'll see
very quickly exactly what the idea is. It's really meant to capture
the fact that the purchasing power of your money can
vary over time, irrespective of the time value of money. And let me explain it this way– at a particular point in
time, let's say time t, you've got a certain
amount of wealth, wt. And the value of the kinds of
things that you like to buy is given by an index. Call it I sub t. So you could think about that
as the price of the basket of goods that you enjoy. OK? So this will include consumer
items, food, clothing. As well, it may include other
items– leisure, entertainment, and so on. And the fact that you have
a certain amount of wealth doesn't really tell
you how happy you are.

It's really how much
you're able to consume. How you use that wealth that
tells you how happy you are. So economists
really like to focus not on total wealth as a measure
of your standard of living, but how you are able
to consume that wealth. So we're going to come up with
a basket of consumption goods and call that price of that
basket, I sub t, all right? Now let's move from time
t to a different point in time, t plus k. So k periods from
now, you're going to have a different
amount of wealth. Hopefully bigger. And presumably, you're going
to be able to consume more. Well, that's presuming
that the prices of what you like to consume don't change.

But if those prices do
change, then in fact, you might not be really
better off in any way. And so in order for you
to tell whether or not you're better off
or worse off, you need to know not only
how much wealth you have, but how much that wealth can
buy you in terms of the stuff that you like to consume. So the idea behind inflation
is to measure the purchasing power of your dollar. And that's completely different
from time value of money. Time value of money simply
says that people are impatient and they prefer money
now to money later. But inflation is a comment
about the purchasing power of that dollar
now versus later. And it can go either way. In other words, it's possible
that a dollar next year will buy you more
than a dollar today because if prices decline, as
they have right now for energy, for example.

Energy is below $100 a barrel. Just a few months ago,
it was at $130 a barrel. So if we had a winter
a few months ago, that would have been really bad
because home heating oil would have been a lot more
expensive than it looks like it's going to be. However, it's still going
to be more expensive than it was two years ago, when
oil was at $40 a barrel. So you need to know
what you're going to consume in order to get a
sense of whether you are better or worse off. And that's what we
measure by this price index, I of t plus k. So when you're looking
at your portfolio, you might ask the
question what's my return on my portfolio. And the way you
calculate that return is look at your wealth at time
t plus k divided by your wealth at time t, subtract 1 from it.

And that's your return, right? That's often called
the nominal return because it's in
name only, meaning it's the actual
number of dollar bills that your wealth will grow to. So if you've got
$1,000 this year, next year you've got
$1,100, your nominal return for your wealth is 10%. That's the number
of dollar bills you'll have more than
you had this year. 10% more. Now if you want
to know how you're doing in terms of your
level of happiness, your purchasing power,
your cost of living, your standard of
living, you've got to look at what's going on
with a cost of living increase. I sub t plus k
divided by I sub t.

And we can write that as a
fixed growth rate, pi, per year. 1 plus pi to the k So let's suppose that all
the prices of the things you love and enjoy– they go up by 10% as well. Well, then have
you made any money? Have you made any progress? You've made money, but
you haven't made progress. You've made 10% in terms of your
return on your initial $1,000. But the stuff that you like
to eat and buy and use– that's also gone up by 10%. So in fact, you can't do any
more consumption next year than you could have this year.

Because while your wealth went
up by 10%, the cost of living went up by 10%. So from a real perspective– real meaning what you
really care about– you haven't really
made any progress. Inflation is a measure of
how much progress we've made. And so when you
engage in analysis of these kinds of
present value problems, you've got to ask the
question whether or not you're focusing on nominal
returns or real returns, OK? And ultimately, as a consumer,
what you all care about is real returns. You want to know whether you're
getting better off in terms of what you can really consume.

So how do you do that. Well, first of all, you
have to change the units. Sorry, question? AUDIENCE: Why pi? ANDREW LO: Why that letter? AUDIENCE: [INAUDIBLE] ANDREW LO: Oh, no, no, no. I'm sorry. Thank you for pointing it out. No, by pi, I just mean a
variable name called pi. I don't mean 3.14159. Only at MIT would I
get that question. I've taught at
other universities and they ask me what
that funny-looking symbol looks like. So yeah, sorry about that. This is just a Greek letter
that denotes a variable. It's like r or something. All right? Thank you. So here, what I've
done is to define a variable called your real
wealth at time t plus k. Real meaning this
is what you really can do with your money
in terms of consuming. What it is is your
nominal wealth divided by the rate of inflation. So in the case of the
example I gave you, where your nominal
wealth goes up by 10% and your inflation rate
goes up by 10%, when you take your nominal
wealth and you divide it by that growth rate in
inflation, what do you get? You get $1,000.

In other words, your wealth
hasn't changed in real terms. OK? So in the example that I gave
you your wealth went up by 10%. Your inflation rate
for a year is also 10%. So if you divide your
total wealth by that index, you're basically
going to get back to your original amount
of wealth, right? So here's the general framework. Your real wealth is going to
be your nominal wealth divided by the rate of inflation. You're dividing by
it because you're using, as your units of
comparison, today's consumption basket. Right? So the way you can look at your
real return, which is denoted 1 plus r real to the k-th power,
your real return over k years is equal to the real wealth at
the end of year k years divided by your wealth today. That's your real rate
of return, right? Because it's how much real
dollars you have at time k. That's just given
by your nominal rate of return of your wealth.

And then divided by
the rate of inflation. OK? So this is the
expression that is the basic relationship between
real and nominal consumption goods. And then we
approximate this ratio with this very, very
simple relationship here. The real rate of
return is approximately equal to the nominal rate of
return minus the inflation rate– not divided by anything. That's the approximation. So getting back to my example. My example of if you
have a 10% nominal growth rate for your investment and
you have a 10% inflation rate, then in that case,
there's no approximation. In fact, your inflation rate,
your real rate of return, is zero, right? 10% minus 10% is zero. Where the approximation
happens is when you have something
a little bit different. For example, suppose the
inflation rate were 10% and suppose your nominal
rate of return was 15%. According to this
approximation, what's your real rate of return? 5%, right. It's not exactly 5% because if
you take 1.15 divided by 1.10, it's not exactly 5%. But it's approximately
equal to that. OK? What this says is that you ought
to think, as a consumer, not just about the
total dollars that's growing but the purchasing
power of those dollars.

OK. For the purposes of
doing NPV calculations, I want to just mention
one rule of thumb that will do you in good
stead, no matter what kind of calculations you do. And that is simply to keep
track of whether you're using nominal or real cash flows. And then to use nominal or
real discount rates to match. In other words,
nominal cash flow should be divided by
nominal discount rates. And real cash flow should be
denominated by real discount rates. Most of the cash flows that you
will get in your analysis will typically be nominal. Nominal meaning that's the
actual number of dollars you will see on those dates. But occasionally, you
may get a forecast that is made in real terms– in terms of purchasing power. And in that case,
you have to just be careful to use the
right interest rate when you're doing your discounting. You have to take into
account inflation. Nominal gets discounted by
nominal, real gets discounted by real.

That's all you have
to remember, OK? Any questions about that? OK. We're now done with
lecture 3 and we're moving on to lecture 4, which
is fixed income securities. And this is the focus of much
of the dislocation in markets today. So this is very topical. And something that
I think you'll find very useful
when we start trying to understand exactly what's
been going on in these markets.

Let me start with a little
bit of an industry overview. And the industry
overview will give you a sense of why these markets
are so important as well as so large. OK. So we're going to
start, as I said, with an overview of
markets and participants. And then I'm going to talk
about evaluation of fixed income securities. It turns out that all of the
hard work that we've done just over the last three
lectures are going to be able to get us
through all of valuation for fixed income securities. In other words, you
now know all that you need to know to price
virtually any fixed income security without default.
Without uncertainty. Remember, we said no
uncertainty until lecture 12. It's a pretty significant
accomplishment because there are lots and
lots of securities out there that are fixed
income securities.

And you now have the
tools– you don't know that you have the
tools yet, but you do, believe me, to price them all. So we're going to go over
the valuation principles and apply them to discount
bonds and coupon bonds. And then I'm going
to talk to you a little bit about uncertainty. I want to bring in interest
rate risk in a very simple way. I want to simply
talk about the fact that interest rates
do change over time and that change can actually
cause some concern as well as some opportunities. I want to discuss what those
opportunities and concerns are. And then I'm going to conclude
by talking about default. I'm going to talk
about corporate bonds. And I probably won't talk
about the subprime issues in this class because I want
to focus on the material that's required. But I will talk about it in this
pro seminar, which is optional.

So you're welcome
to come on Wednesday and we'll go over that material. And if you want, you can
take a look at it yourself. It's pretty self-explanatory so
I think you'll see how it goes. For readings, I'd like you all
to read chapters 23 through 25 of Brealey, Myers, and Allen. You'll have three
lectures to do that. Lectures 4, 5, and 6
will all be focused on fixed income securities.

So let me talk to you a
bit about the industry now. The name fixed income securities
means exactly what it says. What we're going to do now is
to focus on pieces of paper where the payoffs are
fixed and known in advance. Unlike a stock where you buy
a stock and you don't know whether it's going to pay off
at all and the cash flows, the dividends or repurchases or
capital gains are uncertain– you don't have any idea what the
cash flows may or may not be– in contrast of those securities,
fixed income instruments have fixed incomes. So they have very, very
clearly stated payoffs that you know in advance. So from a pricing
perspective, these are probably the simplest
kind of securities that could possibly be constructed, right? Couldn't be simpler than
a piece of paper that says every year on this
date, I will pay you $10,000 of nominal currency, right? That's a fixed income security.

Examples are anything
from treasury securities, securities issued by the
United States Treasury and other foreign treasuries,
to federal agent securities. We know about those now, right? Fannie Mae and Freddie
Mac securities. To corporate
security– securities issued not by the government
or by government sponsored entities, but by
private corporations and public corporations. And then municipal
securities, these are securities issued
by local governments. And then mortgage backed
securities, securities that are payoffs of pools
of other securities, including mortgages. And then the whole mix
of collateralized debt obligations, collateralized
loan obligations, credit default swaps, and other
complex instruments. That's a lot of securities. And to get a sense of how many
securities we're talking about. let me show you the market. This is as of the end
of 2006 because that's the only data that I
could get that is timely.

At the end of 2006,
the US bond market consisted of just tremendous,
tremendous amount of assets. So $6.4 trillion in
mortgage-related securities, 24% of the market. $2.3 trillion in municipals.
$4.2 trillion in treasuries. $2 trillion in asset
backed securities. $3.8 trillion money market. $2.6 trillion in federal
agencies, securities, and so on. These numbers– they
dwarf the stock market. So we're traditionally
focused in financial analysis on pricing stocks
and analyzing stocks. And we get all excited
when Google tries to take over Yahoo and so on. But the size of the markets,
the size of equity markets are dwarfed by fixed
income securities. And again, these are
apples and oranges. And I'm just saying that there
is a hell of a lot more apples and there are oranges.

You can figure out what
you want from that, but these are
really big markets. And on this slide, I
show you the evolution of these markets– how
they've integral over time from 1985 to 2006. And what you'll see is that
the mortgage-related market has just grown by tremendous,
tremendous amounts. As well as federal
agency securities– that's Fannie Mae
and Freddie Mac. And asset backed markets
was nothing in 1985. It didn't exist in '85. And now we're talking about
a $2 trillion market here. So a lot has happened
in the last 20 years. It's been exciting times
for financial markets. And right now,
we're in the midst of some market turmoil because
of that unbridled growth. Now this is the
amount outstanding. This chart shows
you the issuance that is the amount of
debt that's being issued at any given point in time. So the first was an example
of the stock of debt at any point in time.

And now, I'm talking about
the flow of debt year by year. And you can see that as of
2006, mortgage-related bonds were the fastest
growing segment, by far. And that continued up
until 2007 and then the brakes started being
put on to that market. OK? And you can see over
time, the growth of these various different
markets and the fact that federal agency
securities grew but mortgage-related
securities probably was the fastest growing subject
to the asset backed market as well, which is related. Yeah? AUDIENCE: [INAUDIBLE] asset
backed and mortgage-related? ANDREW LO: Mortgage-related is
specifically about mortgages. Asset backed could be any asset. So for example, consumer
credit card loans– you can package that up
and sell claims on that and that would be under
asset backed securities, not under mortgages.

But they're related, obviously. OK. So these numbers
will give you an idea of what's out there, what's
significant and what's not. This gives you a sense of the
amount of trading that goes on. While these securities are
large in size and large in flow, they are not that large
in terms of transactions. So unlike stocks that
trade all the time, we don't have an organized US
bond exchange like the NYSE, where people trade bonds
every minute of the day.

There are bonds being traded
every minute of the day, but they aren't
typically the same ones. Whereas I would argue
that Microsoft and Google are traded every minute
of the trading day. So typically, bonds do
trade, but they don't trade on organized exchanges. And that makes them less liquid. Even the very, very safest
and most liquid bonds do not trade as frequently
as equities and futures. So the liquidity characteristics
can be very, very different for these instruments. And these complex securities,
like collateralized debt obligations, mortgage
backed securities– they trade even less frequently
because they are highly complex and it's not easy to figure
out what their prices are from minute to minute every day. Now the fixed income
market participants that we're going to be focused
on fall into three groups– issuers, intermediaries,
and investors. Issuers, of course, are the
end users of these instruments. They include everything
from governments down to foreign institutions.

These are the folks that issue
pieces of paper that are IOUs and they get cash
in return for that to finance their operations. And in return, they
pay interest, OK? The investors, of
course, are the folks that are buying the paper or
essentially providing loans. So every once in a
while, when I go out with my colleagues for
lunch in the finance group, one of my colleagues will
say, can I sell you a bond, I didn't go to the
cash machine today, and I need you to help
me finance my lunch. These are how finance
professors speak, unfortunately. The idea about
buying somebody bond is you're lending
them money, right? So instead of saying could
you let me $5, we have to say, well, I'm going to issue a
bond, can you buy my bond. The investors are the
ones that are loaning the money to the issuers.

OK? And these include, as I said,
governments, pension funds, insurance companies, banks,
hedge funds, and so on. In the middle of all of
this are the intermediaries. Primary dealers, other
kinds of dealers, investment banks, the
credit rating agencies, the credit enhancers. What do I mean by
credit enhancers? Folks that help credit
markets by providing insurance to the credit, like
private mortgage insurance. And liquidity enhancers. These are the
counter-parties that try to bring buyers
and sellers together to increase the
liquidity of the markets. The dislocation has been going
on in the intermediary sector and of course, the issuers
are having some difficulties now because they're going
to have to make good on these kind of claims. And the people that are
going to be hurt ultimately will be the investors who are
holding pieces of paper that may not be worth as
much as possible. And so the efforts now
at trying to shore up the finances of Fannie Mae and
Freddie Mac, Lehman, Merrill, and all of these
other institutions is really aimed at
trying to help out a combination of the
intermediaries and the issuers.

Because if you don't help out
this group, then what happens is that this group
is going to get hit. So Lehman Brothers, for
example, is an intermediary. They are one of
the biggest dealers in these kinds of securities. Merrill Lynch is also one
of the biggest dealers in these kind of securities. As dealers, they end up taking
exposure on their own books. That's not a great
idea in general because the best
of all worlds is you're the toll collector
that's collecting tolls for traffic going back and
forth and back and forth. You don't take any risk. But if not everybody
wants to go back and forth and back and forth and
back and forth, you might stand ready to do
one side of the business and let other folks do the
other side of the business. But if you're not careful
in laying off your exposure you can end up getting
hurt pretty badly. An example of this that happened
in equity markets in 1987 was when the stock
market crashed. That was a very serious
event on October 19, 1987, where in one single day,
the US stock market lost approximately 20% of its value.

In one day. Now, that's a
serious dislocation. We're going to talk
about that this Friday when we run this trading game. I'm going to have all of you
engage in trading over a very short period of time. So you're going to be under
tremendous pressure as well. You tell me how easy it
is to think on the fly.

What happened that morning
of October 19, 1987, is that the specialists,
the dealers, who are supposed to be
making markets– their job is to
buy when everybody wants to sell and to sell
when everybody wants to buy. They got it there in
the morning at 9:30 and were overwhelmed with
everybody wanting to sell. So they ended up buying– the specialists. And they bought. And as they bought, what
happened to the price? Kept going down. That means more
people wanted to sell. So they kept buying. And as they bought,
what happened? Price kept going down. And it kept going
down all the way. So the stuff that they
bought in the morning was worth 20% less
in the afternoon. And these market makers
also used leverage. So many of their capital
bases were wiped out by that 20% decline in a
day because they were just doing their job. In fact, there was a story– the floor of the New York Stock
Exchange was literally packed.

I mean, it was tighter
than a Tokyo subway train during rush hour, OK? It was packed. I mean literally, you were
elbow to elbow against others. Unfortunately, one
of the market makers had a heart attack
around 1 or 2 o'clock. And he wasn't able
to fall to the ground until the market closed at
four because he was propped up by everybody else desperate
to try to transact. And he died. And somebody who was near
him said, you know, look, I knew the guy was in trouble. But what was I supposed to do. I was 100,000 shares long and
I had to unload my portfolio. I mean, they were trading. That's how desperate
it was on that day. So this kind of intermediation
can be extraordinarily high pressure. And when you're engaged in
an unwinding of portfolios, dislocation can occur. So we're seeing that
right now play out. And it's a little different
because we're dealing with fixed income security. So I'm going to come
back and talk about that.

OK. That's the background
to what we're going to study– these fixed
income markets and fixed income instruments. I'm going to ask you to read
Brealey and Myers so that you can get up to speed on
institutional details. And there are quite
a few, so I would urge you to please
do that reading and make sure that you
understand the basic terms of these markets. What I want to talk about,
though, is the framework. I want to give you a framework
for thinking about evaluating fixed income securities. And really, as I
said, it's a framework that you already know. You already have
that in your mind. I've already changed the way you
think about financial markets by asking you to focus on cash
flows and timing and the time value of money. That's all you need in order to
value fixed income securities. The rest is just
institutional detail, which, while very
important, is not something that we need to
worry about in class. But I'll leave to
you to focus on. So let me give you an example
of valuation and how to do it. It will be a very short one.

You all know how to do this. We've got a sequence of cash
flows for a particular security that I'm going to call a bond. And in particular, I'm going
to call this a coupon bond. Now with a coupon
bond, there are two things you need to know. You need to know
what the coupon is and you need to know
the maturity– how many dates that it pays off. One of the institutional
details that you'll need to know is that coupon bonds
typically pay semiannually. Some coupon bonds can pay
quarterly, but most of them, as a matter of convention,
pay semiannually. But that changes
depending on the market. So you'll need to learn a
little bit about those kind of conventions. I'm not going to
worry about that and I'm going to
abstract from that and simply say that here's a
three year coupon bond that has a principal of $1,000. That's the typical
principal or face value that a bond comes with. So this piece of
paper is an IOU.

And it says, I owe you $1,000
at the end of three years, OK? But I'm not going to
pay you just $1,000 at the end of three years. I'm going to pay you $50 every
year for those three years. So the coupon is a 5% coupon. So when you hear of a coupon
bond that's a 5% three year bond, that term
that I just uttered means that it pays off $1,000
at the end of three years. And in the interim, it pays
off $50 a year as it's coupons. Why is it called a coupon bond? In the old days, the bond
was actually a piece of paper and on the bottom of
it were little coupons. And you'd clip the
coupons and mail them in.

And once a year when you
mail them in, or twice a year when you mail them
in, you get back $50. OK? Nowadays, it's all
done electronically. So first thing you do in order
to value of the cash flow– draw a time line, OK? We're here sitting at
zero, that's today. And you've got
three years to go. One year, two year, three years. At the end of three years,
you get paid your principal– $1,000– plus the coupon.

There are three coupons
for three years. And so at the end of this
bond, when the bond matures, you get paid $1,050. And then $50, $50, and
here we are at date zero. Question– what is this worth? Yeah? AUDIENCE: It depends
on the interest rate. ANDREW LO: Right. AUDIENCE: [INAUDIBLE] interest
rates are exactly 5%, so it's worth just $1000, the same. ANDREW LO: Right. If the interest rate is 5%,
it's worth $1,000 today. That's par. But if the interest rate
is worth less than that– AUDIENCE: Worth
more [INAUDIBLE].. ANDREW LO: Right, exactly. So in general, how do you figure
out the price of this thing? Yeah. AUDIENCE: [INAUDIBLE]
vice versa [INAUDIBLE]?? ANDREW LO: Well no, I was asking
a somewhat different question, which is, how do I figure out
the market value of this bond today times 0. AUDIENCE: [INAUDIBLE] ANDREW LO: Yeah, compute
the net present value, NPV. That's one answer. That was the correct
textbook answer. What's another answer of how do
I figure out the market value? AUDIENCE: Through the market.

ANDREW LO: Exactly. Auction it off. How many people want to pay
me $1,000 for this today? No? $1,001? a thousand and whenever. We can auction it off
and figure out what the price is from the market. But in fact, what
we're doing by doing so is computing the present value. And the way we're doing
it is by figuring out what the price of a dollar
is in date one today. What the price of a dollar
in year two is today.

And what the price of a
dollar is in year three today. Getting those exchange
rates and then converting all of those
different currencies to dollars today. Right? We know this we've
done this many times. So the way that you
figure out valuation is by using discount rates
that we get from the market and applying them to compute
present values, right? Very simple. So really, the components
of evaluation for bonds, if there's no uncertainty,
you already know. We've done it. That was last lecture. And for special cash flows like
annuities and perpetuities, we've got closed form solutions. Formulas, which you can program
up in Excel to figure out. The kind of risks
that we're going to focus on later on in this
lecture and in the lectures after we talk about
uncertainty is inflation risk. We talked about that, right? The fact that when you buy
a bond or you sell a bond, if the purchasing
power changes, that's going to introduce a
new kind of unknown that we need to grapple with.

Credit risk. That's a major form
of risk that we're dealing with in
financial markets today and that we're likely to be
dealing with for years to come. You might like to borrow
from me or lend to me, but what about credit issues. How do you know
that I'm still going to be around a year from
now, two years from now. Timing, which we'll come back
to a little bit later on. Liquidity. And then of course,
what currency. If we're doing
international borrowing, we have an extra dimension of
risk, which is fluctuations in the exchange rate, OK? So for the next
couple of lectures, I want to keep life simple and
talk just about riskless debt.

Riskless in terms of
default. So in particular I'm going to be talking about
US government bonds. All right? And I'll come back
to risky debt later. But for now, let's just focus
on the debt that will not default because you can always
print up dollars to pay off your creditors, right? Those dollars may
not be worth as much as you would like them to be
if you do too much of that, but for now, we're not
going to focus on default.

OK so the first kind
of bond that we're going to try to price is what's
called a pure discount bond. This is a bond that is different
from a coupon bond in the sense that there are no coupons. So it only pays off
one payment at the end. And the reason it's
called the discount bond is because it is
what it sounds like– the price of the bond today
is going to be at a discount from the face value.

If the face value is $1,000
and there's nothing in between, then the price of the banters
can't be greater than $1,000 because money today is worth
more than money next year. So the price today is going
to be lower than $1,000. It's going to be a
discount over $1,000, hence the term pure discount bond. Now there are pure
discount bonds out there. US treasury bills
are examples, where there's one payoff at the
end and nothing in between. But awhile ago,
financial engineers came up with a rather
brilliant idea, which you may not think is
so brilliant because it's so painfully obvious. The government issues
coupon bonds as well. And typically, for
longer maturities, like five years,
15 and 30 years, there are no pure discount bonds
for those longer maturities.

When the government issues them,
they issue them with coupons. But you can imagine
a situation where somebody would like to have
a discount bond for 30 years. And so some clever
financial engineer said, hey, here's what
I'm going to do. I'm going to buy up a lot of
these treasury coupon bonds and I'm going to issue
discount bonds that match exactly the coupon
payments from my treasury bonds. In other words, I'm
going to take the coupons and strip them and offer them
up as separate securities. And I'm going to
call these STRIPS.

And these STRIPS, which
stands for separate trading of registered interest
and principal securities, created a huge market
for essentially what are government
bonds, but that have been pre-processed in
a relatively simple way. Now, this didn't
happen that long ago. Maybe, I don't know, 15 or 20
years ago they created STRIPS. So this is why I'm so excited
about financial markets and why I think all of you
have tremendous opportunities. It's because there
are so many ideas that may seem obvious to you but
are not obvious to the market. And there's no
patent on good ideas. There's no monopoly
on good ideas. You can actually
create tremendous value by coming up with
what you might think of as so simple a
solution but that solves problems for very
large financial institutions. Now how do we
price these things. Well, this is just a one liner. The price of a
discount on is simply equal to its face
value discounted to the present by the
appropriate interest rate.

That's it. Pure and simple. We're now done with pricing
pure discount bonds. There's nothing else to it. OK. It turns out that this is a
really wonderful relationship because if you've got two
of these three variables in this equation,
you've got the third. If I tell you what
the face value is and what the interest rate
is, you've got the price. If I tell you what the price
is and what the face value is, you've got the interest rate. And if I give you the
interest rate of the price, you can actually figure out what
the face value is, all right? So this relationship is
going to be very handy when we look at the prices
of these instruments and we want to now infer
what that says about what's going on with interest rates.

In fact, what I'm going to
show you next time is that when we look at the
newspaper and we take a look at the prices of
discounted coupon bonds, implicit in those prices is
a forecast of the future. This is as close as
any of you are ever going to get to a crystal ball. I'm serious. By looking at prices,
you can tell the future.

You can't do it
perfectly, but neither can Jean Dixon or any of the
other astrologers, right? The point is that this is
our way of figuring out the collective intelligence
of all market participants and what they think of
what was going to happen. And because of that, because of
that kind of market knowledge, I can tell you that
with 99.5% confidence, tomorrow, the Fed will
cut its interest rate. Now how do I know that. I don't know that. The Fed may not. But if you look at
financial markets today, if you look at
treasury prices today, if you look at the Fed funds
features, all of those prices– if you know how to read that,
if you can decipher those tea leaves– it will tell you that tomorrow,
the Fed will cut rates. So I want you to watch tomorrow
to see if I'm right, OK? It would be very embarrassing
and potentially catastrophic if I'm wrong.

So listen carefully. Any questions? Yeah. AUDIENCE: [INAUDIBLE]. ANDREW LO: That's right. In other words, if they
cut rates tomorrow, then they're going
to be shooting one of the very few remaining
bullets that they have. The question is, if a
bear is charging at you and you've got one bullet
left, you're probably going to use it anyway, right? So why don't we return to
this issue on Wednesday since we're out of time? All right, thank you.

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