Collateralized debt obligation (CDO)

WEBVTT
Kind: captions
Language: en

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Welcome back.

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Well, in the last presentation,
we described a

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situation where you had
a bunch of borrowers.

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They needed $1 billion
collectively, because there's

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1000 of them and they each
needed $1 million

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to buy their house.

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And they borrowed the money
essentially from a special

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purpose entity.

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They borrowed it from their
local mortgage broker, who

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then sold it to a bank, or to
an investment bank, who

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created the special purpose
entity, and then they IPO the

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special purpose entity and raise
the money from people

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who bought the mortgage-backed
securities.

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But essentially what happened
is the investors in the

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mortgage-backed securities
provided the money to the

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special purpose entity to

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essentially loan to the borrowers.

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And then the reason why we call
it a security is because,

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not only are these people
getting this 10% a year, but

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if they want to -- let's say
that you had one of these

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mortgage-backed securities and
you paid $1000 for it.

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And you're getting this 10%
a year, but then all of a

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sudden, you think that the whole
mortgage industry is

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about to collapse, a bunch of
people are going to default,

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and you want out.

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If you just gave someone
a loan, there'd be

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no way to get out.

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You'd have to sell that
loan to someone else.

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But if you have a
mortgage-backed security, you

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can actually trade the security
with someone else.

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And they might pay you, who
knows, they might pay more

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than $1000.

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They might pay you less.

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But there will be at least some
type of a market in the

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security, so you could have what
you could call liquidity.

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Liquidity just means that
I have the security

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and I can sell it.

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I could trade it just like I
could trade a share of IBM or

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I could trade a share
of Microsoft.

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But like we said before, this
security, in order to place a

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value on it, you have to do some
type of analysis of what

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you think it's worth.

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Or what you think the real
interest will be after you

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take into account people
pre-paying their mortgage,

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people defaulting on their
mortgage, and other things

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like short-term interest rates,
et cetera, et cetera.

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And there is only maybe a small
group of people who are

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sophisticated enough to be able
to figure that out to

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make some type of models and
who knows if even they're

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sophisticated enough.

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There might be a whole other
class of investors

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here, say this guy.

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He would love to kind of invest
in insecurities, but he

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thinks this is too risky.

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He'd be willing to take a lower
return as long as he was

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allowed to invest in less
risky investments.

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Maybe by law, maybe he's a
pension fund or he's some type

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of a mutual fund, that's forced
to invest in something

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of a certain grade.

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And say that there's another
investor here, and he thinks

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that this is boring.

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You know, 9%, 10%.

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Who cares about that?

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He wants to see bigger
and bigger returns.

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So there's no way for him to
invest in this security and to

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get better returns.

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So now we're going to take this
mortgage-backed security

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and introduce one step further
kind of permutation or

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derivative of what this is.

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That's all derivatives are.

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You've probably heard the term
derivatives and people do a

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lot of hand-waving saying, oh,
it's a more complicated form

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of security.

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All derivative means is you take
one type of asset and you

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slice and dice it in a way to
spread the risk, or whatever.

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And so you create a
derivative asset.

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It's derived from the
original asset.

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So let's see how we could use
this same asset pool, the same

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pool of loans, and satisfy
all of these people.

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Satisfy this guy, who wants
maybe a lower return but lower

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risk, and this guy, who's
willing to take a little bit

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higher risk in exchange
for higher return.

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So now in this situation, we
have the same borrowers.

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They borrowed $1 billion
collectively, right, because

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there's 1000 of them, et
cetera, et cetera.

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And they're still a special
purpose entity, but now,

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instead of just slicing up the
special purpose entity a

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million ways, what we're going
to do is we're going to split

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it up first into three, what
we could call, tranches.

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A tranche is just a bucket,
if you will, of the asset.

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And we're going to call the
three tranches: equity,

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mezzanine, and senior.

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These are the words
that are commonly

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used in this industry.

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A senior just means, if this
entity were to lose money,

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these people get their money
back first. So it's the least

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risk out of all of
the tranches.

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Mezzanine, that just means
the next level or middle.

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And these guys are some
place in between.

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They have a little bit more
risk, and they still get a

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little bit more reward than
senior, but they have less

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risk than this equity tranche.

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Equity tranche.

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These are the people who
first lose money.

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Let's say some of these
borrowers start defaulting.

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It all comes out of the
equity tranche.

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So that's what protects the
senior tranche and the

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mezzanine tranche
from defaults.

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So in this situation what we did
is we raised -- out of the

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$1 billion we needed -- $400
million from the senior

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tranche, $300 million from the
mezzanine tranche, and then

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$300 million from the
equity tranche.

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The $400 million senior tranche
we raised from soon.

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1000 senior securities,
collateralized debt

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obligations.

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These are these, right here.

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Say there were 400,000 of these
and these each cost

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$1000, right?

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Let's say these cost $1000.

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And we issued 400,000
of these.

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So we raised $400 million.

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Let's say we give these
guys a 6% return.

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And you might say, 6%,
that's not much.

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But these guys, it is pretty low
risk, because in order for

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them to not get their 6%, the
value of this $1 billion asset

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or these $1 billion loans, would
have to go down below

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$400 million.

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Maybe I'll do a little bit more
math in another example.

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But I think it'll start
making sense to you.

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For example, every year we said
there's going to be $100

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million in payments, right?

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Because it's 10%.

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$100 million in payments.

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Of that $100 million in
payments, 6% on the $400

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million, that's $24 million
in payments.

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Right?

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So $24 million in payments will
go to the senior tranche.

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Similarly we issued 300,000
shares at $1000 per share on

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the mezzanine tranche.

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This is also 1000.

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This is the mezzanine tranche.

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And let's say they get 7%,
a slightly higher return.

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And these percentages are
usually determined by some

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type of market or what people
are willing to get.

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But let's just say it's
fixed for now.

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Let's say it's 7%.

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So 300,000 shares, seven 7%.

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These guys are going
to get $21 million.

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Right?

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So out of the $100 million every
year, $24 million is

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going to go to these guys, $21
million is going to go to

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these guys, and then whatever's
left over is going

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to go to the equity tranche.

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So the $300 million from equity,
they're going to get

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$55 million assuming that
there are no defaults or

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pre-payments or anything shady
happens with the securities.

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But these guys are going
to get $55 million.

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Or on $300 million, that's
a 16.5% return.

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And I know what you're
thinking.

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Boy, Sal, that sounds amazing.

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Why wouldn't everyone want
to be an equity investor?

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I don't know.

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My pen has stopped working.

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But anyway, I'll try to move
on without my pen.

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So you're saying, why wouldn't
everyone want to

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be an equity investor?

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Well, let me ask
you a question.

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What happens if -- let's go to
that scenario where we talked

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before -- 20% of the borrowers
just say, you know what?

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I can't pay this mortgage
anymore.

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I'm going to hand you back
the keys to these houses.

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And of that 20%, you only
get a 50% return.

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So for each of those $1 million
houses, you're only

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able to sell it for $500,000.

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So then instead of getting $100
million per year, you're

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only going to get $90
million per year.

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I wish I could use my pen.

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Something about my computer
has frozen.

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So instead of $100 million a
year, you're now only going to

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get $90 million a year.

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Right?

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And all of a sudden,
these guys are not

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going to be cut off.

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This guy is still going to get
$24 million, this guy is still

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going to get $21 million, but
now this guy is going to get

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$45 million.

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But he's still getting
above average yield.

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Now let's say it gets
even worse.

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Let's say a bunch of
borrowers start

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defaulting on their loans.

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And instead of getting $90
million per year, you start

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only getting $50 million
in per year.

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Now you pay this guy
$24 million.

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You pay this guy $21 million
-- or this group of guys or

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gals -- $21 million.

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And then all you have left is
$5 million for this guy.

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And $5 million on $300 million,
now he's getting less

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than a 2% return.

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So this guy took on higher
risk for higher reward.

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If everyone pays, sure,
he gets 16.5%.

00:08:38.900 --> 00:08:42.820
But then if you start having a
lot of defaults, if, let's

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say, the return on what you get
every month goes in half,

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this guy takes the entire hit.

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So his return goes to 0%.

00:08:51.130 --> 00:08:53.030
So he had higher risk,
higher reward, while

00:08:53.030 --> 00:08:54.450
these guys get untouched.

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Of course, if enough people
start defaulting, even these

00:08:57.130 --> 00:08:59.440
people start to get hurt.

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So this is a form of a
collateralized debt

00:09:02.250 --> 00:09:03.000
obligation.

00:09:03.000 --> 00:09:05.870
This is actually a
mortgage-backed collateralized

00:09:05.870 --> 00:09:06.560
debt obligation.

00:09:06.560 --> 00:09:12.100
You can actually do this type
of a structure with any type

00:09:12.100 --> 00:09:15.580
of debt obligation that's
backed by assets.

00:09:15.580 --> 00:09:18.260
So we did the situation with
mortgages, but you could do it

00:09:18.260 --> 00:09:19.110
with a bunch of assets.

00:09:19.110 --> 00:09:21.250
You could do it with
corporate debt.

00:09:21.250 --> 00:09:24.450
You could do it with receivables
from a company.

00:09:24.450 --> 00:09:26.880
But what you read about the
most right now in the

00:09:26.880 --> 00:09:29.910
newspapers is mortgage-backed
collateralized debt

00:09:29.910 --> 00:09:30.490
obligations.

00:09:30.490 --> 00:09:33.820
And to some degree, that's
what's been getting a lot of

00:09:33.820 --> 00:09:34.890
these hedge funds in trouble.

00:09:34.890 --> 00:09:38.230
And I think I'll do another
presentation on exactly how

00:09:38.230 --> 00:09:40.370
and why they have gotten
in trouble.

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Look forward to talking to you


Mortgage-backed securities III

WEBVTT
Kind: captions
Language: en

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Welcome back to my series
of presentations on

00:00:03.480 --> 00:00:05.480
mortgage-backed securities.

00:00:05.480 --> 00:00:08.100
So let's review what we've
already gone over.

00:00:08.100 --> 00:00:10.460
So I've already drawn here-- I
actually prepared ahead of

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time-- so I've already drawn
here kind of what we've

00:00:13.580 --> 00:00:14.570
already talked about.

00:00:14.570 --> 00:00:17.560
So we start with borrowers
who need to buy houses.

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Each of them borrowed
$1 million.

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Actually let me write
that down.

00:00:20.890 --> 00:00:24.240
Let me change the
color of my pen.

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Where'd my pen go?

00:00:25.410 --> 00:00:26.110
OK.

00:00:26.110 --> 00:00:27.790
So each of these people
borrowed $1 million.

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OK.

00:00:33.920 --> 00:00:36.230
Each of them borrowed $1 million
and there were 1,000

00:00:36.230 --> 00:00:37.150
of them, right?

00:00:37.150 --> 00:00:39.170
So $1 million times 1,000.

00:00:39.170 --> 00:00:41.250
That's $1 billion that
they needed.

00:00:41.250 --> 00:00:44.460
And they said that they would
pay 10% a year on that money

00:00:44.460 --> 00:00:45.100
that they borrowed.

00:00:45.100 --> 00:00:48.940
So that's 10% for each of them
is $100,000 and then as we

00:00:48.940 --> 00:00:50.500
said, there's 1,000 borrowers.

00:00:50.500 --> 00:00:53.370
So they're going to put in
$100 million, right?

00:00:53.370 --> 00:00:56.030
100,000 times 1,000
is 100 million.

00:00:56.030 --> 00:00:57.070
So just to simplify.

00:00:57.070 --> 00:01:00.000
Keep it in your mind. $1 million
goes to a bunch of

00:01:00.000 --> 00:01:03.050
borrowers, goes to 1,000
borrowers, to be specific.

00:01:03.050 --> 00:01:07.130
And then each year, those
borrowers are going to give

00:01:07.130 --> 00:01:09.280
the special purpose entity--
this is just a corporation

00:01:09.280 --> 00:01:12.560
designed to kind of structure
these mortgage-backed

00:01:12.560 --> 00:01:15.430
securities-- they're going to
give 10% of the billion, or

00:01:15.430 --> 00:01:17.690
$100 million back into this.

00:01:17.690 --> 00:01:20.190
And then we said, OK, well where
does that money for this

00:01:20.190 --> 00:01:22.960
special purpose entity, or for
this corporation, come from?

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Well it comes from the investors
in the actual

00:01:26.150 --> 00:01:27.400
mortgage-backed securities.

00:01:31.440 --> 00:01:36.060
And just to be clear, so
the asset within this

00:01:36.060 --> 00:01:40.175
entity are the loans.

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The loans are the main asset
that's inside of the special

00:01:47.920 --> 00:01:48.470
purpose entity.

00:01:48.470 --> 00:01:51.580
And the loans are just the right
on these 10% payments.

00:01:51.580 --> 00:01:54.430
And so money came from when the
owners of each of these

00:01:54.430 --> 00:01:57.870
mortgage-backed securities--
each, let's say, paid $1,000

00:01:57.870 --> 00:01:59.140
for the mortgage-backed
securities.

00:01:59.140 --> 00:02:01.620
And in return, they're going
to get 10% on their money.

00:02:01.620 --> 00:02:03.750
So each security cost $1,000.

00:02:03.750 --> 00:02:05.040
And then they're going to
they're going to get

00:02:05.040 --> 00:02:06.640
$100 back per month.

00:02:06.640 --> 00:02:08.669
And we said there are a million
of these securities,

00:02:08.669 --> 00:02:12.210
so $1,000 times 1 million,
that's where the $1 billion

00:02:12.210 --> 00:02:13.460
comes from.

00:02:16.760 --> 00:02:18.140
My thing's been acting up.

00:02:18.140 --> 00:02:20.550
That's where the $1 billion
comes from.

00:02:20.550 --> 00:02:22.800
And that essentially is
lent to the borrowers.

00:02:22.800 --> 00:02:24.680
And these guys will get 10%.

00:02:24.680 --> 00:02:28.500
Now one thing I want you to keep
in mind is, they get 10%

00:02:28.500 --> 00:02:33.370
only if every one of these
borrowers pays their loans,

00:02:33.370 --> 00:02:35.760
never defaults, never
pre-pays.

00:02:35.760 --> 00:02:38.300
Pre-paying a mortgage is just
saying, I sold the house.

00:02:38.300 --> 00:02:40.470
I don't need the mortgage
anymore, so I just pay it off.

00:02:40.470 --> 00:02:44.390
So it's only 10%, indefinitely,
if all of the

00:02:44.390 --> 00:02:47.990
borrowers pay all the money
and never default or

00:02:47.990 --> 00:02:49.560
anything like that.

00:02:49.560 --> 00:02:51.670
So this 10% is kind of
in an ideal world.

00:02:51.670 --> 00:02:54.520
Well everyone knows that it's
not going to be exactly 10%.

00:02:54.520 --> 00:02:56.630
Some percentage of these
borrowers are going to default

00:02:56.630 --> 00:02:57.240
on their mortgage.

00:02:57.240 --> 00:02:58.840
Some of them are going
to pay ahead of time.

00:02:58.840 --> 00:03:01.990
And actually that's what the
buyer of the mortgage-backed

00:03:01.990 --> 00:03:04.230
security should try
to figure out.

00:03:04.230 --> 00:03:06.220
And all sorts of buyers are
going to have all sorts of

00:03:06.220 --> 00:03:07.100
different assumptions.

00:03:07.100 --> 00:03:10.350
And this is what you probably
read some articles about,

00:03:10.350 --> 00:03:14.560
these hedge funds with these
computer models to value their

00:03:14.560 --> 00:03:15.930
mortgage-backed securities.

00:03:15.930 --> 00:03:17.610
And that's what those
computer models do.

00:03:17.610 --> 00:03:21.450
They try to look at historical
data and figure out, OK, for a

00:03:21.450 --> 00:03:24.940
given population pool in a given
part of the country,

00:03:24.940 --> 00:03:27.530
what percentage of
them are able to

00:03:27.530 --> 00:03:28.510
pay off their mortgage?

00:03:28.510 --> 00:03:31.140
What percentage of them default
on their mortgage?

00:03:31.140 --> 00:03:34.100
And when they default, what
is kind of the recovery?

00:03:34.100 --> 00:03:37.190
Say they default on a $1 million
mortgage, and then the

00:03:37.190 --> 00:03:39.930
special purpose entity would
get control of that house.

00:03:39.930 --> 00:03:44.070
And then if that house is sold
for $500,000 because the

00:03:44.070 --> 00:03:47.610
property value went down, then
the recovery would be 50%.

00:03:47.610 --> 00:03:50.430
So that's all of the things that
someone needs to factor

00:03:50.430 --> 00:03:52.260
in when they figure out what
will be the real return.

00:03:52.260 --> 00:03:54.030
10% is if everyone pays.

00:03:54.030 --> 00:03:58.120
So let's make some very simple
assumptions for ourselves.

00:03:58.120 --> 00:03:59.760
Let's say we are thinking
about investing in a

00:03:59.760 --> 00:04:02.490
mortgage-backed security and we
want to gauge for ourselves

00:04:02.490 --> 00:04:04.490
what we think the return
is going to be.

00:04:04.490 --> 00:04:09.420
Well let's say we know that this
pool of borrowers that--

00:04:09.420 --> 00:04:16.450
my pen keeps not working--
that 20% will default.

00:04:16.450 --> 00:04:18.529
We're not going to worry about
pre-payment rates and all

00:04:18.529 --> 00:04:19.390
things like that.

00:04:19.390 --> 00:04:20.884
Let's say 20% are going
to default.

00:04:24.180 --> 00:04:27.660
Of these 1,000 borrowers, 200 of
them are just going to lose

00:04:27.660 --> 00:04:28.480
their job or whatever.

00:04:28.480 --> 00:04:30.730
They can't afford a
mortgage anymore.

00:04:30.730 --> 00:04:38.240
And of those 20% that default,
we have a 50% recovery.

00:04:38.240 --> 00:04:43.270
So that means borrower X
defaulted on his loan.

00:04:43.270 --> 00:04:46.450
And then when we go and get
the property-- because the

00:04:46.450 --> 00:04:48.620
loan was secured by the
property-- when we auction off

00:04:48.620 --> 00:04:50.980
the property, we only
get $500,000 for it.

00:04:50.980 --> 00:04:52.350
So we get a 50% recovery.

00:04:52.350 --> 00:04:55.780
50% of the original
value of the loan.

00:04:55.780 --> 00:05:00.820
So if 20% default and then
there's a 50% recovery, then

00:05:00.820 --> 00:05:14.570
on average you're going to get
10% of the loan is worthless.

00:05:14.570 --> 00:05:15.910
And I'm going to make
some kind of

00:05:15.910 --> 00:05:17.750
handwaving assumptions here.

00:05:17.750 --> 00:05:19.760
But you can assume
statistically, and since this

00:05:19.760 --> 00:05:22.230
is a large number of borrowers--
it's 1,000, right?

00:05:22.230 --> 00:05:24.470
If there's only one borrower
it would be hard to kind of

00:05:24.470 --> 00:05:26.650
gauge when he defaults,
if he defaults at all.

00:05:26.650 --> 00:05:28.590
We would just know that
there is a 20% chance.

00:05:28.590 --> 00:05:30.430
But when there's a large number
of borrowers, you can

00:05:30.430 --> 00:05:33.460
kind of do the math and say,
OK, on average 200 of these

00:05:33.460 --> 00:05:35.750
guys are going to default, and
instead of actually getting

00:05:35.750 --> 00:05:40.470
10%, since 10% of the loans are
going to be worthless, I'm

00:05:40.470 --> 00:05:43.940
going to get 10% less
than this 10%.

00:05:43.940 --> 00:05:45.610
So I'm going to get 9%.

00:05:45.610 --> 00:05:48.210
So this is based on the
model that we just

00:05:48.210 --> 00:05:50.500
constructed, right?

00:05:50.500 --> 00:05:51.910
This is the model that
we constructed.

00:05:51.910 --> 00:05:55.080
This is a much simpler model
than what most people use.

00:05:55.080 --> 00:05:58.950
But based on the model that we
just constructed, I think the

00:05:58.950 --> 00:06:00.990
real return we're going to get
on this mortgage-backed

00:06:00.990 --> 00:06:02.570
security is 9%.

00:06:02.570 --> 00:06:06.190
If there was another investor
who assumed a 50% default

00:06:06.190 --> 00:06:09.040
rate, but with a higher
recovery, he or she would have

00:06:09.040 --> 00:06:14.120
a different kind of expected
return from this security.

00:06:14.120 --> 00:06:17.000
So why is this even useful?

00:06:17.000 --> 00:06:17.760
Well think about it.

00:06:17.760 --> 00:06:20.540
Before, in the case we did in
the first video, when someone

00:06:20.540 --> 00:06:25.620
just borrows from the bank,
the bank has very specific

00:06:25.620 --> 00:06:26.670
lending requirements.

00:06:26.670 --> 00:06:29.320
They have their own model.

00:06:29.320 --> 00:06:33.180
So there's a whole class of
borrowers that they might have

00:06:33.180 --> 00:06:34.680
not been able to service.

00:06:34.680 --> 00:06:34.970
Right?

00:06:34.970 --> 00:06:37.830
There might be people with
really good credit scores,

00:06:37.830 --> 00:06:40.730
really good incomes, who don't
have a down payment.

00:06:40.730 --> 00:06:43.210
And if they don't meet what the
bank's requirements are,

00:06:43.210 --> 00:06:44.540
they would never get a loan.

00:06:44.540 --> 00:06:46.430
But there are probably some
investors out there that would

00:06:46.430 --> 00:06:46.970
say, you know what?

00:06:46.970 --> 00:06:50.310
For the right interest rate and
for the right assumptions

00:06:50.310 --> 00:06:53.110
in my model, I'm willing to give
anybody a loan, as long

00:06:53.110 --> 00:06:54.840
as I'm compensated
for it enough.

00:06:54.840 --> 00:06:57.230
And this is what this
mortgage-backed security

00:06:57.230 --> 00:06:58.260
market allows.

00:06:58.260 --> 00:07:02.495
It allows-- let's say this group
of borrowers-- let's say

00:07:02.495 --> 00:07:12.520
this pool of borrowers right
here actually didn't--

00:07:12.520 --> 00:07:14.710
This pool of borrowers
actually aren't the

00:07:14.710 --> 00:07:22.270
traditional-- they don't have
25% down and they don't have

00:07:22.270 --> 00:07:24.340
kind of the traditional
requirements to get a normal

00:07:24.340 --> 00:07:28.290
mortgage-- but if I pool a bunch
of people who don't have

00:07:28.290 --> 00:07:29.630
those traditional requirements,
but they're good

00:07:29.630 --> 00:07:31.740
in other ways-- they have a
high income or high credit

00:07:31.740 --> 00:07:34.940
score-- I can go through this
alternate mechanism to find

00:07:34.940 --> 00:07:37.130
investors that are willing
to loan them money.

00:07:37.130 --> 00:07:39.840
So essentially, from the
borrower's point of view, it

00:07:39.840 --> 00:07:44.260
allows more access to loan
funding that they would have

00:07:44.260 --> 00:07:45.790
otherwise not been able to.

00:07:45.790 --> 00:07:48.770
And from an investor point of
view, it allows another place

00:07:48.770 --> 00:07:51.880
for me to invest in.

00:07:51.880 --> 00:07:55.170
Maybe I feel that the computer
models that I have are really

00:07:55.170 --> 00:07:58.350
good at predicting things like
default rates, and recovery

00:07:58.350 --> 00:08:01.320
rates, and what a
loan is worth.

00:08:01.320 --> 00:08:05.950
And I feel that I can, in some
ways, be a better loan officer

00:08:05.950 --> 00:08:06.480
than the banks.

00:08:06.480 --> 00:08:09.150
And this would be an attractive
place for

00:08:09.150 --> 00:08:10.590
me to invest in.

00:08:10.590 --> 00:08:14.890
It also might just have a risk
reward characteristic that

00:08:14.890 --> 00:08:17.360
doesn't exist in the market
already, and it allows you to

00:08:17.360 --> 00:08:19.600
diversify into one other
asset class.

00:08:19.600 --> 00:08:20.740
So that's the value that it has

00:08:20.740 --> 00:08:22.780
across the entire spectrum.

00:08:22.780 --> 00:08:27.050
Now in the next presentation I'm
going to show how you can,

00:08:27.050 --> 00:08:30.720
I guess, further complicate this
even more, so that you

00:08:30.720 --> 00:08:32.570
can open up the investment
to even a

00:08:32.570 --> 00:08:33.820
larger group of investors.

00:08:33.820 --> 00:08:35.320
Because you can think about it
right now, there's probably

00:08:35.320 --> 00:08:38.530
some people who say, OK, I
already said, some people will

00:08:38.530 --> 00:08:40.760
do these models and try to make
their own assumptions and

00:08:40.760 --> 00:08:43.039
say, OK, this is going
to give me 9% a year.

00:08:43.039 --> 00:08:44.580
But there's a whole bunch of
people who are going to say

00:08:44.580 --> 00:08:46.450
this is just too complicated
for me.

00:08:46.450 --> 00:08:47.740
This seems risky.

00:08:47.740 --> 00:08:49.980
I don't have any fancy models.

00:08:49.980 --> 00:08:51.560
I only like to invest
in things where I

00:08:51.560 --> 00:08:53.120
know I get my money.

00:08:53.120 --> 00:08:55.580
Very highly rated debt
is where I'm going

00:08:55.580 --> 00:08:56.390
to invest my money.

00:08:56.390 --> 00:08:58.850
And there's another group of
people who say, OK, 9%, that's

00:08:58.850 --> 00:09:01.670
nice and everything, but I'm
a hotshot, I'm a gambler.

00:09:01.670 --> 00:09:04.280
9% isn't the type of
returns I want.

00:09:04.280 --> 00:09:07.670
I want to take more risk
and more return.

00:09:07.670 --> 00:09:09.690
And so there should be
something, maybe, for those

00:09:09.690 --> 00:09:10.500
people as well.

00:09:10.500 --> 00:09:12.650
So that's what we're going to
show you in the presentation

00:09:12.650 --> 00:09:15.970
on collateralized debt
obligations.

00:09:15.970 --> 00:09:17.460
See you soon.


Mortgage-backed securities II

WEBVTT
Kind: captions
Language: en

00:00:00.820 --> 00:00:01.700
Welcome back.

00:00:01.700 --> 00:00:04.770
So where we left off is, there
was 1,000 people who all

00:00:04.770 --> 00:00:07.800
needed, let's say, $1
million loans each.

00:00:07.800 --> 00:00:11.260
And they were all going to
pay 10% on their loans.

00:00:11.260 --> 00:00:12.990
And they borrowed it
from this bank.

00:00:12.990 --> 00:00:14.900
It's kind of a standard
commercial bank.

00:00:14.900 --> 00:00:18.160
And this bank says, well you
know, I just handed out $1

00:00:18.160 --> 00:00:20.040
billion and I'm getting these
interest payments.

00:00:20.040 --> 00:00:21.970
And my vaults are empty.

00:00:21.970 --> 00:00:24.450
I want to have money
back in my vaults.

00:00:24.450 --> 00:00:27.310
Or I want to have money back
on my balance sheet.

00:00:27.310 --> 00:00:28.670
So I'm going to sell
these loans.

00:00:28.670 --> 00:00:31.020
I'm going to bundle them all
together and sell them to this

00:00:31.020 --> 00:00:32.189
investment bank.

00:00:32.189 --> 00:00:35.140
And now what is this investment
bank going to do

00:00:35.140 --> 00:00:35.800
with these loans?

00:00:35.800 --> 00:00:36.700
And why is it doing it?

00:00:36.700 --> 00:00:40.220
So let me delete this.

00:00:40.220 --> 00:00:41.630
So we had the investment bank.

00:00:45.650 --> 00:00:47.430
I randomly picked the color
green, but I think it is

00:00:47.430 --> 00:00:49.680
appropriate for the
investment bank.

00:00:49.680 --> 00:00:56.250
So now I have all of the, you
know, me-- that's a little

00:00:56.250 --> 00:00:57.200
smiley face.

00:00:57.200 --> 00:01:03.270
There's 1,000 of me, and we are
now going to pay the 10%.

00:01:03.270 --> 00:01:06.670
We're now going to make all of
our mortgage payments, the 10%

00:01:06.670 --> 00:01:10.010
payment, to this bank,
this investment bank.

00:01:10.010 --> 00:01:12.280
But the investment bank, they're
not in the business of

00:01:12.280 --> 00:01:14.670
servicing loans or keeping loans
on their balance sheets.

00:01:14.670 --> 00:01:17.980
So what they do is, they
create a corporation.

00:01:17.980 --> 00:01:20.630
They create an entity, maybe
a special purpose entity,

00:01:20.630 --> 00:01:21.680
whatever you want to call it.

00:01:21.680 --> 00:01:23.820
So they create a company.

00:01:23.820 --> 00:01:26.170
Let me make that in purple,
another color.

00:01:26.170 --> 00:01:27.420
So they created this company.

00:01:32.730 --> 00:01:44.720
And what they do is, they will
take their rights to these

00:01:44.720 --> 00:01:45.760
payments that they got.

00:01:45.760 --> 00:01:45.960
Right?

00:01:45.960 --> 00:01:49.160
They paid $1 billion to that
first bank in order to get the

00:01:49.160 --> 00:01:51.250
payments from all
of these people.

00:01:51.250 --> 00:01:52.030
And they say, you know what?

00:01:52.030 --> 00:01:54.600
The rights on those payments--
that's the asset.

00:01:54.600 --> 00:01:55.460
They bought all these loans.

00:01:55.460 --> 00:01:58.050
The rights on those payments,
we are now going to transfer

00:01:58.050 --> 00:02:00.690
to this special purpose
entity, to this other

00:02:00.690 --> 00:02:01.560
corporation.

00:02:01.560 --> 00:02:05.150
So now everyone is going to,
essentially-- all their

00:02:05.150 --> 00:02:09.500
mortgage payments are going to
be funnelled into this entity.

00:02:09.500 --> 00:02:11.190
Right?

00:02:11.190 --> 00:02:12.630
And this is a corporation.

00:02:12.630 --> 00:02:16.020
And so what the bank will do
is issue shares in this

00:02:16.020 --> 00:02:16.550
corporation.

00:02:16.550 --> 00:02:20.760
So let's say that it issues,
let's sat for simplicity, a

00:02:20.760 --> 00:02:22.010
hundred shares.

00:02:26.050 --> 00:02:27.300
So what's in this corporation?

00:02:29.760 --> 00:02:33.560
The entire corporation gets the
mortgage payments on the

00:02:33.560 --> 00:02:35.510
$1 billion in loans, right?

00:02:35.510 --> 00:02:36.975
It has $1 billion of
loans outstanding.

00:02:36.975 --> 00:02:38.960
And it is going to
get 10% a year.

00:02:38.960 --> 00:02:42.350
So it's going to get $100
million per year right?

00:02:42.350 --> 00:02:45.140
Because it's a thousand
loans out there.

00:02:45.140 --> 00:02:47.315
It's going to get $100 million
per year for 10 years.

00:02:47.315 --> 00:02:49.220
And at the end of the 10 years
it's also going to get $1

00:02:49.220 --> 00:02:50.880
billion, right?

00:02:50.880 --> 00:02:52.020
That's its asset it has.

00:02:52.020 --> 00:02:55.770
Its asset is the rights on those
payments streams that

00:02:55.770 --> 00:02:58.210
are going to come into
this corporation.

00:02:58.210 --> 00:03:00.530
And it has 100 shares.

00:03:00.530 --> 00:03:02.030
The way I think about
is you can split

00:03:02.030 --> 00:03:04.270
this company 100 ways.

00:03:04.270 --> 00:03:06.590
And I'm doing this to
further confuse you.

00:03:06.590 --> 00:03:10.280
So what is each of those-- the
owner of each of those shares,

00:03:10.280 --> 00:03:12.590
what does it entitle them to?

00:03:12.590 --> 00:03:20.330
Well, it entitles me to 1/100 of
what this corporation gets.

00:03:20.330 --> 00:03:23.400
So if I have a share-- let's
make it look like a share, a

00:03:23.400 --> 00:03:28.080
stock certificate-- I'm going
to get 1/100 of this thing.

00:03:28.080 --> 00:03:29.530
And normally you wouldn't
have 100 shares.

00:03:29.530 --> 00:03:31.440
You would have, let's say,
a million shares.

00:03:31.440 --> 00:03:32.840
Actually let me make it a
million shares, just because I

00:03:32.840 --> 00:03:35.530
think that's, in some strange
way, more realistic.

00:03:35.530 --> 00:03:39.600
So let's say there are
a million shares.

00:03:39.600 --> 00:03:42.100
So if there are 1 million
shares, each share will get 1

00:03:42.100 --> 00:03:44.380
millionth of the cash
flow stream that's

00:03:44.380 --> 00:03:46.170
entitled to this entity.

00:03:46.170 --> 00:03:50.180
So instead of getting $100
million every year, it gets

00:03:50.180 --> 00:03:51.110
one millionth of that.

00:03:51.110 --> 00:03:55.390
So it gets $100 per year.

00:03:55.390 --> 00:03:57.940
And then on the last year,
instead of getting $1 billion

00:03:57.940 --> 00:04:01.030
it gets $1000.

00:04:01.030 --> 00:04:04.230
So what the bank will do is
it'll take these shares and

00:04:04.230 --> 00:04:05.890
then it'll sell it to
the general public.

00:04:05.890 --> 00:04:08.380
It'll IPO it, essentially.

00:04:08.380 --> 00:04:09.420
You can think of it that way.

00:04:09.420 --> 00:04:12.360
And tons of people will buy it,
especially hedge funds,

00:04:12.360 --> 00:04:15.635
and pension funds, and mutual
funds, and bond investors.

00:04:18.370 --> 00:04:22.029
And it's important to think
about how the money's flowing.

00:04:22.029 --> 00:04:26.960
So now when they sell these
shares in this entity, people

00:04:26.960 --> 00:04:29.620
are going to give them, well,
hopefully more than what they

00:04:29.620 --> 00:04:30.840
paid for it, right?

00:04:30.840 --> 00:04:33.830
Maybe there's a lot of demand
for this type of asset, where

00:04:33.830 --> 00:04:36.080
I get this type of
income stream.

00:04:36.080 --> 00:04:38.950
So maybe once they sell all the
shares, they get, I don't

00:04:38.950 --> 00:04:41.760
know, they get $1.1 billion
for them, right?

00:04:41.760 --> 00:04:44.702
So this is the investors.

00:04:44.702 --> 00:04:48.360
And the investors collectively
buy these

00:04:48.360 --> 00:04:49.700
shares for $1.1 billion.

00:04:49.700 --> 00:04:55.280
Essentially, let's say they
paid $1.1 billion for a

00:04:55.280 --> 00:04:59.470
million shares, so they
paid $1,100 per share.

00:04:59.470 --> 00:05:00.720
Right?

00:05:02.400 --> 00:05:04.840
Each of the investors paid
$1,100 for each of these

00:05:04.840 --> 00:05:08.430
shares, so that $1.1 billion
goes into this

00:05:08.430 --> 00:05:09.630
special purpose entity.

00:05:09.630 --> 00:05:11.630
And if you think about
it, the bank made out

00:05:11.630 --> 00:05:12.620
like a bandit, right?

00:05:12.620 --> 00:05:17.890
Because the bank paid $1 billion
for the rights to

00:05:17.890 --> 00:05:23.520
these mortgage payments, and
it's getting $1.1 billion from

00:05:23.520 --> 00:05:24.340
the investors.

00:05:24.340 --> 00:05:27.190
And all the bank has to do is
kind of set this whole legal

00:05:27.190 --> 00:05:29.150
structure up and service
the loans.

00:05:29.150 --> 00:05:30.350
It actually doesn't even have
to service the loans.

00:05:30.350 --> 00:05:31.580
We'll go into that later.

00:05:31.580 --> 00:05:35.520
So let me summarize, I guess.

00:05:35.520 --> 00:05:36.980
Just because I know this
can be a little bit

00:05:36.980 --> 00:05:38.230
of a daunting subject.

00:05:41.280 --> 00:05:43.800
Let me summarize.

00:05:43.800 --> 00:05:47.200
And this purple I don't like.

00:05:47.200 --> 00:05:47.830
Anyway.

00:05:47.830 --> 00:05:50.315
So you have tons of investors.

00:05:50.315 --> 00:05:52.730
So, each of these
is an investor.

00:05:52.730 --> 00:05:54.690
Actually a mortgage,
a borrower.

00:05:54.690 --> 00:05:56.030
All of these people need
to buy houses.

00:05:56.030 --> 00:05:59.670
These are all smiley faces.

00:05:59.670 --> 00:06:00.980
They all need to buy houses.

00:06:00.980 --> 00:06:07.370
And then they collectively
get $1 billion.

00:06:07.370 --> 00:06:08.830
Right? $1 million each.

00:06:08.830 --> 00:06:13.080
And they each use that $1
million to buy their house.

00:06:13.080 --> 00:06:18.100
And then that $1 billion
initially came from just their

00:06:18.100 --> 00:06:19.350
local bank.

00:06:21.790 --> 00:06:25.800
And when the $1 billion came
from that local bank, all the

00:06:25.800 --> 00:06:28.640
payments, the interest payments,
went to the bank.

00:06:28.640 --> 00:06:31.600
But then an investment bank came
along and said, well no,

00:06:31.600 --> 00:06:33.195
I want to buy the rights
to those payments.

00:06:36.088 --> 00:06:38.910
And an investment bank came
along and says, well, I'm

00:06:38.910 --> 00:06:40.160
going to give you $1 billion.

00:06:44.020 --> 00:06:45.640
And now instead of
you getting the

00:06:45.640 --> 00:06:47.720
payments, I get the payments.

00:06:47.720 --> 00:06:52.080
And then the bank sets up a
special purpose entity.

00:06:52.080 --> 00:06:54.130
Essentially it sells
a bunch of shares.

00:06:54.130 --> 00:06:55.380
Let's say it sells
a million shares.

00:07:00.190 --> 00:07:04.560
And let's say it was able to
sell each of those shares for

00:07:04.560 --> 00:07:12.950
$1,100 from the investing
public.

00:07:12.950 --> 00:07:16.270
So it raises $1.1
billion, right?

00:07:16.270 --> 00:07:20.180
So the value of this company is
$1.1 billion that now goes

00:07:20.180 --> 00:07:21.030
to the bank.

00:07:21.030 --> 00:07:24.180
And now the payment stream
instead of going to-- let me

00:07:24.180 --> 00:07:28.340
do a different color-- now the
payment stream goes to this

00:07:28.340 --> 00:07:32.580
special purpose entity
instead of the bank.

00:07:32.580 --> 00:07:35.080
And the bank essentially made
out like a bandit because it

00:07:35.080 --> 00:07:40.920
paid $1 billion and it got $1.1
so it made $100 million

00:07:40.920 --> 00:07:42.010
just for doing this
transaction.

00:07:42.010 --> 00:07:44.280
I'm not saying that's how much
a bank actually would make,

00:07:44.280 --> 00:07:48.150
but this shows you why every
person is kind of, what

00:07:48.150 --> 00:07:50.040
they're doing in this
value chain.

00:07:50.040 --> 00:07:52.600
And as I said before, this
bank also probably did

00:07:52.600 --> 00:07:53.310
something similar.

00:07:53.310 --> 00:07:57.050
They probably took some fees or
sold the loans for slightly

00:07:57.050 --> 00:07:59.300
more than they issued
the loans for.

00:07:59.300 --> 00:08:07.920
So these shares-- each of these
one million shares--

00:08:07.920 --> 00:08:10.400
this is a mortgage-backed
security.

00:08:14.900 --> 00:08:15.400
And it makes sense.

00:08:15.400 --> 00:08:16.040
It's a security.

00:08:16.040 --> 00:08:19.690
A security is an ownership
that's tradable in a company.

00:08:19.690 --> 00:08:24.100
And that company has the right
to payments that are secured

00:08:24.100 --> 00:08:25.120
by mortgages.

00:08:25.120 --> 00:08:28.420
So if all these people promised
they would pay, and

00:08:28.420 --> 00:08:32.590
they're going to pay to this
special purpose entity.

00:08:32.590 --> 00:08:36.429
But if, by chance, one of these
people lose their jobs

00:08:36.429 --> 00:08:41.000
or they can't pay, or for
whatever reason, instead of

00:08:41.000 --> 00:08:44.440
the payments, this entity is
going to have the rights to

00:08:44.440 --> 00:08:45.130
their property.

00:08:45.130 --> 00:08:46.890
And that's why we
say that it's a

00:08:46.890 --> 00:08:48.240
mortgage-backed security.

00:08:48.240 --> 00:08:50.980
So it's not just a promise
to get money.

00:08:50.980 --> 00:08:53.470
The money is actually backed
by people's mortgages.

00:08:53.470 --> 00:08:55.660
And of course, then this entity
is going to, if this

00:08:55.660 --> 00:08:58.970
guy defaults on his loan--
he's one of a million, so

00:08:58.970 --> 00:09:01.200
statistically you might be
able to predict that.

00:09:01.200 --> 00:09:03.900
I don't to put too much stock in
these statistical models--

00:09:03.900 --> 00:09:06.780
then this entity will just have
that property auctioned

00:09:06.780 --> 00:09:07.520
off or sold.

00:09:07.520 --> 00:09:10.570
And the cash flow will
come back to it.

00:09:10.570 --> 00:09:12.510
So that's what a mortgage-backed
security is.

00:09:12.510 --> 00:09:15.980
Hopefully I didn't confuse
you too much.

00:09:15.980 --> 00:09:19.260
My next presentation, I'm going
to take it to a further

00:09:19.260 --> 00:09:22.430
level of confusion and show you
what a collateralized debt

00:09:22.430 --> 00:09:23.430
obligation is.

00:09:23.430 --> 00:09:27.150
And then I'll do a more
philosophical video on why

00:09:27.150 --> 00:09:30.190
these things even exist, and
why they're useful, and why

00:09:30.190 --> 00:09:35.190
people may benefit or may not
benefit from these things.


Mortgage-backed securities I

WEBVTT
Kind: captions
Language: en

00:00:00.910 --> 00:00:04.760
Welcome to my presentation on
mortgage-backed securities.

00:00:04.760 --> 00:00:05.730
Let's get started.

00:00:05.730 --> 00:00:07.560
And this is going to be part
of a whole new series of

00:00:07.560 --> 00:00:10.840
presentations, because I think
what's happening right now in

00:00:10.840 --> 00:00:14.670
the credit markets is pretty
significant from, I guess, a

00:00:14.670 --> 00:00:16.510
personal finance point of
view and just from a

00:00:16.510 --> 00:00:17.730
historic point of view.

00:00:17.730 --> 00:00:20.130
And I want to do a whole set
of videos just so people

00:00:20.130 --> 00:00:23.870
understand, I guess, how
everything fits together, and

00:00:23.870 --> 00:00:25.470
what the possible repercussions
could be.

00:00:25.470 --> 00:00:26.690
But we have to start
with the basics.

00:00:26.690 --> 00:00:28.170
So what is a mortgage-backed
security?

00:00:28.170 --> 00:00:29.940
You've probably read
a lot about these.

00:00:29.940 --> 00:00:33.440
So historically, let's think
about what historically

00:00:33.440 --> 00:00:37.100
happens when I went to get a
loan for a house, let's say,

00:00:37.100 --> 00:00:37.850
20 years ago.

00:00:37.850 --> 00:00:38.920
And I'm going to simplify
some things.

00:00:38.920 --> 00:00:40.250
And later we can do
a more nuanced.

00:00:44.000 --> 00:00:46.000
Where'd my pen go?

00:00:46.000 --> 00:00:48.150
Let's say I need $100,000.

00:00:48.150 --> 00:00:50.210
No, let me say $1 million,
because that's actually closer

00:00:50.210 --> 00:00:52.710
to how much houses cost now.

00:00:52.710 --> 00:00:57.080
Let's say I need a $1 million
loan to buy a house, right?

00:00:57.080 --> 00:00:58.990
This is going to be a mortgage
that's going to be

00:00:58.990 --> 00:01:00.160
backed by my house.

00:01:00.160 --> 00:01:03.150
And when I say backed by my
house, or secured by my house,

00:01:03.150 --> 00:01:08.230
that means that I'm going to
borrow $1 million from a bank,

00:01:08.230 --> 00:01:10.780
and if I can't pay back
the loan, then the

00:01:10.780 --> 00:01:11.590
bank gets my house.

00:01:11.590 --> 00:01:13.210
That's all it means.

00:01:13.210 --> 00:01:15.800
And oftentimes it'll only be
secured by the house, which

00:01:15.800 --> 00:01:17.310
means that I could just give
them back the keys.

00:01:17.310 --> 00:01:19.760
They get the house and I have
no other responsibility, but

00:01:19.760 --> 00:01:21.250
of course my credit
gets messed up.

00:01:21.250 --> 00:01:22.690
But I need a $1 million loan.

00:01:22.690 --> 00:01:28.280
The traditional way I got a $1
million loan is I would go and

00:01:28.280 --> 00:01:30.550
talk to the bank.

00:01:30.550 --> 00:01:33.260
This is the bank.

00:01:33.260 --> 00:01:34.720
They have the money.

00:01:34.720 --> 00:01:41.830
And then they would give me $1
million and I would pay them

00:01:41.830 --> 00:01:46.340
some type of interest. I'll
make up a number.

00:01:46.340 --> 00:01:48.410
The interest rates obviously
change, and we'll do future

00:01:48.410 --> 00:01:50.730
presentations on what causes the
interest rates to change.

00:01:50.730 --> 00:01:55.890
But let's say I would pay them
10% interest. And for the sake

00:01:55.890 --> 00:01:59.660
of simplicity, I'm going to
assume that the loans in this

00:01:59.660 --> 00:02:01.690
presentation are interest-only
loans.

00:02:01.690 --> 00:02:04.800
In a traditional mortgage, you
actually, your payment has

00:02:04.800 --> 00:02:06.950
some part interest and
some part principal.

00:02:06.950 --> 00:02:10.419
Principal is actually when
you're paying down the loan.

00:02:10.419 --> 00:02:12.530
The math is a little bit more
difficult with that, so what

00:02:12.530 --> 00:02:15.030
we're going to do in this case
is assume that I only pay the

00:02:15.030 --> 00:02:17.770
interest portion, and at the
end of the loan I pay the

00:02:17.770 --> 00:02:18.800
whole loan amount.

00:02:18.800 --> 00:02:23.470
So let's say that this
is a 10-year loan.

00:02:23.470 --> 00:02:27.530
So for each year of the 10
years, I'm going to pay

00:02:27.530 --> 00:02:33.290
$100,000 in interest. $100,000
per year, right?

00:02:33.290 --> 00:02:38.540
And then in year 10, I'm going
to pay the $100,000 and I'm

00:02:38.540 --> 00:02:41.490
also going to pay back
the $1 million.

00:02:41.490 --> 00:02:44.150
Right?

00:02:44.150 --> 00:02:50.550
Year 1, 2, 3, dot, dot,
dot, dot, 9, 10.

00:02:50.550 --> 00:02:52.310
So in year one, I
pay $100,000.

00:02:52.310 --> 00:02:53.720
Year two, I pay $100,000.

00:02:53.720 --> 00:02:55.030
Year three, I pay $100,000.

00:02:55.030 --> 00:02:56.030
Dot, dot, dot, dot.

00:02:56.030 --> 00:02:57.650
Year nine, I pay $100,000.

00:02:57.650 --> 00:03:00.340
And then year 10, I pay the
$100,000 plus I pay back the

00:03:00.340 --> 00:03:01.030
$1 million.

00:03:01.030 --> 00:03:04.300
So I pay back $1.1 million.

00:03:04.300 --> 00:03:08.180
So that's kind of how the cash
is going to be transferred

00:03:08.180 --> 00:03:09.830
between me and the bank.

00:03:09.830 --> 00:03:11.725
And this is how a-- I don't
want to say a traditional

00:03:11.725 --> 00:03:13.240
loan, because this isn't
a traditional loan, an

00:03:13.240 --> 00:03:17.630
interest-only loan-- but for the
sake of this presentation,

00:03:17.630 --> 00:03:19.410
how it's different than a
mortgage-backed security, the

00:03:19.410 --> 00:03:21.990
important thing to realize
is that the bank would

00:03:21.990 --> 00:03:23.710
have kept the loan.

00:03:23.710 --> 00:03:25.780
These payments I would have been
making would have been

00:03:25.780 --> 00:03:27.010
directly to the bank.

00:03:27.010 --> 00:03:28.540
And that's what the
business that,

00:03:28.540 --> 00:03:30.800
historically, banks were in.

00:03:30.800 --> 00:03:38.770
Another person, you-- and you
have a hat-- let's say you're

00:03:38.770 --> 00:03:40.610
extremely wealthy and
you would put $1

00:03:40.610 --> 00:03:42.090
million into the bank.

00:03:42.090 --> 00:03:42.340
Right?

00:03:42.340 --> 00:03:44.320
That's just your life savings
or you inherited

00:03:44.320 --> 00:03:45.260
it from your uncle.

00:03:45.260 --> 00:03:47.710
And the bank would pay you,
I don't know, 5%.

00:03:51.840 --> 00:03:55.120
And then take that $1 million,
give it to me, and get 10% on

00:03:55.120 --> 00:03:56.680
what I just borrowed.

00:03:56.680 --> 00:03:58.330
And then the bank makes
the difference, right?

00:03:58.330 --> 00:04:01.360
It's paying you 5% percent and
then it's getting 10% from me.

00:04:01.360 --> 00:04:03.790
And we can go later into how
they can pull this off, like

00:04:03.790 --> 00:04:05.270
what happens when you have
to withdraw the money,

00:04:05.270 --> 00:04:05.960
et cetera, et cetera.

00:04:05.960 --> 00:04:09.220
But the important thing to
realize is that these payments

00:04:09.220 --> 00:04:11.210
I make are to the bank.

00:04:11.210 --> 00:04:15.220
That's how loans worked before
the mortgage-backed security

00:04:15.220 --> 00:04:17.320
industry really got developed.

00:04:17.320 --> 00:04:20.550
Now let's do the example with
a mortgage-backed security.

00:04:23.270 --> 00:04:24.460
Now there's still me.

00:04:24.460 --> 00:04:29.040
I still exist. And I still
need $1 million.

00:04:31.950 --> 00:04:34.100
Let's say I still
go to the bank.

00:04:34.100 --> 00:04:35.460
Let's say I go to the bank.

00:04:35.460 --> 00:04:36.710
The bank is still there.

00:04:41.740 --> 00:04:45.550
And like before, the bank
gives me $1 million.

00:04:48.380 --> 00:04:52.320
And then I give the
bank 10% per year.

00:04:52.320 --> 00:04:52.840
Right?

00:04:52.840 --> 00:04:54.940
So it looks very similar
to our old model.

00:04:54.940 --> 00:04:57.900
But in the old model,
the bank would keep

00:04:57.900 --> 00:04:59.040
these payments itself.

00:04:59.040 --> 00:05:03.650
And that $1 million it had is
now used to pay for my house.

00:05:03.650 --> 00:05:05.810
Then there was an innovation.

00:05:05.810 --> 00:05:08.370
Instead of having to get more
deposits in order to keep

00:05:08.370 --> 00:05:10.750
giving out loans, the bank said,
well, why don't I sell

00:05:10.750 --> 00:05:14.030
these loans to a third
party and let them do

00:05:14.030 --> 00:05:15.140
something with it?

00:05:15.140 --> 00:05:16.550
And I know that that might
be a little confusing.

00:05:16.550 --> 00:05:17.640
How do you sell a loan?

00:05:17.640 --> 00:05:18.890
Well let's say there's me.

00:05:18.890 --> 00:05:21.510
And let's say there's
a thousand of me.

00:05:21.510 --> 00:05:22.020
Right?

00:05:22.020 --> 00:05:24.310
There's a bunch of Sals
in the world.

00:05:24.310 --> 00:05:24.820
Right?

00:05:24.820 --> 00:05:28.080
And we each are borrowing
money from the bank.

00:05:28.080 --> 00:05:30.740
So there's a thousand of me.

00:05:30.740 --> 00:05:31.050
Right?

00:05:31.050 --> 00:05:32.460
I'm just saying any kind
of large number.

00:05:32.460 --> 00:05:34.040
It doesn't have to
be a thousand.

00:05:34.040 --> 00:05:36.220
And collectively we
have borrowed a

00:05:36.220 --> 00:05:37.430
thousand times a million.

00:05:37.430 --> 00:05:42.190
So we've collectively borrowed
$1 billion from the bank.

00:05:42.190 --> 00:05:44.570
And we are collectively paying
10% on that, right?

00:05:44.570 --> 00:05:47.330
Because each of us are going to
pay 10% per year, so we're

00:05:47.330 --> 00:05:49.470
each going to pay 10%
on that $1 billion.

00:05:49.470 --> 00:05:49.750
Right?

00:05:49.750 --> 00:05:52.930
So 10% on that $1 billion is
$100 million in interest. So

00:05:52.930 --> 00:05:58.220
this 10% equals $100 million.

00:05:58.220 --> 00:06:02.810
Now the bank says, OK, all the
$1 billion that I had in my

00:06:02.810 --> 00:06:05.830
vaults, or whatever-- I guess
now there's no physical money,

00:06:05.830 --> 00:06:09.500
but in my databases-- is now
out in people's pockets.

00:06:09.500 --> 00:06:10.800
I want to get more money.

00:06:10.800 --> 00:06:13.470
So what the bank does is it
takes all these loans

00:06:13.470 --> 00:06:17.200
together, that $1 billion in
loans, and it says, hey,

00:06:17.200 --> 00:06:22.060
investment bank-- so that's
another bank-- why don't you

00:06:22.060 --> 00:06:23.750
give me $1 billion?

00:06:26.490 --> 00:06:28.850
So the investment bank gives
them $1 billion.

00:06:28.850 --> 00:06:33.110
And then instead of me and the
other thousands of me paying

00:06:33.110 --> 00:06:38.430
the money to this bank, we're
now paying it to this new

00:06:38.430 --> 00:06:40.990
party, right?

00:06:40.990 --> 00:06:43.020
I'm making my picture
very confusing.

00:06:43.020 --> 00:06:44.480
So what just happened?

00:06:44.480 --> 00:06:48.420
When this bank sold the loans--
grouped all of the

00:06:48.420 --> 00:06:50.460
loans together and it folded it
into a big, kind of did it

00:06:50.460 --> 00:06:52.750
on a wholesale basis--
it's sold a thousand

00:06:52.750 --> 00:06:54.090
loans to this bank.

00:06:54.090 --> 00:06:58.330
So this bank paid $1 billion
for the right to get the

00:06:58.330 --> 00:07:00.870
interest and principal payment
on those loans.

00:07:00.870 --> 00:07:06.280
So all that happened is, this
guy got the cash and then this

00:07:06.280 --> 00:07:08.850
bank will now get the
set of payments.

00:07:08.850 --> 00:07:10.930
So you might wonder, why
did this bank do it?

00:07:10.930 --> 00:07:14.210
Well I kind of glazed over the
details, but he probably got a

00:07:14.210 --> 00:07:16.550
lot of fees for doing this, or
maybe he just likes giving

00:07:16.550 --> 00:07:18.130
loans to his customers,
whatever.

00:07:18.130 --> 00:07:20.610
But the actual right answer
is that he got

00:07:20.610 --> 00:07:22.300
fees for doing this.

00:07:22.300 --> 00:07:24.110
And he's actually probably going
to transfer a little bit

00:07:24.110 --> 00:07:26.130
less value to this guy.

00:07:26.130 --> 00:07:28.630
Now, hopefully you understand
the notion of actually

00:07:28.630 --> 00:07:29.610
transferring the loan.

00:07:29.610 --> 00:07:31.980
This guy pays money and now the
payments are essentially

00:07:31.980 --> 00:07:33.840
going to be funnelled to him.

00:07:33.840 --> 00:07:35.810
I only have two minutes left
in this presentation, so in

00:07:35.810 --> 00:07:39.530
the next presentation I'm going
to focus on what this

00:07:39.530 --> 00:07:43.300
guy can now do with the
loan to turn it into a

00:07:43.300 --> 00:07:44.630
mortgage-backed security.

00:07:44.630 --> 00:07:46.250
And this guy's an investment
bank instead of

00:07:46.250 --> 00:07:48.070
a commercial bank.

00:07:48.070 --> 00:07:49.820
That detail is not that
important in understanding

00:07:49.820 --> 00:07:52.020
what a mortgage-backed security
is, but that will

00:07:52.020 --> 00:07:54.820
have to wait until the
next presentation.

00:07:54.820 --> 00:07:56.340
See you soon.


Return on capital

WEBVTT
Kind: captions
Language: en

00:00:01.160 --> 00:00:04.660
Welcome to my presentation
on return on capital.

00:00:04.660 --> 00:00:06.950
Let me write that down.

00:00:06.950 --> 00:00:08.060
I'm using the wrong color.

00:00:08.060 --> 00:00:09.260
Let me use a nicer color.

00:00:09.260 --> 00:00:10.510
Let me go to white.

00:00:20.700 --> 00:00:23.750
I want to do this presentation
first, because I think this is

00:00:23.750 --> 00:00:26.420
really going to give you the big
picture on how you should

00:00:26.420 --> 00:00:29.100
think about what something
is worth.

00:00:29.100 --> 00:00:31.140
Whether you should invest
your money into it.

00:00:31.140 --> 00:00:33.890
And how you should weigh the
different options you have in

00:00:33.890 --> 00:00:36.450
terms of what you actually have
to do with your money, in

00:00:36.450 --> 00:00:37.500
terms of where you
want to put it.

00:00:37.500 --> 00:00:38.310
Do you want to put
it in the bank?

00:00:38.310 --> 00:00:39.130
Do you want to buy a house?

00:00:39.130 --> 00:00:40.740
Do you want to pay off
your credit cards?

00:00:40.740 --> 00:00:41.900
Et cetera, et cetera.

00:00:41.900 --> 00:00:44.860
So let's just define
return on capital.

00:00:44.860 --> 00:00:47.570
And just so you know, I'm not
necessarily going to be strict

00:00:47.570 --> 00:00:51.270
on the accounting conventions,
or the GAP conventions --

00:00:51.270 --> 00:00:52.840
that's the accounting
conventions in this country.

00:00:52.840 --> 00:00:56.290
I'm going to do it more on a
hands-on, how Joe Investors

00:00:56.290 --> 00:00:58.470
should think about
their money.

00:00:58.470 --> 00:01:03.360
So in this scenario, I define
return on capital as just the

00:01:03.360 --> 00:01:17.470
cash you get per year divided by
the total cash you put in.

00:01:23.080 --> 00:01:26.730
And, well, I don't want
to just say, cash.

00:01:26.730 --> 00:01:28.010
There's other ways to
measure return.

00:01:28.010 --> 00:01:30.640
But actually, to keep it simple,
let's just say cash.

00:01:30.640 --> 00:01:32.750
So let's think about
how this works out.

00:01:32.750 --> 00:01:35.170
Let's say, I have an idea.

00:01:35.170 --> 00:01:36.630
I have a restaurant.

00:01:36.630 --> 00:01:40.530
And that restaurant, it'll
cost $1 million.

00:01:40.530 --> 00:01:47.835
It'll cost $1 million investment
in this restaurant.

00:01:50.590 --> 00:01:52.210
It's going to be a $1
million investment.

00:01:52.210 --> 00:01:57.500
And let's say that, per year,
after paying all the expenses,

00:01:57.500 --> 00:02:01.670
after paying the utility, after
paying the employees,

00:02:01.670 --> 00:02:04.690
after repairing, and
maintenance, and after paying

00:02:04.690 --> 00:02:07.900
taxes, everything, let's
say this restaurant

00:02:07.900 --> 00:02:11.790
makes $100,000 a year.

00:02:11.790 --> 00:02:13.170
And that's after taxes
and everything.

00:02:13.170 --> 00:02:14.400
That's what goes
into my pocket.

00:02:14.400 --> 00:02:17.470
So in this situation, my return
on capital, the way

00:02:17.470 --> 00:02:23.885
I've defined it, is $100,000
divided by $1 million, or we

00:02:23.885 --> 00:02:29.880
could just say a thousand
thousand dollars, equals 10%.

00:02:29.880 --> 00:02:30.560
Pretty straightforward.

00:02:30.560 --> 00:02:32.560
You're probably saying,
Sal, this is silly.

00:02:32.560 --> 00:02:33.610
Why are you wasting my time?

00:02:33.610 --> 00:02:36.230
Well, maybe it is.

00:02:36.230 --> 00:02:38.890
But I think you'll find that
this is going to lay a

00:02:38.890 --> 00:02:42.060
foundation that will eventually
blow your mind.

00:02:42.060 --> 00:02:44.590
So let's keep going.

00:02:44.590 --> 00:02:45.840
Let me do another.

00:02:52.510 --> 00:02:55.260
OK, so I said the restaurant
-- let's make it a pizza

00:02:55.260 --> 00:03:00.140
restaurant -- let's just say,
the restaurant return on

00:03:00.140 --> 00:03:05.110
capital is equal to 10%.

00:03:05.110 --> 00:03:05.570
Right?

00:03:05.570 --> 00:03:09.540
I can put in $1 million and I'll
get in $100,000 per year.

00:03:09.540 --> 00:03:10.910
That's where I got 10%.

00:03:10.910 --> 00:03:11.990
Let me write that down.

00:03:11.990 --> 00:03:25.430
I get $100,000 per year off
of $1 million investment.

00:03:25.430 --> 00:03:28.720
Now, that's one project.

00:03:28.720 --> 00:03:31.140
I'm not going to factor in
things like risk and

00:03:31.140 --> 00:03:32.550
probabilities just yet.

00:03:32.550 --> 00:03:35.380
Let's just say, for sure, I know
that if I put my money

00:03:35.380 --> 00:03:38.830
here, I'm going to get
10% on my money.

00:03:38.830 --> 00:03:40.810
And let's say the other
option with my

00:03:40.810 --> 00:03:46.365
money is a beauty parlor.

00:03:57.570 --> 00:03:59.330
And let's say that that
also costs $1 million.

00:04:08.180 --> 00:04:16.269
And this beauty parlor gets
me $50,000 a year.

00:04:16.269 --> 00:04:19.050
I think it's very obvious to you
already which investment

00:04:19.050 --> 00:04:20.279
you'd rather invest in.

00:04:20.279 --> 00:04:24.250
Because the return on capital on
this beauty parlor is only

00:04:24.250 --> 00:04:27.020
50,000 divided by a
million, or 5%.

00:04:27.020 --> 00:04:27.910
So this is obvious.

00:04:27.910 --> 00:04:30.980
You'd rather do the restaurant
than a beauty parlor.

00:04:30.980 --> 00:04:35.870
And in general, after adjusting
for risk, you always

00:04:35.870 --> 00:04:37.970
want to go with the project
that has the

00:04:37.970 --> 00:04:39.910
higher return on capital.

00:04:39.910 --> 00:04:42.670
And, later on, there will be
nuances in terms of when you

00:04:42.670 --> 00:04:43.400
get that return.

00:04:43.400 --> 00:04:46.710
Maybe you would rather have a
slightly lower return if you

00:04:46.710 --> 00:04:47.900
get the money faster.

00:04:47.900 --> 00:04:52.515
Or a slightly higher return if
you're taking on risks, et

00:04:52.515 --> 00:04:53.100
cetera, et cetera.

00:04:53.100 --> 00:04:55.900
Or to compensate for risk.

00:04:55.900 --> 00:04:57.460
So we know we want to
do the restaurant.

00:04:57.460 --> 00:05:00.730
But do we definitely want
to do the restaurant?

00:05:00.730 --> 00:05:04.990
We'd rather do the restaurant
than the beauty parlor, right?

00:05:04.990 --> 00:05:08.490
But my question to you is, do
we definitely want to do the

00:05:08.490 --> 00:05:09.280
restaurant?

00:05:09.280 --> 00:05:12.710
And this is where the return
on capital becomes

00:05:12.710 --> 00:05:13.180
interesting.

00:05:13.180 --> 00:05:15.340
Because what matters, before
we put the money into the

00:05:15.340 --> 00:05:18.070
restaurant, is to think
about what the cost of

00:05:18.070 --> 00:05:19.400
that money is to us.

00:05:19.400 --> 00:05:21.930
And this is what I think will
be a little bit of a new

00:05:21.930 --> 00:05:22.830
concept to you.

00:05:22.830 --> 00:05:25.730
So I'm going to introduce you,
now, to the notion of a cost

00:05:25.730 --> 00:05:27.431
of capital.

00:05:27.431 --> 00:05:29.850
So let me erase this.

00:05:32.350 --> 00:05:33.470
OK.

00:05:33.470 --> 00:05:34.860
So the restaurant costs
$1 million.

00:05:40.270 --> 00:05:47.320
And it gives me $100,000
a year.

00:05:47.320 --> 00:05:52.190
And that's a 10% return
on capital.

00:05:52.190 --> 00:05:53.680
Now, let's say I have to
borrow all the money.

00:05:53.680 --> 00:05:56.360
And there's some bank that's
willing to give me all the

00:05:56.360 --> 00:05:57.980
money for this restaurant.

00:05:57.980 --> 00:06:11.280
And the interest rate on this
loan is, let's say, 15%.

00:06:11.280 --> 00:06:16.090
Is it still a good idea for me
to open up the restaurant?

00:06:16.090 --> 00:06:19.170
Well, if I have a loan and I
have to borrow the whole

00:06:19.170 --> 00:06:21.880
amount -- so I'm going to have
a loan for $1 million to buy

00:06:21.880 --> 00:06:24.850
that same restaurant.

00:06:24.850 --> 00:06:28.830
And I'm going to be charged 15%
in interest every year .

00:06:28.830 --> 00:06:30.690
And I'm not going to take taxes,
and the fact that you

00:06:30.690 --> 00:06:32.470
could deduct taxes, et cetera,
et cetera , into

00:06:32.470 --> 00:06:33.930
account just yet.

00:06:33.930 --> 00:06:36.580
Let's assume that my total
cost is 15% per year in

00:06:36.580 --> 00:06:43.440
interest. So I'm going to have
to spend $150,000 per year in

00:06:43.440 --> 00:06:46.640
interest.

00:06:46.640 --> 00:06:50.000
So my question to you is, does
it still make sense for me to

00:06:50.000 --> 00:06:51.450
open up this restaurant?

00:06:51.450 --> 00:06:53.920
Every year, I'm going to be
making $100,000 from the

00:06:53.920 --> 00:06:55.270
restaurant itself.

00:06:55.270 --> 00:07:00.740
But I'm going to be paying
$150,000 a year in interest.

00:07:00.740 --> 00:07:03.870
So you'll probably say, Sal,
once again, you have just

00:07:03.870 --> 00:07:04.990
restated the obvious.

00:07:04.990 --> 00:07:06.890
No, you would not want to
do this restaurant.

00:07:06.890 --> 00:07:09.890
Because every year,
$50,000 will be

00:07:09.890 --> 00:07:11.710
burning out of your pocket.

00:07:11.710 --> 00:07:13.830
Now, you might think that this
is obvious, but I'm going to

00:07:13.830 --> 00:07:16.750
show you many, many examples of
where people are actively

00:07:16.750 --> 00:07:17.210
doing this.

00:07:17.210 --> 00:07:20.720
People who you would otherwise
assume could do

00:07:20.720 --> 00:07:21.660
this type of math.

00:07:21.660 --> 00:07:23.930
And it's especially happening
in the housing market.

00:07:23.930 --> 00:07:24.780
But anyway.

00:07:24.780 --> 00:07:27.090
So in this situation, you
wouldn't want to invest in it.

00:07:27.090 --> 00:07:30.140
And a very simple way of
thinking about this is you'd

00:07:30.140 --> 00:07:35.410
only want to invest, you only
want to do a project, if your

00:07:35.410 --> 00:07:41.430
return on capital is greater
than your cost of capital.

00:07:46.720 --> 00:07:49.925
This is the only time that you
want to invest in a project.

00:07:52.540 --> 00:07:54.770
With that said, I'm not
going to go back to

00:07:54.770 --> 00:07:55.730
what we just did.

00:07:55.730 --> 00:07:57.930
I just showed you something that
we thought was obvious,

00:07:57.930 --> 00:08:02.250
but I'm going to re-ask
you a question.

00:08:02.250 --> 00:08:05.430
So we had the restaurant.

00:08:05.430 --> 00:08:06.725
And we have the beauty parlor.

00:08:06.725 --> 00:08:08.790
Let's call it BP for short.

00:08:08.790 --> 00:08:11.420
They both cost $1 million.

00:08:11.420 --> 00:08:13.630
Let me write ROC.

00:08:13.630 --> 00:08:16.490
The ROC of the restaurant,
we said, was 10%.

00:08:16.490 --> 00:08:19.100
And the ROC on the beauty
parlor, we said, was 5%.

00:08:19.100 --> 00:08:21.090
So right now, superficially, it
looks like the restaurant

00:08:21.090 --> 00:08:24.020
is just a better project.

00:08:24.020 --> 00:08:28.640
But then we said the cost of
capital, so the interest rate.

00:08:28.640 --> 00:08:30.680
How much does it cost for us
to get that $1 million?

00:08:30.680 --> 00:08:35.530
The interest rate to borrow
money for a restaurant is 15%.

00:08:35.530 --> 00:08:38.210
And we said that this is
not a good investment.

00:08:38.210 --> 00:08:40.440
Because our cost of capital
is higher than

00:08:40.440 --> 00:08:41.080
our return on capital.

00:08:41.080 --> 00:08:42.929
And you could do the math
and figure it out.

00:08:42.929 --> 00:08:45.070
But what if there was some kind
of government program?

00:08:45.070 --> 00:08:48.390
They just felt that there
weren't enough beauty parlors

00:08:48.390 --> 00:08:49.130
in the country.

00:08:49.130 --> 00:08:52.740
And they were willing to give
you a really cheap loan to buy

00:08:52.740 --> 00:08:53.820
a beauty parlor.

00:08:53.820 --> 00:08:55.910
And the government program, they
said, we're going to give

00:08:55.910 --> 00:09:00.560
you a low-interest loan of 2%.

00:09:00.560 --> 00:09:02.570
So my question to you is,
now, which project

00:09:02.570 --> 00:09:03.790
would you rather do?

00:09:03.790 --> 00:09:06.150
Superficially, it looks like
the restaurant was better.

00:09:06.150 --> 00:09:09.120
You get a 10% return,
as opposed to 5%.

00:09:09.120 --> 00:09:11.660
But your cost of capital, the
interest rate you would have

00:09:11.660 --> 00:09:14.000
to pay on a loan for the beauty
parlor, all of a sudden

00:09:14.000 --> 00:09:15.600
looks a little bit better.

00:09:15.600 --> 00:09:17.860
In fact, this is actually
a good investment.

00:09:17.860 --> 00:09:20.620
Because your cost of capital
is less than

00:09:20.620 --> 00:09:21.700
your return on capital.

00:09:21.700 --> 00:09:22.830
We can even do the math.

00:09:22.830 --> 00:09:27.500
Every year the beauty parlor
will generate $50,000.

00:09:27.500 --> 00:09:31.260
And you'll be paying $20,000
in interest. So you'll be

00:09:31.260 --> 00:09:34.280
netting $30,000 without having
to put any money for yourself.

00:09:34.280 --> 00:09:35.480
You'll be borrowing
all the money.

00:09:35.480 --> 00:09:37.510
So clearly this is a
good investment.

00:09:37.510 --> 00:09:42.910
So that's it, now, for the intro
on return on capital and

00:09:42.910 --> 00:09:43.790
cost of capital.

00:09:43.790 --> 00:09:45.640
And in my next presentations,
I'll go into a little bit more

00:09:45.640 --> 00:09:48.810
detail and do a few more
nuanced examples.


The unit circle definition of trigonometric function

WEBVTT
Kind: captions
Language: en

00:00:00.910 --> 00:00:03.370
We're now going to study the
unit circle a little bit more,

00:00:03.370 --> 00:00:08.370
and see how it extends, I guess
we could say, the traditional

00:00:08.370 --> 00:00:10.770
SOH-CAH-TOA definitions
of functions.

00:00:10.770 --> 00:00:14.590
And how we can actually use it
to solve for angles that the

00:00:14.590 --> 00:00:18.280
SOH-CAH-TOA definition of the
trig functions actually

00:00:18.280 --> 00:00:19.560
doesn't help us with.

00:00:19.560 --> 00:00:21.830
So let's just, as a
review, remember what

00:00:21.830 --> 00:00:22.760
SOH-CAH-TOA told us.

00:00:25.450 --> 00:00:26.670
I'll write it up here
in this corner.

00:00:31.460 --> 00:00:32.910
I don't want to get confusing,
because I don't want to

00:00:32.910 --> 00:00:33.700
write over too much.

00:00:33.700 --> 00:00:37.260
SOH, CAH, TOA.

00:00:37.260 --> 00:00:37.690
I'm sorry.

00:00:37.690 --> 00:00:39.120
I got it all jumbled up here.

00:00:39.120 --> 00:00:43.730
That told us that if we have a
right angle that the sine of an

00:00:43.730 --> 00:00:47.920
angle in the right angle is
equal to the opposite side

00:00:47.920 --> 00:00:49.070
over the hypotenuse.

00:00:49.070 --> 00:00:51.210
The cosine of an angle is
equal to the adjacent

00:00:51.210 --> 00:00:52.600
side over hypotenuse.

00:00:52.600 --> 00:00:54.810
And the tangent side is
equal to the opposite

00:00:54.810 --> 00:00:55.750
over the adjacent side.

00:00:55.750 --> 00:00:56.940
And this worked fine for us.

00:00:56.940 --> 00:00:59.820
But if you think about it,
what happens when that angle

00:00:59.820 --> 00:01:00.980
approaches 90 degrees?

00:01:00.980 --> 00:01:03.790
Because you can't have two 90
degree angles in a right angle.

00:01:03.790 --> 00:01:06.890
Or what happens when that angle
is greater than 90 degrees?

00:01:06.890 --> 00:01:08.900
Or what if it went negative?

00:01:08.900 --> 00:01:11.780
And that's why, if you remember
from the previous video,

00:01:11.780 --> 00:01:14.560
we needed the unit
circle definition.

00:01:14.560 --> 00:01:18.100
So let's review the unit
circle definition.

00:01:18.100 --> 00:01:21.180
Let me erase this.

00:01:21.180 --> 00:01:21.670
Dum di-dum di-dum.

00:01:25.010 --> 00:01:27.060
I actually got this unit
circle-- I think I got

00:01:27.060 --> 00:01:27.850
it from Wikipedia.

00:01:27.850 --> 00:01:30.900
But I want to give due
credit to whoever I did

00:01:30.900 --> 00:01:34.610
it get for, this drawing
of the unit circle.

00:01:34.610 --> 00:01:37.730
But the unit circle
kind of extends that

00:01:37.730 --> 00:01:38.770
SOH-CAH-TOA definition.

00:01:38.770 --> 00:01:41.560
It tells us if we have a unit
circle-- and this is a picture

00:01:41.560 --> 00:01:44.290
of a unit circle here-- a unit
circle is just a circle

00:01:44.290 --> 00:01:48.100
centered at the origin,
centered at the point 0, 0,

00:01:48.100 --> 00:01:49.910
and it has a radius of 1.

00:01:49.910 --> 00:01:54.850
So it intersects the x-axis
at 1, 0 and negative 1, 0.

00:01:54.850 --> 00:01:59.440
It intersects the y-axis at
0, 1 and 0, negative 1.

00:01:59.440 --> 00:02:05.000
If we have a unit circle we
define-- let's start with the

00:02:05.000 --> 00:02:09.170
cosine of theta-- we define the
cosine of theta as let's take

00:02:09.170 --> 00:02:14.960
an angle that's between two
radiuses in this unit circle.

00:02:14.960 --> 00:02:19.600
And one radius is going to
be the positive x-axis

00:02:19.600 --> 00:02:21.330
between 0 and 1.

00:02:21.330 --> 00:02:24.550
So one radius is going
to be this line here.

00:02:24.550 --> 00:02:30.620
And then we have the angle is
the angle between you can kind

00:02:30.620 --> 00:02:33.380
of view that as the base
radius and some other radius.

00:02:33.380 --> 00:02:37.760
So let's say this
case right here.

00:02:37.760 --> 00:02:41.020
And this would be our angle.

00:02:41.020 --> 00:02:45.550
The unit circle definition
tells us that the cosine of

00:02:45.550 --> 00:02:51.110
this angle is equal to the
x-coordinate where this radius

00:02:51.110 --> 00:02:55.850
intersects the unit circle, and
that the sine of this function

00:02:55.850 --> 00:02:59.055
is equal to the y-coordinate
where this point intersects

00:02:59.055 --> 00:03:00.370
the unit circle.

00:03:00.370 --> 00:03:04.570
So for example, in this case--
if you can read behind

00:03:04.570 --> 00:03:07.770
my line-- this says 30
degrees equals pi/6.

00:03:07.770 --> 00:03:14.090
So this angle right here is
30 degrees, or pi/6 radians.

00:03:18.000 --> 00:03:21.720
And what this definition tells
us is that the sine of 30

00:03:21.720 --> 00:03:27.240
degrees is 1/2, and that the
cosine of 30 degrees is

00:03:27.240 --> 00:03:29.990
square root of 3/2.

00:03:29.990 --> 00:03:31.990
And what I want to show you is
that this unit circle

00:03:31.990 --> 00:03:35.050
definition actually coincides
with our SOH-CAH-TOA

00:03:35.050 --> 00:03:37.490
definition, but then
it extends it.

00:03:37.490 --> 00:03:40.320
So let's see how we can get
from that SOH-CAH-TOA

00:03:40.320 --> 00:03:42.840
definition to this unit circle
definition, and why they're

00:03:42.840 --> 00:03:44.300
actually consistent
with each other.

00:03:44.300 --> 00:03:49.410
So let me erase some of
what I have written here.

00:03:49.410 --> 00:03:52.340
Let me get the eraser tool.

00:03:52.340 --> 00:03:54.995
I'm going to erase what I had.

00:03:59.270 --> 00:04:08.450
So let me go back to the pen
tool, make it small again.

00:04:08.450 --> 00:04:09.310
OK.

00:04:09.310 --> 00:04:11.400
I think I'm all set.

00:04:11.400 --> 00:04:14.150
So let's go back to that theta.

00:04:14.150 --> 00:04:17.410
Let's say that this
is the theta.

00:04:17.410 --> 00:04:23.100
And as we said, this angle
is 30 degrees or pi/6.

00:04:23.100 --> 00:04:28.710
Let's drop a line from
that point to the x-axis.

00:04:28.710 --> 00:04:30.590
And as we see this line is
perpendicular, so this

00:04:30.590 --> 00:04:31.740
is a 90 degree angle.

00:04:35.730 --> 00:04:39.510
And if this is a 30 degree
angle here-- this is 30.

00:04:39.510 --> 00:04:39.750
Right?

00:04:39.750 --> 00:04:42.450
Theta equals 30.

00:04:42.450 --> 00:04:43.730
This is 30, this is 90.

00:04:43.730 --> 00:04:44.380
What is this angle?

00:04:44.380 --> 00:04:45.955
Well, this is a 60 degree
angle, because they

00:04:45.955 --> 00:04:47.100
add up to 180.

00:04:47.100 --> 00:04:49.440
So this is a 30-60-90 triangle.

00:04:49.440 --> 00:04:50.410
Interesting.

00:04:50.410 --> 00:04:53.320
And what do you remember
about 30-60-90 triangles?

00:04:53.320 --> 00:04:57.570
Well, the side opposite the
30 degree side is 1/2 the

00:04:57.570 --> 00:04:59.530
length of the hypotenuse.

00:04:59.530 --> 00:05:00.390
I hope you remember that.

00:05:00.390 --> 00:05:02.790
I don't want to
confuse you too much.

00:05:02.790 --> 00:05:06.160
So this is the side opposite
the 30 degree side.

00:05:06.160 --> 00:05:07.280
Right?

00:05:07.280 --> 00:05:08.390
And what's the hypotenuse?

00:05:08.390 --> 00:05:09.490
This is the hypotenuse.

00:05:09.490 --> 00:05:11.200
And what's the length
of this hypotenuse?

00:05:11.200 --> 00:05:13.360
Well it's 1, because this is a
unit circle and this is the

00:05:13.360 --> 00:05:14.990
radius of the unit circle.

00:05:14.990 --> 00:05:18.870
So the length of this
hypotenuse is 1, and so the

00:05:18.870 --> 00:05:21.300
length of this side, which
is opposite the 30 degree

00:05:21.300 --> 00:05:23.490
angle, is going to be 1/2.

00:05:23.490 --> 00:05:23.740
Right?

00:05:23.740 --> 00:05:28.560
And I'm just using the
30-60-90 triangles that we've

00:05:28.560 --> 00:05:30.450
done previous videos on.

00:05:30.450 --> 00:05:34.170
And what's the side opposite
the 60 degree side?

00:05:34.170 --> 00:05:36.070
Well once again it's
square root of 3/2

00:05:36.070 --> 00:05:38.230
times the hypotenuse.

00:05:38.230 --> 00:05:39.860
And so it's square root of 3/2.

00:05:42.670 --> 00:05:43.180
Right?

00:05:43.180 --> 00:05:46.260
So we can figure out that this
side is square root of 3/2,

00:05:46.260 --> 00:05:49.750
and that this side is 1/2.

00:05:49.750 --> 00:05:51.760
So a couple of things
we can figure out.

00:05:51.760 --> 00:05:53.650
Just by looking at this we can
immediately say, well what's

00:05:53.650 --> 00:05:56.240
the coordinate of this point?

00:05:56.240 --> 00:05:58.440
Well it's x-coordinate
is right here.

00:05:58.440 --> 00:05:58.800
Right?

00:05:58.800 --> 00:06:01.510
It's x-coordinate would
be square root of 3/2.

00:06:01.510 --> 00:06:02.810
That's this right here.

00:06:02.810 --> 00:06:04.080
This distance.

00:06:04.080 --> 00:06:07.970
And it's y-coordinate would be
the length of this side of

00:06:07.970 --> 00:06:09.260
the right triangle, or 1/2.

00:06:09.260 --> 00:06:10.410
And there we have
it right here.

00:06:10.410 --> 00:06:11.850
It was already written for us.

00:06:11.850 --> 00:06:13.850
The x-coordinate is the
square root of 3/2 and

00:06:13.850 --> 00:06:16.170
the y-coordinate is 1/2.

00:06:16.170 --> 00:06:20.160
And now what I want to show you
is why this x-coordinate can be

00:06:20.160 --> 00:06:23.820
taken as the cosine of theta,
and why this y-coordinate can

00:06:23.820 --> 00:06:25.340
be taken as the sine of theta.

00:06:25.340 --> 00:06:27.170
Well what does
SOH-CAH-TOA tell us?

00:06:27.170 --> 00:06:29.410
Well let's start
with the cosine.

00:06:29.410 --> 00:06:30.940
So SOH, CAH, TOA.

00:06:30.940 --> 00:06:31.400
So CAH.

00:06:34.920 --> 00:06:37.795
Cosine is adjacent over
hypotenuse, right?

00:06:45.120 --> 00:06:48.790
Well, in this triangle I just
drew, what is the adjacent

00:06:48.790 --> 00:06:50.490
side to this angle?

00:06:50.490 --> 00:06:50.613
Right?

00:06:50.613 --> 00:06:52.120
Because we're trying to figure
out the cosine of this

00:06:52.120 --> 00:06:54.170
angle, this 30 degrees.

00:06:54.170 --> 00:06:57.220
Well the adjacent side to this
angle is, of course, this side.

00:06:57.220 --> 00:06:58.170
Right?

00:06:58.170 --> 00:07:00.260
So adjacent is
square root of 3/2.

00:07:00.260 --> 00:07:02.060
We figured that out just now.

00:07:02.060 --> 00:07:03.320
And what's the hypotenuse?

00:07:03.320 --> 00:07:08.050
Well the hypotenuse is this
side, which has length 1

00:07:08.050 --> 00:07:10.830
because it was the unit circle
and that's the radius of it.

00:07:10.830 --> 00:07:13.540
So the cosine of this angle
using the SOH-CAH-TOA

00:07:13.540 --> 00:07:16.630
definition is square root
of 3-- the adjacent side--

00:07:16.630 --> 00:07:18.230
over the hypotenuse 1.

00:07:18.230 --> 00:07:20.935
So square root of 3/2 over
1, which is the square root

00:07:20.935 --> 00:07:25.070
of 3/2, which was the same
thing as the x-coordinate.

00:07:25.070 --> 00:07:27.060
Similarly, we can look at SOH.

00:07:27.060 --> 00:07:30.660
Sine equals opposite
over hypotenuse.

00:07:35.920 --> 00:07:37.010
Well what's the opposite side?

00:07:37.010 --> 00:07:38.410
It's 1/2.

00:07:38.410 --> 00:07:40.470
And the hypotenuse is 1 here.

00:07:40.470 --> 00:07:43.450
So the sine is just 1/2 over 1.

00:07:43.450 --> 00:07:44.940
And so we have it here.

00:07:44.940 --> 00:07:47.220
So that's why the unit circle
definition isn't kind of a

00:07:47.220 --> 00:07:50.180
replacing definition for the
SOH-CAH-TOA definition, it's

00:07:50.180 --> 00:07:52.960
really just an extension that
allows us-- I mean, for 30

00:07:52.960 --> 00:07:55.940
degrees SOH-CAH-TOA worked, for
45 degrees SOH-CAH-TOA worked,

00:07:55.940 --> 00:07:57.750
for 60 degrees it would work.

00:07:57.750 --> 00:07:59.490
But once you get to 90 it
becomes a little bit more

00:07:59.490 --> 00:08:01.980
difficult if you use
traditional SOH-CAH-TOA and you

00:08:01.980 --> 00:08:04.310
try to draw a right triangle
that has two 90 degree angles

00:08:04.310 --> 00:08:05.410
in it-- because you couldn't.

00:08:05.410 --> 00:08:08.480
And especially once you get to
angles that are larger than 90

00:08:08.480 --> 00:08:11.190
or angles that actually
could even go negative.

00:08:11.190 --> 00:08:14.650
It's not drawn here in the unit
circle, but 330 degrees is the

00:08:14.650 --> 00:08:17.140
same thing as negative 30
degrees, because you could go

00:08:17.140 --> 00:08:18.060
either way in the circle.

00:08:18.060 --> 00:08:19.340
And you could keep going
around the circle.

00:08:19.340 --> 00:08:22.480
You could figure out the sine
or the cosine of, you know, 1

00:08:22.480 --> 00:08:25.590
million degrees if you just
keep going around the circle.

00:08:25.590 --> 00:08:28.460
So hopefully this gives you
a sense of the unit circle

00:08:28.460 --> 00:08:31.250
definition of the sine
and cosine functions.

00:08:31.250 --> 00:08:33.240
And, of course, the tangent
function is always just the

00:08:33.240 --> 00:08:37.310
sine over the cosine,
or the y over the x.

00:08:37.310 --> 00:08:39.250
And you could use the
unit circle definition

00:08:39.250 --> 00:08:40.440
for that as well.

00:08:40.440 --> 00:08:44.170
And I'll leave it for you as an
exercise to try to derive all

00:08:44.170 --> 00:08:48.490
of these other values using
this unit circle, and using

00:08:48.490 --> 00:08:52.930
what you already know about
30-60-90 triangles and what you

00:08:52.930 --> 00:08:56.650
already know about 45-45-90
triangles, or what you

00:08:56.650 --> 00:08:57.670
already know about the
Pythagorean theorem.

00:08:57.670 --> 00:09:01.320
And you should be able to
figure out all of these values

00:09:01.320 --> 00:09:03.570
going around the unit circle.

00:09:03.570 --> 00:09:06.270
Hopefully that was helpful.

00:09:06.270 --> 00:09:07.772
See you soon.