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Prof: So we're talking now about mortgages and how to
value them, and if you remember now a
mortgage-- so the first mortgages,
by the way, that we know of,
come from Babylonian times.
It's not like some American invented the mortgage or
something.
This was 3,500-3,800 years old and we have on these cuneiform
tablets these mortgages.
And so the idea of a mortgage is you make a promise,
you back your promise with collateral,
so if you don't keep the promise they can take your
house, and there's some way of getting
out of the promise because everybody knows the collateral,
you might want to leave the home, and then you have to have
some way of dissolving the promise because the promise
involves many payments over time.
So it's making a promise, backing it with collateral,
and finding a way to dissolve the promise at prearranged terms
in case you want to end it by prepaying.
And that prepaying is called the refinancing option.
And because there's a refinancing option it makes the
mortgage a much more complicated thing,
and a much more interesting thing, and something that,
for example, a hedge fund could imagine that
it could make money trading.
So I just want to give you a slight indication of how that
could happen.
So as we said if you have a typical mortgage,
say the mortgage rate is 8 percent--
maybe this is a different answer than I did--
so here we have an 8 percent mortgage with a 6 percent
interest rate to begin with.
Now, if it's an 8 percent mortgage the guy's going to have
to pay much more than 8 percent a year because a mortgage,
remember, there are level payments.
We're talking about fixed rate mortgages.
You pay the same amount every single year for 30 years,
now you're really paying monthly and I've ignored the
monthly business because it's just too many months and there
are 360 of them.
So I'm thinking of it as an annual payment.
You have to pay, of course, more than 8 dollars
a year because if the mortgage rate were 8 percent and you had
a balloon payment on the end, you'd pay 8,8, 8,108.
That's the way they used to work, but they were changed.
So you could imagine the old fashioned mortgage would pay
8,8, 8,8, 8,108; if you didn't pay your 8
somewhere along the line they'd confiscate your whole house and
then take what was owed out of it and you could get out of it
by paying 100.
The new mortgages instead of paying 8 every year for 30 years
you pay 8.88 every year for 30 years because if you discount
payments of 8.8 for 30 years at 8 percent you get 100.
So the present value is 100 at the agreed upon discounting rate
or mortgage rate 8 percent.
And so you see how important this discount rate is.
And the remaining balance, however, goes down because
every time you're paying you're paying more than the 8 percent
interest.
You're paying in the first year 8.8 instead of 8 and so that gap
of .88 is used to reduce the balance from 100 to 99.117.
And so you see the balance is going down over time and making
the lender safer and safer because the same house is
backing it.
So it's called an amortizing mortgage.
Now, why is it difficult to value?
Because you have the option, any time you want,
and there's a good reason for that option,
any time you want you have the option of getting out of the
mortgage and just saying, "Okay, I've paid 3
payments of 8.88, I don't want to do it anymore.
I want to pay off 97.13 and then let's call it quits."
And they say, "Okay,"
and there's nothing they can do about it.
Now, when are you going to exercise that option?
You're going to exercise that option either because you have
to move, that's the intention of it,
or you'll exercise it when it's most advantageous to you.
Now, why could it become advantageous to exercise it?
Well, you don't really want to exercise the option and this is
the way most people think of it backwards.
They think, "Oh, the interest rates are going
down.
That means I'll get a new mortgage with a lower interest
rate."
They're hoping for exactly the wrong thing.
If the interest rates go up what they've got is a much
better mortgage because they're continuing to buy at the same 8
percent interest and maybe interest rates in the economy
have become 12 percent and they're actually making money.
So people who borrow in times of high inflation do better.
When there are times of deflation the borrowers get
crushed.
Irving Fisher said one of the main reasons for the Depression
being so bad is all the entrepreneurial people in the
country, as usual, were borrowing,
and then there was a deflation and so they were getting
crushed.
And the very people who drive the economy were being hurt the
most.
And so that feedback, he said, was responsible for
part of the severity of the Depression.
So you see interest rates can go up or down and what happens?
When they go up, if they go up high enough to 19
percent you think, "My, gosh,
I've made a fortune holding this mortgage.
I'm still borrowing at 8 percent and I can invest my
money at 19 percent."
So you've made a fortune and the poor lender's gotten
crushed.
On the other hand if the interest rates go way down here,
so the present value of what you owe if you kept paying it
becomes huge, you don't have to face that big
loss because you just prepay at whatever the remaining balance
is there and then you've protected your downside.
So by paying attention and deciding when the optimal time
to prepay is, you can save yourself a lot of
money and thereby cost the bank a lot of money.
So when exactly should you prepay?
When should you exercise your options?
Well, in this example if you never exercised it you'd be
handing the bank, effectively,
120 dollars even though they lent you 20 [correction:
lent you 100].
So the bank would have made a 20 percent profit on you.
But if you exercise your option optimally you're going to make
not 100-- the bank is not going to get
100 dollars out of you, they're going to even get less
than 100 dollars.
They're going to get 98 dollars out of you.
So when exactly should you be exercising your option?
Well, we went over this last time.
I'll do it once again.
So remember, the payment you owed was
8.88,8.88, blah, blah, blah, 8.88.
The remaining balance started, of course, at 100 and then it
went down to 99.11 and then it kept going down from there.
So since I can't remember the numbers let's just call this
B_1, the remaining balance which
happened to be, you know, it was 99.11 the
first time.
Let's call this B_1, then I went to B_2,
B_3 etcetera and then B_30 is equal to 0,
no remaining balance after that.
So we said, what should you do--I'm going to do the
calculation now a little bit differently--
I said after every payment of 8.88 you could always say to
yourself, "Do I want to continue or
do I want to pay my option?"
Now, you notice that if I had divided this by B_1,
say, if you had a mortgage that was a little bit smaller,
barely over a 1 dollar for example,
that would divide everything by B_1.
The payments would all be divided by B_1 and the
remaining balances would all be divided by B_1.
So I could always scale this thing up or down.
There's nothing fancy about 100, nothing important about
100.
If the original loan was for 200 you just double all your
payments and double all your remaining balances.
What could be more obvious than that?
So I want to think in those terms of a mortgage that always
has 1 dollar left.
So suppose at any stage you had 1 dollar left in your mortgage.
Your remaining balance was 1.
So let's say at any node, let's ask the question,
what is the value of 1 dollar of remaining balance?
So if you start at 100 and you haven't prepaid,
here you've got B_2 dollars.
Of course, whatever the value of that is divided by
B_2, that's the value of 1 dollar.
So I'm just going to figure out the value of 1 dollar of
remaining balance and I'm going to call that W,
let's say.
I'll call that W of some node S.
So where am I?
I'm in some node in this interest rate tree,
right?
Here's our interest rate tree, and I'm anywhere just here,
and I'm doing backward induction so for all successor
nodes I figured out what 1 dollar of remaining balance is.
And let's say it's in period 1,2, 3,4, 5, so I'm in period 5,
B_5.
So what is the remaining balance at this node which I
call S?
So it's some node right there of--oh no, I've lost it.
So W_S is going to be what?
It's going to be the minimum of 1, you could just pay it if you
wanted to, or you could wait.
1 over (1 r_S), and then what would you have to
do, you would have to make your payment.
Well, what's your payment?
The payment is this 8.88 but divided by B_5 plus
the remaining balance of 1 dollar.
So (B_6 over B_5) times the
remainder times W_Sup.
Now, why is this right?
I hope it is right by the way.
I should have thought of this a little before.
So this is the remainder of 1 dollar left.
So if I divide by B_5 here I'm not going to have a
remaining balance of B_6.
I'm going to have a remaining balance of B_6 over
B_5.
So if I started with 1 dollar of remaining balance then I know
that in the next period I'm going to have B_6 over
B_5 dollars of remaining balance left.
It doesn't sound too convincing, by the way.
Well, it's right, and that happens with
probability 1 half.
And then with the other probability 1 half,
plus I make the payment, but I go down instead of up and
so I have B_6 over B_5 but I have
W_Sdown, and that's also times 1 half.
So either I pay off my remaining dollar or I end up
with this many dollars.
Assuming I had a 1 dollar of remaining balance I'm either
going to pay it off, the remaining balance,
or I'm going to have this much left next period and 1 dollar of
remaining balance is going to be that.
So that's it.
So I know now by working this backwards I can tell what 1
dollar at the beginning is worth.
And so it's exactly the same calculation I did before except
I'm talking about 1 dollar.
I'm always figuring out 1 dollar of remaining balance
instead of the whole thing.
Present value of callable, so here's present value of 1
dollar of principal.
And so remember the present value of a callable mortgage was
98.8.
Here the present value of 1 dollar,
figuring it out that way, is .98, obviously it's divided
by 100, but the key is that now you can
see just by looking at it where the 1s are is where the guy
decided to prepay.
So it's the same thing as before, but you see before you
couldn't tell very easily from the numbers when I did the 100.
Sorry, that didn't quite make it.
Before when I did the present value with the 100 all these
numbers were 98s and 97s.
I mean, where has he prepaid?
It's hard to tell where the prepayment is.
If I do it all in terms of 1 dollar of remaining balance then
just by looking at the screen I can tell where the guy prepaid
because there are 1s there.
So I know where he's prepaid.
Wherever the 1s are that means he's prepaid.
So I can tell very easily what he did.
All right, that's the only purpose of doing the same
calculation in a somewhat trickier way.
So if you think about it a second you see I've just divided
by--I've always reduced things to if you had 1 dollar left.
All right, so this tells us what to do, when the guy should
prepay and when he shouldn't prepay.
So if you're now in the world looking at what's happening you
can find the historical record of how people have prepaid.
So let's just look at the historical record,
for example.
Here, if you can see this, this is blown up as big as it
goes.
So this is what you might see as the historical record of
percentage prepayments annualized from '86 to '99,
say.
So you notice that they're very low here, and then they get to
be very high, and then they get low again,
and then they get high again.
So why do you think that happened?
So what is this?
This is prepayments for a particular mortgage,
8 percent.
You take all the people in the country who started in 1986 with
8 percent mortgages.
There's a huge crowd of those because that was about what the
mortgage rate was that year.
So a huge collection of people got these mortgages in '86 and
you keep track of what percentage of them prepaid,
really every month, but you write the annualized
rate, and then this is the record.
So why do you think it changed so dramatically like that?
What's the explanation?
Student: Stock market.
Prof: What?
Student: Stock market.
Prof: It looks like the stock market,
but I assure you the stock market had almost nothing to do
with it.
Why would prepayments be so low, and then be so high,
then be low, then be high?
What do you think was happening?
Student: Interest rate change.
Prof: Interest rate.
We just did that.
We just solved that.
That was the whole point of what we were doing.
So you tell me, what do you think happened in
'93?
This is September '93.
I don't know if you can read that.
What do you think was going on then?
Student: Interest rates got low.
Prof: Interest rates got low, exactly.
So you may not remember this because you were barely born.
In the early '90s there was a recession and then the
government cut the interest rates.
In the '90s, the early '90s there was a
recession and the government kept cutting interest rates
further, and further and further.
There was this huge decline in interest rates through the early
'90s, and so what happened?
All these people who, in '86, who had these 8 percent
mortgages--the new interest rates were lower and so they all
prepaid.
You got this shocking amount of prepayment.
So this graph, which seems sort of surprising
and looks like the stock market, turns out to have nothing to do
with the stock market.
It has to do with where the interest rates are.
Well, do you think interest rates explain everything?
No.
What else could you notice about the--escape.
What else have we learned here by doing these calculations?
Well, what we've learned so far is that if the interest rates in
the economy are at 6 percent, that's where they started,
remember we said they started at 6 percent and there was 16
percent volatility.
Here I had 20 percent volatility.
It doesn't matter.
I mean, that's a plausible amount of volatility,
a little high, but that volatility.
The mortgage rate of 8 percent is not going to give a value of
100.
It's going to cheat the bank if the homeowners are acting
rationally.
The bank could get 120 if the people weren't acting
rationally.
They were just never exercising their option.
It they're exercising their option optimally the thing was
only worth 98.
Now, I told you at that time the interest rates should have
been around 7 and 1 half percent,
not 8 percent given this 6 percent interest rate in the
economy.
The mortgage rate should be 7 and 1 half percent.
So we deduced last time that obviously not everybody's acting
optimally.
Well, you can tell that looking at this diagram.
How do you know that not everybody's acting optimally?
Remember these are '86 mortgages, so everybody's taking
them out at the same time within a few months of each other,
the same 8 percent mortgage.
How can you tell from this graph that they're not
exercising their option optimally?
It's completely obvious.
Just looking at it for one second you can say,
"Oh, these people can't be exercising their option
optimally," why is that?
Yes?
Student: They should be exercising all at the same time
if they were acting rationally.
Prof: So as he says we've just done the calculation
with those 1s and 0s.
I told you when the right time to exercise the option is,
so, everybody's got the same circumstance.
Every single person if all they're trying to do is minimize
the present value of their payments they should all be
prepaying at the same time.
Here you see that very few people are prepaying,
but it's getting up to almost 10 percent so probably this is a
stupid time to prepay, but the point is still 10
percent of them are prepaying.
And over here when presumably you ought to prepay,
in the entire year, right, they have 12 chances
during the year.
It takes them an entire year and only 60 percent of them have
figured out that they should prepay.
So you know they're not acting optimally.
So just from that graph that would tell you,
and you have further evidence of that.
That's evidence that they aren't acting optimally.
Furthermore you have evidence that the banks don't expect them
to be acting optimally because the banks aren't charging them 8
or 9 percent interest, which is what they would need
to pay to get the thing worth 100,
they're charging them 7 and 1 half percent interest which for
the optimal pre-payer is worth much less than 100 to the bank.
So the banks wouldn't do that.
They would just go out of business if they did something
stupid like that.
They wouldn't do that unless they thought that the homeowners
weren't acting, at least not all of them
acting, optimally.
So suppose you had to predict how people are going to act in
the future and you wanted to trade on that?
What would you do?
How would you think about predicting it?
So this is the data that you have.
What would you do?
You have this data.
These are 8 percent things.
You also have 9 percent mortgages issued the year
before, and then maybe a year before
that there were 8 and 1 half percent interest and you have
that history, and you've got all these
different pools and all these different histories.
How would you think about figuring out a prepayment--how
would you predict prepayments?
Well, the way economists, macro economists at least in
the old days, used to make predictions,
they would say, "Hum, the first quarter
looks pretty good."
What are they predicting now?
Now, they're saying unemployment is probably going
to keep rising for the next quarter or two well until the
next year, but at that point things are
going to turn around and we expect the economy to get
stronger, come out of its recession and
unemployment should gradually improve from its high which we
expect will be 10 and 1 half percent to something back down
to 6 percent by the end of 2011.
That's more or less the economists' prediction.
Now, can you make a prediction like that about prepayments?
Would it make sense to make a prediction about that?
Why is that an utterly stupid kind of prediction?
What is the essence of good prediction?
If you wanted to predict something and you were going to
lose a lot of money if your prediction was wrong how would
you refine your prediction compared to what I just gave as
a sample prediction?
Yep?
Student: You have to have a number of scenarios and
>
to each one.
Prof: Exactly.
So what he said is if you're even the slightest bit
sophisticated you're not going to make a bald non-contingent
prediction.
Things are going to get worse the next two quarters,
then they're going to start getting better,
then things are going to get as well as they're going to get
after two years.
You'll solve the problem after two years.
What happens if another war breaks out in Iraq?
What if Iran bombs Israel?
What if there's another crash in commercial real estate?
How could that prediction possibly turn out to be true?
It's a sure thing it's going to be wrong.
It's just impossible that's going to be right because the
guy making the prediction has made no contingencies built in
his prediction.
You know that guy's making a prediction for free.
Someone may be paying him to hear him, but he's not going to
be penalized if his prediction is wrong.
No one in their right mind would make such a prediction.
So the first thing you should do in predicting prepayments is
to realize that you've got a tree of possible futures,
and given this tree of possible futures you're going to predict
different prepayments depending on where you go on the tree.
So you see, prediction is not a simple one event--it's not a one
shot thing.
Just as he so aptly put it, it's a many scenario thing.
You have to predict on many, many scenarios what you think
will happen and that makes your prediction much better because,
of course, if there is a war in Iraq,
and if there is a catastrophe in Afghanistan,
and if Iran does bomb Israel, and if the commercial real
estate market collapses things are going to be a lot worse than
this original guy's prediction.
So everybody knows that, so why not make the prediction
more sensible?
So, on Wall Street that's what everybody's done for 20 years.
Now, they haven't done it for 30 years.
It's just 20 years that they've been doing that.
So when I got to Kidder Peabody in 1990 they were making these
one scenario predictions.
It's a long story which I'll tell maybe Sunday night.
I ended up in charge of the Research Department and so we
made, you know, other firms were doing this
already, we made scenario predictions, okay?
So now what kind of scenario predictions are you going to
make?
When you make contingent predictions there are an awful
lot of them.
You can't even write them all down, so what you have to do is
you have to have a model.
So what kind of model should you have?
I'll tell you now what the standard guys were doing on Wall
Street at the time.
They were saying--here's interest rate,
sorry.
Here's the present value of a mortgage.
Here's the present value of a callable mortgage,
present value of 1 dollar of principal, so realistic
prepayments.
So if we go over here we'll see that people said,
"Look, from this graph it's clear,"
they would say, "that when interest rates
went down people prepay more so why don't we have a function
that looks like this?"
So, prepay, that's the percentage of remaining balance
that is paid off.
So what does that mean?
Remember, after you've made your coupon payment you have a
remaining balance, B_5.
You could pay all of it, or none of it,
or half of it.
So the prepay is what percentage of the
B_5--that's just after you've paid, right?
So, B_2 lets do that one.
B_2, just after you've paid 8.88 the
remaining balance has now been reduced to B_2.
You could, in addition to the 8.88, pay off all of that
B_2.
Typically some people who are alert and think it's a good time
to prepay will pay all of B_2.
Others will pay none of B_2.
So if you aggregate over the whole collection of people the
prepay percentages, out of the sums of all their
B_2s what percentage of them are going to pay off.
So we look at the aggregate prepayment.
That's the old fashioned way.
And we say, "What percentage of the remaining
balance is paid off?"
So you'd make a function like this.
You'd say, "Well, prepaid might equal 10
percent."
Why am I picking 10 percent?
So if you go back to this picture you see that prepayments
seem to be around 10 percent when nothing's happening.
So you say 10 percent plus maybe you're going to get some
more prepayments so you might write--well, I just wrote down a
function plus the min.
The min, say, of .60 because it never seems
to get over 60 percent if you look at that you see it never
gets over 60 percent really.
So the min of 60 and 15 times the max of 0 and (M -
r_S - sigma over 133).
That would be a kind of prepayment function.
So what does this say?
What happens?
You're normally going to pay--so this is this whole
function here, so I should write this as .1
plus, can you see that over there,
maybe not, so this plus .1.
So there's a baseline of 10 percent and if the interest rate
is high, so the interest rate is above
the mortgage rate no one else is going to prepay because this is
going to be a negative number and this will be 0.
So you're just going to do .1,10 percent.
On the other hand, as the interest rate gets low
and falls far enough below the mortgage rate people are going
to say to themselves, "Ah-ha!
I have a big incentive to prepay now.
Maybe interest rates have gone down so far I can no longer hope
they're going to go back up above the mortgage rate.
I should start prepaying more."
So more people are going to prepay and this thing is going
to go up.
I just multiply it by some constant, but it'll never go up
more than 60 percent.
That's what this function says.
And sigma, this is the volatility--all right,
so let's just leave that aside.
So there's a prepayment function that seems to sort of
capture what's going on.
It's usually around 10 percent when there's no incentive.
It never gets above 60 percent, but as the incentive to prepay,
as interest rates get lower and the incentive to prepay
increases, more and more people prepay.
That's kind of the idea.
All right, and then you would fit fancier curves than that.
You would look at M - r_T and you would fit
a curve that looks like this.
So if there's just a little bit of incentive to prepay,
the rates are a little bit lower than the mortgage rate,
nobody does it.
Then quickly a lot of people do it and then they stop doing it.
So this is like 60 percent and most of the time you're around
10 percent, and you try and fit this curve.
You're going to have millions of parameters and since you have
so much data you could fit parameters.
That was the old fashioned way and that's how people would
predict prepayments.
Now, that's not going to turn out to be such a great way,
but it certainly teaches you something.
So let's look at what happens if you now--with those realistic
prepayments you compute the value of a mortgage.
So this is the prepayment that you'd get for the different
rates and so you can see that as the rates go down the total
prepayment is going up.
And by the way, it's more than 60 percent
because you've got this 10 percent added to the 60 percent,
so the most it could be is 70 percent,
which it hits over here.
So you get 70 percent as the maximum prepayments,
and as interest rates get higher no one prepays except the
10 percent of guys.
Now, by the way, why are people prepaying over
here even when the rates are so high?
It's because some people are moving or they're getting
divorced and they have to sell their house.
So obviously you're going to get some prepayments no matter
what.
People have to prepay, and why is it that people never
prepay more than 60 percent historically or 70 percent,
because not everybody pays attention.
Now, I called them the dumb guys last time,
but as I said, I probably fit into that
category.
It's people who are distracted and doing other things.
They're just not paying attention and so they don't
realize.
They don't know what's going on, so they don't realize they
should be prepaying.
So as interest rates go down more people prepay.
As interest rates go up less people prepay.
And if you did some historical thing and figured out the right
parameters you'd get a prepayment function.
So how did I figure out this was 15?
How did I figure out this was .6?
Why should I divide this by 133?
What's sigma?
Once you get those parameters historically you now have a
well-determined behavior rule of what people are going to prepay,
and from that you can figure out what the prices are of any
mortgage by backward induction.
So how would you do it again by backward induction?
The same we always did it.
Over here, what would you do over here?
How would you change this rule?
Well, you would just be feeding in the prepayment function.
So what would the prepayment function be?
Well, people wouldn't be doing a minimum here,
right?
They're not deciding whether or not to prepay,
they're just prepaying.
So let's get rid of that.
They're prepaying.
So this is the value of 1 dollars left of principal.
So some of them are prepaying and that's the function,
so prepay, and that depends on what node you're at.
And here it says what percentage of the remaining
balance is being prepaid.
So that tells you, that rule, who's prepaying,
and then with the rest of the money that's going on until next
time 1 minus that same thing, 1 minus prepay times exactly
what we had before.
So this part of 1 dollar got prepaid immediately so that's
the cash that went to the mortgage holder.
The rest of the cash got saved until next time and here's what
happens to it.
You have to make your coupon, then you have a remaining
balance, and then whatever is going to happen is going to
happen.
So you'll study this and you'll figure out I'm sure.
It takes a little bit of effort to see that through,
but with half an hour staring at it you'll understand how this
works and you'll read it in a spreadsheet so you can figure
out the value of a mortgage.
You get a value of a mortgage, and now we can start doing
experiments by changing the parameters and see how the
mortgage works.
Now, before I do that I want to say that there's a better way to
do this.
I mean, maybe these numbers are estimated--what's a better way
of doing it?
How did I do it at Ellington, how did we--I mean at Kidder
Peabody?
How did we predict prepayments?
What's another way at looking at prepayments?
Let me tell you something that's missing.
I used to ask people who wanted to work at Kidder Peabody or
Ellington the following little simple puzzle,
and most of the genius mathematicians always got this
answer wrong.
Of course we hired them anyway, but they'd always get this
wrong.
So the question is, suppose you've got a group of
people like this and you figure out what the value of the
mortgage is, and interest rates have been
constant all this time.
Let's suppose for one month interest rates shoot down,
interest rates collapse and half the pool,
60 percent of the pool disappears.
So now you've only got 40 percent of the people left you
had before, and then interest rates return to exactly where
they were to begin with.
Should the pool that's left be worth 40 percent of the pool
that you had just here, or more than 40 percent,
or less than 40 percent?
So remember, you had 100 people here.
You're the bank who's lent them the money.
You're valuing the mortgage payments they're going to make
to you, you're getting a certain amount
of money from them, 60 percent of them suddenly
disappeared in 1 month leaving 40 left,
but now interest rates are back exactly where they were before.
Is the value of the mortgage starting here with the 40
percent pool worth 40 percent of what it was originally,
more than 40 percent or less than 40 percent?
What do you think?
Yes?
Student: Is it worth more than 40 percent because
those people don't understand interest rates and therefore
they're not >
option properly and >
their mortgages?
Prof: Exactly.
So that's an incredibly important point.
It's called the opposite of adverse selection.
Every one of these events is selecting the people left not
adversely, not perversely,
what's the opposite of adversely,
favorably to you, so the guys who are left are
all losers, but that's who you want to deal
with.
You don't want to trade with the geniuses.
You want to trade with the guy who's not paying any attention.
So the guys left are the people who are never going to prepay or
hardly ever going to prepay and so it's much better.
Now, this function doesn't capture that at all,
right?
It doesn't say anything.
It just says your prepayment's depending on where you are.
So whether you were here or here you're going to get the
same prepayment, but we know that that's not
going to be the case.
In fact, it's clear that over here there must have been a much
bigger incentive than there was over there.
So the prepayments are the same, but actually interest
rates here were vastly lower than interest rates there.
So this is not such a good function.
So how would you improve?
What would you do to take into account this adverse selection,
or actually pro-verse selection?
What is the opposite of adverse?
Well, it doesn't matter.
What would you think to do?
Your whole livelihood depends on it, millions,
trillions of dollars at stake here.
You've got to model prepayments correctly, so how would you
think of doing this?
Just give me some sense of what a hedge fund does or what anyone
in this market would have to do.
Well, most of them did this.
So what would you do?
Yeah?
Student: Buy up old mortgages, because the market is
probably under estimating their value.
Prof: Well you would buy it up when?
Student: Right after...
Prof: Right here you'd buy it up, right there,
but what model would you use to predict prepayments?
Not this one, so how would you imagine doing
it.
You would imagine making a model just like your intuition,
so what does that mean doing?
Someone's asking you to run a research department,
make a model of forecasting prepayments.
All the data you have is aggregate data like that.
You can't observe individual homeowners in those days.
They wouldn't give you the information.
I'll explain all that Sunday night.
So this is the kind of data you have, what the whole group of
people is doing every year, but what would you do to build
the model?
Adverse selection is very important or pro-verse
selection.
It's embarrassing I don't remember the word,
favorable selection, a very important thing.
So how would you capture that in your model?
Yep?
Student: Would you split it into two groups and then
model it separately?
Prof: So maybe another thing you could do,
what if you instead of having this function that says what the
aggregate's going to do all the data's aggregate,
so all you can do is test against aggregate data.
But suppose you said, "The world,
all we can see is the aggregate, but the people really
acting are individuals acting, not the aggregate.
It's the sum of individual activities, so what we should do
now is have different kinds of people."
Oh gosh, sorry.
It was there already.
So let's go back to where we were before, so realistic.
What you ought to do is you ought to say,
well, 8 percent--remember we had two kinds of people already.
We've already got two kinds of people, sorry.
We've got these guys, the guys who never call,
so they're people.
That's a kind of person.
And suppose you go down here and you have the people who are
optimally prepaying?
Suppose you imagine that half the people were optimally
prepaying and half the people never prepaid?
Well, would that explain this favorable selection?
Absolutely it would explain it because when you went through
your little tree and you went here,
and here, and here, and here, by the time you got
down here all those people, all the optimal pre-payers
they're all prepaying.
So you start off with half-optimal guys and
half-asleep guys.
Once you get down here all the optimal guys have disappeared
and the pool that's left is all asleep,
so of course the pool is worth much more here given the
interest rate than it was over here.
In fact, if it goes back then again to here where it was
before--sorry that's same line.
If it goes back to here--have I done this right?
No, I've got to go back twice here and then here.
So once it goes back to here if it goes here,
here, here and here then the pool is going to be much more
valuable here than it started there.
There are half as many people, but it's worth much more than
half of what it was there.
So the way to do this is to break--so then you're looking at
the individuals.
You're saying one class of people is very smart,
or one class of people is very alert, it's a much better word,
one class of people is very alert.
One class of people is very un-alert and as you go through
the tree the alert people are going to disappear faster than
the non-alert people and that's why you're going to have a
favorable selection of people who's left in the pool.
Well, of course, there are no extremes of
perfectly rational or perfectly asleep in the economy so what
you can do is you can make people in between.
How do you make them in between?
Well, suppose that, for example,
I only did one thing.
Suppose it's costly to prepay?
Some people just say to themselves, "I'm going to
have to take a whole day off of work.
I'm not going to write my paper.
I might lose some business that I was going to do that day.
A whole bunch of stuff I'm losing, so I'm going to subtract
that.
I'm not going to prepay.
I'm not going to even think about doing it unless I can get
at least a certain benefit from having done it."
So you can add a cost of prepaying and people aren't
going to prepay unless the gain that they have by prepaying
exceeds the cost of doing the prepayments.
So to take the simplest case let's suppose the very act of--
never mind the thinking and all that--
the very act of prepaying, going to the bank literally
costs you money.
So if you have a value, if the thing is 100 and you can
prepay, you know, if you do your
calculations and don't prepay today it's worth 98 and if you
prepay today the remaining balance is 94 you're saving 4
dollars, but if the cost of prepayment
is 5 you're still not going to do it.
So you get a guy with a high cost of prepaying,
an infinite cost of prepaying, he's going to look like he's
totally un-alert.
A guy with zero cost of paying is going to look like he's
totally alert.
So you can have gradations of rationality, and you can have
different dimensions.
So you can have cost of prepaying and you can have
alertness.
What's the percentage of time you're actually paying attention
that month?
What fraction of the months do you actually pay attention,
and you can have a distribution of people, different costs and
different alertnesses.
So that's the model that I built.
It's a simplified form of it.
It gives you an idea.
So here's this burnout effect that I showed that if you take
the same coupons, but an older one rather than
a--an older one that's burned out will always prepay slower,
so the pink one is always less than the blue one because it
went through an opportunity to prepay.
So here you start with a pool of guys on the right,
and then after a while, after time has gone down a lot
of them have prepaid.
So here's alertness and cost.
So you describe a person by what his cost of prepaying is
and how alert he is.
The more alert he is and the lower the cost of prepaying the
closer to rational he is.
The less alert he is, the higher the cost of
prepaying the closer to the totally dumb guy he is.
And so you could have a whole normally distributed
distribution of people and over time those groups are going to
be reduced because a lot of them are prepaying,
but they won't be reduce symmetrically.
The low cost high alertness guys are going to disappear much
faster and the pool's going to get more and more favorable to
you.
And so anyway, all you have to do is
parameterize the cost, what the distribution of people
in the population, what the standard deviation and
expectation of cost is and of alertness is,
and that tells you what this distribution looks like.
So you're fitting four numbers and you've got thousands of
pools and hundreds and hundreds of months,
and fitting four parameters you can end up fitting all the data.
So look at what happens here.
So here's the same data.
So I just tell you I know that in a population,
given what I've calculated in the '90s there,
I know what fraction of the people have this cost and that
alertness, what fraction of the people are
so close to dumb that their costs are astronomical and their
alertness is tiny, what fraction of the people
have almost no cost and a very high alertness,
so I'm only estimating four parameters because I'm assuming
it's normally distributed.
Given that fixed pool of people I apply that to the beginning of
every single mortgage and I just crank out what would those guys
do.
In the tree if they knew what the volatilities were when would
they decide to prepay, and then I have to follow a
scenario out in the future and I say,
"Well, along this path which guy would prepay and which
guy wouldn't prepay and what would the total prepayments look
along that path?"
And so this has generated the pink line from the model with no
knowledge of the world except I fit those parameters and look
how close it is to what actually happened.
So it turns out that it was incredibly easy to predict,
contingently predict what prepayments were going to be and
therefore to be able to value mortgages.
And this was a secret that not many people,
you know, a bunch of people understood,
but not that many understood, and so for years we were
trading at our hedge fund, first at Kidder and then at
Ellington with this ability to contingently forecast
prepayments at a very high rate.
And why was it so stable, the prediction,
and so reliable?
It's because the class of people stayed pretty much the
same and every year there'd be the same kinds of people with
the same kinds of behavior.
Some were very alert.
Some were very not alert, but the distribution of types
was more or less the same and you could predict with pretty
good accuracy what was going to happen from year to year.
Of course, then after 2003 or so the class of people started
to radically change and many more people who never got
mortgages before got them and it became much harder to predict
what they were going to do.
But so in the old days it was pretty easy to predict.
And why was it so easy to predict?
Because it was an agent based model, agent based.
So, by the way, I added this volatility here,
so these guys who just ran regressions they had to have a
volatility or something parameter.
So you see as volatility goes up the prepayments are slower.
Well, they just had to notice that and build it right into
their function.
I didn't even have to think of that or burnout.
None of those things did I have to think about because if you're
a guy optimizing here and volatility goes up,
so you reset the tree so that the interest rates can change
faster.
The option is worth more so you're going to wait longer.
You're not going to just exercise it right away because
you've got a chance that prices will really go up so you can
wait a little longer, afford to wait longer.
So prepayments will slow down.
So all I'm saying, all of this is just to say that
if you have the right-- so it's agent based,
it's contingent predictions, those two things together
enable you to make quite reliable predictions about the
future if you're in a stable environment.
And so what seems like a bewildering amount of stuff
turns out to be pretty easy to explain.
So now what happens?
So do you have any questions here or should I--yes?
Student: You said you assume that those two parameters
are normally distributed.
Did you select among some sort of variance?
Prof: Some sort of what?
Student: Variance.
Prof: I had to figure out what the mean and the
variance is.
There's mean and variance of cost and mean and variance of
alertness to get that distribution,
right?
So how do I know what the population--so let me just put
the picture up again.
So who are the hyper rational guys?
They are the people with the really high alertness up there
and the really low cost, so they're the guys back there.
They're the hyper--or maybe it was the guys,
you know, one of these corners with very high alertness and
very low cost.
I forgot which way the scale works.
It might be going down.
So anyway, the guys with very high alertness and very low
costs are the hyper rational people.
At the other corner you've got the guys who have very low
alertness and very high costs.
They're the people who you're going to make a lot of money on
if you're the bank.
So how do I know how many people are of each type?
Well, I don't.
I have to fit this distribution.
But you see I have so much data.
I've got this kind of curve.
This kind of curve I've got for every starting year for the
whole history and there's so many different interest rates
and so many different-- so I'm applying that same
population at the beginning of every single curve and then
seeing what happens to my prediction versus what really
happened.
So I've got thousands, and thousands,
and thousands of data points and only four parameters to fit.
So I pick the four parameters to fit the data as much as
possible.
If I assumed everybody was perfectly alert instead of that
curve that I showed you, I put a huge crowd here of
perfectly rational people then I would have found that I would
have gotten prepayments at 100 percent up there and at 0 all
the way over here and so it wouldn't have fit that curve.
So that's how I knew that there couldn't be that many perfectly
rational people.
Yes?
Student: How can you know for sure that there are
only two patterns?
Prof: You mean how do I know cost and alertness,
maybe there's some other factors?
Yes, well there probably are other factors.
So what would you commonsensically think are the
factors?
What keeps people from prepaying?
I think the most obvious one is it's a huge hassle and they're
not paying attention.
So those are the first two that I thought of.
Could you think of another one?
Student: Maybe their age.
Prof: Their age, exactly.
So maybe demography has an effect on it.
So maybe, for example, you get more sophisticated the
older you get.
So that was another factor we put in.
So I'm not telling you all the factors, but these were the two
main factors.
Another factor was growing sophistication.
We called it the smart factor.
That's another factor.
So over time you get more sophisticated.
So anyway, the point is with a few of these factors you got a
pretty good fit, and it was pretty reliable,
and you could predict what was going to happen contingently.
So now if you want to trade mortgages what are some of the
interesting things that happen?
The first interesting thing to notice is that what do you think
happens as the interest rate goes down?
So the first thing to notice is--so I'll just ask you two
questions.
Let's go on the other side.
I'm running out of room.
Suppose that you have the mortgage value,
what you get in the tree?
So in this tree that we've built, here's the tree,
it's going like that, and at every node we're
predicting-- for each class of people we're
predicting where his 1s are.
So that class is prepaying.
The other class is not as smart so they're not prepaying here,
but maybe when things get really low they'll start
prepaying here.
So each class of people, each cost, alertness type has
its own tree.
They're the same tree, but it's own behavior on the
tree, and then I add them all together.
So what happens with the starting interest rate?
So here we had .06 and this value was 98 or something,
right?
Now, suppose the interest rate went down to .05.
I drew this picture of interest and mortgage value.
What do you think happens?
So the interest starts--this is '98,6 percent is there.
As the interest rate goes down what do you think happens to the
value of the mortgage?
If you're a bank and you've fixed--the mortgage rate is 8
percent.
That's a fixed mortgage rate, but now you've moved in the
tree from here to here.
Do you think your mortgage is going to go up in value or down
in value?
Student: It's going up.
Prof: It's going to go up because the interest rates
are lower and the present value of the payments is getting
higher.
So if the interest rate goes down the mortgage is going to go
up like that, typically.
But will it keep going up like this and this?
If it were a bond it would go up like that,
right?
A bond, a 1 year bond which owed 1 over 1 r would keep going
up and up the value before it got negative,
say.
It would go up.
As r got negative it would go way up like that.
So does the mortgage keep going up like that?
As the interest rate goes down is the value of the mortgage
going to get higher and higher and higher?
Suppose the guy's optimal, what's going to happen?
This is 100 here.
What'll happen?
Yep?
Student: He's going to prepay.
Prof: He's going to eventually figure out that he
should prepay so it'll go like this.
If he's perfectly optimal he'll never let it go above 100.
So it's going to go something like this.
As the interest rate gets higher you get crushed,
and as the interest rate gets lower you don't get the full
upside because he's prepaying at 100.
He's never letting it go above 100, right?
So if he's not so optimal maybe your value will go up,
but not so astronomically high.
So this idea that the mortgage curve, instead of being like
this goes like that, this is what was called
negative convexity.
Now, the next thing to know is suppose that the guys are partly
irrational so it's going above 100.
So it's starting to go like this.
Then what do you think?
As the interest gets really low what's going to happen?
All right, you just said it, so.
If the guy was rational, perfectly rational it would go
like that.
He'd never let it go above 100, but now suppose guys are not
totally rational?
What's going to happen is they're going to,
sort of--as rates get a little bit low they're going to
overlook the fact that they should prepay.
So now it's advantageous to you.
Things are worth more than 100, but if rates get incredibly low
even the dumbest guy, the highest cost guy is going
to realize he has an advantage to prepay and so things are
going to go back down like that.
So the value's going to be quite complicated.
So this is the mortgage value as a function of interest rates.
Just common sense will tell you this.
In a typical bond as the interest rate gets lower the
present value gets higher.
You should expect a curve like that, but because of the option
if it were rationally exercised the curve would never get above
100.
It would have to go like that.
But now if people are irrational you can take
advantage of them and get more than 100 out of them.
But if the situation gets so favorable to you it becomes
blindingly obvious, eventually to them,
that they're getting screwed, and eventually they act and
bring it all the way back to 100 again.
So this value of the mortgage looks like that.
So that's a very tricky thing.
I'll even write, very tricky.
So if you don't know what you're doing you could easily
get yourself hurt holding mortgages.
You could suddenly find yourself losing money holding
mortgages.
So that's my next subject here.
I want to talk about hedging.
So we know something now about valuing mortgages.
Now I want to talk about hedging, and what hedge funds
do, and what everyone on Wall Street should be doing which is
hedging.
So if you hold a mortgage you're going to hold it because
maybe you can lend 100 to a bunch of people but actually get
a value that's more than 100.
So it looks like you're here, but if interest rates change a
little bit suddenly this huge value you thought you had might
collapse back down to 100, or the interest rates might go
up and it might collapse to way below 100.
So you look like you're well off, but there are scenarios
where you could lose money and you want to protect yourself
against that.
So how do you go about doing it?
What does hedging mean?
And I want to put it in the context, the old context of the
World Series which we started with before.
So it's easier to understand there,
and so many of you will have thought about this before so
you'll be able to answer it, but if I put it in the mortgage
context it would seem just too difficult.
I don't know why I did that.
So the World Series--I'm going to lower it in a second.
So suppose that the Yankees have a 60 percent chance,
I said beating the Dodgers, I thought the Dodgers would be
in the World Series, a 60 percent chance of winning
any game against the Phillies in the World Series.
And you are a *** and your fellow bookies all understand
that it's 60 percent.
So some naive Philly fan comes to you and says I want to bet
100 dollars that the Phillies win the World Series.
Should you take the bet or not?
Yes you should take the bet because 60 percent of the time
you're going to win 100 dollars--no.
Yes you should take the bet.
If he bet on one game you would make, with 60 percent
probability you'd win 100 and with 40 percent probability
you'd lose 100.
So that means on average your expectation is equal to 20.
So if he's willing to bet 100 dollars on the Phillies winning
the first game of the series with you,
you know that your expected chance of winning is 20 dollars.
You're expecting to win 20 dollars from the guy.
Now, suppose he's willing to make the same bet,
100 dollars for the entire series?
What's your chance of winning and what's your expected profit
from him?
Is it less than 20,20, or more than 20?
Student: More than 20.
Prof: More than 20.
It's going to turn out to be, so a 7 game series,
it's going to turn out to be 42 which we're going to figure out
in a second.
But what's your risk?
What's your risk?
In either case you might lose 100 dollars.
The Phillies, they're probably going to lose,
but there's a chance something goes crazy and some unknown guy
hits five home runs in the first four games or something,
and some other unknown guy hits another four home runs and you
lose the World Series.
You could lose 100 dollars, and maybe the guy's not betting
100 dollars but 100 thousand dollars or a hundred million
dollars.
You know you've got a favorable bet, but you don't want to run
the risk of losing even though there's not that high a chance
you're going to lose.
What can you do about it?
Well, you know that there are these other bookies out there
who every game are willing to bet at odds 60/40 either
direction on the Phillies or the Yankees because they just all
know-- they're just like you.
You all know that the odds are 60 percent for the Yankees
winning every game.
So suppose this naive guy, the Phillies fan,
comes up to you and bets 100 dollars on the World Series that
the Phillies will win.
You don't want to run the risk of losing 100 dollars.
You know there are these other bookies who are willing to take
bets a game at a time 60/40 odds.
What should you be doing?
What would you do?
Yes?
Student: Bet on the Phillies winning because they
give you better odds so you're guaranteed your profit.
Prof: So what would you do?
So this guy's come to you, and you're not going to be able
to give the-- we're going to find out exactly
what you should do in one second,
but let's just see how far you can get by reason without
calculation.
So this guy's come to you and said, "I'm betting 100
dollars on the Phillies winning the World Series."
This is the night before the first game.
Every *** is standing by ready to take bets at 30 to 20
odds.
What would you do?
Student: You'd bet with the *** that the Phillies
would win because...
Prof: That what?
Student: That the Phillies would win.
Prof: Yeah, how much?
Student: 100 dollars.
Prof: You'd bet the whole 100 dollars?
Student: Well, you get better odds,
so.
Prof: But would you bet the whole 100 dollars on the
first game?
The guy's only bet 100 dollars on the whole series.
Student: You'd bet 80 >
dollars.
Prof: So it's not so obvious what to do,
right, but he's got exactly the right idea.
You can hedge your bet.
So here we are.
I shouldn't have put that down.
Don't tell me I turned it off.
That would just kill me.
God, I meant to hit mute.
I think I hit off.
Oh, how dumb?
So you would bet on the--while that warms up.
I can see it.
All right, so what happens is you'll have a tree which looks
like this and like this, like this and like this,
like this and like this and let's say we go out a few games
like this.
Now, this is a 1,2, 3 game series.
All right, so I've done it.
Here's the start of World Series.
This is the World Series spreadsheet you had before.
Now, here's the start.
Here's game 1,2, 3,4, 5,6, 7.
So if the Yankees win the series they get 100 dollars.
You get 100 dollars, sorry.
Oh, what an idiot.
So every time you end up above the start, win more than you
lose, you get 100 dollars.
On the other hand, if you lose more than you win
you lose 100 dollars, and so ctrl,
copy.
Here is losing 100 dollars.
So now this tree, remember from doing it before,
is just by backward induction.
If you look at this thing up there it says you get,
60 percent I think was the number we figured out over here,
so right?
So 60 percent is the probability of the Yankees
winning a game.
So you take any node like this one you're always taking 60
percent of the value up here plus 40 percent of the value
here.
So if you do that you find out that the value to you is 42
dollars, just what we said.
So let's put that in the middle of the screen.
So the value is 42 dollars.
Now, if the Yankees win the first game you're in much better
shape.
So winning the first game means you moved up to this node here.
All of a sudden you went from 42 dollars to 64 dollars.
And if the Yankees lost the first game you would have gone
down to that value which is like 9 dollars.
Your expected winnings when the Yankees are down a game,
you know, they're still a better team so actually it's
more likely even after losing the first game that the Yankees
would still win the series.
So you see the risk that you're running and you can calculate
this.
So what should you do in the very first game?
This tells you that your expected winnings is 42.
Of course .6 times 64 that's 38.4 .4 times 9 is 3.6.
That is 42 dollars.
So that's 42 because it's the average of this and this,
and 64 is the average of .6 of this and .4 of that.
So what should you do?
Well, on average you're going to make 42 dollars.
What's the essence of hedging?
You want to guarantee that you make 42 dollars no matter what
happens.
No matter who wins the series you want to end up with 42 extra
dollars assuming the interest rate is 0 from the beginning to
the end of the series.
So how can you arrange that?
What can you do?
Well, so that's the mystery.
I'll give you one second to try and think it through.
You should get this.
What would you do here?
Are there no baseball bookies in the--yep?
Student: Didn't we just bring this up before like with
our hedge funds?
Can we put something else aside that you view at a percentage
rate that you think you can trust and then you can trust the
rest of it to whatever the real probabilities are?
Prof: Well, you can bet with another ***
at 60 to 40 odds.
If the Yankees win the first game you're just doing great.
If the Yankees lose the first game you're looking to be in a
little bit of trouble.
So the point is you're not going to get the payoffs until
the very end either plus 100 or minus 100,
but already by the first game you're either doing better than
you were before or worse than you were before.
You're already, in effect, suffering some risk
at the very beginning.
So this is one of the great ideas of finance.
You shouldn't hedge the final outcome.
You should hedge next day's outcome.
If you're marking to market that's what you'd have to do.
Marking to market you'd have to say my position now--my bet is
worth 64 dollars.
The Yankees lost the first game, the bet would be worth 9
dollars.
So what does it mean to protect yourself?
Not just protect yourself against what's happening at the
end, that's really what you want to
do, but in order to do that you should protect yourself every
day against what could happen.
So every day you should end up with 42 here and 42 there
because, after all, that's what you're trying to
lock in.
No matter who wins the first game you should still say I'm 42
dollars ahead because I got myself in this position.
So how could you do that?
Well, let's bet at 3 to 2 odds, right, 60/40 is 3 to 2 odds.
Let's make a bet with another *** at 22 and 33 here.
So 22--I put it in the wrong place.
This is the 33 and this is 22, but plus 33 and minus 22.
So what are you doing here?
Notice that this is 2 times 11, this is 3 times 11.
This is 60/40 odds.
I'm betting on the Phillies.
If the Phillies win one game I collect 33 dollars.
That's what I should do that he said.
He said, "Go to the *** across the street and bet on one
game, not the whole series.
Bet on one game with that *** across the street,
33 dollars versus 22 dollars."
Let's say you can only bet 1 game at a time with the other
bookies, actually, maybe you were saying
all along bet on the whole series,
but let's say you can only bet one game at a time with the
other bookies.
You'd bet 33 dollars on the Phillies in the first game.
That naive Philly fan has put up 100 dollars on the series.
You're, in the first game, going to put 33 dollars.
You've taken his bet so you're hoping the Yankees win,
but that's bad to be in a position where you have to hope.
You don't want to do that.
So you take his bet on the Phillies because he's given you
100 to 100 odds.
That's even odds even though you know the Yankees have a 60
percent change of winning.
You go to the *** across the street and you bet at 60/40 odds
on the Phillies, but you don't bet the whole
100.
You only bet 33 dollars of it.
So if you win you get 33 dollars.
If you lose you only have to pay the guy 22.
So what's going to happen?
After the first day this position is going to be worth 42
and this position is also going to be worth 42,
exactly where you started.
So because a win in the first game is going to put you so far
ahead in your bet with the first naive Philly better,
and a loss in the first game is going to put you so far behind,
you hedge that possibility by going 33/22 in favor of the
Phillies.
You take a big bet on the Yankees and then you make a
smaller bet on the Phillies that cancels out part of the big bet
on the Yankees, but you've made the two at
different odds and so on net you're still going to be 42
dollars ahead.
Let's just pause for a second and see if you got that.
So by doing this you can't possibly lose any money.
And now you're going to repeat this bet down here and here.
So in the next--you see where do things go next?
Here you're down 8 dollars.
If you lost again you'd be down 32 dollars.
Now things would really be bad.
After the Yankees lost two games in a row your original bet
would look terrible, but things aren't so bad
because you bet on the Phillies here.
You already made 33 dollars.
So how much money do you think you should be betting on the
Phillies down here?
Well, you want to lock in 42 dollars at every node no matter
what happens.
This 42 dollars, by making the right offsetting
bet you can keep 42 everywhere, here until the very end,
and so no matter what happened you can always end up with 42
dollars.
That's the essence of hedging.
So let's just say it again what the idea is.
It's a great idea and we don't have time to go through all the
details, but the great idea is this.
You've made some gigantic bet with somebody.
Why do you bet with anybody?
Because you think you know more than they do.
The whole essence of trading and finance is you think you
understand the world better than somebody else.
So understand it means you think something's going to turn
out one way that the other guy doesn't really know is going to
happen.
So you're making a bet on whether you're right or wrong.
So when you say you know you don't know for sure.
You just have a better idea than he does,
so you want to use your idea without running the risk.
So how can you do it?
If your idea is really correct there may be a way so that you
can eliminate the luck.
So here if you really know the odds are 60/40,
your class of bookies knows the odds are 60/40,
and some other guys who doesn't know thinks the odds are 50/50
and is willing to bet against you,
you can lock in your 42 dollars for sure.
You don't just take a bet and hope you win.
You can take a bet and then hedge it to lock in your profit
for sure, step by step,
and that's what we have to explain how that dynamic hedging
works.
So I have to stop.