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 bookie 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 bookie is standing by

ready to take bets at 30 to 20 odds.

What would you do?

Student: You'd bet with

the bookie 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 bookie 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

bookie 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 bookie

across the street and bet on one game, not the whole series.

Bet on one game with that

bookie 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 bookie 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.

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