WEBVTT

00:01.650 --> 00:04.710
Prof: So we're talking
now about mortgages and how to

00:04.713 --> 00:08.723
value them,
and if you remember now a

00:08.724 --> 00:12.024
mortgage--
so the first mortgages,

00:12.022 --> 00:14.342
by the way,
that we know of,

00:14.339 --> 00:16.559
come from Babylonian times.

00:16.560 --> 00:19.860
It's not like some American
invented the mortgage or

00:19.862 --> 00:20.642
something.

00:20.640 --> 00:26.690
This was 3,500-3,800 years old
and we have on these cuneiform

00:26.688 --> 00:29.308
tablets these mortgages.

00:29.310 --> 00:35.760
And so the idea of a mortgage
is you make a promise,

00:35.760 --> 00:37.830
you back your promise with
collateral,

00:37.830 --> 00:41.040
so if you don't keep the
promise they can take your

00:41.041 --> 00:43.611
house,
and there's some way of getting

00:43.612 --> 00:47.472
out of the promise because
everybody knows the collateral,

00:47.470 --> 00:49.810
you might want to leave the
home, and then you have to have

00:49.805 --> 00:51.935
some way of dissolving the
promise because the promise

00:51.940 --> 00:53.430
involves many payments over
time.

00:53.430 --> 00:56.340
So it's making a promise,
backing it with collateral,

00:56.340 --> 01:00.010
and finding a way to dissolve
the promise at prearranged terms

01:00.011 --> 01:02.541
in case you want to end it by
prepaying.

01:02.539 --> 01:06.609
And that prepaying is called
the refinancing option.

01:06.608 --> 01:10.088
And because there's a
refinancing option it makes the

01:10.088 --> 01:12.898
mortgage a much more complicated
thing,

01:12.900 --> 01:16.190
and a much more interesting
thing, and something that,

01:16.188 --> 01:18.808
for example,
a hedge fund could imagine that

01:18.805 --> 01:20.625
it could make money trading.

01:20.629 --> 01:23.799
So I just want to give you a
slight indication of how that

01:23.796 --> 01:24.626
could happen.

01:24.629 --> 01:27.949
So as we said if you have a
typical mortgage,

01:27.950 --> 01:30.800
say the mortgage rate is 8
percent--

01:30.799 --> 01:32.969
maybe this is a different
answer than I did--

01:32.970 --> 01:36.860
so here we have an 8 percent
mortgage with a 6 percent

01:36.864 --> 01:39.074
interest rate to begin with.

01:39.069 --> 01:42.329
Now, if it's an 8 percent
mortgage the guy's going to have

01:42.325 --> 01:45.805
to pay much more than 8 percent
a year because a mortgage,

01:45.810 --> 01:46.920
remember, there are level
payments.

01:46.920 --> 01:48.560
We're talking about fixed rate
mortgages.

01:48.560 --> 01:51.770
You pay the same amount every
single year for 30 years,

01:51.769 --> 01:54.429
now you're really paying
monthly and I've ignored the

01:54.433 --> 01:57.463
monthly business because it's
just too many months and there

01:57.455 --> 01:58.475
are 360 of them.

01:58.480 --> 02:01.140
So I'm thinking of it as an
annual payment.

02:01.140 --> 02:04.110
You have to pay,
of course, more than 8 dollars

02:04.108 --> 02:08.038
a year because if the mortgage
rate were 8 percent and you had

02:08.044 --> 02:12.114
a balloon payment on the end,
you'd pay 8,8, 8,108.

02:12.110 --> 02:15.280
That's the way they used to
work, but they were changed.

02:15.280 --> 02:18.970
So you could imagine the old
fashioned mortgage would pay

02:18.972 --> 02:21.542
8,8, 8,8, 8,108;
if you didn't pay your 8

02:21.536 --> 02:25.086
somewhere along the line they'd
confiscate your whole house and

02:25.090 --> 02:28.530
then take what was owed out of
it and you could get out of it

02:28.530 --> 02:29.620
by paying 100.

02:29.620 --> 02:33.700
The new mortgages instead of
paying 8 every year for 30 years

02:33.697 --> 02:37.707
you pay 8.88 every year for 30
years because if you discount

02:37.706 --> 02:41.646
payments of 8.8 for 30 years at
8 percent you get 100.

02:41.650 --> 02:46.020
So the present value is 100 at
the agreed upon discounting rate

02:46.016 --> 02:48.056
or mortgage rate 8 percent.

02:48.060 --> 02:52.560
And so you see how important
this discount rate is.

02:52.560 --> 02:56.040
And the remaining balance,
however, goes down because

02:56.043 --> 03:00.133
every time you're paying you're
paying more than the 8 percent

03:00.128 --> 03:00.998
interest.

03:01.000 --> 03:06.640
You're paying in the first year
8.8 instead of 8 and so that gap

03:06.638 --> 03:11.828
of .88 is used to reduce the
balance from 100 to 99.117.

03:11.830 --> 03:14.840
And so you see the balance is
going down over time and making

03:14.838 --> 03:17.398
the lender safer and safer
because the same house is

03:17.396 --> 03:18.146
backing it.

03:18.150 --> 03:20.310
So it's called an amortizing
mortgage.

03:20.310 --> 03:22.610
Now, why is it difficult to
value?

03:22.610 --> 03:25.820
Because you have the option,
any time you want,

03:25.818 --> 03:27.958
and there's a good reason for
that option,

03:27.960 --> 03:30.710
any time you want you have the
option of getting out of the

03:30.711 --> 03:33.471
mortgage and just saying,
"Okay, I've paid 3

03:33.473 --> 03:35.973
payments of 8.88,
I don't want to do it anymore.

03:35.970 --> 03:41.420
I want to pay off 97.13 and
then let's call it quits."

03:41.419 --> 03:42.319
And they say,
"Okay,"

03:42.318 --> 03:43.608
and there's nothing they can do
about it.

03:43.610 --> 03:46.170
Now, when are you going to
exercise that option?

03:46.169 --> 03:49.469
You're going to exercise that
option either because you have

03:49.465 --> 03:51.715
to move,
that's the intention of it,

03:51.718 --> 03:55.238
or you'll exercise it when it's
most advantageous to you.

03:55.240 --> 03:58.910
Now, why could it become
advantageous to exercise it?

03:58.910 --> 04:01.750
Well, you don't really want to
exercise the option and this is

04:01.750 --> 04:03.800
the way most people think of it
backwards.

04:03.800 --> 04:05.860
They think, "Oh,
the interest rates are going

04:05.855 --> 04:06.145
down.

04:06.150 --> 04:08.480
That means I'll get a new
mortgage with a lower interest

04:08.479 --> 04:09.029
rate."

04:09.030 --> 04:12.040
They're hoping for exactly the
wrong thing.

04:12.038 --> 04:15.128
If the interest rates go up
what they've got is a much

04:15.128 --> 04:18.738
better mortgage because they're
continuing to buy at the same 8

04:18.742 --> 04:21.952
percent interest and maybe
interest rates in the economy

04:21.947 --> 04:25.617
have become 12 percent and
they're actually making money.

04:25.620 --> 04:29.980
So people who borrow in times
of high inflation do better.

04:29.980 --> 04:32.710
When there are times of
deflation the borrowers get

04:32.713 --> 04:33.263
crushed.

04:33.259 --> 04:36.469
Irving Fisher said one of the
main reasons for the Depression

04:36.466 --> 04:39.246
being so bad is all the
entrepreneurial people in the

04:39.245 --> 04:41.135
country,
as usual, were borrowing,

04:41.141 --> 04:43.741
and then there was a deflation
and so they were getting

04:43.740 --> 04:44.270
crushed.

04:44.269 --> 04:47.229
And the very people who drive
the economy were being hurt the

04:47.225 --> 04:47.565
most.

04:47.569 --> 04:50.529
And so that feedback,
he said, was responsible for

04:50.531 --> 04:53.011
part of the severity of the
Depression.

04:53.009 --> 04:56.369
So you see interest rates can
go up or down and what happens?

04:56.370 --> 04:58.820
When they go up,
if they go up high enough to 19

04:58.819 --> 05:00.539
percent you think,
"My, gosh,

05:00.540 --> 05:02.940
I've made a fortune holding
this mortgage.

05:02.939 --> 05:08.139
I'm still borrowing at 8
percent and I can invest my

05:08.136 --> 05:10.986
money at 19 percent."

05:10.990 --> 05:13.230
So you've made a fortune and
the poor lender's gotten

05:13.228 --> 05:13.658
crushed.

05:13.660 --> 05:17.170
On the other hand if the
interest rates go way down here,

05:17.170 --> 05:20.570
so the present value of what
you owe if you kept paying it

05:20.574 --> 05:23.514
becomes huge,
you don't have to face that big

05:23.507 --> 05:27.397
loss because you just prepay at
whatever the remaining balance

05:27.401 --> 05:30.721
is there and then you've
protected your downside.

05:30.720 --> 05:34.110
So by paying attention and
deciding when the optimal time

05:34.105 --> 05:36.705
to prepay is,
you can save yourself a lot of

05:36.706 --> 05:39.786
money and thereby cost the bank
a lot of money.

05:39.790 --> 05:41.940
So when exactly should you
prepay?

05:41.940 --> 05:43.730
When should you exercise your
options?

05:43.730 --> 05:46.150
Well, in this example if you
never exercised it you'd be

05:46.149 --> 05:47.629
handing the bank,
effectively,

05:47.625 --> 05:50.205
120 dollars even though they
lent you 20 [correction:

05:50.206 --> 05:51.046
lent you 100].

05:51.050 --> 05:54.610
So the bank would have made a
20 percent profit on you.

05:54.610 --> 06:02.720
But if you exercise your option
optimally you're going to make

06:02.716 --> 06:05.146
not 100--
the bank is not going to get

06:05.151 --> 06:07.111
100 dollars out of you,
they're going to even get less

06:07.113 --> 06:07.773
than 100 dollars.

06:07.769 --> 06:09.949
They're going to get 98 dollars
out of you.

06:09.949 --> 06:14.559
So when exactly should you be
exercising your option?

06:14.560 --> 06:16.750
Well, we went over this last
time.

06:16.750 --> 06:18.580
I'll do it once again.

06:18.579 --> 06:23.249
So remember,
the payment you owed was

06:23.254 --> 06:27.934
8.88,8.88, blah,
blah, blah, 8.88.

06:27.930 --> 06:34.170
The remaining balance started,
of course, at 100 and then it

06:34.172 --> 06:40.522
went down to 99.11 and then it
kept going down from there.

06:40.519 --> 06:44.039
So since I can't remember the
numbers let's just call this

06:44.040 --> 06:46.250
B_1,
the remaining balance which

06:46.254 --> 06:49.224
happened to be,
you know, it was 99.11 the

06:49.220 --> 06:50.250
first time.

06:50.250 --> 06:52.860
Let's call this B_1,
then I went to B_2,

06:52.860 --> 06:59.110
B_3 etcetera and then
B_30 is equal to 0,

06:59.110 --> 07:01.380
no remaining balance after that.

07:01.379 --> 07:03.669
So we said, what should you
do--I'm going to do the

07:03.666 --> 07:05.676
calculation now a little bit
differently--

07:05.680 --> 07:10.380
I said after every payment of
8.88 you could always say to

07:10.379 --> 07:13.409
yourself,
"Do I want to continue or

07:13.413 --> 07:15.733
do I want to pay my
option?"

07:15.730 --> 07:19.650
Now, you notice that if I had
divided this by B_1,

07:19.649 --> 07:23.369
say, if you had a mortgage that
was a little bit smaller,

07:23.370 --> 07:30.670
barely over a 1 dollar for
example,

07:30.670 --> 07:33.190
that would divide everything by
B_1.

07:33.190 --> 07:36.260
The payments would all be
divided by B_1 and the

07:36.261 --> 07:39.441
remaining balances would all be
divided by B_1.

07:39.440 --> 07:41.410
So I could always scale this
thing up or down.

07:41.410 --> 07:45.790
There's nothing fancy about
100, nothing important about

07:45.791 --> 07:46.271
100.

07:46.269 --> 07:49.869
If the original loan was for
200 you just double all your

07:49.872 --> 07:53.092
payments and double all your
remaining balances.

07:53.089 --> 07:54.439
What could be more obvious than
that?

07:54.440 --> 07:57.930
So I want to think in those
terms of a mortgage that always

07:57.927 --> 07:59.127
has 1 dollar left.

07:59.129 --> 08:04.999
So suppose at any stage you had
1 dollar left in your mortgage.

08:05.000 --> 08:08.690
Your remaining balance was 1.

08:08.689 --> 08:18.969
So let's say at any node,
let's ask the question,

08:18.968 --> 08:30.318
what is the value of 1 dollar
of remaining balance?

08:30.319 --> 08:33.319
So if you start at 100 and you
haven't prepaid,

08:33.315 --> 08:35.915
here you've got B_2
dollars.

08:35.918 --> 08:38.588
Of course, whatever the value
of that is divided by

08:38.586 --> 08:41.036
B_2,
that's the value of 1 dollar.

08:41.038 --> 08:45.268
So I'm just going to figure out
the value of 1 dollar of

08:45.267 --> 08:48.797
remaining balance and I'm going
to call that W,

08:48.803 --> 08:49.883
let's say.

08:49.879 --> 08:52.369
I'll call that W of some node S.

08:52.370 --> 08:53.580
So where am I?

08:53.580 --> 08:59.250
I'm in some node in this
interest rate tree,

08:59.254 --> 09:00.314
right?

09:00.308 --> 09:03.528
Here's our interest rate tree,
and I'm anywhere just here,

09:03.528 --> 09:06.388
and I'm doing backward
induction so for all successor

09:06.389 --> 09:09.689
nodes I figured out what 1
dollar of remaining balance is.

09:09.690 --> 09:16.920
And let's say it's in period
1,2, 3,4, 5, so I'm in period 5,

09:16.921 --> 09:18.851
B_5.

09:18.850 --> 09:21.620
So what is the remaining
balance at this node which I

09:21.620 --> 09:22.100
call S?

09:22.100 --> 09:27.860
So it's some node right there
of--oh no, I've lost it.

09:27.860 --> 09:32.470
So W_S is going to be
what?

09:32.470 --> 09:38.780
It's going to be the minimum of
1, you could just pay it if you

09:38.775 --> 09:41.925
wanted to, or you could wait.

09:41.928 --> 09:46.918
1 over (1 r_S),
and then what would you have to

09:46.923 --> 09:50.673
do, you would have to make your
payment.

09:50.669 --> 09:52.149
Well, what's your payment?

09:52.149 --> 10:08.249
The payment is this 8.88 but
divided by B_5 plus

10:08.250 --> 10:18.420
the remaining balance of 1
dollar.

10:18.418 --> 10:25.498
So (B_6 over
B_5) times the

10:25.498 --> 10:30.728
remainder times W_Sup.

10:30.730 --> 10:32.740
Now, why is this right?

10:32.740 --> 10:34.130
I hope it is right by the way.

10:34.129 --> 10:41.799
I should have thought of this a
little before.

10:41.798 --> 10:44.658
So this is the remainder of 1
dollar left.

10:44.658 --> 10:47.638
So if I divide by B_5
here I'm not going to have a

10:47.639 --> 10:49.509
remaining balance of
B_6.

10:49.509 --> 10:54.269
I'm going to have a remaining
balance of B_6 over

10:54.274 --> 10:55.594
B_5.

10:55.590 --> 10:59.580
So if I started with 1 dollar
of remaining balance then I know

10:59.576 --> 11:03.426
that in the next period I'm
going to have B_6 over

11:03.431 --> 11:06.831
B_5 dollars of
remaining balance left.

11:06.830 --> 11:16.530
It doesn't sound too
convincing, by the way.

11:16.528 --> 11:19.048
Well, it's right,
and that happens with

11:19.053 --> 11:20.453
probability 1 half.

11:20.450 --> 11:24.350
And then with the other
probability 1 half,

11:24.350 --> 11:29.880
plus I make the payment,
but I go down instead of up and

11:29.879 --> 11:35.109
so I have B_6 over
B_5 but I have

11:35.106 --> 11:41.696
W_Sdown,
and that's also times 1 half.

11:41.700 --> 11:48.130
So either I pay off my
remaining dollar or I end up

11:48.133 --> 11:51.353
with this many dollars.

11:51.350 --> 11:55.340
Assuming I had a 1 dollar of
remaining balance I'm either

11:55.340 --> 11:58.360
going to pay it off,
the remaining balance,

11:58.357 --> 12:02.237
or I'm going to have this much
left next period and 1 dollar of

12:02.240 --> 12:04.810
remaining balance is going to be
that.

12:04.809 --> 12:07.469
So that's it.

12:07.470 --> 12:11.600
So I know now by working this
backwards I can tell what 1

12:11.599 --> 12:14.179
dollar at the beginning is
worth.

12:14.178 --> 12:17.018
And so it's exactly the same
calculation I did before except

12:17.015 --> 12:18.405
I'm talking about 1 dollar.

12:18.408 --> 12:21.128
I'm always figuring out 1
dollar of remaining balance

12:21.125 --> 12:22.635
instead of the whole thing.

12:22.639 --> 12:25.779
Present value of callable,
so here's present value of 1

12:25.779 --> 12:27.059
dollar of principal.

12:27.058 --> 12:31.568
And so remember the present
value of a callable mortgage was

12:31.565 --> 12:32.095
98.8.

12:32.100 --> 12:34.110
Here the present value of 1
dollar,

12:34.110 --> 12:38.170
figuring it out that way,
is .98, obviously it's divided

12:38.171 --> 12:41.201
by 100,
but the key is that now you can

12:41.201 --> 12:45.491
see just by looking at it where
the 1s are is where the guy

12:45.486 --> 12:47.036
decided to prepay.

12:47.038 --> 12:50.218
So it's the same thing as
before, but you see before you

12:50.219 --> 12:53.919
couldn't tell very easily from
the numbers when I did the 100.

12:53.918 --> 12:56.188
Sorry, that didn't quite make
it.

12:56.190 --> 12:59.220
Before when I did the present
value with the 100 all these

12:59.216 --> 13:00.646
numbers were 98s and 97s.

13:00.649 --> 13:02.009
I mean, where has he prepaid?

13:02.009 --> 13:04.029
It's hard to tell where the
prepayment is.

13:04.028 --> 13:07.108
If I do it all in terms of 1
dollar of remaining balance then

13:07.105 --> 13:10.225
just by looking at the screen I
can tell where the guy prepaid

13:10.230 --> 13:11.820
because there are 1s there.

13:11.820 --> 13:13.290
So I know where he's prepaid.

13:13.288 --> 13:15.458
Wherever the 1s are that means
he's prepaid.

13:15.460 --> 13:17.510
So I can tell very easily what
he did.

13:17.509 --> 13:20.779
All right, that's the only
purpose of doing the same

13:20.779 --> 13:23.409
calculation in a somewhat
trickier way.

13:23.408 --> 13:26.088
So if you think about it a
second you see I've just divided

13:26.085 --> 13:28.895
by--I've always reduced things
to if you had 1 dollar left.

13:28.899 --> 13:32.099
All right, so this tells us
what to do, when the guy should

13:32.101 --> 13:34.201
prepay and when he shouldn't
prepay.

13:34.200 --> 13:38.620
So if you're now in the world
looking at what's happening you

13:38.620 --> 13:43.040
can find the historical record
of how people have prepaid.

13:43.038 --> 13:45.968
So let's just look at the
historical record,

13:45.966 --> 13:46.916
for example.

13:46.918 --> 13:55.618
Here, if you can see this,
this is blown up as big as it

13:55.621 --> 13:56.731
goes.

13:56.730 --> 14:04.280
So this is what you might see
as the historical record of

14:04.282 --> 14:10.892
percentage prepayments
annualized from '86 to '99,

14:10.890 --> 14:11.970
say.

14:11.970 --> 14:15.100
So you notice that they're very
low here, and then they get to

14:15.101 --> 14:17.211
be very high,
and then they get low again,

14:17.206 --> 14:18.896
and then they get high again.

14:18.899 --> 14:20.799
So why do you think that
happened?

14:20.799 --> 14:21.519
So what is this?

14:21.519 --> 14:24.759
This is prepayments for a
particular mortgage,

14:24.764 --> 14:25.634
8 percent.

14:25.629 --> 14:29.899
You take all the people in the
country who started in 1986 with

14:29.903 --> 14:31.423
8 percent mortgages.

14:31.418 --> 14:34.058
There's a huge crowd of those
because that was about what the

14:34.058 --> 14:35.378
mortgage rate was that year.

14:35.379 --> 14:38.599
So a huge collection of people
got these mortgages in '86 and

14:38.596 --> 14:41.436
you keep track of what
percentage of them prepaid,

14:41.440 --> 14:44.020
really every month,
but you write the annualized

14:44.019 --> 14:46.209
rate,
and then this is the record.

14:46.210 --> 14:49.070
So why do you think it changed
so dramatically like that?

14:49.070 --> 14:49.970
What's the explanation?

14:49.970 --> 14:50.630
Student: Stock market.

14:50.629 --> 14:51.309
Prof: What?

14:51.309 --> 14:52.709
Student: Stock market.

14:52.710 --> 14:54.370
Prof: It looks like the
stock market,

14:54.368 --> 14:56.568
but I assure you the stock
market had almost nothing to do

14:56.567 --> 14:57.027
with it.

14:57.029 --> 14:59.449
Why would prepayments be so
low, and then be so high,

14:59.453 --> 15:00.763
then be low,
then be high?

15:00.759 --> 15:01.849
What do you think was happening?

15:01.850 --> 15:02.510
Student: Interest rate
change.

15:02.509 --> 15:03.439
Prof: Interest rate.

15:03.440 --> 15:04.240
We just did that.

15:04.240 --> 15:05.570
We just solved that.

15:05.570 --> 15:07.020
That was the whole point of
what we were doing.

15:07.019 --> 15:09.839
So you tell me,
what do you think happened in

15:09.844 --> 15:10.234
'93?

15:10.230 --> 15:12.840
This is September '93.

15:12.840 --> 15:14.260
I don't know if you can read
that.

15:14.259 --> 15:15.419
What do you think was going on
then?

15:15.418 --> 15:18.448
Student: Interest rates
got low.

15:18.450 --> 15:20.770
Prof: Interest rates got
low, exactly.

15:20.769 --> 15:24.489
So you may not remember this
because you were barely born.

15:24.490 --> 15:28.270
In the early '90s there was a
recession and then the

15:28.270 --> 15:30.940
government cut the interest
rates.

15:30.940 --> 15:32.650
In the '90s,
the early '90s there was a

15:32.652 --> 15:35.132
recession and the government
kept cutting interest rates

15:35.131 --> 15:36.801
further, and further and
further.

15:36.798 --> 15:39.908
There was this huge decline in
interest rates through the early

15:39.913 --> 15:41.373
'90s, and so what happened?

15:41.370 --> 15:44.780
All these people who,
in '86, who had these 8 percent

15:44.784 --> 15:48.664
mortgages--the new interest
rates were lower and so they all

15:48.660 --> 15:49.450
prepaid.

15:49.450 --> 15:51.360
You got this shocking amount of
prepayment.

15:51.360 --> 15:54.920
So this graph,
which seems sort of surprising

15:54.918 --> 16:00.018
and looks like the stock market,
turns out to have nothing to do

16:00.015 --> 16:02.115
with the stock market.

16:02.120 --> 16:04.350
It has to do with where the
interest rates are.

16:04.350 --> 16:08.800
Well, do you think interest
rates explain everything?

16:08.799 --> 16:09.519
No.

16:09.519 --> 16:15.739
What else could you notice
about the--escape.

16:15.740 --> 16:23.160
What else have we learned here
by doing these calculations?

16:23.158 --> 16:29.408
Well, what we've learned so far
is that if the interest rates in

16:29.413 --> 16:33.853
the economy are at 6 percent,
that's where they started,

16:33.847 --> 16:36.647
remember we said they started
at 6 percent and there was 16

16:36.654 --> 16:37.724
percent volatility.

16:37.720 --> 16:39.910
Here I had 20 percent
volatility.

16:39.909 --> 16:40.679
It doesn't matter.

16:40.678 --> 16:43.778
I mean, that's a plausible
amount of volatility,

16:43.784 --> 16:46.234
a little high,
but that volatility.

16:46.230 --> 16:53.720
The mortgage rate of 8 percent
is not going to give a value of

16:53.721 --> 16:54.461
100.

16:54.460 --> 16:57.420
It's going to cheat the bank if
the homeowners are acting

16:57.422 --> 16:58.112
rationally.

16:58.110 --> 17:01.240
The bank could get 120 if the
people weren't acting

17:01.235 --> 17:02.045
rationally.

17:02.048 --> 17:04.788
They were just never exercising
their option.

17:04.788 --> 17:07.868
It they're exercising their
option optimally the thing was

17:07.865 --> 17:08.725
only worth 98.

17:08.730 --> 17:10.980
Now, I told you at that time
the interest rates should have

17:10.981 --> 17:12.381
been around 7 and 1 half
percent,

17:12.380 --> 17:15.770
not 8 percent given this 6
percent interest rate in the

17:15.770 --> 17:16.400
economy.

17:16.400 --> 17:18.170
The mortgage rate should be 7
and 1 half percent.

17:18.170 --> 17:21.350
So we deduced last time that
obviously not everybody's acting

17:21.353 --> 17:21.993
optimally.

17:21.990 --> 17:25.220
Well, you can tell that looking
at this diagram.

17:25.220 --> 17:28.840
How do you know that not
everybody's acting optimally?

17:28.838 --> 17:32.068
Remember these are '86
mortgages, so everybody's taking

17:32.067 --> 17:35.597
them out at the same time within
a few months of each other,

17:35.596 --> 17:37.506
the same 8 percent mortgage.

17:37.509 --> 17:42.409
How can you tell from this
graph that they're not

17:42.406 --> 17:46.076
exercising their option
optimally?

17:46.079 --> 17:47.409
It's completely obvious.

17:47.410 --> 17:49.910
Just looking at it for one
second you can say,

17:49.910 --> 17:53.120
"Oh, these people can't be
exercising their option

17:53.117 --> 17:54.957
optimally,"
why is that?

17:54.960 --> 17:55.740
Yes?

17:55.740 --> 17:58.970
Student: They should be
exercising all at the same time

17:58.971 --> 18:00.721
if they were acting rationally.

18:00.720 --> 18:03.810
Prof: So as he says
we've just done the calculation

18:03.805 --> 18:05.045
with those 1s and 0s.

18:05.048 --> 18:08.258
I told you when the right time
to exercise the option is,

18:08.258 --> 18:10.778
so, everybody's got the same
circumstance.

18:10.778 --> 18:13.988
Every single person if all
they're trying to do is minimize

18:13.986 --> 18:16.916
the present value of their
payments they should all be

18:16.915 --> 18:18.625
prepaying at the same time.

18:18.630 --> 18:21.330
Here you see that very few
people are prepaying,

18:21.328 --> 18:25.828
but it's getting up to almost
10 percent so probably this is a

18:25.826 --> 18:29.346
stupid time to prepay,
but the point is still 10

18:29.347 --> 18:31.427
percent of them are prepaying.

18:31.430 --> 18:34.680
And over here when presumably
you ought to prepay,

18:34.684 --> 18:37.744
in the entire year,
right, they have 12 chances

18:37.740 --> 18:39.070
during the year.

18:39.068 --> 18:42.788
It takes them an entire year
and only 60 percent of them have

18:42.791 --> 18:45.151
figured out that they should
prepay.

18:45.150 --> 18:48.820
So you know they're not acting
optimally.

18:48.818 --> 18:50.898
So just from that graph that
would tell you,

18:50.896 --> 18:52.826
and you have further evidence
of that.

18:52.828 --> 18:55.958
That's evidence that they
aren't acting optimally.

18:55.960 --> 18:59.410
Furthermore you have evidence
that the banks don't expect them

18:59.407 --> 19:02.907
to be acting optimally because
the banks aren't charging them 8

19:02.913 --> 19:06.143
or 9 percent interest,
which is what they would need

19:06.138 --> 19:08.248
to pay to get the thing worth
100,

19:08.250 --> 19:11.970
they're charging them 7 and 1
half percent interest which for

19:11.974 --> 19:15.954
the optimal pre-payer is worth
much less than 100 to the bank.

19:15.950 --> 19:17.260
So the banks wouldn't do that.

19:17.259 --> 19:19.109
They would just go out of
business if they did something

19:19.109 --> 19:19.749
stupid like that.

19:19.750 --> 19:23.270
They wouldn't do that unless
they thought that the homeowners

19:23.265 --> 19:25.545
weren't acting,
at least not all of them

19:25.549 --> 19:26.839
acting, optimally.

19:26.838 --> 19:31.578
So suppose you had to predict
how people are going to act in

19:31.582 --> 19:35.202
the future and you wanted to
trade on that?

19:35.200 --> 19:38.110
What would you do?

19:38.108 --> 19:40.358
How would you think about
predicting it?

19:40.358 --> 19:41.748
So this is the data that you
have.

19:41.750 --> 19:43.950
What would you do?

19:43.950 --> 19:44.710
You have this data.

19:44.710 --> 19:46.050
These are 8 percent things.

19:46.048 --> 19:48.718
You also have 9 percent
mortgages issued the year

19:48.722 --> 19:50.562
before,
and then maybe a year before

19:50.564 --> 19:53.184
that there were 8 and 1 half
percent interest and you have

19:53.180 --> 19:55.040
that history,
and you've got all these

19:55.040 --> 19:57.340
different pools and all these
different histories.

19:57.338 --> 20:03.828
How would you think about
figuring out a prepayment--how

20:03.832 --> 20:07.612
would you predict prepayments?

20:07.608 --> 20:10.878
Well, the way economists,
macro economists at least in

20:10.882 --> 20:14.332
the old days,
used to make predictions,

20:14.327 --> 20:17.517
they would say,
"Hum, the first quarter

20:17.520 --> 20:18.880
looks pretty good."

20:18.880 --> 20:20.450
What are they predicting now?

20:20.450 --> 20:24.060
Now, they're saying
unemployment is probably going

20:24.058 --> 20:28.178
to keep rising for the next
quarter or two well until the

20:28.183 --> 20:30.783
next year,
but at that point things are

20:30.777 --> 20:33.537
going to turn around and we
expect the economy to get

20:33.538 --> 20:35.988
stronger,
come out of its recession and

20:35.991 --> 20:39.581
unemployment should gradually
improve from its high which we

20:39.577 --> 20:43.097
expect will be 10 and 1 half
percent to something back down

20:43.101 --> 20:45.351
to 6 percent by the end of 2011.

20:45.348 --> 20:47.958
That's more or less the
economists' prediction.

20:47.960 --> 20:51.490
Now, can you make a prediction
like that about prepayments?

20:51.490 --> 20:53.480
Would it make sense to make a
prediction about that?

20:53.480 --> 20:59.460
Why is that an utterly stupid
kind of prediction?

20:59.460 --> 21:03.940
What is the essence of good
prediction?

21:03.940 --> 21:06.940
If you wanted to predict
something and you were going to

21:06.938 --> 21:10.048
lose a lot of money if your
prediction was wrong how would

21:10.045 --> 21:13.145
you refine your prediction
compared to what I just gave as

21:13.152 --> 21:14.572
a sample prediction?

21:14.569 --> 21:15.249
Yep?

21:15.250 --> 21:16.680
Student: You have to
have a number of scenarios and

21:16.682 --> 21:17.312
>

21:17.311 --> 21:17.691
to each one.

21:17.690 --> 21:18.680
Prof: Exactly.

21:18.680 --> 21:22.620
So what he said is if you're
even the slightest bit

21:22.623 --> 21:27.283
sophisticated you're not going
to make a bald non-contingent

21:27.276 --> 21:28.456
prediction.

21:28.460 --> 21:30.740
Things are going to get worse
the next two quarters,

21:30.740 --> 21:32.290
then they're going to start
getting better,

21:32.288 --> 21:36.918
then things are going to get as
well as they're going to get

21:36.917 --> 21:38.327
after two years.

21:38.328 --> 21:39.618
You'll solve the problem after
two years.

21:39.618 --> 21:43.338
What happens if another war
breaks out in Iraq?

21:43.339 --> 21:45.169
What if Iran bombs Israel?

21:45.170 --> 21:49.750
What if there's another crash
in commercial real estate?

21:49.750 --> 21:53.010
How could that prediction
possibly turn out to be true?

21:53.009 --> 21:54.939
It's a sure thing it's going to
be wrong.

21:54.940 --> 21:57.650
It's just impossible that's
going to be right because the

21:57.647 --> 22:00.497
guy making the prediction has
made no contingencies built in

22:00.500 --> 22:01.420
his prediction.

22:01.420 --> 22:03.460
You know that guy's making a
prediction for free.

22:03.460 --> 22:06.070
Someone may be paying him to
hear him, but he's not going to

22:06.070 --> 22:07.930
be penalized if his prediction
is wrong.

22:07.930 --> 22:10.930
No one in their right mind
would make such a prediction.

22:10.930 --> 22:14.710
So the first thing you should
do in predicting prepayments is

22:14.713 --> 22:18.313
to realize that you've got a
tree of possible futures,

22:18.308 --> 22:22.048
and given this tree of possible
futures you're going to predict

22:22.045 --> 22:25.775
different prepayments depending
on where you go on the tree.

22:25.778 --> 22:32.108
So you see, prediction is not a
simple one event--it's not a one

22:32.113 --> 22:33.423
shot thing.

22:33.420 --> 22:37.380
Just as he so aptly put it,
it's a many scenario thing.

22:37.380 --> 22:40.000
You have to predict on many,
many scenarios what you think

22:40.001 --> 22:43.041
will happen and that makes your
prediction much better because,

22:43.038 --> 22:44.848
of course, if there is a war in
Iraq,

22:44.848 --> 22:46.678
and if there is a catastrophe
in Afghanistan,

22:46.680 --> 22:49.840
and if Iran does bomb Israel,
and if the commercial real

22:49.837 --> 22:53.397
estate market collapses things
are going to be a lot worse than

22:53.398 --> 22:55.408
this original guy's prediction.

22:55.410 --> 22:59.780
So everybody knows that,
so why not make the prediction

22:59.784 --> 23:01.084
more sensible?

23:01.078 --> 23:06.528
So, on Wall Street that's what
everybody's done for 20 years.

23:06.528 --> 23:09.138
Now, they haven't done it for
30 years.

23:09.140 --> 23:12.110
It's just 20 years that they've
been doing that.

23:12.108 --> 23:18.378
So when I got to Kidder Peabody
in 1990 they were making these

23:18.383 --> 23:21.163
one scenario predictions.

23:21.160 --> 23:24.600
It's a long story which I'll
tell maybe Sunday night.

23:24.598 --> 23:27.658
I ended up in charge of the
Research Department and so we

23:27.663 --> 23:29.963
made, you know,
other firms were doing this

23:29.962 --> 23:32.592
already, we made scenario
predictions, okay?

23:32.588 --> 23:35.028
So now what kind of scenario
predictions are you going to

23:35.025 --> 23:35.325
make?

23:35.328 --> 23:38.778
When you make contingent
predictions there are an awful

23:38.776 --> 23:39.666
lot of them.

23:39.670 --> 23:43.430
You can't even write them all
down, so what you have to do is

23:43.428 --> 23:45.118
you have to have a model.

23:45.118 --> 23:49.718
So what kind of model should
you have?

23:49.720 --> 23:53.890
I'll tell you now what the
standard guys were doing on Wall

23:53.890 --> 23:55.400
Street at the time.

23:55.400 --> 24:00.210
They were saying--here's
interest rate,

24:00.207 --> 24:01.217
sorry.

24:01.220 --> 24:02.640
Here's the present value of a
mortgage.

24:02.640 --> 24:04.910
Here's the present value of a
callable mortgage,

24:04.906 --> 24:07.366
present value of 1 dollar of
principal, so realistic

24:07.367 --> 24:08.137
prepayments.

24:08.140 --> 24:12.850
So if we go over here we'll see
that people said,

24:12.848 --> 24:15.638
"Look, from this graph
it's clear,"

24:15.638 --> 24:19.648
they would say,
"that when interest rates

24:19.653 --> 24:25.313
went down people prepay more so
why don't we have a function

24:25.306 --> 24:28.176
that looks like this?"

24:28.180 --> 24:39.530
So, prepay, that's the
percentage of remaining balance

24:39.529 --> 24:43.599
that is paid off.

24:43.599 --> 24:45.719
So what does that mean?

24:45.720 --> 24:48.410
Remember, after you've made
your coupon payment you have a

24:48.407 --> 24:50.057
remaining balance,
B_5.

24:50.058 --> 24:52.848
You could pay all of it,
or none of it,

24:52.846 --> 24:54.016
or half of it.

24:54.019 --> 24:56.709
So the prepay is what
percentage of the

24:56.712 --> 25:00.542
B_5--that's just after
you've paid, right?

25:00.538 --> 25:02.068
So, B_2 lets do that
one.

25:02.068 --> 25:03.928
B_2,
just after you've paid 8.88 the

25:03.925 --> 25:06.315
remaining balance has now been
reduced to B_2.

25:06.318 --> 25:09.198
You could, in addition to the
8.88, pay off all of that

25:09.204 --> 25:10.064
B_2.

25:10.058 --> 25:12.878
Typically some people who are
alert and think it's a good time

25:12.884 --> 25:14.834
to prepay will pay all of
B_2.

25:14.828 --> 25:17.818
Others will pay none of
B_2.

25:17.818 --> 25:21.168
So if you aggregate over the
whole collection of people the

25:21.169 --> 25:23.819
prepay percentages,
out of the sums of all their

25:23.820 --> 25:26.830
B_2s what percentage
of them are going to pay off.

25:26.828 --> 25:29.728
So we look at the aggregate
prepayment.

25:29.730 --> 25:31.220
That's the old fashioned way.

25:31.220 --> 25:34.760
And we say, "What
percentage of the remaining

25:34.763 --> 25:36.793
balance is paid off?"

25:36.788 --> 25:38.538
So you'd make a function like
this.

25:38.538 --> 25:41.578
You'd say, "Well,
prepaid might equal 10

25:41.576 --> 25:42.676
percent."

25:42.680 --> 25:44.830
Why am I picking 10 percent?

25:44.828 --> 25:51.728
So if you go back to this
picture you see that prepayments

25:51.734 --> 25:58.524
seem to be around 10 percent
when nothing's happening.

25:58.519 --> 26:03.269
So you say 10 percent plus
maybe you're going to get some

26:03.273 --> 26:08.453
more prepayments so you might
write--well, I just wrote down a

26:08.451 --> 26:10.661
function plus the min.

26:10.660 --> 26:13.250
The min, say,
of .60 because it never seems

26:13.252 --> 26:16.832
to get over 60 percent if you
look at that you see it never

26:16.834 --> 26:18.814
gets over 60 percent really.

26:18.808 --> 26:31.748
So the min of 60 and 15 times
the max of 0 and (M -

26:31.750 --> 26:40.550
r_S - sigma over 133).

26:40.548 --> 26:43.128
That would be a kind of
prepayment function.

26:43.130 --> 26:47.770
So what does this say?

26:47.769 --> 26:48.739
What happens?

26:48.740 --> 26:51.780
You're normally going to
pay--so this is this whole

26:51.784 --> 26:55.244
function here,
so I should write this as .1

26:55.239 --> 26:58.349
plus, can you see that over
there,

26:58.349 --> 27:02.969
maybe not, so this plus .1.

27:02.970 --> 27:08.460
So there's a baseline of 10
percent and if the interest rate

27:08.464 --> 27:10.704
is high,
so the interest rate is above

27:10.695 --> 27:13.315
the mortgage rate no one else is
going to prepay because this is

27:13.316 --> 27:15.476
going to be a negative number
and this will be 0.

27:15.480 --> 27:19.850
So you're just going to do
.1,10 percent.

27:19.848 --> 27:22.678
On the other hand,
as the interest rate gets low

27:22.680 --> 27:26.290
and falls far enough below the
mortgage rate people are going

27:26.294 --> 27:28.494
to say to themselves,
"Ah-ha!

27:28.486 --> 27:30.466
I have a big incentive to
prepay now.

27:30.470 --> 27:32.910
Maybe interest rates have gone
down so far I can no longer hope

27:32.912 --> 27:35.042
they're going to go back up
above the mortgage rate.

27:35.038 --> 27:37.808
I should start prepaying
more."

27:37.808 --> 27:41.148
So more people are going to
prepay and this thing is going

27:41.154 --> 27:41.804
to go up.

27:41.798 --> 27:46.398
I just multiply it by some
constant, but it'll never go up

27:46.402 --> 27:48.262
more than 60 percent.

27:48.259 --> 27:49.539
That's what this function says.

27:49.538 --> 27:53.128
And sigma, this is the
volatility--all right,

27:53.134 --> 27:55.834
so let's just leave that aside.

27:55.828 --> 27:58.438
So there's a prepayment
function that seems to sort of

27:58.439 --> 27:59.719
capture what's going on.

27:59.720 --> 28:03.200
It's usually around 10 percent
when there's no incentive.

28:03.200 --> 28:06.450
It never gets above 60 percent,
but as the incentive to prepay,

28:06.450 --> 28:08.150
as interest rates get lower and
the incentive to prepay

28:08.150 --> 28:10.230
increases,
more and more people prepay.

28:10.230 --> 28:12.040
That's kind of the idea.

28:12.038 --> 28:16.238
All right, and then you would
fit fancier curves than that.

28:16.240 --> 28:19.700
You would look at M -
r_T and you would fit

28:19.698 --> 28:21.758
a curve that looks like this.

28:21.759 --> 28:23.889
So if there's just a little bit
of incentive to prepay,

28:23.890 --> 28:26.060
the rates are a little bit
lower than the mortgage rate,

28:26.059 --> 28:26.809
nobody does it.

28:26.808 --> 28:29.698
Then quickly a lot of people do
it and then they stop doing it.

28:29.700 --> 28:33.560
So this is like 60 percent and
most of the time you're around

28:33.557 --> 28:36.447
10 percent, and you try and fit
this curve.

28:36.450 --> 28:38.870
You're going to have millions
of parameters and since you have

28:38.865 --> 28:40.445
so much data you could fit
parameters.

28:40.450 --> 28:44.500
That was the old fashioned way
and that's how people would

28:44.497 --> 28:46.057
predict prepayments.

28:46.058 --> 28:48.978
Now, that's not going to turn
out to be such a great way,

28:48.980 --> 28:51.120
but it certainly teaches you
something.

28:51.118 --> 28:55.488
So let's look at what happens
if you now--with those realistic

28:55.493 --> 28:59.083
prepayments you compute the
value of a mortgage.

28:59.078 --> 29:03.728
So this is the prepayment that
you'd get for the different

29:03.730 --> 29:08.550
rates and so you can see that as
the rates go down the total

29:08.546 --> 29:10.746
prepayment is going up.

29:10.750 --> 29:12.460
And by the way,
it's more than 60 percent

29:12.462 --> 29:15.122
because you've got this 10
percent added to the 60 percent,

29:15.118 --> 29:16.818
so the most it could be is 70
percent,

29:16.819 --> 29:19.019
which it hits over here.

29:19.019 --> 29:22.399
So you get 70 percent as the
maximum prepayments,

29:22.402 --> 29:26.422
and as interest rates get
higher no one prepays except the

29:26.419 --> 29:28.039
10 percent of guys.

29:28.038 --> 29:30.698
Now, by the way,
why are people prepaying over

29:30.702 --> 29:33.012
here even when the rates are so
high?

29:33.009 --> 29:35.309
It's because some people are
moving or they're getting

29:35.307 --> 29:37.257
divorced and they have to sell
their house.

29:37.259 --> 29:40.449
So obviously you're going to
get some prepayments no matter

29:40.453 --> 29:40.843
what.

29:40.838 --> 29:43.658
People have to prepay,
and why is it that people never

29:43.657 --> 29:46.527
prepay more than 60 percent
historically or 70 percent,

29:46.529 --> 29:48.709
because not everybody pays
attention.

29:48.710 --> 29:51.100
Now, I called them the dumb
guys last time,

29:51.103 --> 29:53.273
but as I said,
I probably fit into that

29:53.269 --> 29:54.009
category.

29:54.009 --> 29:56.219
It's people who are distracted
and doing other things.

29:56.220 --> 29:58.050
They're just not paying
attention and so they don't

29:58.045 --> 29:58.405
realize.

29:58.410 --> 30:00.590
They don't know what's going
on, so they don't realize they

30:00.585 --> 30:01.405
should be prepaying.

30:01.410 --> 30:03.570
So as interest rates go down
more people prepay.

30:03.568 --> 30:05.348
As interest rates go up less
people prepay.

30:05.348 --> 30:09.028
And if you did some historical
thing and figured out the right

30:09.032 --> 30:11.752
parameters you'd get a
prepayment function.

30:11.750 --> 30:14.420
So how did I figure out this
was 15?

30:14.420 --> 30:16.390
How did I figure out this was
.6?

30:16.390 --> 30:18.720
Why should I divide this by 133?

30:18.720 --> 30:19.630
What's sigma?

30:19.630 --> 30:23.390
Once you get those parameters
historically you now have a

30:23.386 --> 30:27.946
well-determined behavior rule of
what people are going to prepay,

30:27.950 --> 30:31.120
and from that you can figure
out what the prices are of any

30:31.124 --> 30:32.934
mortgage by backward induction.

30:32.930 --> 30:35.170
So how would you do it again by
backward induction?

30:35.170 --> 30:36.620
The same we always did it.

30:36.618 --> 30:42.968
Over here, what would you do
over here?

30:42.970 --> 30:54.070
How would you change this rule?

30:54.068 --> 30:57.508
Well, you would just be feeding
in the prepayment function.

30:57.509 --> 31:09.189
So what would the prepayment
function be?

31:09.190 --> 31:11.190
Well, people wouldn't be doing
a minimum here,

31:11.192 --> 31:11.552
right?

31:11.548 --> 31:13.348
They're not deciding whether or
not to prepay,

31:13.348 --> 31:14.348
they're just prepaying.

31:14.349 --> 31:18.149
So let's get rid of that.

31:18.150 --> 31:19.690
They're prepaying.

31:19.690 --> 31:24.250
So this is the value of 1
dollars left of principal.

31:24.250 --> 31:28.070
So some of them are prepaying
and that's the function,

31:28.065 --> 31:31.875
so prepay, and that depends on
what node you're at.

31:31.880 --> 31:34.970
And here it says what
percentage of the remaining

31:34.971 --> 31:36.711
balance is being prepaid.

31:36.710 --> 31:39.560
So that tells you,
that rule, who's prepaying,

31:39.558 --> 31:43.638
and then with the rest of the
money that's going on until next

31:43.638 --> 31:51.018
time 1 minus that same thing,
1 minus prepay times exactly

31:51.018 --> 31:54.758
what we had before.

31:54.759 --> 31:57.999
So this part of 1 dollar got
prepaid immediately so that's

31:57.999 --> 32:00.499
the cash that went to the
mortgage holder.

32:00.500 --> 32:07.330
The rest of the cash got saved
until next time and here's what

32:07.327 --> 32:09.117
happens to it.

32:09.118 --> 32:13.898
You have to make your coupon,
then you have a remaining

32:13.898 --> 32:18.858
balance, and then whatever is
going to happen is going to

32:18.855 --> 32:19.825
happen.

32:19.828 --> 32:25.408
So you'll study this and you'll
figure out I'm sure.

32:25.410 --> 32:29.070
It takes a little bit of effort
to see that through,

32:29.068 --> 32:33.128
but with half an hour staring
at it you'll understand how this

32:33.133 --> 32:37.003
works and you'll read it in a
spreadsheet so you can figure

32:36.998 --> 32:39.128
out the value of a mortgage.

32:39.130 --> 32:41.990
You get a value of a mortgage,
and now we can start doing

32:41.986 --> 32:44.686
experiments by changing the
parameters and see how the

32:44.690 --> 32:45.660
mortgage works.

32:45.660 --> 32:50.400
Now, before I do that I want to
say that there's a better way to

32:50.396 --> 32:51.146
do this.

32:51.150 --> 32:55.460
I mean, maybe these numbers are
estimated--what's a better way

32:55.460 --> 32:56.450
of doing it?

32:56.450 --> 33:00.890
How did I do it at Ellington,
how did we--I mean at Kidder

33:00.890 --> 33:01.670
Peabody?

33:01.670 --> 33:03.810
How did we predict prepayments?

33:03.808 --> 33:08.478
What's another way at looking
at prepayments?

33:08.480 --> 33:14.560
Let me tell you something
that's missing.

33:14.558 --> 33:18.078
I used to ask people who wanted
to work at Kidder Peabody or

33:18.077 --> 33:20.937
Ellington the following little
simple puzzle,

33:20.940 --> 33:24.180
and most of the genius
mathematicians always got this

33:24.183 --> 33:25.123
answer wrong.

33:25.118 --> 33:27.998
Of course we hired them anyway,
but they'd always get this

33:27.996 --> 33:28.396
wrong.

33:28.400 --> 33:32.010
So the question is,
suppose you've got a group of

33:32.012 --> 33:36.232
people like this and you figure
out what the value of the

33:36.230 --> 33:38.880
mortgage is,
and interest rates have been

33:38.883 --> 33:40.063
constant all this time.

33:40.058 --> 33:43.648
Let's suppose for one month
interest rates shoot down,

33:43.648 --> 33:46.428
interest rates collapse and
half the pool,

33:46.425 --> 33:48.995
60 percent of the pool
disappears.

33:49.000 --> 33:51.780
So now you've only got 40
percent of the people left you

33:51.780 --> 33:54.710
had before, and then interest
rates return to exactly where

33:54.713 --> 33:56.133
they were to begin with.

33:56.130 --> 34:00.320
Should the pool that's left be
worth 40 percent of the pool

34:00.319 --> 34:03.719
that you had just here,
or more than 40 percent,

34:03.715 --> 34:05.735
or less than 40 percent?

34:05.740 --> 34:08.490
So remember,
you had 100 people here.

34:08.489 --> 34:10.959
You're the bank who's lent them
the money.

34:10.960 --> 34:13.640
You're valuing the mortgage
payments they're going to make

34:13.639 --> 34:15.439
to you,
you're getting a certain amount

34:15.438 --> 34:18.348
of money from them,
60 percent of them suddenly

34:18.353 --> 34:21.413
disappeared in 1 month leaving
40 left,

34:21.409 --> 34:25.189
but now interest rates are back
exactly where they were before.

34:25.190 --> 34:27.850
Is the value of the mortgage
starting here with the 40

34:27.849 --> 34:30.809
percent pool worth 40 percent of
what it was originally,

34:30.809 --> 34:32.979
more than 40 percent or less
than 40 percent?

34:32.980 --> 34:33.940
What do you think?

34:33.940 --> 34:35.780
Yes?

34:35.780 --> 34:37.990
Student: Is it worth
more than 40 percent because

34:37.992 --> 34:40.282
those people don't understand
interest rates and therefore

34:40.284 --> 34:41.734
they're not
>

34:41.733 --> 34:43.503
option properly and
>

34:43.503 --> 34:44.473
their mortgages?

34:44.469 --> 34:45.339
Prof: Exactly.

34:45.340 --> 34:47.900
So that's an incredibly
important point.

34:47.900 --> 34:49.900
It's called the opposite of
adverse selection.

34:49.900 --> 34:55.230
Every one of these events is
selecting the people left not

34:55.233 --> 34:57.563
adversely,
not perversely,

34:57.563 --> 35:00.163
what's the opposite of
adversely,

35:00.159 --> 35:02.739
favorably to you,
so the guys who are left are

35:02.744 --> 35:04.614
all losers,
but that's who you want to deal

35:04.605 --> 35:04.805
with.

35:04.809 --> 35:07.029
You don't want to trade with
the geniuses.

35:07.030 --> 35:09.160
You want to trade with the guy
who's not paying any attention.

35:09.159 --> 35:12.339
So the guys left are the people
who are never going to prepay or

35:12.342 --> 35:15.072
hardly ever going to prepay and
so it's much better.

35:15.070 --> 35:18.550
Now, this function doesn't
capture that at all,

35:18.545 --> 35:19.145
right?

35:19.150 --> 35:20.470
It doesn't say anything.

35:20.469 --> 35:23.739
It just says your prepayment's
depending on where you are.

35:23.739 --> 35:27.109
So whether you were here or
here you're going to get the

35:27.110 --> 35:29.750
same prepayment,
but we know that that's not

35:29.746 --> 35:31.276
going to be the case.

35:31.280 --> 35:34.250
In fact, it's clear that over
here there must have been a much

35:34.248 --> 35:36.438
bigger incentive than there was
over there.

35:36.440 --> 35:39.230
So the prepayments are the
same, but actually interest

35:39.228 --> 35:42.228
rates here were vastly lower
than interest rates there.

35:42.230 --> 35:45.590
So this is not such a good
function.

35:45.590 --> 35:47.510
So how would you improve?

35:47.510 --> 35:50.830
What would you do to take into
account this adverse selection,

35:50.829 --> 35:52.679
or actually pro-verse
selection?

35:52.679 --> 35:58.089
What is the opposite of adverse?

35:58.090 --> 36:01.270
Well, it doesn't matter.

36:01.269 --> 36:03.709
What would you think to do?

36:03.710 --> 36:06.270
Your whole livelihood depends
on it, millions,

36:06.266 --> 36:08.366
trillions of dollars at stake
here.

36:08.369 --> 36:11.359
You've got to model prepayments
correctly, so how would you

36:11.356 --> 36:12.486
think of doing this?

36:12.489 --> 36:15.949
Just give me some sense of what
a hedge fund does or what anyone

36:15.951 --> 36:17.821
in this market would have to do.

36:17.820 --> 36:20.670
Well, most of them did this.

36:20.670 --> 36:23.390
So what would you do?

36:23.389 --> 36:24.329
Yeah?

36:24.329 --> 36:29.559
Student: Buy up old
mortgages, because the market is

36:29.561 --> 36:33.171
probably under estimating their
value.

36:33.170 --> 36:34.620
Prof: Well you would buy
it up when?

36:34.619 --> 36:36.619
Student: Right after...

36:36.619 --> 36:40.329
Prof: Right here you'd
buy it up, right there,

36:40.327 --> 36:44.177
but what model would you use to
predict prepayments?

36:44.179 --> 36:49.599
Not this one,
so how would you imagine doing

36:49.599 --> 36:50.229
it.

36:50.230 --> 36:56.290
You would imagine making a
model just like your intuition,

36:56.286 --> 36:59.576
so what does that mean doing?

36:59.579 --> 37:01.829
Someone's asking you to run a
research department,

37:01.829 --> 37:03.759
make a model of forecasting
prepayments.

37:03.760 --> 37:06.170
All the data you have is
aggregate data like that.

37:06.170 --> 37:08.720
You can't observe individual
homeowners in those days.

37:08.719 --> 37:10.329
They wouldn't give you the
information.

37:10.329 --> 37:12.489
I'll explain all that Sunday
night.

37:12.489 --> 37:18.779
So this is the kind of data you
have, what the whole group of

37:18.782 --> 37:24.762
people is doing every year,
but what would you do to build

37:24.760 --> 37:26.230
the model?

37:26.230 --> 37:29.100
Adverse selection is very
important or pro-verse

37:29.097 --> 37:29.827
selection.

37:29.829 --> 37:32.379
It's embarrassing I don't
remember the word,

37:32.380 --> 37:35.110
favorable selection,
a very important thing.

37:35.110 --> 37:37.880
So how would you capture that
in your model?

37:37.880 --> 37:38.670
Yep?

37:38.670 --> 37:41.630
Student: Would you split
it into two groups and then

37:41.628 --> 37:42.748
model it separately?

37:42.750 --> 37:47.940
Prof: So maybe another
thing you could do,

37:47.940 --> 37:51.710
what if you instead of having
this function that says what the

37:51.706 --> 37:54.916
aggregate's going to do all the
data's aggregate,

37:54.920 --> 37:57.100
so all you can do is test
against aggregate data.

37:57.099 --> 38:00.959
But suppose you said,
"The world,

38:00.960 --> 38:03.830
all we can see is the
aggregate, but the people really

38:03.831 --> 38:06.661
acting are individuals acting,
not the aggregate.

38:06.659 --> 38:09.649
It's the sum of individual
activities, so what we should do

38:09.653 --> 38:12.033
now is have different kinds of
people."

38:12.030 --> 38:15.060
Oh gosh, sorry.

38:15.059 --> 38:19.699
It was there already.

38:19.699 --> 38:27.709
So let's go back to where we
were before, so realistic.

38:27.710 --> 38:30.770
What you ought to do is you
ought to say,

38:30.769 --> 38:35.589
well, 8 percent--remember we
had two kinds of people already.

38:35.590 --> 38:37.580
We've already got two kinds of
people, sorry.

38:37.579 --> 38:41.899
We've got these guys,
the guys who never call,

38:41.900 --> 38:43.820
so they're people.

38:43.820 --> 38:45.170
That's a kind of person.

38:45.170 --> 38:48.330
And suppose you go down here
and you have the people who are

38:48.331 --> 38:49.511
optimally prepaying?

38:49.510 --> 38:52.510
Suppose you imagine that half
the people were optimally

38:52.512 --> 38:55.072
prepaying and half the people
never prepaid?

38:55.070 --> 38:59.630
Well, would that explain this
favorable selection?

38:59.630 --> 39:02.590
Absolutely it would explain it
because when you went through

39:02.585 --> 39:04.485
your little tree and you went
here,

39:04.489 --> 39:09.109
and here, and here,
and here, by the time you got

39:09.105 --> 39:13.965
down here all those people,
all the optimal pre-payers

39:13.974 --> 39:15.734
they're all prepaying.

39:15.730 --> 39:18.570
So you start off with
half-optimal guys and

39:18.572 --> 39:19.862
half-asleep guys.

39:19.860 --> 39:22.590
Once you get down here all the
optimal guys have disappeared

39:22.592 --> 39:24.542
and the pool that's left is all
asleep,

39:24.539 --> 39:27.689
so of course the pool is worth
much more here given the

39:27.690 --> 39:29.910
interest rate than it was over
here.

39:29.909 --> 39:34.679
In fact, if it goes back then
again to here where it was

39:34.684 --> 39:37.554
before--sorry that's same line.

39:37.550 --> 39:40.350
If it goes back to here--have I
done this right?

39:40.349 --> 39:42.629
No, I've got to go back twice
here and then here.

39:42.630 --> 39:45.530
So once it goes back to here if
it goes here,

39:45.532 --> 39:49.292
here, here and here then the
pool is going to be much more

39:49.291 --> 39:51.931
valuable here than it started
there.

39:51.929 --> 39:54.739
There are half as many people,
but it's worth much more than

39:54.744 --> 39:56.084
half of what it was there.

39:56.079 --> 40:00.069
So the way to do this is to
break--so then you're looking at

40:00.072 --> 40:01.292
the individuals.

40:01.289 --> 40:03.839
You're saying one class of
people is very smart,

40:03.838 --> 40:07.148
or one class of people is very
alert, it's a much better word,

40:07.148 --> 40:09.208
one class of people is very
alert.

40:09.210 --> 40:12.010
One class of people is very
un-alert and as you go through

40:12.010 --> 40:14.910
the tree the alert people are
going to disappear faster than

40:14.909 --> 40:17.709
the non-alert people and that's
why you're going to have a

40:17.710 --> 40:20.610
favorable selection of people
who's left in the pool.

40:20.610 --> 40:24.010
Well, of course,
there are no extremes of

40:24.010 --> 40:29.110
perfectly rational or perfectly
asleep in the economy so what

40:29.112 --> 40:33.282
you can do is you can make
people in between.

40:33.280 --> 40:34.570
How do you make them in between?

40:34.570 --> 40:36.360
Well, suppose that,
for example,

40:36.360 --> 40:37.690
I only did one thing.

40:37.690 --> 40:40.120
Suppose it's costly to prepay?

40:40.119 --> 40:41.889
Some people just say to
themselves, "I'm going to

40:41.887 --> 40:43.187
have to take a whole day off of
work.

40:43.190 --> 40:45.100
I'm not going to write my paper.

40:45.099 --> 40:48.579
I might lose some business that
I was going to do that day.

40:48.579 --> 40:52.569
A whole bunch of stuff I'm
losing, so I'm going to subtract

40:52.568 --> 40:53.048
that.

40:53.050 --> 40:54.960
I'm not going to prepay.

40:54.960 --> 40:58.020
I'm not going to even think
about doing it unless I can get

40:58.023 --> 41:00.933
at least a certain benefit from
having done it."

41:00.929 --> 41:04.159
So you can add a cost of
prepaying and people aren't

41:04.161 --> 41:07.841
going to prepay unless the gain
that they have by prepaying

41:07.835 --> 41:10.745
exceeds the cost of doing the
prepayments.

41:10.750 --> 41:14.480
So to take the simplest case
let's suppose the very act of--

41:14.480 --> 41:15.730
never mind the thinking and all
that--

41:15.730 --> 41:18.980
the very act of prepaying,
going to the bank literally

41:18.983 --> 41:20.093
costs you money.

41:20.090 --> 41:24.590
So if you have a value,
if the thing is 100 and you can

41:24.586 --> 41:26.796
prepay,
you know, if you do your

41:26.802 --> 41:30.202
calculations and don't prepay
today it's worth 98 and if you

41:30.202 --> 41:33.372
prepay today the remaining
balance is 94 you're saving 4

41:33.373 --> 41:35.663
dollars,
but if the cost of prepayment

41:35.664 --> 41:37.614
is 5 you're still not going to
do it.

41:37.610 --> 41:39.770
So you get a guy with a high
cost of prepaying,

41:39.766 --> 41:42.486
an infinite cost of prepaying,
he's going to look like he's

41:42.485 --> 41:43.465
totally un-alert.

41:43.469 --> 41:46.129
A guy with zero cost of paying
is going to look like he's

41:46.130 --> 41:46.890
totally alert.

41:46.889 --> 41:51.589
So you can have gradations of
rationality, and you can have

41:51.594 --> 41:53.464
different dimensions.

41:53.460 --> 41:58.450
So you can have cost of
prepaying and you can have

41:58.447 --> 41:59.667
alertness.

41:59.670 --> 42:03.250
What's the percentage of time
you're actually paying attention

42:03.246 --> 42:04.006
that month?

42:04.010 --> 42:06.760
What fraction of the months do
you actually pay attention,

42:06.760 --> 42:09.700
and you can have a distribution
of people, different costs and

42:09.704 --> 42:10.964
different alertnesses.

42:10.960 --> 42:14.270
So that's the model that I
built.

42:14.269 --> 42:16.379
It's a simplified form of it.

42:16.380 --> 42:18.410
It gives you an idea.

42:18.409 --> 42:23.279
So here's this burnout effect
that I showed that if you take

42:23.278 --> 42:26.628
the same coupons,
but an older one rather than

42:26.625 --> 42:30.375
a--an older one that's burned
out will always prepay slower,

42:30.380 --> 42:33.930
so the pink one is always less
than the blue one because it

42:33.931 --> 42:36.381
went through an opportunity to
prepay.

42:36.380 --> 42:39.960
So here you start with a pool
of guys on the right,

42:39.961 --> 42:43.761
and then after a while,
after time has gone down a lot

42:43.757 --> 42:45.547
of them have prepaid.

42:45.550 --> 42:48.050
So here's alertness and cost.

42:48.050 --> 42:53.150
So you describe a person by
what his cost of prepaying is

42:53.154 --> 42:55.164
and how alert he is.

42:55.159 --> 42:57.699
The more alert he is and the
lower the cost of prepaying the

42:57.704 --> 42:58.874
closer to rational he is.

42:58.869 --> 43:01.599
The less alert he is,
the higher the cost of

43:01.601 --> 43:04.971
prepaying the closer to the
totally dumb guy he is.

43:04.969 --> 43:07.949
And so you could have a whole
normally distributed

43:07.945 --> 43:11.645
distribution of people and over
time those groups are going to

43:11.650 --> 43:14.810
be reduced because a lot of them
are prepaying,

43:14.809 --> 43:17.109
but they won't be reduce
symmetrically.

43:17.110 --> 43:20.550
The low cost high alertness
guys are going to disappear much

43:20.547 --> 43:24.037
faster and the pool's going to
get more and more favorable to

43:24.043 --> 43:24.513
you.

43:24.510 --> 43:28.210
And so anyway,
all you have to do is

43:28.213 --> 43:32.233
parameterize the cost,
what the distribution of people

43:32.226 --> 43:35.256
in the population,
what the standard deviation and

43:35.255 --> 43:38.365
expectation of cost is and of
alertness is,

43:38.369 --> 43:40.549
and that tells you what this
distribution looks like.

43:40.550 --> 43:43.380
So you're fitting four numbers
and you've got thousands of

43:43.376 --> 43:45.606
pools and hundreds and hundreds
of months,

43:45.610 --> 43:50.520
and fitting four parameters you
can end up fitting all the data.

43:50.519 --> 43:52.019
So look at what happens here.

43:52.019 --> 43:53.779
So here's the same data.

43:53.780 --> 43:57.540
So I just tell you I know that
in a population,

43:57.539 --> 44:01.929
given what I've calculated in
the '90s there,

44:01.929 --> 44:04.819
I know what fraction of the
people have this cost and that

44:04.820 --> 44:07.270
alertness,
what fraction of the people are

44:07.269 --> 44:10.679
so close to dumb that their
costs are astronomical and their

44:10.679 --> 44:13.879
alertness is tiny,
what fraction of the people

44:13.882 --> 44:17.322
have almost no cost and a very
high alertness,

44:17.320 --> 44:19.520
so I'm only estimating four
parameters because I'm assuming

44:19.518 --> 44:20.578
it's normally distributed.

44:20.579 --> 44:24.549
Given that fixed pool of people
I apply that to the beginning of

44:24.554 --> 44:28.534
every single mortgage and I just
crank out what would those guys

44:28.527 --> 44:28.967
do.

44:28.969 --> 44:32.269
In the tree if they knew what
the volatilities were when would

44:32.268 --> 44:35.208
they decide to prepay,
and then I have to follow a

44:35.210 --> 44:37.510
scenario out in the future and I
say,

44:37.510 --> 44:40.230
"Well, along this path
which guy would prepay and which

44:40.228 --> 44:42.988
guy wouldn't prepay and what
would the total prepayments look

44:42.992 --> 44:44.192
along that path?"

44:44.190 --> 44:47.130
And so this has generated the
pink line from the model with no

44:47.130 --> 44:50.020
knowledge of the world except I
fit those parameters and look

44:50.021 --> 44:52.241
how close it is to what actually
happened.

44:52.239 --> 44:57.329
So it turns out that it was
incredibly easy to predict,

44:57.329 --> 45:00.769
contingently predict what
prepayments were going to be and

45:00.773 --> 45:03.313
therefore to be able to value
mortgages.

45:03.309 --> 45:05.389
And this was a secret that not
many people,

45:05.389 --> 45:06.789
you know, a bunch of people
understood,

45:06.789 --> 45:09.469
but not that many understood,
and so for years we were

45:09.472 --> 45:12.702
trading at our hedge fund,
first at Kidder and then at

45:12.699 --> 45:16.029
Ellington with this ability to
contingently forecast

45:16.027 --> 45:18.307
prepayments at a very high rate.

45:18.309 --> 45:21.009
And why was it so stable,
the prediction,

45:21.005 --> 45:22.215
and so reliable?

45:22.219 --> 45:24.879
It's because the class of
people stayed pretty much the

45:24.882 --> 45:27.792
same and every year there'd be
the same kinds of people with

45:27.791 --> 45:29.321
the same kinds of behavior.

45:29.320 --> 45:30.320
Some were very alert.

45:30.320 --> 45:33.070
Some were very not alert,
but the distribution of types

45:33.065 --> 45:36.015
was more or less the same and
you could predict with pretty

45:36.016 --> 45:39.116
good accuracy what was going to
happen from year to year.

45:39.119 --> 45:42.879
Of course, then after 2003 or
so the class of people started

45:42.876 --> 45:46.246
to radically change and many
more people who never got

45:46.253 --> 45:50.143
mortgages before got them and it
became much harder to predict

45:50.137 --> 45:52.237
what they were going to do.

45:52.239 --> 45:54.569
But so in the old days it was
pretty easy to predict.

45:54.570 --> 45:55.990
And why was it so easy to
predict?

45:55.989 --> 46:03.089
Because it was an agent based
model, agent based.

46:03.090 --> 46:05.430
So, by the way,
I added this volatility here,

46:05.427 --> 46:08.397
so these guys who just ran
regressions they had to have a

46:08.400 --> 46:10.420
volatility or something
parameter.

46:10.420 --> 46:14.480
So you see as volatility goes
up the prepayments are slower.

46:14.480 --> 46:17.620
Well, they just had to notice
that and build it right into

46:17.621 --> 46:18.561
their function.

46:18.559 --> 46:20.539
I didn't even have to think of
that or burnout.

46:20.539 --> 46:23.929
None of those things did I have
to think about because if you're

46:23.927 --> 46:26.507
a guy optimizing here and
volatility goes up,

46:26.510 --> 46:29.700
so you reset the tree so that
the interest rates can change

46:29.695 --> 46:30.185
faster.

46:30.190 --> 46:32.950
The option is worth more so
you're going to wait longer.

46:32.949 --> 46:34.959
You're not going to just
exercise it right away because

46:34.961 --> 46:37.161
you've got a chance that prices
will really go up so you can

46:37.161 --> 46:39.461
wait a little longer,
afford to wait longer.

46:39.460 --> 46:41.550
So prepayments will slow down.

46:41.550 --> 46:43.390
So all I'm saying,
all of this is just to say that

46:43.389 --> 46:47.349
if you have the right--
so it's agent based,

46:47.353 --> 46:53.533
it's contingent predictions,
those two things together

46:53.527 --> 46:57.067
enable you to make quite
reliable predictions about the

46:57.065 --> 46:59.945
future if you're in a stable
environment.

46:59.949 --> 47:04.089
And so what seems like a
bewildering amount of stuff

47:04.085 --> 47:07.405
turns out to be pretty easy to
explain.

47:07.409 --> 47:11.039
So now what happens?

47:11.039 --> 47:16.439
So do you have any questions
here or should I--yes?

47:16.440 --> 47:19.640
Student: You said you
assume that those two parameters

47:19.639 --> 47:21.079
are normally distributed.

47:21.079 --> 47:23.179
Did you select among some sort
of variance?

47:23.179 --> 47:24.199
Prof: Some sort of what?

47:24.199 --> 47:25.269
Student: Variance.

47:25.268 --> 47:27.158
Prof: I had to figure
out what the mean and the

47:27.159 --> 47:27.659
variance is.

47:27.659 --> 47:31.369
There's mean and variance of
cost and mean and variance of

47:31.373 --> 47:33.593
alertness to get that
distribution,

47:33.588 --> 47:34.238
right?

47:34.239 --> 47:40.789
So how do I know what the
population--so let me just put

47:40.789 --> 47:43.529
the picture up again.

47:43.530 --> 47:46.370
So who are the hyper rational
guys?

47:46.369 --> 47:48.919
They are the people with the
really high alertness up there

47:48.920 --> 47:51.470
and the really low cost,
so they're the guys back there.

47:51.469 --> 47:55.249
They're the hyper--or maybe it
was the guys,

47:55.246 --> 48:00.336
you know, one of these corners
with very high alertness and

48:00.338 --> 48:01.918
very low cost.

48:01.920 --> 48:03.480
I forgot which way the scale
works.

48:03.480 --> 48:05.630
It might be going down.

48:05.630 --> 48:08.320
So anyway, the guys with very
high alertness and very low

48:08.315 --> 48:10.135
costs are the hyper rational
people.

48:10.139 --> 48:13.449
At the other corner you've got
the guys who have very low

48:13.449 --> 48:15.339
alertness and very high costs.

48:15.340 --> 48:17.640
They're the people who you're
going to make a lot of money on

48:17.635 --> 48:18.435
if you're the bank.

48:18.440 --> 48:21.550
So how do I know how many
people are of each type?

48:21.550 --> 48:22.740
Well, I don't.

48:22.739 --> 48:25.999
I have to fit this distribution.

48:26.000 --> 48:27.960
But you see I have so much data.

48:27.960 --> 48:30.340
I've got this kind of curve.

48:30.340 --> 48:33.930
This kind of curve I've got for
every starting year for the

48:33.934 --> 48:37.474
whole history and there's so
many different interest rates

48:37.465 --> 48:40.675
and so many different--
so I'm applying that same

48:40.681 --> 48:44.201
population at the beginning of
every single curve and then

48:44.195 --> 48:47.525
seeing what happens to my
prediction versus what really

48:47.525 --> 48:48.385
happened.

48:48.389 --> 48:50.649
So I've got thousands,
and thousands,

48:50.648 --> 48:54.598
and thousands of data points
and only four parameters to fit.

48:54.599 --> 48:56.939
So I pick the four parameters
to fit the data as much as

48:56.940 --> 48:57.410
possible.

48:57.409 --> 49:01.069
If I assumed everybody was
perfectly alert instead of that

49:01.067 --> 49:04.497
curve that I showed you,
I put a huge crowd here of

49:04.501 --> 49:08.491
perfectly rational people then I
would have found that I would

49:08.492 --> 49:12.352
have gotten prepayments at 100
percent up there and at 0 all

49:12.353 --> 49:16.413
the way over here and so it
wouldn't have fit that curve.

49:16.409 --> 49:20.629
So that's how I knew that there
couldn't be that many perfectly

49:20.632 --> 49:21.862
rational people.

49:21.860 --> 49:22.740
Yes?

49:22.739 --> 49:25.449
Student: How can you
know for sure that there are

49:25.452 --> 49:26.442
only two patterns?

49:26.440 --> 49:28.500
Prof: You mean how do I
know cost and alertness,

49:28.496 --> 49:29.826
maybe there's some other
factors?

49:29.829 --> 49:32.719
Yes, well there probably are
other factors.

49:32.719 --> 49:36.039
So what would you
commonsensically think are the

49:36.041 --> 49:36.751
factors?

49:36.750 --> 49:38.520
What keeps people from
prepaying?

49:38.518 --> 49:41.558
I think the most obvious one is
it's a huge hassle and they're

49:41.561 --> 49:42.711
not paying attention.

49:42.710 --> 49:44.110
So those are the first two that
I thought of.

49:44.110 --> 49:45.530
Could you think of another one?

49:45.530 --> 49:46.810
Student: Maybe their age.

49:46.809 --> 49:48.479
Prof: Their age, exactly.

49:48.480 --> 49:51.880
So maybe demography has an
effect on it.

49:51.880 --> 49:55.300
So maybe, for example,
you get more sophisticated the

49:55.304 --> 49:56.364
older you get.

49:56.360 --> 49:58.930
So that was another factor we
put in.

49:58.929 --> 50:04.319
So I'm not telling you all the
factors, but these were the two

50:04.322 --> 50:05.652
main factors.

50:05.650 --> 50:08.050
Another factor was growing
sophistication.

50:08.050 --> 50:12.620
We called it the smart factor.

50:12.619 --> 50:14.669
That's another factor.

50:14.670 --> 50:18.350
So over time you get more
sophisticated.

50:18.349 --> 50:23.659
So anyway, the point is with a
few of these factors you got a

50:23.657 --> 50:26.847
pretty good fit,
and it was pretty reliable,

50:26.846 --> 50:30.246
and you could predict what was
going to happen contingently.

50:30.250 --> 50:36.250
So now if you want to trade
mortgages what are some of the

50:36.246 --> 50:39.716
interesting things that happen?

50:39.719 --> 50:44.909
The first interesting thing to
notice is that what do you think

50:44.907 --> 50:48.337
happens as the interest rate
goes down?

50:48.340 --> 50:55.520
So the first thing to notice
is--so I'll just ask you two

50:55.521 --> 50:57.061
questions.

50:57.059 --> 50:58.369
Let's go on the other side.

50:58.369 --> 50:59.259
I'm running out of room.

50:59.260 --> 51:03.310
Suppose that you have the
mortgage value,

51:03.313 --> 51:06.053
what you get in the tree?

51:06.050 --> 51:09.740
So in this tree that we've
built, here's the tree,

51:09.739 --> 51:13.279
it's going like that,
and at every node we're

51:13.282 --> 51:16.182
predicting--
for each class of people we're

51:16.179 --> 51:17.889
predicting where his 1s are.

51:17.889 --> 51:19.709
So that class is prepaying.

51:19.710 --> 51:23.090
The other class is not as smart
so they're not prepaying here,

51:23.085 --> 51:25.795
but maybe when things get
really low they'll start

51:25.797 --> 51:26.847
prepaying here.

51:26.849 --> 51:30.149
So each class of people,
each cost, alertness type has

51:30.153 --> 51:31.093
its own tree.

51:31.090 --> 51:33.090
They're the same tree,
but it's own behavior on the

51:33.094 --> 51:34.744
tree, and then I add them all
together.

51:34.739 --> 51:47.239
So what happens with the
starting interest rate?

51:47.239 --> 51:52.149
So here we had .06 and this
value was 98 or something,

51:52.148 --> 51:52.888
right?

51:52.889 --> 51:56.289
Now, suppose the interest rate
went down to .05.

51:56.289 --> 52:03.449
I drew this picture of interest
and mortgage value.

52:03.449 --> 52:04.809
What do you think happens?

52:04.809 --> 52:08.729
So the interest starts--this is
'98,6 percent is there.

52:08.730 --> 52:13.600
As the interest rate goes down
what do you think happens to the

52:13.596 --> 52:15.476
value of the mortgage?

52:15.480 --> 52:20.470
If you're a bank and you've
fixed--the mortgage rate is 8

52:20.469 --> 52:21.359
percent.

52:21.360 --> 52:24.950
That's a fixed mortgage rate,
but now you've moved in the

52:24.947 --> 52:26.547
tree from here to here.

52:26.550 --> 52:34.480
Do you think your mortgage is
going to go up in value or down

52:34.476 --> 52:35.926
in value?

52:35.929 --> 52:37.829
Student: It's going up.

52:37.829 --> 52:40.349
Prof: It's going to go
up because the interest rates

52:40.351 --> 52:42.831
are lower and the present value
of the payments is getting

52:42.831 --> 52:43.311
higher.

52:43.309 --> 52:46.949
So if the interest rate goes
down the mortgage is going to go

52:46.951 --> 52:48.531
up like that,
typically.

52:48.530 --> 52:50.560
But will it keep going up like
this and this?

52:50.559 --> 52:52.449
If it were a bond it would go
up like that,

52:52.449 --> 52:52.809
right?

52:52.809 --> 52:56.949
A bond, a 1 year bond which
owed 1 over 1 r would keep going

52:56.945 --> 52:59.885
up and up the value before it
got negative,

52:59.889 --> 53:00.449
say.

53:00.449 --> 53:02.179
It would go up.

53:02.179 --> 53:06.609
As r got negative it would go
way up like that.

53:06.610 --> 53:09.440
So does the mortgage keep going
up like that?

53:09.440 --> 53:14.400
As the interest rate goes down
is the value of the mortgage

53:14.398 --> 53:18.158
going to get higher and higher
and higher?

53:18.159 --> 53:20.569
Suppose the guy's optimal,
what's going to happen?

53:20.570 --> 53:23.990
This is 100 here.

53:23.989 --> 53:26.839
What'll happen?

53:26.840 --> 53:27.570
Yep?

53:27.570 --> 53:29.070
Student: He's going to
prepay.

53:29.070 --> 53:31.580
Prof: He's going to
eventually figure out that he

53:31.583 --> 53:33.323
should prepay so it'll go like
this.

53:33.320 --> 53:36.310
If he's perfectly optimal he'll
never let it go above 100.

53:36.309 --> 53:38.019
So it's going to go something
like this.

53:38.018 --> 53:40.768
As the interest rate gets
higher you get crushed,

53:40.771 --> 53:44.041
and as the interest rate gets
lower you don't get the full

53:44.039 --> 53:46.389
upside because he's prepaying at
100.

53:46.389 --> 53:52.359
He's never letting it go above
100, right?

53:52.360 --> 53:55.880
So if he's not so optimal maybe
your value will go up,

53:55.878 --> 53:58.068
but not so astronomically high.

53:58.070 --> 54:02.680
So this idea that the mortgage
curve, instead of being like

54:02.681 --> 54:06.101
this goes like that,
this is what was called

54:06.101 --> 54:07.931
negative convexity.

54:07.929 --> 54:16.579
Now, the next thing to know is
suppose that the guys are partly

54:16.577 --> 54:21.737
irrational so it's going above
100.

54:21.739 --> 54:25.389
So it's starting to go like
this.

54:25.389 --> 54:26.979
Then what do you think?

54:26.980 --> 54:33.550
As the interest gets really low
what's going to happen?

54:33.550 --> 54:34.940
All right, you just said it, so.

54:34.940 --> 54:37.730
If the guy was rational,
perfectly rational it would go

54:37.730 --> 54:38.350
like that.

54:38.349 --> 54:42.069
He'd never let it go above 100,
but now suppose guys are not

54:42.070 --> 54:43.270
totally rational?

54:43.268 --> 54:45.338
What's going to happen is
they're going to,

54:45.340 --> 54:48.000
sort of--as rates get a little
bit low they're going to

54:48.001 --> 54:50.271
overlook the fact that they
should prepay.

54:50.269 --> 54:51.749
So now it's advantageous to you.

54:51.750 --> 54:55.200
Things are worth more than 100,
but if rates get incredibly low

54:55.202 --> 54:58.592
even the dumbest guy,
the highest cost guy is going

54:58.588 --> 55:02.618
to realize he has an advantage
to prepay and so things are

55:02.615 --> 55:05.085
going to go back down like that.

55:05.090 --> 55:07.470
So the value's going to be
quite complicated.

55:07.469 --> 55:10.919
So this is the mortgage value
as a function of interest rates.

55:10.920 --> 55:12.490
Just common sense will tell you
this.

55:12.489 --> 55:16.359
In a typical bond as the
interest rate gets lower the

55:16.356 --> 55:18.436
present value gets higher.

55:18.440 --> 55:21.690
You should expect a curve like
that, but because of the option

55:21.693 --> 55:25.003
if it were rationally exercised
the curve would never get above

55:25.003 --> 55:25.433
100.

55:25.429 --> 55:26.919
It would have to go like that.

55:26.920 --> 55:28.890
But now if people are
irrational you can take

55:28.885 --> 55:31.295
advantage of them and get more
than 100 out of them.

55:31.300 --> 55:35.060
But if the situation gets so
favorable to you it becomes

55:35.063 --> 55:37.583
blindingly obvious,
eventually to them,

55:37.579 --> 55:40.569
that they're getting screwed,
and eventually they act and

55:40.574 --> 55:42.574
bring it all the way back to 100
again.

55:42.570 --> 55:44.540
So this value of the mortgage
looks like that.

55:44.539 --> 55:46.239
So that's a very tricky thing.

55:46.239 --> 55:50.409
I'll even write, very tricky.

55:50.409 --> 55:54.169
So if you don't know what
you're doing you could easily

55:54.172 --> 55:56.822
get yourself hurt holding
mortgages.

55:56.820 --> 55:59.260
You could suddenly find
yourself losing money holding

55:59.257 --> 55:59.817
mortgages.

55:59.820 --> 56:02.220
So that's my next subject here.

56:02.219 --> 56:05.809
I want to talk about hedging.

56:05.809 --> 56:09.919
So we know something now about
valuing mortgages.

56:09.920 --> 56:15.490
Now I want to talk about
hedging, and what hedge funds

56:15.487 --> 56:21.787
do, and what everyone on Wall
Street should be doing which is

56:21.789 --> 56:23.049
hedging.

56:23.050 --> 56:26.490
So if you hold a mortgage
you're going to hold it because

56:26.485 --> 56:30.105
maybe you can lend 100 to a
bunch of people but actually get

56:30.105 --> 56:32.125
a value that's more than 100.

56:32.130 --> 56:35.170
So it looks like you're here,
but if interest rates change a

56:35.173 --> 56:38.273
little bit suddenly this huge
value you thought you had might

56:38.269 --> 56:41.329
collapse back down to 100,
or the interest rates might go

56:41.333 --> 56:43.433
up and it might collapse to way
below 100.

56:43.429 --> 56:45.829
So you look like you're well
off, but there are scenarios

56:45.831 --> 56:48.321
where you could lose money and
you want to protect yourself

56:48.320 --> 56:49.050
against that.

56:49.050 --> 56:50.310
So how do you go about doing it?

56:50.309 --> 56:51.549
What does hedging mean?

56:51.550 --> 56:56.820
And I want to put it in the
context, the old context of the

56:56.820 --> 57:00.820
World Series which we started
with before.

57:00.820 --> 57:02.820
So it's easier to understand
there,

57:02.820 --> 57:05.800
and so many of you will have
thought about this before so

57:05.800 --> 57:09.730
you'll be able to answer it,
but if I put it in the mortgage

57:09.726 --> 57:12.806
context it would seem just too
difficult.

57:12.809 --> 57:13.629
I don't know why I did that.

57:13.630 --> 57:17.130
So the World Series--I'm going
to lower it in a second.

57:17.130 --> 57:21.120
So suppose that the Yankees
have a 60 percent chance,

57:21.119 --> 57:23.529
I said beating the Dodgers,
I thought the Dodgers would be

57:23.534 --> 57:26.614
in the World Series,
a 60 percent chance of winning

57:26.612 --> 57:30.192
any game against the Phillies in
the World Series.

57:30.190 --> 57:33.990
And you are a bookie and your
fellow bookies all understand

57:33.985 --> 57:35.485
that it's 60 percent.

57:35.489 --> 57:39.529
So some naive Philly fan comes
to you and says I want to bet

57:39.525 --> 57:43.145
100 dollars that the Phillies
win the World Series.

57:43.150 --> 57:46.550
Should you take the bet or not?

57:46.550 --> 57:49.030
Yes you should take the bet
because 60 percent of the time

57:49.034 --> 57:50.694
you're going to win 100
dollars--no.

57:50.690 --> 57:52.210
Yes you should take the bet.

57:52.210 --> 57:56.050
If he bet on one game you would
make, with 60 percent

57:56.045 --> 58:00.175
probability you'd win 100 and
with 40 percent probability

58:00.177 --> 58:01.577
you'd lose 100.

58:01.579 --> 58:06.679
So that means on average your
expectation is equal to 20.

58:06.679 --> 58:09.919
So if he's willing to bet 100
dollars on the Phillies winning

58:09.916 --> 58:12.126
the first game of the series
with you,

58:12.130 --> 58:15.570
you know that your expected
chance of winning is 20 dollars.

58:15.570 --> 58:19.090
You're expecting to win 20
dollars from the guy.

58:19.090 --> 58:21.540
Now, suppose he's willing to
make the same bet,

58:21.541 --> 58:23.461
100 dollars for the entire
series?

58:23.460 --> 58:31.680
What's your chance of winning
and what's your expected profit

58:31.681 --> 58:33.191
from him?

58:33.190 --> 58:36.150
Is it less than 20,20,
or more than 20?

58:36.150 --> 58:37.800
Student: More than 20.

58:37.800 --> 58:39.130
Prof: More than 20.

58:39.130 --> 58:41.780
It's going to turn out to be,
so a 7 game series,

58:41.777 --> 58:45.197
it's going to turn out to be 42
which we're going to figure out

58:45.197 --> 58:46.077
in a second.

58:46.079 --> 58:48.609
But what's your risk?

58:48.610 --> 58:49.650
What's your risk?

58:49.650 --> 58:53.250
In either case you might lose
100 dollars.

58:53.250 --> 58:56.610
The Phillies,
they're probably going to lose,

58:56.610 --> 58:59.830
but there's a chance something
goes crazy and some unknown guy

58:59.826 --> 59:02.986
hits five home runs in the first
four games or something,

59:02.989 --> 59:05.849
and some other unknown guy hits
another four home runs and you

59:05.846 --> 59:06.966
lose the World Series.

59:06.969 --> 59:09.679
You could lose 100 dollars,
and maybe the guy's not betting

59:09.675 --> 59:12.285
100 dollars but 100 thousand
dollars or a hundred million

59:12.289 --> 59:12.849
dollars.

59:12.849 --> 59:15.619
You know you've got a favorable
bet, but you don't want to run

59:15.619 --> 59:18.339
the risk of losing even though
there's not that high a chance

59:18.344 --> 59:19.484
you're going to lose.

59:19.480 --> 59:25.030
What can you do about it?

59:25.030 --> 59:28.650
Well, you know that there are
these other bookies out there

59:28.648 --> 59:31.948
who every game are willing to
bet at odds 60/40 either

59:31.954 --> 59:35.764
direction on the Phillies or the
Yankees because they just all

59:35.760 --> 59:37.250
know--
they're just like you.

59:37.250 --> 59:40.270
You all know that the odds are
60 percent for the Yankees

59:40.268 --> 59:41.398
winning every game.

59:41.400 --> 59:45.050
So suppose this naive guy,
the Phillies fan,

59:45.052 --> 59:50.152
comes up to you and bets 100
dollars on the World Series that

59:50.150 --> 59:52.360
the Phillies will win.

59:52.360 --> 59:54.750
You don't want to run the risk
of losing 100 dollars.

59:54.750 --> 59:58.250
You know there are these other
bookies who are willing to take

59:58.251 --> 1:00:00.261
bets a game at a time 60/40
odds.

1:00:00.260 --> 1:00:02.400
What should you be doing?

1:00:02.400 --> 1:00:11.910
What would you do?

1:00:11.909 --> 1:00:13.169
Yes?

1:00:13.170 --> 1:00:15.550
Student: Bet on the
Phillies winning because they

1:00:15.552 --> 1:00:17.982
give you better odds so you're
guaranteed your profit.

1:00:17.980 --> 1:00:19.090
Prof: So what would you
do?

1:00:19.090 --> 1:00:21.430
So this guy's come to you,
and you're not going to be able

1:00:21.432 --> 1:00:23.262
to give the--
we're going to find out exactly

1:00:23.260 --> 1:00:24.630
what you should do in one
second,

1:00:24.630 --> 1:00:27.630
but let's just see how far you
can get by reason without

1:00:27.626 --> 1:00:28.386
calculation.

1:00:28.389 --> 1:00:30.819
So this guy's come to you and
said, "I'm betting 100

1:00:30.818 --> 1:00:33.288
dollars on the Phillies winning
the World Series."

1:00:33.289 --> 1:00:36.109
This is the night before the
first game.

1:00:36.110 --> 1:00:41.230
Every bookie is standing by
ready to take bets at 30 to 20

1:00:41.231 --> 1:00:41.861
odds.

1:00:41.860 --> 1:00:44.490
What would you do?

1:00:44.489 --> 1:00:47.129
Student: You'd bet with
the bookie that the Phillies

1:00:47.128 --> 1:00:48.128
would win because...

1:00:48.130 --> 1:00:48.820
Prof: That what?

1:00:48.820 --> 1:00:50.260
Student: That the
Phillies would win.

1:00:50.260 --> 1:00:51.230
Prof: Yeah, how much?

1:00:51.230 --> 1:00:56.040
Student: 100 dollars.

1:00:56.039 --> 1:00:57.339
Prof: You'd bet the
whole 100 dollars?

1:00:57.340 --> 1:01:00.310
Student: Well,
you get better odds,

1:01:00.307 --> 1:01:00.667
so.

1:01:00.670 --> 1:01:02.560
Prof: But would you bet
the whole 100 dollars on the

1:01:02.556 --> 1:01:02.976
first game?

1:01:02.980 --> 1:01:05.920
The guy's only bet 100 dollars
on the whole series.

1:01:05.920 --> 1:01:08.510
Student: You'd bet 80
>

1:01:08.510 --> 1:01:09.000
dollars.

1:01:09.000 --> 1:01:11.450
Prof: So it's not so
obvious what to do,

1:01:11.451 --> 1:01:13.851
right, but he's got exactly the
right idea.

1:01:13.849 --> 1:01:21.419
You can hedge your bet.

1:01:21.420 --> 1:01:22.530
So here we are.

1:01:22.530 --> 1:01:27.270
I shouldn't have put that down.

1:01:27.269 --> 1:01:28.919
Don't tell me I turned it off.

1:01:28.920 --> 1:01:32.880
That would just kill me.

1:01:32.880 --> 1:01:33.830
God, I meant to hit mute.

1:01:33.829 --> 1:01:39.069
I think I hit off.

1:01:39.070 --> 1:01:40.510
Oh, how dumb?

1:01:40.510 --> 1:01:52.460
So you would bet on the--while
that warms up.

1:01:52.460 --> 1:01:56.430
I can see it.

1:01:56.429 --> 1:02:00.579
All right, so what happens is
you'll have a tree which looks

1:02:00.579 --> 1:02:04.589
like this and like this,
like this and like this,

1:02:04.588 --> 1:02:09.688
like this and like this and
let's say we go out a few games

1:02:09.686 --> 1:02:10.826
like this.

1:02:10.829 --> 1:02:14.479
Now, this is a 1,2,
3 game series.

1:02:14.480 --> 1:02:15.290
All right, so I've done it.

1:02:15.289 --> 1:02:18.709
Here's the start of World
Series.

1:02:18.710 --> 1:02:21.350
This is the World Series
spreadsheet you had before.

1:02:21.349 --> 1:02:23.159
Now, here's the start.

1:02:23.159 --> 1:02:29.099
Here's game 1,2, 3,4, 5,6, 7.

1:02:29.099 --> 1:02:39.389
So if the Yankees win the
series they get 100 dollars.

1:02:39.389 --> 1:02:42.039
You get 100 dollars, sorry.

1:02:42.039 --> 1:02:51.189
Oh, what an idiot.

1:02:51.190 --> 1:02:54.990
So every time you end up above
the start, win more than you

1:02:54.985 --> 1:02:56.815
lose, you get 100 dollars.

1:02:56.820 --> 1:03:01.140
On the other hand,
if you lose more than you win

1:03:01.144 --> 1:03:04.184
you lose 100 dollars,
and so ctrl,

1:03:04.181 --> 1:03:05.011
copy.

1:03:05.010 --> 1:03:10.490
Here is losing 100 dollars.

1:03:10.489 --> 1:03:12.739
So now this tree,
remember from doing it before,

1:03:12.744 --> 1:03:14.284
is just by backward induction.

1:03:14.280 --> 1:03:18.800
If you look at this thing up
there it says you get,

1:03:18.800 --> 1:03:24.040
60 percent I think was the
number we figured out over here,

1:03:24.043 --> 1:03:25.223
so right?

1:03:25.219 --> 1:03:27.799
So 60 percent is the
probability of the Yankees

1:03:27.804 --> 1:03:28.764
winning a game.

1:03:28.760 --> 1:03:35.470
So you take any node like this
one you're always taking 60

1:03:35.469 --> 1:03:42.059
percent of the value up here
plus 40 percent of the value

1:03:42.059 --> 1:03:43.119
here.

1:03:43.119 --> 1:03:47.159
So if you do that you find out
that the value to you is 42

1:03:47.155 --> 1:03:49.205
dollars, just what we said.

1:03:49.210 --> 1:03:52.420
So let's put that in the middle
of the screen.

1:03:52.420 --> 1:03:55.340
So the value is 42 dollars.

1:03:55.340 --> 1:03:59.720
Now, if the Yankees win the
first game you're in much better

1:03:59.724 --> 1:04:00.324
shape.

1:04:00.320 --> 1:04:04.130
So winning the first game means
you moved up to this node here.

1:04:04.130 --> 1:04:13.560
All of a sudden you went from
42 dollars to 64 dollars.

1:04:13.559 --> 1:04:18.709
And if the Yankees lost the
first game you would have gone

1:04:18.706 --> 1:04:22.766
down to that value which is like
9 dollars.

1:04:22.768 --> 1:04:25.418
Your expected winnings when the
Yankees are down a game,

1:04:25.420 --> 1:04:27.640
you know, they're still a
better team so actually it's

1:04:27.639 --> 1:04:30.149
more likely even after losing
the first game that the Yankees

1:04:30.150 --> 1:04:31.450
would still win the series.

1:04:31.449 --> 1:04:34.319
So you see the risk that you're
running and you can calculate

1:04:34.324 --> 1:04:34.664
this.

1:04:34.659 --> 1:04:37.829
So what should you do in the
very first game?

1:04:37.829 --> 1:04:41.639
This tells you that your
expected winnings is 42.

1:04:41.639 --> 1:04:50.359
Of course .6 times 64 that's
38.4 .4 times 9 is 3.6.

1:04:50.360 --> 1:04:52.650
That is 42 dollars.

1:04:52.650 --> 1:04:56.610
So that's 42 because it's the
average of this and this,

1:04:56.606 --> 1:05:00.486
and 64 is the average of .6 of
this and .4 of that.

1:05:00.489 --> 1:05:04.009
So what should you do?

1:05:04.010 --> 1:05:06.820
Well, on average you're going
to make 42 dollars.

1:05:06.820 --> 1:05:08.380
What's the essence of hedging?

1:05:08.380 --> 1:05:11.380
You want to guarantee that you
make 42 dollars no matter what

1:05:11.380 --> 1:05:11.880
happens.

1:05:11.880 --> 1:05:15.410
No matter who wins the series
you want to end up with 42 extra

1:05:15.414 --> 1:05:18.894
dollars assuming the interest
rate is 0 from the beginning to

1:05:18.893 --> 1:05:20.403
the end of the series.

1:05:20.400 --> 1:05:22.150
So how can you arrange that?

1:05:22.150 --> 1:05:29.360
What can you do?

1:05:29.360 --> 1:05:31.750
Well, so that's the mystery.

1:05:31.750 --> 1:05:34.240
I'll give you one second to try
and think it through.

1:05:34.239 --> 1:05:36.249
You should get this.

1:05:36.250 --> 1:05:45.930
What would you do here?

1:05:45.929 --> 1:05:51.109
Are there no baseball bookies
in the--yep?

1:05:51.110 --> 1:05:54.350
Student: Didn't we just
bring this up before like with

1:05:54.347 --> 1:05:55.317
our hedge funds?

1:05:55.320 --> 1:05:58.820
Can we put something else aside
that you view at a percentage

1:05:58.822 --> 1:06:02.272
rate that you think you can
trust and then you can trust the

1:06:02.266 --> 1:06:05.416
rest of it to whatever the real
probabilities are?

1:06:05.420 --> 1:06:07.560
Prof: Well,
you can bet with another bookie

1:06:07.559 --> 1:06:08.389
at 60 to 40 odds.

1:06:08.389 --> 1:06:11.629
If the Yankees win the first
game you're just doing great.

1:06:11.630 --> 1:06:15.970
If the Yankees lose the first
game you're looking to be in a

1:06:15.972 --> 1:06:17.742
little bit of trouble.

1:06:17.739 --> 1:06:20.159
So the point is you're not
going to get the payoffs until

1:06:20.161 --> 1:06:22.111
the very end either plus 100 or
minus 100,

1:06:22.110 --> 1:06:24.700
but already by the first game
you're either doing better than

1:06:24.704 --> 1:06:26.784
you were before or worse than
you were before.

1:06:26.780 --> 1:06:28.890
You're already,
in effect, suffering some risk

1:06:28.893 --> 1:06:30.023
at the very beginning.

1:06:30.018 --> 1:06:33.008
So this is one of the great
ideas of finance.

1:06:33.010 --> 1:06:36.210
You shouldn't hedge the final
outcome.

1:06:36.210 --> 1:06:38.230
You should hedge next day's
outcome.

1:06:38.230 --> 1:06:40.680
If you're marking to market
that's what you'd have to do.

1:06:40.679 --> 1:06:44.249
Marking to market you'd have to
say my position now--my bet is

1:06:44.248 --> 1:06:45.358
worth 64 dollars.

1:06:45.360 --> 1:06:48.070
The Yankees lost the first
game, the bet would be worth 9

1:06:48.065 --> 1:06:48.545
dollars.

1:06:48.550 --> 1:06:50.580
So what does it mean to protect
yourself?

1:06:50.579 --> 1:06:53.039
Not just protect yourself
against what's happening at the

1:06:53.041 --> 1:06:54.861
end,
that's really what you want to

1:06:54.864 --> 1:06:57.894
do, but in order to do that you
should protect yourself every

1:06:57.893 --> 1:06:59.563
day against what could happen.

1:06:59.559 --> 1:07:02.589
So every day you should end up
with 42 here and 42 there

1:07:02.594 --> 1:07:05.194
because, after all,
that's what you're trying to

1:07:05.186 --> 1:07:05.846
lock in.

1:07:05.849 --> 1:07:09.109
No matter who wins the first
game you should still say I'm 42

1:07:09.106 --> 1:07:12.036
dollars ahead because I got
myself in this position.

1:07:12.039 --> 1:07:13.829
So how could you do that?

1:07:13.829 --> 1:07:22.489
Well, let's bet at 3 to 2 odds,
right, 60/40 is 3 to 2 odds.

1:07:22.489 --> 1:07:29.159
Let's make a bet with another
bookie at 22 and 33 here.

1:07:29.159 --> 1:07:31.599
So 22--I put it in the wrong
place.

1:07:31.599 --> 1:07:38.359
This is the 33 and this is 22,
but plus 33 and minus 22.

1:07:38.360 --> 1:07:39.870
So what are you doing here?

1:07:39.869 --> 1:07:42.879
Notice that this is 2 times 11,
this is 3 times 11.

1:07:42.880 --> 1:07:44.350
This is 60/40 odds.

1:07:44.349 --> 1:07:46.879
I'm betting on the Phillies.

1:07:46.880 --> 1:07:49.860
If the Phillies win one game I
collect 33 dollars.

1:07:49.860 --> 1:07:51.720
That's what I should do that he
said.

1:07:51.719 --> 1:07:54.859
He said, "Go to the bookie
across the street and bet on one

1:07:54.862 --> 1:07:56.312
game, not the whole series.

1:07:56.309 --> 1:08:00.859
Bet on one game with that
bookie across the street,

1:08:00.860 --> 1:08:04.230
33 dollars versus 22
dollars."

1:08:04.230 --> 1:08:06.550
Let's say you can only bet 1
game at a time with the other

1:08:06.550 --> 1:08:08.160
bookies,
actually, maybe you were saying

1:08:08.161 --> 1:08:09.511
all along bet on the whole
series,

1:08:09.510 --> 1:08:12.380
but let's say you can only bet
one game at a time with the

1:08:12.382 --> 1:08:13.192
other bookies.

1:08:13.190 --> 1:08:16.710
You'd bet 33 dollars on the
Phillies in the first game.

1:08:16.710 --> 1:08:21.080
That naive Philly fan has put
up 100 dollars on the series.

1:08:21.078 --> 1:08:24.568
You're, in the first game,
going to put 33 dollars.

1:08:24.569 --> 1:08:27.109
You've taken his bet so you're
hoping the Yankees win,

1:08:27.106 --> 1:08:29.976
but that's bad to be in a
position where you have to hope.

1:08:29.979 --> 1:08:31.129
You don't want to do that.

1:08:31.130 --> 1:08:34.730
So you take his bet on the
Phillies because he's given you

1:08:34.731 --> 1:08:35.871
100 to 100 odds.

1:08:35.868 --> 1:08:38.338
That's even odds even though
you know the Yankees have a 60

1:08:38.337 --> 1:08:39.527
percent change of winning.

1:08:39.529 --> 1:08:43.079
You go to the bookie across the
street and you bet at 60/40 odds

1:08:43.082 --> 1:08:45.512
on the Phillies,
but you don't bet the whole

1:08:45.507 --> 1:08:45.957
100.

1:08:45.960 --> 1:08:47.910
You only bet 33 dollars of it.

1:08:47.908 --> 1:08:49.858
So if you win you get 33
dollars.

1:08:49.859 --> 1:08:52.279
If you lose you only have to
pay the guy 22.

1:08:52.279 --> 1:08:54.009
So what's going to happen?

1:08:54.010 --> 1:08:58.420
After the first day this
position is going to be worth 42

1:08:58.421 --> 1:09:02.051
and this position is also going
to be worth 42,

1:09:02.046 --> 1:09:04.406
exactly where you started.

1:09:04.408 --> 1:09:09.018
So because a win in the first
game is going to put you so far

1:09:09.018 --> 1:09:13.318
ahead in your bet with the first
naive Philly better,

1:09:13.319 --> 1:09:16.369
and a loss in the first game is
going to put you so far behind,

1:09:16.368 --> 1:09:22.538
you hedge that possibility by
going 33/22 in favor of the

1:09:22.537 --> 1:09:23.747
Phillies.

1:09:23.750 --> 1:09:27.110
You take a big bet on the
Yankees and then you make a

1:09:27.108 --> 1:09:31.178
smaller bet on the Phillies that
cancels out part of the big bet

1:09:31.177 --> 1:09:34.077
on the Yankees,
but you've made the two at

1:09:34.077 --> 1:09:37.477
different odds and so on net
you're still going to be 42

1:09:37.478 --> 1:09:38.528
dollars ahead.

1:09:38.529 --> 1:09:42.329
Let's just pause for a second
and see if you got that.

1:09:42.328 --> 1:09:45.958
So by doing this you can't
possibly lose any money.

1:09:45.960 --> 1:09:49.260
And now you're going to repeat
this bet down here and here.

1:09:49.260 --> 1:09:54.480
So in the next--you see where
do things go next?

1:09:54.479 --> 1:09:57.049
Here you're down 8 dollars.

1:09:57.050 --> 1:10:00.020
If you lost again you'd be down
32 dollars.

1:10:00.020 --> 1:10:01.340
Now things would really be bad.

1:10:01.340 --> 1:10:05.350
After the Yankees lost two
games in a row your original bet

1:10:05.354 --> 1:10:08.404
would look terrible,
but things aren't so bad

1:10:08.400 --> 1:10:11.240
because you bet on the Phillies
here.

1:10:11.239 --> 1:10:14.139
You already made 33 dollars.

1:10:14.140 --> 1:10:19.980
So how much money do you think
you should be betting on the

1:10:19.975 --> 1:10:22.085
Phillies down here?

1:10:22.090 --> 1:10:26.110
Well, you want to lock in 42
dollars at every node no matter

1:10:26.108 --> 1:10:27.128
what happens.

1:10:27.130 --> 1:10:29.920
This 42 dollars,
by making the right offsetting

1:10:29.923 --> 1:10:33.413
bet you can keep 42 everywhere,
here until the very end,

1:10:33.408 --> 1:10:36.898
and so no matter what happened
you can always end up with 42

1:10:36.899 --> 1:10:37.549
dollars.

1:10:37.550 --> 1:10:39.350
That's the essence of hedging.

1:10:39.350 --> 1:10:42.530
So let's just say it again what
the idea is.

1:10:42.529 --> 1:10:44.859
It's a great idea and we don't
have time to go through all the

1:10:44.859 --> 1:10:46.309
details, but the great idea is
this.

1:10:46.310 --> 1:10:49.240
You've made some gigantic bet
with somebody.

1:10:49.239 --> 1:10:51.019
Why do you bet with anybody?

1:10:51.020 --> 1:10:52.740
Because you think you know more
than they do.

1:10:52.738 --> 1:10:55.788
The whole essence of trading
and finance is you think you

1:10:55.789 --> 1:10:58.459
understand the world better than
somebody else.

1:10:58.460 --> 1:11:01.670
So understand it means you
think something's going to turn

1:11:01.671 --> 1:11:05.111
out one way that the other guy
doesn't really know is going to

1:11:05.109 --> 1:11:05.729
happen.

1:11:05.729 --> 1:11:11.039
So you're making a bet on
whether you're right or wrong.

1:11:11.038 --> 1:11:13.318
So when you say you know you
don't know for sure.

1:11:13.319 --> 1:11:16.249
You just have a better idea
than he does,

1:11:16.252 --> 1:11:20.362
so you want to use your idea
without running the risk.

1:11:20.359 --> 1:11:21.529
So how can you do it?

1:11:21.529 --> 1:11:26.129
If your idea is really correct
there may be a way so that you

1:11:26.131 --> 1:11:28.051
can eliminate the luck.

1:11:28.050 --> 1:11:31.180
So here if you really know the
odds are 60/40,

1:11:31.180 --> 1:11:34.060
your class of bookies knows the
odds are 60/40,

1:11:34.060 --> 1:11:36.890
and some other guys who doesn't
know thinks the odds are 50/50

1:11:36.891 --> 1:11:38.611
and is willing to bet against
you,

1:11:38.609 --> 1:11:42.399
you can lock in your 42 dollars
for sure.

1:11:42.399 --> 1:11:45.929
You don't just take a bet and
hope you win.

1:11:45.930 --> 1:11:49.810
You can take a bet and then
hedge it to lock in your profit

1:11:49.814 --> 1:11:51.394
for sure,
step by step,

1:11:51.390 --> 1:11:54.840
and that's what we have to
explain how that dynamic hedging

1:11:54.835 --> 1:11:55.365
works.

1:11:55.369 --> 1:12:05.099
So I have to stop.

1:12:05.100 --> 1:12:10.000