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