WEBVTT 00:00.960 --> 00:06.440 We're talking about the theory of debt and interest rates. 00:06.440 --> 00:09.850 So, I want to talk about a number of technical topics 00:09.850 --> 00:15.240 first. We're going to start with a model, an Irving Fisher 00:15.240 --> 00:22.370 model of interest. And then I'm going to talk about 00:22.370 --> 00:28.270 present values, and discount bonds, compound interest, 00:28.270 --> 00:32.520 conventional bonds, the term structure of interest rates, 00:32.520 --> 00:33.670 and forward rates. 00:33.670 --> 00:35.880 These are all technical things. 00:35.880 --> 00:39.360 And then, I want to get back and think about what really 00:39.360 --> 00:41.060 goes on in debt markets. 00:44.020 --> 00:45.920 There's two assignments for this lecture. 00:45.920 --> 00:52.610 One is several chapters out of the Fabozzi et al. manuscript. 00:52.610 --> 00:55.500 And then, there's a chapter from my forthcoming book that 00:55.500 --> 00:59.220 I'm currently writing, but that is the most meager 00:59.220 --> 01:01.890 chapter that I've given you yet. 01:01.890 --> 01:08.140 The book is not done, so I think the real reference for 01:08.140 --> 01:10.880 this is the Fabozzi et al. 01:10.880 --> 01:12.380 manuscript, at this point. 01:18.260 --> 01:22.240 And then, Oliver will give a TA section that will clarify, 01:22.240 --> 01:24.140 I think, some of the points. 01:24.140 --> 01:29.100 So anyway, what we're talking about today is interest rates. 01:29.100 --> 01:33.200 The percent that you earn on a loan, or that you pay on a 01:33.200 --> 01:36.120 loan, depending on what side of it you are. 01:36.120 --> 01:39.750 And interest rates go back thousands of years. 01:39.750 --> 01:41.350 It's an old idea. 01:43.870 --> 01:49.710 Typically, it's a few percent a year, right? 01:49.710 --> 01:53.050 The first question we want to try to think about is what 01:53.050 --> 01:54.000 explains that. 01:54.000 --> 01:57.100 Why is it a few percent a year? 01:57.100 --> 01:58.910 And why not something completely different? 02:05.710 --> 02:07.920 And why is it even a positive number? 02:07.915 --> 02:12.585 Do you ever think of negative interest rates? 02:12.590 --> 02:15.880 Well, these are basic questions. 02:15.880 --> 02:21.500 So, I wanted to start with the history of thought and an 02:21.500 --> 02:28.120 economist from the 19th century, Eugen von 02:28.120 --> 02:37.570 Boehm-Bawerk, who wrote a book on the theory of interest in 02:37.570 --> 02:39.720 the late nineteen century. 02:39.720 --> 02:44.050 Actually it was 1884. 02:44.050 --> 02:52.140 And it's a long, very verbose account of what causes 02:52.140 --> 02:54.180 interest rates. 02:54.180 --> 02:58.000 But basically, he came up with three explanations. 02:58.000 --> 03:02.990 Why is the interest rate something like 5%, or 3%, or 03:02.990 --> 03:06.110 7%, or something in that range? 03:06.110 --> 03:09.570 And he said, there's really three causes. 03:09.570 --> 03:12.300 One of them is technical progress. 03:12.300 --> 03:16.440 That, as the economy gets more and more scientific 03:16.440 --> 03:19.540 information about how to do things, things get more 03:19.540 --> 03:20.550 productive. 03:20.550 --> 03:24.700 So, maybe the 3% percent, or the 5%, whatever it is, is the 03:24.700 --> 03:26.310 rate of technical progress. 03:26.310 --> 03:31.470 That's how fast technology is improving. 03:31.470 --> 03:33.820 But that's not the only cause that von 03:33.820 --> 03:36.700 Boehm-Bawerk talked about. 03:36.700 --> 03:43.310 Another one was advantages to roundaboutness. 03:43.310 --> 03:46.350 That must be some translation from his German. 03:46.350 --> 03:51.040 But the idea is that more roundabout production is more 03:51.040 --> 03:51.550 productive. 03:51.550 --> 03:54.380 This isn't technical progress. 03:54.380 --> 03:58.760 If someone can ask you to make something directly right now, 03:58.760 --> 04:02.130 you've got to use the simplest and the most direct way to do 04:02.130 --> 04:03.800 it, if you're going to do it right now. 04:03.800 --> 04:06.070 But if you have time, you can do it in a 04:06.070 --> 04:06.910 more roundabout way. 04:06.910 --> 04:10.530 You can make tools first and do something else that makes 04:10.529 --> 04:13.169 you a more efficient producer of this. 04:13.170 --> 04:16.420 And so, maybe the interest rate is a measure of the 04:16.420 --> 04:20.420 advantages to roundaboutness. 04:20.420 --> 04:24.540 And the third cause that von Boehm-Bawerk gave is time 04:24.540 --> 04:25.870 preference. 04:25.870 --> 04:28.770 That people just prefer the present over the future. 04:28.770 --> 04:30.710 They're impatient. 04:30.710 --> 04:32.930 This is behavioral economics, I suppose. 04:32.930 --> 04:34.520 This is psychology. 04:34.520 --> 04:38.350 That, you know, you've got a box of candy sitting there. 04:38.350 --> 04:41.580 And you're looking at it and you're saying, well, I should 04:41.580 --> 04:44.040 really enjoy that next year. 04:44.040 --> 04:45.860 Well, maybe it would spoil by next year. 04:45.860 --> 04:46.920 Next month. 04:46.920 --> 04:48.800 But somehow you don't. 04:48.800 --> 04:51.520 You have an impulse to consume now. 04:51.520 --> 04:54.440 So, maybe the rate of interest is the rate of time 04:54.440 --> 04:55.690 preference. 04:57.700 --> 04:59.330 Why is the interest rate 5%? 04:59.330 --> 05:03.110 It's because people are 5% happier to get something now 05:03.110 --> 05:06.230 than to get it in the future. 05:06.230 --> 05:11.190 So, he left that train of thought for us. 05:11.190 --> 05:14.010 This was not Mathematical Economics. 05:14.010 --> 05:19.000 It was Literary Economics. 05:19.000 --> 05:25.990 But the next person I want to mention in the history of 05:25.990 --> 05:34.720 thought is Irving Fisher, who was a professor at Yale 05:34.720 --> 05:35.890 University. 05:35.890 --> 05:47.970 But he wrote a book in 1930 called The Theory of Interest. 05:47.970 --> 05:53.050 And it is the all-time classic, I 05:53.050 --> 05:58.130 think, on this topic. 05:58.130 --> 06:02.560 So, Irving Fisher is talked about in your textbook by 06:02.560 --> 06:03.700 Fabozzi et al. 06:03.700 --> 06:08.060 He's talked about in many textbooks. 06:08.060 --> 06:10.660 He graduated from Yale. 06:10.660 --> 06:12.380 I mention this, since you're Yale undergrads. 06:12.380 --> 06:13.790 He was a Yale undergrad. 06:13.786 --> 06:18.316 He graduated, maybe it was in 1885. 06:18.320 --> 06:22.390 And he got the first Economics Ph.D. at Yale University in 06:22.390 --> 06:24.190 the 1890's. 06:24.190 --> 06:27.480 And he just stayed here in New Haven all his life. 06:27.480 --> 06:31.730 And if you were living in New Haven in the early twentieth 06:31.730 --> 06:36.930 century, you'd know him because he was a jogger. 06:36.930 --> 06:38.160 Nobody else jogged. 06:38.160 --> 06:41.300 He would exercise and run around campus, so everyone 06:41.300 --> 06:42.700 would see him. 06:42.700 --> 06:45.930 In the 1910's or '20's, nobody did that. 06:45.930 --> 06:46.620 But he did. 06:46.620 --> 06:51.500 He was a health nut, among other things. 06:51.500 --> 06:53.860 I could talk a lot about him, he's a fascinating guy. 06:53.860 --> 06:56.020 I'll tell you one more story about him. 06:56.020 --> 06:59.100 He would invite students to his house for dinner. 06:59.100 --> 07:02.960 And he would explain to them before dinner that he believed 07:02.960 --> 07:08.010 that proper eating required that you chew every bite 100 07:08.010 --> 07:09.960 times before you swallow it. 07:09.960 --> 07:12.310 So, he would tell his students to do that. 07:12.310 --> 07:14.350 And it slowed down conversation at 07:14.350 --> 07:16.130 dinner a great deal. 07:16.125 --> 07:17.705 But that's not what he's known for. 07:17.710 --> 07:20.870 What he's known for is, among other things, his theory of 07:20.870 --> 07:25.130 interest. So, this is what's talked about in your textbook 07:25.130 --> 07:30.310 and I wanted to start out with Irving Fisher because -- 07:30.310 --> 07:32.710 by the way, I don't know when this room was built. 07:32.705 --> 07:35.345 Does anyone know? 07:35.350 --> 07:36.450 Because he died in '47. 07:36.450 --> 07:41.560 He probably lectured from this same blackboard, right? 07:41.560 --> 07:44.620 So, I don't know, this same slate, it could be, right? 07:44.620 --> 07:46.310 It could go back to that time. 07:46.310 --> 07:49.490 So, I'm going to put back on the board what he had on this 07:49.490 --> 07:58.920 board, I'm assuming in some time in the 1930's. 07:58.920 --> 08:02.020 What your author, your textbook author, Fabozzi, 08:02.020 --> 08:05.600 emphasizes for a theory of interest is something that 08:05.600 --> 08:08.800 came from Fisher that's very simple. 08:08.800 --> 08:12.630 And he says, the interest rate -- 08:12.630 --> 08:15.900 this is Fabozzi's distillation of Irving Fisher -- 08:15.900 --> 08:21.810 the interest rate is the intersection of a supply and 08:21.810 --> 08:24.660 demand curve for savings. 08:24.659 --> 08:29.019 So, I'm going to put saving, s, on this axis. 08:29.020 --> 08:31.990 And on this axis, I'm going to put the interest 08:31.990 --> 08:35.120 rate, call that r. 08:35.120 --> 08:38.700 I don't know why we commonly use r for interest. It's not 08:38.700 --> 08:41.780 the first letter, it's in the middle of the word. 08:41.780 --> 08:47.110 And the idea is that there's a supply of saving at any time. 08:47.110 --> 08:50.630 That people then wish to put in the bank or someplace else 08:50.630 --> 08:55.250 to earn interest. And the theory is that the higher the 08:55.250 --> 08:58.410 interest rate, the more people will save. So, we have an 08:58.410 --> 09:00.920 upward-sloping supply curve. 09:00.920 --> 09:04.520 Now this S means supply, whereas this S 09:04.520 --> 09:07.620 down here means saving. 09:07.620 --> 09:13.600 And then there's a demand for investment capital, right? 09:13.600 --> 09:18.400 The bank lends out your savings to businesses, and the 09:18.400 --> 09:20.700 businesses want to know what the interest rate is. 09:20.700 --> 09:26.050 The lower the interest rate, the more they'll demand. 09:26.050 --> 09:32.010 So, we have a demand curve for saving. 09:32.010 --> 09:37.460 And then the intersection of the two is the interest rate. 09:37.460 --> 09:39.470 Well, it gives the interest rate on this axis and the 09:39.470 --> 09:41.530 amount of saving on the other axis. 09:41.530 --> 09:44.440 That's a very simple story. 09:44.440 --> 09:46.740 And that's what Fabozzi et al. 09:46.740 --> 09:48.400 covers in your text. 09:48.400 --> 09:52.470 But I wanted to go back to another diagram that Fabozzi 09:52.470 --> 09:55.420 et al. did not include in your textbook, but it also comes 09:55.420 --> 10:07.480 from the 1930 book, The Theory of Interest. That is a diagram 10:07.480 --> 10:10.590 that shows a two-period story. 10:10.590 --> 10:14.340 And the thing I liked about this two-period diagram is 10:14.340 --> 10:18.670 that it brings out the von Boehm-Bawerk causes of 10:18.670 --> 10:22.550 interest rate in a very succinct way. 10:22.550 --> 10:25.360 So, this is the second Irving Fisher diagram. 10:29.840 --> 10:32.180 I'm going to do a little story telling about this. 10:32.180 --> 10:34.180 Remember the book, Robinson Crusoe. 10:34.175 --> 10:37.885 It was written by Jonathan Swift in the 1700's. 10:37.890 --> 10:41.310 It was the story of a man named Robinson Crusoe, who was 10:41.310 --> 10:48.420 marooned on an island all by himself and had to live on his 10:48.420 --> 10:50.650 own with no help. 10:50.650 --> 10:54.140 This is a famous story called a Robinson Cruise economy. 10:54.140 --> 10:57.300 There's only one person in the economy, so, of course, 10:57.296 --> 10:59.026 there's no trade. 10:59.025 --> 11:03.055 But we'll move to a little bit of trade. 11:03.060 --> 11:05.060 I'm just telling you a story of the rate of -- there'll be 11:05.060 --> 11:07.200 a rate of interest on Robinson Crusoe's island. 11:12.275 --> 11:18.345 I'm going to show here consumption today. 11:23.510 --> 11:29.140 And on this axis, consumption next year. 11:32.968 --> 11:34.218 All right. 11:36.350 --> 11:37.690 I don't remember the novel. 11:37.690 --> 11:39.240 Did anyone here read it? 11:39.240 --> 11:41.910 Somebody must have read Robinson Crusoe. 11:41.910 --> 11:45.520 But I'm not going to be true to the story. 11:45.520 --> 11:48.050 The story I'm going to tell is that Robinson 11:48.050 --> 11:51.450 Crusoe has some food. 11:51.450 --> 11:53.710 That's all that the whole economy just does. 11:53.710 --> 11:55.180 Let's say it's grain. 11:55.180 --> 11:56.850 I don't know how he got that on the island. 11:56.850 --> 11:58.060 But he's got grain. 11:58.060 --> 12:01.080 And he's deciding how much to eat this year, and how much to 12:01.080 --> 12:03.080 plant for next year. 12:03.080 --> 12:06.810 So, the total amount of grain he has is right here. 12:06.810 --> 12:10.960 So, that is his endowment of grain. 12:10.960 --> 12:12.900 That's the maximum he could eat. 12:12.900 --> 12:17.010 But if he eats it all, there won't be any grain to plant 12:17.010 --> 12:19.810 for next year, OK? 12:19.810 --> 12:24.920 So, he better not eat it all, or he'll starve next year. 12:24.920 --> 12:29.310 Now, in a simple linear production -- 12:29.310 --> 12:34.420 with technology that's linear, he can choose to set aside a 12:34.420 --> 12:37.270 certain amount of grain, which is the difference between what 12:37.270 --> 12:40.820 he has and what he's consuming. 12:40.820 --> 12:43.560 And then that will produce grain next period. 12:43.560 --> 12:46.690 So, I'm going to draw a straight line. 12:46.690 --> 12:48.470 That's supposed to be a straight line. 12:48.470 --> 12:50.560 These are all supposed to be straight lines here. 12:56.560 --> 13:02.740 And that is his choice set under linear technology. 13:02.740 --> 13:07.990 I'm drawing it with no decreasing returns. 13:07.990 --> 13:14.420 The idea is that for every bushel of grain that he 13:14.420 --> 13:17.750 plants, he gets two bushels next year, or 13:17.750 --> 13:20.420 whatever it is, OK? 13:20.420 --> 13:24.190 And so, if he were to consume nothing this period, 13:24.190 --> 13:26.200 he would have -- 13:26.200 --> 13:30.650 if I drew this thing with the right slope of minus 2 -- 13:30.650 --> 13:32.400 he would have twice as much. 13:32.400 --> 13:35.790 This is the maximum he could have next period, OK? 13:35.790 --> 13:38.250 And so, he could consume anywhere along this line. 13:41.960 --> 13:47.860 And this would be the simplest Robinson Crusoe economy. 13:47.860 --> 13:49.890 So, what does he do? 13:49.890 --> 13:53.500 Remember from elementary micro theory, he has indifference 13:53.500 --> 13:55.730 curves between consumption today 13:55.730 --> 13:57.340 and consumption tomorrow. 13:57.340 --> 13:58.430 Remember these? 13:58.430 --> 14:00.890 These are like contours of his utility. 14:00.885 --> 14:02.785 And we typically draw them like this. 14:06.890 --> 14:07.520 So, what does he do? 14:07.520 --> 14:13.180 He maximizes his utility and chooses a point with the 14:13.180 --> 14:16.150 highest indifference curve touching the production 14:16.150 --> 14:18.240 possibility frontier. 14:18.240 --> 14:21.130 This is the PPF, the 14:21.130 --> 14:23.970 production possibility frontier. 14:23.970 --> 14:27.470 And that determines the amount that he consumes and the 14:27.470 --> 14:28.310 amount that he saves. 14:28.310 --> 14:31.450 And he consumes this amount here. 14:31.450 --> 14:35.490 And the difference between his endowment and his consumption 14:35.490 --> 14:38.420 is his saving. 14:38.420 --> 14:42.660 And then next period, he consumes this amount. 14:42.660 --> 14:44.910 All right, that's simple micro theory. 14:44.910 --> 14:46.160 That's familiar to you? 14:50.410 --> 14:53.290 So, in this case the interest rate, the slope 14:53.290 --> 14:54.610 of this line -- 14:54.605 --> 15:01.805 this slope is equal to minus 1 plus r where r is 15:01.810 --> 15:03.800 the interest rate. 15:03.800 --> 15:05.930 So, in this case, I've told a very simple story. 15:05.930 --> 15:08.920 It has only one von Boehm-Bawerk cause, its 15:08.920 --> 15:09.960 roundaboutness. 15:09.960 --> 15:13.810 But maybe there's technical progress, too, I don't know. 15:13.810 --> 15:16.730 It has maybe a couple of his causes. 15:16.730 --> 15:20.630 If, as time goes by, Robinson Crusoe figures out better how 15:20.630 --> 15:22.780 to grow grain, there could be a 15:22.780 --> 15:26.190 technical progress component. 15:26.190 --> 15:29.770 But preferences don't matter in this story, the preferences 15:29.770 --> 15:32.330 I represented by his indifference curves. 15:32.330 --> 15:35.260 And since I've got a linear production possibility 15:35.260 --> 15:39.570 frontier, impatience doesn't matter. 15:39.570 --> 15:45.150 The interest rate in this case is decided by the technology, 15:45.150 --> 15:47.090 the slope of the curve. 15:47.090 --> 15:49.620 So, we don't have all of von Boehm-Bawerk causes yet. 15:52.900 --> 15:53.840 Next step. 15:53.840 --> 15:57.030 That was the simplest Irving Fisher story. 15:57.030 --> 16:00.890 The next step is, let's suppose, however, that there 16:00.890 --> 16:04.930 are diminishing returns to investment in grain. 16:04.930 --> 16:08.620 That means, for example, maybe when he grows a little bit of 16:08.620 --> 16:12.200 it he's very good at it and he produces a big crop. 16:12.200 --> 16:15.510 But as he tries to grow more grain, he gets less 16:15.510 --> 16:15.950 productive. 16:15.950 --> 16:18.460 Maybe he has to do it on the worst land or he's running out 16:18.460 --> 16:21.370 of water, or something is not going right. 16:21.370 --> 16:24.120 Then we would change the production possibility 16:24.120 --> 16:28.020 frontier, so that it concaves down. 16:31.280 --> 16:33.490 Something like that. 16:33.490 --> 16:34.180 You see what I'm saying? 16:34.180 --> 16:35.850 Diminishing returns to investment. 16:38.480 --> 16:42.500 As you keep trying to add more and more grain to your 16:42.500 --> 16:47.880 production, as you save more and more, you get less and 16:47.880 --> 16:50.250 less return. 16:50.250 --> 16:52.420 So now, we have a new production possibility 16:52.420 --> 16:58.720 frontier that is more complicated. 16:58.720 --> 17:00.510 So now, what happens? 17:00.510 --> 17:04.160 Forget this straight line, which I drew first, and now 17:04.160 --> 17:07.990 consider a new production possibility frontier that's 17:07.990 --> 17:09.600 curved downward. 17:09.599 --> 17:11.929 Well, what does Robinson Crusoe do? 17:11.930 --> 17:16.500 Well, Robinson Crusoe picks the highest indifference curve 17:16.500 --> 17:20.460 that touches this production possibility frontier. 17:20.460 --> 17:23.390 So, that means he finds an indifference curve that's 17:23.390 --> 17:25.560 tangent to it. 17:25.560 --> 17:27.950 And he chooses that point. 17:27.950 --> 17:29.200 OK? 17:32.880 --> 17:35.890 So, this is what Robinson Crusoe would do. 17:35.890 --> 17:42.380 Now, the interest rate is the slope of the tangency between 17:42.375 --> 17:44.135 the indifference curve and the 17:44.140 --> 17:46.970 production possibility frontier. 17:46.970 --> 17:48.630 It's the same for both. 17:48.630 --> 17:52.400 And this was the insight that von Boehm-Bawerk maybe had a 17:52.400 --> 17:55.060 little trouble getting. 17:55.060 --> 17:57.660 There's two different things determining the interest rate. 17:57.660 --> 18:02.390 One of them is the production possibility frontier, and the 18:02.390 --> 18:04.780 other one is the indifference curves. 18:04.780 --> 18:08.880 Now, we have all of von Boehm-Bawerk causes. 18:08.880 --> 18:13.640 We've got roundaboutness, we have technical progress, and 18:13.640 --> 18:15.270 we have impatience. 18:15.270 --> 18:20.730 Well, the impatience would be reflected by the slope of the 18:20.730 --> 18:22.990 indifference curves. 18:22.990 --> 18:24.330 So, let me put it this way. 18:24.330 --> 18:30.790 Suppose Robinson Crusoe really wanted to consume a lot today. 18:30.790 --> 18:33.270 He was very impatient. 18:33.270 --> 18:36.910 That means that his indifference curves -- 18:36.910 --> 18:39.440 did you give me colored chalk? 18:39.440 --> 18:41.420 STUDENT: There's a little bit of yellow. 18:41.420 --> 18:43.680 PROFESSOR ROBERT SHILLER: Oh, we have a little yellow. 18:43.675 --> 18:46.045 All right. 18:46.050 --> 18:49.380 Suppose Robinson Crusoe is very impatient. 18:49.380 --> 18:50.370 He wants to consume. 18:50.370 --> 18:53.140 Now, he doesn't care about the future. 18:53.140 --> 18:57.420 Then, his indifference curves might look -- 18:57.420 --> 18:59.060 I'll just draw a tangency -- 18:59.060 --> 19:00.770 his indifference might look different. 19:00.770 --> 19:02.450 They might look like this. 19:05.270 --> 19:07.960 So, he would have a tangency further to the right, 19:07.960 --> 19:11.000 consuming more today and less in the future. 19:13.790 --> 19:15.830 Now, the slope here is different than 19:15.830 --> 19:17.900 the slope here, right? 19:17.900 --> 19:20.350 Because I haven't changed the production possibility 19:20.350 --> 19:22.990 frontier but I've moved to a different point on the 19:22.990 --> 19:25.380 production possibility frontier. 19:25.380 --> 19:29.670 So, you can see that if Robinson Crusoe becomes more 19:29.670 --> 19:34.900 impatient, his interest rate goes up. 19:34.900 --> 19:37.390 Now you understand that the interest rate in the Robinson 19:37.390 --> 19:42.160 Crusoe economy is not just about Robinson Crusoe. 19:42.160 --> 19:44.960 Even though there's only one person in this economy, it's 19:44.960 --> 19:50.290 about all of Eugen von Boehm-Bawerk's causes. 19:50.290 --> 19:53.190 The technology is represented by the technical progress and 19:53.190 --> 19:56.240 the roundaboutness, and the preferences are represented by 19:56.240 --> 19:59.560 the indifference curves. 19:59.560 --> 20:04.580 And you can see that the actual rate of interest in his 20:04.580 --> 20:10.790 economy is determined by the tangency. 20:10.790 --> 20:13.510 Now on the other hand, suppose Robinson Crusoe were very 20:13.510 --> 20:16.810 patient and really wants to live for the future. 20:16.810 --> 20:20.640 Then the highest indifference curve that touches the 20:20.640 --> 20:22.380 production possibility frontier might 20:22.380 --> 20:26.210 get up here, right? 20:26.210 --> 20:29.170 Now that's another Robinson Crusoe with a different 20:29.170 --> 20:31.860 personality who's more patient. 20:31.860 --> 20:37.720 Then the tangency would be up here and the interest rate 20:37.720 --> 20:43.350 would be much lower, because the interest rate would be the 20:43.350 --> 20:47.940 slope of the line that goes through that tangency point, 20:47.940 --> 20:53.160 tangent to both the indifference curve and the 20:53.160 --> 20:55.930 production possibility frontier. 20:55.930 --> 20:57.940 So. this is just a one-person economy. 20:57.935 --> 21:01.275 Is this clear? 21:01.280 --> 21:02.970 So, I've drawn a lot of lines, maybe I should 21:02.970 --> 21:04.220 start all over again. 21:08.100 --> 21:10.760 We've now gotten all of von Boehm-Bawerk's causes of 21:10.760 --> 21:15.870 interest. And we've got an interest rate. 21:15.870 --> 21:20.080 We've tied it to production -- 21:20.080 --> 21:22.790 technology, represented by the production possibility 21:22.790 --> 21:26.100 frontier, and taste, represented by the 21:26.100 --> 21:28.220 indifference curve. 21:28.220 --> 21:31.280 But now I want to add a person to the economy. 21:31.275 --> 21:34.335 So, let me start all over again. 21:34.340 --> 21:38.300 There's two Robinson Crusoes in this island. 21:38.300 --> 21:41.160 And let's start out with autonomy. 21:41.160 --> 21:42.890 They haven't discovered each other yet. 21:42.890 --> 21:44.680 They're on opposite sides of the island. 21:47.540 --> 21:49.460 They have the same technology. 21:49.460 --> 21:52.950 They have the same production possibility frontier, but they 21:52.950 --> 21:56.830 live on opposite sides of the island, and they don't trade 21:56.826 --> 21:57.516 with each other. 21:57.520 --> 21:59.400 So, let me start out again. 21:59.396 --> 22:01.966 This is the same diagram. 22:01.970 --> 22:09.040 We have consumption today, and consumption next year, again. 22:09.040 --> 22:13.360 And we have a production possibility frontier. 22:13.360 --> 22:15.300 That's the same curve that I drew before. 22:15.300 --> 22:18.520 And the technology is the same for both of them. 22:18.520 --> 22:21.090 And let's suppose they have the same endowment. 22:21.090 --> 22:27.340 But let's suppose that Crusoe A is very patient, and Crusoe 22:27.340 --> 22:30.220 B is very impatient. 22:30.220 --> 22:36.990 So, Crusoe A, his indifference curves form a 22:36.990 --> 22:38.880 tangency down here. 22:38.876 --> 22:42.636 So, this is A. And Crusoe B's indifference 22:42.640 --> 22:45.680 curves are up here. 22:45.676 --> 22:52.586 This is B. And so, they are planning to plant. 22:52.590 --> 22:56.450 That means that Crusoe A will be saving very little. 22:56.450 --> 22:57.830 I mean, will be consuming a lot. 23:00.350 --> 23:03.700 A is the impatient one, the way I've drawn it. 23:03.700 --> 23:07.160 Consuming a lot now and not saving much for the future, 23:07.160 --> 23:09.150 but is maximizing his utility. 23:09.150 --> 23:12.070 That's why we have the highest indifference curve shown here 23:12.070 --> 23:13.830 with this tangent. 23:13.830 --> 23:18.980 And Crusoe B is the very patient one. 23:18.980 --> 23:22.700 And is consuming very little this year and plans to consume 23:22.700 --> 23:25.040 a lot next year. 23:25.040 --> 23:26.800 So, let's say they're about to plant, 23:26.800 --> 23:28.210 according to these tastes. 23:28.210 --> 23:29.970 And then they find each other. 23:29.970 --> 23:32.490 Now, they realize, there's two of us on this island. 23:32.490 --> 23:36.000 Now, we're getting a real economy with two people. 23:36.000 --> 23:39.570 So, what should they do? 23:39.570 --> 23:42.790 Well, the obvious thing is that there are gains to trade. 23:42.790 --> 23:45.970 And the kind of trade would be in the loan market. 23:51.740 --> 23:56.390 This Crusoe B is suffering a lot of diminishing returns to 23:56.390 --> 23:57.920 production. 23:57.920 --> 24:01.480 So, he really shouldn't be planting so much grain, 24:01.480 --> 24:03.570 because he's not getting much return for it. 24:03.570 --> 24:06.380 Whereas this other guy on the other side of the island has 24:06.380 --> 24:10.720 very high productivity. 24:10.720 --> 24:13.220 He can produce a lot for a little bit of grain. 24:13.220 --> 24:18.220 So, he should tell Crusoe A, you should plant some of this 24:18.220 --> 24:20.880 grain for me. 24:20.880 --> 24:22.130 You are more productive, because you're 24:22.130 --> 24:24.000 not doing as much. 24:24.000 --> 24:29.640 Well, in short, what will happen is, they'll do it 24:29.640 --> 24:30.970 through a loan. 24:30.970 --> 24:32.610 I will loan you so much grain. 24:32.610 --> 24:33.860 There's no money. 24:36.230 --> 24:37.610 A wants to consume a lot. 24:37.610 --> 24:45.020 So, B will say, instead of planting so much, we'll strike 24:45.020 --> 24:49.670 a loan to allow you to consume along your tastes. 24:49.670 --> 24:52.420 And what will happen in the economy is, we'll find an 24:52.420 --> 24:55.660 interest rate for the economy that looks something -- 24:55.656 --> 24:58.666 I'm going to draw a tangency. 24:58.670 --> 25:02.580 Like, that's supposed to be a straight line. 25:02.580 --> 25:09.350 And on this tangent line, we have Crusoe B has maximized 25:09.350 --> 25:13.670 his utilitiy subject to that tangent line constraint. 25:13.670 --> 25:20.730 And Crusoe A maximized his utility subject to the same 25:20.730 --> 25:23.210 constraint. 25:23.210 --> 25:27.800 And it has to be such a way that the borrowing market as 25:27.800 --> 25:30.510 shown over here clears. 25:30.510 --> 25:34.970 And when we have that kind of equilibrium, you can see that 25:34.970 --> 25:41.020 both A and B have achieved higher utility than they did 25:41.020 --> 25:43.020 when they didn't trade. 25:43.020 --> 25:47.530 So, this is the function of a lending market. 25:47.530 --> 25:53.170 So, A who wants to -- did I say that right? 25:53.170 --> 25:56.430 A, who wants to consume a lot this period -- 25:56.430 --> 25:58.970 the production point is here. 25:58.970 --> 26:03.410 And B lends this amount of consumption to A, so that A 26:03.410 --> 26:05.420 can consume a lot. 26:05.420 --> 26:08.490 He can consume this much. 26:08.490 --> 26:12.330 And B, since he's lent it to A, consumes only this much 26:12.330 --> 26:14.370 this period. 26:14.371 --> 26:16.491 But you see they're both better off. 26:16.490 --> 26:20.150 They've both achieved a higher utility. 26:23.520 --> 26:25.570 And what is the interest rate in the economy? 26:25.570 --> 26:29.160 The interest rate is the slope of this line. 26:29.160 --> 26:32.800 Well, the slope of this line is minus 1 plus 26:32.795 --> 26:35.345 the interest rate. 26:35.350 --> 26:39.430 So, that is the Fisher theory of interest. 26:39.430 --> 26:41.430 And now, it's much more complicated. 26:41.430 --> 26:44.090 You can see how all of Eugene von Boehm-Bawerk's 26:44.090 --> 26:46.770 causes play a role. 26:46.770 --> 26:50.860 But the interest rate is not something you could have read 26:50.860 --> 26:54.530 off from any one person's utility. 26:54.530 --> 26:57.210 It's not just impatience. 26:57.210 --> 26:58.810 We're both complicated people. 26:58.810 --> 27:01.340 We both have a whole set of indifference curves. 27:01.340 --> 27:05.510 And it's not necessarily easy to define whether or how 27:05.510 --> 27:09.380 impatient am I. It interacts with the production 27:09.380 --> 27:12.920 possibility frontier in a complicated way to produce a 27:12.920 --> 27:14.750 market interest rate. 27:14.750 --> 27:19.870 So, this is the model for the interest of the economy that 27:19.870 --> 27:22.350 Irving Fisher developed. 27:22.350 --> 27:25.400 And so, I wanted to just take that as a given. 27:25.400 --> 27:30.380 Now, when you put it this way, it all looks indisputable that 27:30.380 --> 27:32.450 the loan market is a good thing, right? 27:35.850 --> 27:39.630 I can't think of any criticism of the two Robinson Crusoes 27:39.630 --> 27:42.480 going together and making a loan. 27:42.480 --> 27:46.020 There's nothing bad about this loan, right? 27:46.020 --> 27:50.000 They're just both consuming more as a result. 27:50.000 --> 27:53.370 But I want to come back to criticisms of lending at the 27:53.370 --> 27:57.610 end of this lecture, because I want to try to make this 27:57.610 --> 28:00.280 course into something that talks about the purpose of 28:00.280 --> 28:03.270 finance and the real purpose of finance. 28:03.270 --> 28:07.880 And this story is not the whole story about real people 28:07.880 --> 28:10.720 and how they interact with the lending market. 28:10.720 --> 28:16.460 But before I do that, though, I want to do some arithmetic 28:16.460 --> 28:19.720 of finance. 28:19.715 --> 28:25.405 Let me move on to what I said I would talk about, mainly 28:25.410 --> 28:29.420 different kinds of bonds and present values. 28:29.420 --> 28:34.230 The Irving Fisher story was very simple, and it had only 28:34.230 --> 28:35.750 two periods. 28:35.750 --> 28:45.400 So, that's too simple for our purposes. 28:45.400 --> 28:50.670 So, what I want to talk about now is different kinds of loan 28:50.670 --> 28:52.490 instruments. 28:52.490 --> 28:55.680 And the first and the simplest is the discount bond. 29:01.180 --> 29:05.070 When you make a loan to someone, you could do it 29:05.070 --> 29:09.220 between a company or between a government and someone. 29:09.220 --> 29:14.080 A discount bond pays a fixed amount at a future date, and 29:14.080 --> 29:16.250 it sells at a discount today. 29:16.250 --> 29:21.820 It pays no interest. I mean it doesn't have annual interest 29:21.820 --> 29:22.410 or anything like that. 29:22.410 --> 29:27.100 It merely specifies this bond is worth so many dollars or 29:27.100 --> 29:31.280 euros as of a future date. 29:31.280 --> 29:32.710 And why would you buy it? 29:32.710 --> 29:35.410 Because you pay less than that amount. 29:35.410 --> 29:47.220 So, let's say that it's worth $100 in T periods. 29:47.220 --> 29:50.170 T years. 29:50.170 --> 29:53.560 I'll say T years. 29:53.560 --> 30:02.540 And I made that a capital T. So, what is a discount bond 30:02.540 --> 30:03.980 worth today? 30:03.980 --> 30:07.730 Now, we have an issue of compounding, which I want to 30:07.730 --> 30:10.590 come to in a minute, but let's assume, first of all, that 30:10.590 --> 30:12.420 we're using annual 30:12.420 --> 30:14.250 compounding, and T is in years. 30:19.570 --> 30:26.650 Then, the price of the discount bond today, the price 30:26.650 --> 30:37.120 today, is equal to $100 all over 1 plus 30:37.120 --> 30:40.280 r to the T-th power. 30:40.280 --> 30:45.290 Where T is the number of years to maturity. 30:45.290 --> 30:47.420 T years to maturity. 30:56.270 --> 31:05.280 And that's the formula. 31:05.280 --> 31:14.280 In other words, 1 plus r to the T-th power is equal to 100 31:14.280 --> 31:23.340 over P. So 100 over P is the ratio of my final value to my 31:23.340 --> 31:26.830 initial investment value if I invest in a discount bond. 31:26.830 --> 31:30.280 And I want to convert that to an annual interest rate. 31:30.280 --> 31:37.430 So, this is the formula that allows me to do that. 31:37.430 --> 31:45.390 So, r is also called yield to maturity. 31:45.390 --> 31:49.500 And the maturity is T, the time when the 31:49.500 --> 31:51.340 discount bond matures. 31:51.340 --> 31:56.320 So, it says if it's paying an interest rate, r, once per 31:56.320 --> 31:57.820 year for T years -- 32:02.800 --> 32:06.060 We can infer an interest rate on it even though the bond 32:06.060 --> 32:09.470 itself has a price, not an interest rate. 32:09.470 --> 32:11.520 I mean, we can calculate the interest rate 32:11.520 --> 32:12.770 by using this formula. 32:19.660 --> 32:22.960 Now, let me come back to compounding. 32:22.960 --> 32:26.400 This is elementary, but let me just talk about putting money 32:26.400 --> 32:29.190 in the bank here. 32:29.190 --> 32:30.490 So, compounding. 32:35.780 --> 32:41.420 If you have annual compounding, and you have an 32:41.420 --> 32:45.660 interest rate of r, and you put your money in the bank 32:45.660 --> 32:50.170 with annual compounding, and the interest rate is r, that 32:50.170 --> 32:52.980 means you don't earn interest on interest 32:52.980 --> 32:54.250 until after a year. 32:57.900 --> 33:03.700 If you put in $1 today, 1/2 a year later you'll have 1 plus 33:03.700 --> 33:06.460 r over 2 dollars, right? 33:06.460 --> 33:08.470 With an interest rate r. 33:11.780 --> 33:19.650 3/4 of a year later, you'll have 1 plus 3/4r dollars. 33:19.650 --> 33:23.830 And then a full year later you'll have 1 plus r. 33:23.830 --> 33:27.690 But now, after one year, you start earning interest 33:27.690 --> 33:30.100 on the 1 plus r. 33:30.100 --> 33:37.680 So, a 1/2 year after that, you would have 1 plus r times 1 33:37.680 --> 33:41.320 plus r over 2. 33:41.320 --> 33:46.200 And then two years later, you'd have 1 plus r 33:46.200 --> 33:48.870 squared, and so on. 33:48.870 --> 33:51.030 That's annual compounding. 33:51.030 --> 33:54.560 But the bank could offer you a different formula. 33:54.560 --> 33:58.000 They could offer you 33:58.000 --> 34:01.060 every-six-months compounding -- 34:01.060 --> 34:03.340 twice-a-year compounding. 34:03.340 --> 34:06.590 Then, here's the difference, after 1/2 a year, you'd have 1 34:06.586 --> 34:11.446 plus r over 2, as before. 34:11.449 --> 34:16.159 But now, after 3/4 of a year, you would have, instead, 1 34:16.160 --> 34:24.050 plus r over 2 times 1 plus r over 4, and so on. 34:24.050 --> 34:25.120 Now, what Fabozzi et al. 34:25.120 --> 34:28.530 likes to do is compounding every six months. 34:28.530 --> 34:33.240 This is what might make the textbook a little confusing. 34:33.239 --> 34:36.399 Because we naturally think of annual compounding. 34:36.400 --> 34:39.210 A year seems like a natural interval. 34:39.210 --> 34:42.630 But in finance, six months is more natural. 34:42.630 --> 34:46.420 Because, by convention, a lot of bonds pay 34:46.420 --> 34:48.880 coupons every six months. 34:48.880 --> 34:50.010 So, Fabozzi et al. 34:50.010 --> 34:55.050 uses the letter z to mean r over 2. 34:55.050 --> 34:59.510 And his time intervals are six months long. 34:59.510 --> 35:02.810 So, that means that the formula that Fabozzi et al. 35:02.810 --> 35:07.020 gives for a discount bond assumes a different 35:07.020 --> 35:09.600 compounding interval. 35:09.600 --> 35:10.810 The Fabozzi et al. 35:10.810 --> 35:12.620 assumption. 35:12.620 --> 35:21.620 He writes P equals 100 all over 1 plus z to the lower 35:21.620 --> 35:27.280 case t, where the lower case t is 2T. 35:27.280 --> 35:29.300 And so, that's the Fabozzi et al. 35:29.300 --> 35:33.320 formula for the price of a discount bond. 35:33.320 --> 35:36.720 Of course, it only applies at every six months interval. 35:36.720 --> 35:39.710 He's not showing what it is at six and a half months, or 35:39.710 --> 35:42.070 something like that. 35:42.070 --> 35:44.900 So, is that clear about compounding and 35:44.900 --> 35:46.150 about discount bonds? 35:52.100 --> 35:55.710 Now, a fundamental concept in finance is 35:55.710 --> 35:58.930 present discounted value. 35:58.930 --> 36:01.680 If you have a payment coming in the future -- 36:04.470 --> 36:23.460 So, I have a payment in T years or 2T six months, or we 36:23.460 --> 36:24.710 could say semesters. 36:28.970 --> 36:34.330 Then, the present value, depending on how I compound -- 36:34.330 --> 36:37.800 Well, let's talk about annual compounding. 36:37.800 --> 36:42.800 The present discounted value of a payment in T years is 36:42.800 --> 36:53.720 just the amount, which is $ x divided by 1 plus r to the T. 36:53.720 --> 36:58.140 Or if you're compounding every six months, it would be x all 36:58.140 --> 37:08.480 over 1 plus z to the lower case t. 37:08.480 --> 37:10.190 Lower case t equals 2T. 37:13.600 --> 37:16.670 So, whenever we ask a question about present values we'll 37:16.670 --> 37:19.570 have to make clear what compounding interval we're 37:19.570 --> 37:20.820 talking about. 37:23.830 --> 37:24.720 By the way there's also -- 37:24.720 --> 37:26.610 I shouldn't say by the way, it's fundamental. 37:26.610 --> 37:30.650 There's also continuous compounding. 37:30.650 --> 37:35.830 I talked about compounding annually, or twice a year. 37:35.830 --> 37:37.980 I can do it four times a year. 37:37.980 --> 37:42.400 If I do it four times a year, that means I pay 1/4 of the 37:42.400 --> 37:45.790 interest after three months, and then I start earning 37:45.790 --> 37:50.790 interest on interest after three months, and so on. 37:54.830 --> 37:59.620 What if you compound really often? 37:59.620 --> 38:02.840 You could do daily compounding. 38:02.840 --> 38:07.460 That would mean you would start earning interest on 38:07.460 --> 38:11.200 interest 365 times a year. 38:11.200 --> 38:13.490 The limit is continuous compounding. 38:18.410 --> 38:26.680 And the formula for continuous compounding is e to the rT, 38:26.680 --> 38:32.620 where e is the natural number 2.718. 38:32.620 --> 38:35.520 r is the continuously compounded interest rate. 38:35.522 --> 38:40.832 So, your balance equals the initial amount -- 38:40.825 --> 38:42.215 what did I say? 38:42.220 --> 38:47.000 $1 times e to the rT. 38:47.000 --> 38:48.250 That's continuous compounding. 38:53.690 --> 38:56.700 The unfortunate thing is that present values allow us to 38:56.700 --> 39:00.690 compute present values in different ways, depending on 39:00.690 --> 39:04.210 what kind of compounding I'm assuming. 39:04.210 --> 39:08.920 But if I have a sequence of payments coming in, the 39:08.920 --> 39:11.670 present discounted value of the sequence -- 39:11.670 --> 39:14.550 and suppose they come in once a year -- 39:14.550 --> 39:18.640 then it'd be natural to use annual compounding. 39:18.640 --> 39:24.260 And then the present discounted value, PDV, is the 39:24.260 --> 39:26.350 summation of the payments. 39:26.350 --> 39:28.310 And what am I calling them here? 39:31.260 --> 39:36.970 x sub i all over 1 plus r. 39:36.970 --> 39:43.130 Oh no, I say x sub t over one plus r to the t, from t equals 39:43.130 --> 39:45.450 1 to infinity. 39:45.450 --> 39:50.330 And that's the present discounted value for annual 39:50.330 --> 39:53.200 compounding of annual payments. 39:53.200 --> 39:58.140 And suppose the payments are coming in every six months, as 39:58.140 --> 40:02.600 they do with corporate bonds, then it might be natural to do 40:02.600 --> 40:06.140 compounding every six months. 40:06.140 --> 40:13.770 So then, we do PDV is equal to the summation, t equals 1 to 40:13.770 --> 40:21.930 infinity, x sub t, all over 1 plus r over 2 to the t. 40:24.660 --> 40:27.440 If I wanted to do continuous compounding -- suppose I have 40:27.440 --> 40:30.270 payments that are coming in continually -- 40:30.270 --> 40:33.880 then the present bond's discounted value would be the 40:33.880 --> 40:42.680 integral from 0 to infinity of x sub t e to the minus rt dt. 40:42.680 --> 40:45.090 And that would be a continuously compounded 40:45.090 --> 40:50.100 present value for a continuous stream of payments. 40:50.100 --> 40:54.870 So, if someone is offering me payments over time, then the 40:54.870 --> 41:03.100 payments have to be summed somehow into a present value. 41:10.210 --> 41:13.730 In finance, it often happens that people are promising to 41:13.730 --> 41:17.900 pay you something at various future intervals over time, 41:17.900 --> 41:21.740 and you have to recognize that payments in the future are 41:21.740 --> 41:23.980 worth less than payments today. 41:23.980 --> 41:28.820 Just as a discount bond is worth $100 in five years, but 41:28.820 --> 41:33.030 it's not worth $100 today, it's worth 100 all over 1 plus 41:33.030 --> 41:35.330 r to the T, appropriately compounded. 41:39.890 --> 41:41.270 And that's true generally. 41:41.270 --> 41:44.050 Anything in the future is worth less. 41:44.050 --> 41:47.510 So, present discounted value is one of the most fundamental 41:47.510 --> 41:50.030 concepts in finance. 41:50.030 --> 41:53.590 That whenever someone is offering me a payment stream 41:53.590 --> 41:56.590 in the future, you discount it to the 41:56.590 --> 41:58.470 present using these formulas. 41:58.470 --> 42:02.220 So, for example, if you are lending to your friend to buy 42:02.220 --> 42:06.990 a house, and the person is promising to pay you over the 42:06.990 --> 42:09.910 years, then you've got to figure out, well, what is that 42:09.910 --> 42:11.540 payment worth right now? 42:11.540 --> 42:15.180 And you would take the present value of it. 42:15.180 --> 42:18.690 There's a few present value formulas that are essential. 42:21.420 --> 42:24.370 And I'm going to just briefly mention them. 42:28.004 --> 42:33.784 The present value of a consol, or perpetuity. 42:36.990 --> 42:41.960 A perpetuity or a consol is an instrument that pays the same 42:41.960 --> 42:43.910 payment every period forever. 42:46.587 --> 42:49.427 It was named after the British consols that were issued in 42:49.430 --> 42:50.610 the 18th century. 42:50.610 --> 42:53.350 They were British government debt that had 42:53.350 --> 42:54.770 no expiration date. 42:54.770 --> 42:57.380 And the British government promised to pay 42:57.380 --> 43:04.120 you forever an amount. 43:04.120 --> 43:06.360 OK, what is the present value? 43:06.360 --> 43:08.470 Now, we'll call the amount that the 43:08.470 --> 43:10.490 consol pays its coupon. 43:13.180 --> 43:18.460 And let's say the coupon were GBP 1 per year. 43:18.460 --> 43:24.320 If it was paying GBP 1 per year, and we're using annual 43:24.320 --> 43:29.140 compounding, then the present discounted value is equal to 43:29.140 --> 43:34.900 GBP 1 over the interest rate. 43:37.660 --> 43:40.840 That's very simple, because this bond will 43:40.840 --> 43:43.140 always pay you GBP 1. 43:43.140 --> 43:47.600 And so, what is the interest rate on it? 43:47.600 --> 43:52.120 Your GBP 1 is equal r over the present discounted value. 43:52.120 --> 43:56.730 So, the prices of the bond of the consol should be the 43:56.730 --> 43:58.850 payment divided by the interest rate. 44:01.750 --> 44:09.730 Another formula is the formula for an annuity. 44:09.730 --> 44:14.230 An annuity is a different kind of payment stream. 44:14.230 --> 44:19.800 It's a consol for a while and then it stops. 44:19.800 --> 44:22.630 An annuity pays a fixed payment each 44:22.630 --> 44:29.990 period until maturity. 44:32.950 --> 44:36.060 So, it pays, let's say, GBP x. 44:36.060 --> 44:38.150 Let's not say GBP 1. 44:38.150 --> 44:42.680 If it pays GBP x every year, then the present 44:42.680 --> 44:43.930 discounted value -- 44:46.820 --> 44:58.100 it pays GBP x from t equals 1 to T. And then it stops. 44:58.100 --> 45:01.250 T is the last payment. 45:01.250 --> 45:10.470 Then the formula is x over r, times 1 minus 1 all over 1 45:10.470 --> 45:14.330 plus r to the T-th power. 45:14.330 --> 45:18.310 So, that's the annuity formula. 45:18.305 --> 45:21.365 And that's very important, because a lot of financial 45:21.370 --> 45:22.990 instruments are annuities. 45:22.990 --> 45:27.610 The most important example being a home mortgage, a 45:27.610 --> 45:30.020 traditional home mortgage. 45:30.020 --> 45:35.600 You might take out a 30-year mortgage when you buy a house. 45:35.600 --> 45:38.810 And the mortgage will generally say in the United 45:38.810 --> 45:41.330 States -- it's not so common in other countries -- but in 45:41.330 --> 45:46.210 the United States it will say you pay a fixed amount -- 45:48.940 --> 45:50.440 well, usually it's monthly, but let's say 45:50.440 --> 45:52.440 annually for now -- 45:52.440 --> 45:58.460 a fixed amount every year as your mortgage payment. 45:58.460 --> 46:01.080 And then you pay that continually until 30 years 46:01.080 --> 46:03.960 have elapsed, and then you're done. 46:03.960 --> 46:05.210 No more payments. 46:09.020 --> 46:12.950 The final thing I want to talk about is a corporate bond, or 46:12.950 --> 46:17.450 a conventional bond, which is a combination of an annuity 46:17.450 --> 46:19.650 and a discount bond. 46:19.650 --> 46:24.180 And so, a conventional corporate bond, or government 46:24.180 --> 46:29.190 bond, pays a coupon every six months. 46:29.192 --> 46:45.162 So, a conventional bond pays coupon c, an amount c, in 46:45.160 --> 46:49.750 dollars, pounds, or whatever currency, every six months. 46:57.120 --> 47:06.160 And principal plus c at the end. 47:12.050 --> 47:18.110 So, that means that it's really an annuity and a 47:18.110 --> 47:20.640 discount bond together, right? 47:20.640 --> 47:28.770 And so, the present discounted value for the conventional 47:28.770 --> 47:33.030 bond would be the sum of the present discounted value using 47:33.030 --> 47:38.030 the annuity formula for x equals c plus the present 47:38.030 --> 47:42.400 discounted value of the principal, which is 47:42.400 --> 47:44.320 given by the -- 47:44.320 --> 47:46.880 well, it would be this one, where you have r over 2, 47:46.880 --> 47:49.900 because it's every six months. 47:49.900 --> 47:52.230 And then the final -- 47:52.230 --> 47:55.400 I think it's the final concept I want to get at before 47:55.400 --> 47:59.400 talking a little bit about other matters. 47:59.400 --> 48:04.110 I want to talk about forward rates, and the term structure 48:04.110 --> 48:05.830 of interest rates. 48:05.830 --> 48:12.260 Now, at every point in time there are interest rates of 48:12.260 --> 48:16.060 various maturities quoted. 48:16.060 --> 48:24.630 And we want to define the forward rates implicit in 48:24.630 --> 48:27.050 those maturity formulas. 48:27.050 --> 48:29.760 And this is covered carefully in your textbook 48:29.762 --> 48:30.672 of Fabozzi et al. 48:30.670 --> 48:34.360 I'm just going to do a very simple exposition of it. 48:51.690 --> 49:03.730 The concept of a forward rate, forward interest rate, is due 49:03.730 --> 49:12.550 to Sir John Hicks, in his 1939 book, Value and Capital. 49:25.820 --> 49:30.160 About 20 years ago, I was writing a chapter for the 49:30.160 --> 49:35.090 Handbook of Monetary Economics about interest rates. 49:35.090 --> 49:41.930 And I was trying to confirm who invented the concept of 49:41.930 --> 49:42.970 forward interest rates. 49:42.970 --> 49:46.600 So, I'll build a little story around this. 49:46.600 --> 49:50.730 I thought it was Sir John Hicks, reading his 1939 book, 49:50.730 --> 49:53.130 and I couldn't find any earlier reference. 49:53.130 --> 49:56.700 So, I asked my research assistant, can you confirm for 49:56.700 --> 49:59.290 me that the concept of a forward interest 49:59.290 --> 50:01.880 rate is due to Hicks. 50:01.880 --> 50:07.780 And my graduate student looked around and tried to find 50:07.780 --> 50:10.460 earlier references to it and he could not. 50:10.460 --> 50:13.020 Then, one day the graduate came to me and said -- this is 50:13.020 --> 50:14.210 like 20 years ago. 50:14.205 --> 50:17.295 The graduate said, why don't you ask Hicks? 50:17.295 --> 50:19.655 And I said, wait a minute. 50:19.660 --> 50:22.590 This book was written in 1939. 50:22.590 --> 50:25.070 Is that man still alive? 50:25.070 --> 50:26.610 And he said, I think he is. 50:26.610 --> 50:30.530 So, I wrote to the United Kingdom. 50:30.530 --> 50:31.750 I found his address. 50:31.750 --> 50:34.520 I forget, Cambridge or Oxford. 50:34.520 --> 50:36.800 And I said, did you invent the concept of 50:36.800 --> 50:39.100 forward interest rates? 50:39.100 --> 50:42.870 And then six months went by and I got no answer. 50:42.870 --> 50:45.230 Then I got a paper letter -- 50:45.230 --> 50:47.920 they didn't have email in those days -- 50:47.920 --> 50:49.710 from Sir John Hicks. 50:49.710 --> 50:52.340 And it was written with trembling handwriting. 50:52.340 --> 50:56.790 And he said, my apologies for taking so long to answer. 50:56.790 --> 50:58.910 My health isn't good. 50:58.910 --> 51:04.170 But he said, to answer your question, he said, maybe I did 51:04.170 --> 51:06.820 invent the concept of forward interest rates. 51:06.820 --> 51:08.590 But he said, well maybe it wasn't. 51:08.590 --> 51:11.630 Maybe it was from coffee hour at the London School of 51:11.630 --> 51:15.690 Economics, where he was visiting in the 1920's. 51:15.690 --> 51:17.440 So, here we go. 51:17.440 --> 51:21.040 Sir John Hicks is reminiscing to me about what happened in 51:21.040 --> 51:30.980 coffee time in the 1920's. 51:30.980 --> 51:34.350 I'm just trying to convey what he told me they were thinking. 51:34.350 --> 51:37.810 At any point of time, you open the newspaper and you see 51:37.810 --> 51:41.060 interest rates quoted for various maturities. 51:41.060 --> 51:43.360 That's called the term structure of interest rates. 51:46.880 --> 51:51.220 For example, you will find Treasury -- 51:51.220 --> 51:54.120 well, you'll find one-year rate quotes, there'll be a 51:54.120 --> 51:55.370 yield on one-year bonds. 51:55.370 --> 51:57.820 There'll be a yield on two years. 51:57.820 --> 52:00.510 There'll be a yield quoted on three-year bonds. 52:00.510 --> 52:01.370 Right? 52:01.370 --> 52:04.510 Let me tell you right now, for most of the world today, if 52:04.510 --> 52:08.850 you want to borrow money for one year, it's really cheap. 52:08.850 --> 52:12.630 In Europe, or the U.K., U.S., over much of the 52:12.630 --> 52:14.050 world it's like 1%. 52:14.045 --> 52:18.025 In the U.S., it's less than 1%. 52:18.030 --> 52:21.060 It depends on who you are, what your borrowing rate will 52:21.060 --> 52:22.820 be, depending on your credit history. 52:22.820 --> 52:25.790 But if you have excellent credit, one-year interest 52:25.790 --> 52:27.170 rates are really low. 52:27.170 --> 52:31.950 But if you want to borrow for 10 years, it's more like 3.5%. 52:31.950 --> 52:35.510 It's higher, right? 52:35.510 --> 52:37.930 And if you want to borrow for 30 years, they might charge 52:37.925 --> 52:39.175 you 4% or 5%. 52:41.850 --> 52:45.480 This is the term structure of interest rates, and it's 52:45.475 --> 52:48.175 quoted every day in the newspaper. 52:48.180 --> 52:51.280 Well, I should say, I'm thinking 1925. 52:51.280 --> 52:54.330 In 1925, you'd go to the newspaper to see it. 52:54.330 --> 52:56.290 Now you go to the internet to see it. 52:56.290 --> 52:58.740 So, newspapers don't carry this anymore. 52:58.740 --> 53:03.110 But I'm still in the mode of thinking of Sir John Hicks. 53:03.110 --> 53:04.630 We're in 1925. 53:04.630 --> 53:09.950 So, you open up the newspaper in 1925 and you get the yield 53:09.950 --> 53:12.620 to maturity, or the interest rate on various maturities. 53:15.770 --> 53:17.010 All for today. 53:17.010 --> 53:20.380 Everything that's quoted in today's paper is an interest 53:20.380 --> 53:24.570 rate between now, today, and so many years in the future. 53:24.570 --> 53:28.310 The one-year interest rate quoted is the rate between now 53:28.310 --> 53:30.540 and one year from now, right? 53:30.540 --> 53:34.320 And the two-year interest rate quoted is the rate from now to 53:34.320 --> 53:37.890 two years from now, and so on. 53:37.890 --> 53:40.980 So, Hicks and his coffee hour people were saying, well, it 53:40.980 --> 53:43.430 seems kind of one-dimensional, because all the rates that are 53:43.430 --> 53:47.260 quoted are rates between now and some future date. 53:47.260 --> 53:50.960 But what about between two future dates. 53:50.960 --> 53:54.200 And then they thought about this at coffee hours, and 53:54.200 --> 53:57.160 someone said, well, it's kind of unnecessary to quote them, 53:57.160 --> 54:02.130 because they're all implicit in the term structure today. 54:02.130 --> 54:04.390 And this is where the concept of forward 54:04.390 --> 54:05.740 interest rate comes. 54:05.740 --> 54:08.630 And it's explained in Fabozzi et al. 54:08.630 --> 54:13.910 But I thought, I'm going to just try to explain it in the 54:13.910 --> 54:14.560 simplest term. 54:14.560 --> 54:16.830 Once we get the concept, it's easy. 54:16.830 --> 54:20.520 And I'm going to assume annual 54:20.520 --> 54:23.630 compounding to simplify things. 54:23.630 --> 54:29.570 But Fabozzi, he being a good financier, does it in 54:29.570 --> 54:30.820 six-month compounding. 54:33.150 --> 54:39.340 So, now the year is 1925, and we're in coffee hour. 54:45.520 --> 55:01.650 Suppose I expect to have GBP 100 to invest in '26. 55:01.650 --> 55:06.790 It's '25 now, this is a whole year from 1926, OK? 55:06.790 --> 55:11.280 And I want to lock in the interest rate now. 55:11.280 --> 55:13.780 Is there any way to do that? 55:13.780 --> 55:17.810 I mean, I could try to go to some banker and say, can you 55:17.810 --> 55:21.610 promise me that you'll give me an interest rate in 55:21.610 --> 55:23.410 1926 for one year. 55:23.410 --> 55:27.240 The banker might do it, you know, but I don't need to go 55:27.240 --> 55:29.500 to a banker to do that. 55:29.500 --> 55:35.190 Once I have all of these bonds available, and if I can both 55:35.190 --> 55:40.950 go long and short them, then I can lock it in. 55:40.950 --> 55:44.420 So, here's what I want to do. 55:44.420 --> 55:46.950 This is what they were discussing at coffee hour. 55:46.950 --> 55:55.740 Buy, in 1925, two-year bonds in an amount -- 55:55.740 --> 55:59.200 you've got to buy the amount right -- 55:59.195 --> 56:05.835 you've got to buy 1 plus r sub 2, which is the two-year 56:05.840 --> 56:14.470 yield, squared, all over 1 plus r sub 1 bonds. 56:17.090 --> 56:20.290 Discount bonds. 56:20.290 --> 56:24.710 They'll mature in two years. 56:24.710 --> 56:44.100 And then I have to short, in 1925, one-period bond that 56:44.100 --> 56:49.390 matures at GBP 100 So, suppose I do that, what happens after 56:49.390 --> 56:50.740 one period? 56:50.740 --> 56:53.990 Well, after one period, I owe GBP 100, right? 56:53.990 --> 56:58.790 Because I just shorted a one-period bond. 57:02.740 --> 57:07.090 So, I pay GBP 100, that's like investing GBP 100. 57:07.090 --> 57:14.310 At the end, I get this amount times GBP 100, right? 57:14.310 --> 57:17.670 Because this is the number of bonds that I bought. 57:17.670 --> 57:20.380 So, what is the return that I get? 57:20.380 --> 57:24.840 The return that I get is the ratio -- 57:24.840 --> 57:35.310 well, we'll call that the forward rate between '26 and 57:35.310 --> 57:42.390 '27 as quoted in 1925. 57:42.390 --> 57:47.140 And so, that forward rate, we'll say 1 plus the forward 57:47.140 --> 58:00.720 rate, f, is equal to 1 plus r sub 2, squared, all over 1 58:00.720 --> 58:04.950 plus r sub 1. 58:04.950 --> 58:08.300 It's just the amount that I get. 58:08.300 --> 58:13.660 What I'll get if I bought this number of bonds, I get GBP 100 58:13.660 --> 58:20.030 times this number in two periods in 1927, but I put out 58:20.030 --> 58:22.830 GBP 100 in 1926. 58:22.830 --> 58:30.590 So, the ratio of the amount that I got at the end, in '27, 58:30.590 --> 58:33.140 to the amount that I put in in '26 is given by this. 58:33.140 --> 58:37.020 So, that's 1 plus the interest rate I got on the bond. 58:37.020 --> 58:42.490 So, you can compute forward rates. 58:42.490 --> 58:46.830 I'm just showing it for a one-year ahead forward rate 58:46.830 --> 58:50.300 for a one-year loan. 58:50.300 --> 58:54.760 But you can compute it for any periods further in the future 58:54.760 --> 58:56.910 over any maturity. 58:56.910 --> 59:00.450 And this is the formula given, it's on page 227 59:00.450 --> 59:01.640 of Fabozzi et al. 59:01.640 --> 59:05.730 I'm not going to show you the general formula. 59:05.730 --> 59:09.820 The expectations theory of the term structure is 59:09.820 --> 59:12.900 a theory that -- 59:12.900 --> 59:13.510 I'll write it down. 59:13.510 --> 59:22.960 Expectations theory says that the forward rate equals the 59:22.960 --> 59:24.540 expected spot rate. 59:29.590 --> 59:30.880 So, do you see what I'm saying? 59:30.880 --> 59:36.340 Here in 1925, I open The London Times, and right there 59:36.340 --> 59:40.610 I have printed the whole term structure today. 59:40.610 --> 59:44.350 And I can then compute, using forward rate formulas, the 59:44.350 --> 59:48.560 implied interest rates for every year in the future. 59:48.560 --> 59:53.070 Even out to 2010, they could have computed -- 59:53.070 --> 59:54.940 if they had bonds that were that long -- 59:54.940 --> 59:56.360 I think they had a few. 59:56.360 --> 59:57.970 Let's see, 1925. 59:57.970 --> 1:00:00.390 Some bonds go out 100 years. 1:00:00.390 --> 1:00:05.200 If you wanted to do the one-year rate in 1925, for the 1:00:05.200 --> 1:00:09.860 year 2011, you'd have to find a pair of bonds. 1:00:09.860 --> 1:00:13.120 One of them maturing in 2011, and another 1:00:13.120 --> 1:00:15.120 one maturing in 2012. 1:00:15.120 --> 1:00:17.850 And if you did that, you could get an interest 1:00:17.850 --> 1:00:19.820 rate for this year. 1:00:19.820 --> 1:00:24.070 So, that was kind of the realization that Hicks got, 1:00:24.070 --> 1:00:26.480 that the whole future is laid out here in 1:00:26.480 --> 1:00:27.880 this morning's paper. 1:00:27.880 --> 1:00:29.560 All the interest rates for -- 1:00:29.560 --> 1:00:31.080 maybe not out to 2011 -- 1:00:31.080 --> 1:00:34.180 but out to a long time in the future. 1:00:34.180 --> 1:00:36.750 And so, what determines those interest rates. 1:00:36.750 --> 1:00:40.740 So, Hicks, in his book, wrote, the simplest theory is the 1:00:40.740 --> 1:00:46.190 theory that these forward rates are just predictions of 1:00:46.190 --> 1:00:48.580 interest rates on those future dates. 1:00:48.580 --> 1:00:51.680 So, we could go back and see, what were they predicting? 1:00:51.680 --> 1:00:55.440 They weren't thinking so clearly, definitively, about 1:00:55.440 --> 1:00:57.880 2011, but they must've been, because they were trading 1:00:57.880 --> 1:00:59.580 these bonds. 1:00:59.580 --> 1:01:07.080 And so, you could test whether the expectations theory, 1:01:07.080 --> 1:01:09.970 whether people are forming rational expectations by 1:01:09.970 --> 1:01:14.480 looking at those forecasts and seeing, were they right? 1:01:14.480 --> 1:01:17.600 Now there's a huge literature on this, but 1:01:17.600 --> 1:01:19.530 Hicks said that -- 1:01:19.530 --> 1:01:20.910 I'll just stop with this -- 1:01:20.910 --> 1:01:27.640 Hicks said that the expectations theory doesn't 1:01:27.640 --> 1:01:31.780 quite work, because there's a risk premium. 1:01:31.780 --> 1:01:36.150 That the forward rates tend to be above the optimally 1:01:36.150 --> 1:01:39.430 forecasted future spot rates -- 1:01:39.430 --> 1:01:43.220 spot meaning, you know, as quoted on that date -- 1:01:43.220 --> 1:01:44.540 because of risk. 1:01:44.540 --> 1:01:47.600 And people are uncertain about the future, so they demand a 1:01:47.600 --> 1:01:51.570 higher forward rate then they expect to see 1:01:51.570 --> 1:01:54.020 happening in the spot rate. 1:01:54.020 --> 1:01:58.990 So, I will stop talking technical things. 1:01:58.990 --> 1:02:00.520 I wanted to say something. 1:02:00.520 --> 1:02:05.780 I have so much more to say, but I'll have to 1:02:05.780 --> 1:02:08.720 limit due to time. 1:02:08.720 --> 1:02:12.600 What I've laid out here is a theory of interest rates. 1:02:12.600 --> 1:02:14.590 And I've done some interest rate calculations. 1:02:14.590 --> 1:02:18.860 And I've pointed out the remarkable institutions we 1:02:18.860 --> 1:02:24.110 have that have interest rates for all intervals, 1:02:24.110 --> 1:02:26.980 out maybe 100 years. 1:02:26.980 --> 1:02:30.160 And so, it's all kind of like the whole future is planned in 1:02:30.160 --> 1:02:31.430 these markets. 1:02:31.430 --> 1:02:33.590 It seems impressive, doesn't it? 1:02:39.390 --> 1:02:41.830 And when I told you the Robinson Crusoe story, didn't 1:02:41.830 --> 1:02:42.980 that sound good? 1:02:42.980 --> 1:02:47.050 Like when the two Robinson Crusoes discover each other, 1:02:47.050 --> 1:02:49.950 aren't they obviously doing the right thing to make a loan 1:02:49.950 --> 1:02:51.200 from one to the other? 1:02:53.810 --> 1:02:57.160 And I like that. 1:02:57.160 --> 1:02:59.220 I think basically everything I've said here 1:02:59.220 --> 1:03:01.310 is basically right. 1:03:01.310 --> 1:03:04.140 But I wanted to say that one of the themes of this course 1:03:04.135 --> 1:03:08.855 is about human behavior and behavioral economics. 1:03:08.860 --> 1:03:14.820 And I wanted to talk a little bit about borrowing and 1:03:14.820 --> 1:03:19.990 lending, and how it actually plays out in the real world. 1:03:19.990 --> 1:03:26.120 And how our attitudes are changing, our regulatory 1:03:26.120 --> 1:03:28.640 attitudes are changing. 1:03:28.640 --> 1:03:31.970 So, let me just step back. 1:03:31.970 --> 1:03:34.640 You know, I think this literature, involving Irving 1:03:34.640 --> 1:03:37.600 Fisher and von Boehm-Bawerk, and many others who've 1:03:37.600 --> 1:03:39.420 contributed to the understanding of interest 1:03:39.420 --> 1:03:44.450 rates, is very powerful and important. 1:03:44.450 --> 1:03:48.950 And it supersedes anything that had been written in the 1:03:48.950 --> 1:03:51.100 last thousands of years. 1:03:51.100 --> 1:03:54.660 They had interest rates for thousands of years, but that 1:03:54.660 --> 1:03:58.820 simple diagram, that Fisher-diagram, came just a 1:03:58.820 --> 1:03:59.660 short time ago. 1:03:59.660 --> 1:04:02.530 It's hardly long ago at all. 1:04:02.530 --> 1:04:05.770 But I wanted to step back and think about what people said 1:04:05.770 --> 1:04:10.380 about interest rates going way back in time. 1:04:10.380 --> 1:04:17.110 And so, I was going to quote the Bible. 1:04:17.110 --> 1:04:20.570 There's a Latin word. 1:04:23.500 --> 1:04:26.330 Do you know this word? 1:04:26.332 --> 1:04:29.082 [WRITES USURA] 1:04:29.080 --> 1:04:32.920 Do you know what that means in Latin? 1:04:32.920 --> 1:04:37.850 Well actually our English word "use" comes from it. 1:04:37.850 --> 1:04:39.100 I don't know how to pronounce it. ''Usura'' 1:04:39.100 --> 1:04:41.960 in Latin means use. 1:04:41.960 --> 1:04:46.460 And it means also interest. Because, what is interest? 1:04:46.460 --> 1:04:48.520 You're giving someone the use of the money. 1:04:48.520 --> 1:04:49.480 You're not giving them the money. 1:04:49.480 --> 1:04:52.140 They're getting the use of the money. 1:04:52.140 --> 1:04:55.130 And they had other words for interest. But this ancient 1:04:55.130 --> 1:05:00.100 word had a negative connotation. 1:05:00.100 --> 1:05:04.640 It kind of meant something immoral. 1:05:04.640 --> 1:05:10.690 And so, we have a word called usury. 1:05:10.692 --> 1:05:11.752 You know this word. 1:05:11.750 --> 1:05:15.290 This is English now. 1:05:15.290 --> 1:05:18.730 It goes back more than 2000 years. 1:05:18.730 --> 1:05:20.060 I actually have it here in Latin. 1:05:20.060 --> 1:05:22.540 I'm just curious about these things, but I can't 1:05:22.540 --> 1:05:23.790 pronounce it right. 1:05:27.050 --> 1:05:29.990 It must have been written in Greek, or Aramaic, or 1:05:29.990 --> 1:05:34.260 something originally, but it uses the word, "usury," usura. 1:05:34.260 --> 1:05:38.910 But the quotation, it says in Exodus, "If thou lend money to 1:05:38.910 --> 1:05:44.750 any of my people that is poor by thee, thou shalt not be to 1:05:44.750 --> 1:05:47.880 him as an usurer. 1:05:47.880 --> 1:05:51.720 Neither shalt thou lay upon him usury." Now 1:05:51.720 --> 1:05:53.280 what does that mean? 1:05:53.280 --> 1:05:57.370 Because usura could mean both interest and excessive 1:05:57.370 --> 1:06:00.950 interest. So, it's not clear what the Bible is 1:06:00.950 --> 1:06:02.860 saying about lending. 1:06:02.860 --> 1:06:05.710 It sounds like it's telling you you can't lend -- 1:06:05.710 --> 1:06:09.400 you can lend someone money, but don't take any interest. 1:06:09.400 --> 1:06:12.100 That's what it seems to be saying but it's ambiguous. 1:06:12.100 --> 1:06:13.940 I was going to quote the Koran. 1:06:13.940 --> 1:06:15.780 I don't speak Arabic. 1:06:15.780 --> 1:06:19.090 I think there's a similar ambiguity in Arabic. 1:06:22.820 --> 1:06:26.390 And I'm quoting an English translation of the Koran: "Oh 1:06:26.390 --> 1:06:27.810 you who believe. 1:06:27.810 --> 1:06:31.580 Be careful of Allah, and give up the interest that is 1:06:31.580 --> 1:06:34.800 outstanding." Or usura. 1:06:37.310 --> 1:06:41.330 That has been interpreted by modern Islamic scholars as 1:06:41.330 --> 1:06:47.530 that charging interest is ungodly. 1:06:47.530 --> 1:06:50.950 And it was interpreted by Christian scholars. 1:06:50.950 --> 1:06:53.110 They go back and they try to figure out what was meant, and 1:06:53.110 --> 1:06:54.920 they couldn't figure it out, either, then. 1:06:54.920 --> 1:06:58.230 Times change over the centuries. 1:06:58.230 --> 1:07:03.710 But for thousands of years the Catholic Church -- or maybe 1:07:03.710 --> 1:07:04.210 not thousands. 1:07:04.210 --> 1:07:05.640 I don't know the whole history of this. 1:07:05.640 --> 1:07:08.280 It depends on which century you're talking about. 1:07:08.280 --> 1:07:11.920 But for many centuries, the Catholic Church interpreted 1:07:11.920 --> 1:07:15.690 this, as do many Muslims today, 1:07:15.690 --> 1:07:17.760 that interest is immoral. 1:07:17.760 --> 1:07:21.790 And therefore, the only people who were allowed to loan were 1:07:21.790 --> 1:07:24.990 Jews, because they weren't subject to the -- 1:07:24.990 --> 1:07:27.900 even though it's actually the Book of Exodus -- 1:07:27.900 --> 1:07:30.940 but they weren't subject to the same interpretation. 1:07:30.940 --> 1:07:34.490 So, it was considered immoral. 1:07:34.490 --> 1:07:37.050 I wonder, why is that? 1:07:37.050 --> 1:07:38.180 Why is it immoral? 1:07:38.180 --> 1:07:41.340 Because we just saw the logic of it. 1:07:44.480 --> 1:07:48.220 Now, the Robinson Crusoe story. 1:07:48.220 --> 1:07:51.360 I had two different men on the other side of the island. 1:07:51.360 --> 1:07:54.190 And I had one of them wanting consumption today and of one 1:07:54.190 --> 1:07:56.500 of them wanting consumption later. 1:07:56.500 --> 1:07:58.960 Your first question is, maybe they 1:07:58.960 --> 1:08:00.270 were wrong to be different. 1:08:00.270 --> 1:08:02.540 Maybe they should both be doing the same thing. 1:08:02.540 --> 1:08:06.160 Why is one of them different than the other? 1:08:06.160 --> 1:08:09.120 The guy who's going to consume a lot today, maybe I should 1:08:09.120 --> 1:08:10.310 have a word with this guy. 1:08:10.310 --> 1:08:11.980 You know, don't do it, you're going to be 1:08:11.979 --> 1:08:13.249 really hungry next year. 1:08:13.250 --> 1:08:15.010 Why are you doing this? 1:08:15.010 --> 1:08:19.270 So, instead of forming a loan between the two, we should 1:08:19.270 --> 1:08:20.540 advise them. 1:08:20.540 --> 1:08:23.880 And maybe they don't need a loan. 1:08:23.880 --> 1:08:28.590 So, this comes back to what are we doing with our loans. 1:08:28.590 --> 1:08:33.330 And are we giving people good advice? 1:08:33.330 --> 1:08:35.100 Or do we have a tendency in the 1:08:35.100 --> 1:08:40.350 financial world to be usurious? 1:08:40.350 --> 1:08:44.340 Are we going after and victimizing people by lending 1:08:44.340 --> 1:08:47.150 them money? 1:08:47.149 --> 1:08:50.069 I think that there is a problem. 1:08:50.069 --> 1:08:55.469 And these thousands of years of history of concern about 1:08:55.470 --> 1:09:00.870 usury have to do with real problems that develop. 1:09:00.870 --> 1:09:04.340 So, just in preparing for this lecture, on an impulse, I got 1:09:04.340 --> 1:09:05.700 on to Google. 1:09:05.700 --> 1:09:10.740 And I searched on vacation loans. 1:09:10.740 --> 1:09:16.600 I found 1.6 million websites that were encouraging you to 1:09:16.600 --> 1:09:20.460 take out a loan to go on a vacation. 1:09:20.460 --> 1:09:24.040 Now, is that socially conscious? 1:09:24.040 --> 1:09:25.880 I was wondering about that. 1:09:25.880 --> 1:09:29.330 Is it ever right to borrow money to go on a vacation? 1:09:29.330 --> 1:09:31.720 I mean, I've thought about it. 1:09:31.720 --> 1:09:35.600 And then I remembered, Franco Modigliani, who was one of the 1:09:35.600 --> 1:09:38.420 authors of your textbook, and he was my teacher. 1:09:38.420 --> 1:09:41.200 I still remember these moments from classroom. 1:09:41.200 --> 1:09:47.010 And he was teaching us about these subjects. 1:09:47.010 --> 1:09:50.150 He was thinking about examples of investments -- 1:09:50.152 --> 1:09:51.232 and he said, you know what? 1:09:51.230 --> 1:09:56.960 One of the best investments I can think of is a honeymoon. 1:09:56.960 --> 1:09:59.760 When you get married, you go on a vacation. 1:09:59.760 --> 1:10:02.150 Now, why are you doing that? 1:10:02.150 --> 1:10:05.100 Is it for fun? 1:10:05.100 --> 1:10:05.910 Probably not. 1:10:05.910 --> 1:10:08.120 In fact, I have a suspicion that most 1:10:08.120 --> 1:10:10.410 honeymoons are not fun. 1:10:14.170 --> 1:10:17.900 I think it's just people are too uptight and tense. 1:10:17.900 --> 1:10:19.340 What have we just done? 1:10:19.340 --> 1:10:22.300 And I bet that's right. 1:10:22.300 --> 1:10:24.530 So, why do you do it? 1:10:24.530 --> 1:10:27.020 Well, you do it as an investment, right? 1:10:27.020 --> 1:10:29.210 You want this photograph album. 1:10:29.205 --> 1:10:30.385 You want the memories. 1:10:30.390 --> 1:10:32.570 You're kind of bonding. 1:10:32.570 --> 1:10:34.950 I think he's absolutely right. 1:10:34.950 --> 1:10:37.330 You should go on a honeymoon. 1:10:37.330 --> 1:10:38.460 So, I did another search. 1:10:38.460 --> 1:10:41.530 I searched on honeymoon loans. 1:10:41.530 --> 1:10:43.830 And I got 1.7 million hits. 1:10:43.830 --> 1:10:45.630 It beat vacation loans. 1:10:45.630 --> 1:10:48.600 So, there are many lenders ready to lend. 1:10:48.600 --> 1:10:50.170 And you should do it. 1:10:50.170 --> 1:10:55.540 If you're just getting married and you don't have any money, 1:10:55.540 --> 1:11:03.170 go to the usurious guy and ask for the honeymoon loan. 1:11:03.170 --> 1:11:05.040 So, I'm not sure whether it's bad. 1:11:05.040 --> 1:11:06.550 This is a question. 1:11:06.550 --> 1:11:08.050 I think that there are abusers. 1:11:08.050 --> 1:11:10.970 And I wanted to just close with Elizabeth Warren. 1:11:13.590 --> 1:11:16.420 I first met her just a few years ago. 1:11:16.420 --> 1:11:17.770 Well, actually, I remember her book. 1:11:17.770 --> 1:11:20.750 She wrote some important books. 1:11:20.750 --> 1:11:24.670 She's a Harvard law professor who wrote books. 1:11:24.670 --> 1:11:28.760 One of her books was published by Yale, called The Fragile 1:11:28.760 --> 1:11:30.020 Middle Class. 1:11:30.020 --> 1:11:32.790 And it's about people who go into bankruptcy. 1:11:32.790 --> 1:11:36.030 And she points out that in the U.S., even back in the old 1:11:36.030 --> 1:11:38.920 days when the economy was good, we had a million 1:11:38.920 --> 1:11:41.300 personal bankruptcies a year. 1:11:41.300 --> 1:11:43.910 This is because of borrowing. 1:11:43.910 --> 1:11:47.300 You don't know how many bankruptcies there are, 1:11:47.300 --> 1:11:51.190 because people are ashamed when they declare bankruptcy. 1:11:51.190 --> 1:11:53.180 And they try to cover it up from as 1:11:53.180 --> 1:11:55.030 many people as possible. 1:11:55.030 --> 1:11:58.600 There are as many personal bankruptcies in a normal year 1:11:58.600 --> 1:12:00.370 as there are divorces. 1:12:00.370 --> 1:12:01.680 But you don't hear about them. 1:12:01.680 --> 1:12:04.020 You hear about all kinds of divorces. 1:12:04.020 --> 1:12:06.460 People are ashamed of divorces, too. 1:12:06.460 --> 1:12:09.430 But they can't cover them up because everybody knows. 1:12:09.430 --> 1:12:12.190 But they can pretty well cover up a bankruptcy, and so they 1:12:12.190 --> 1:12:13.830 don't talk about it. 1:12:13.830 --> 1:12:17.370 So, what Elizabeth Warren is saying, she thinks that the 1:12:17.370 --> 1:12:20.320 lending industry is victimizing people. 1:12:20.320 --> 1:12:25.400 It's advertising for vacation loans and the like, and then 1:12:25.400 --> 1:12:29.080 they don't tell people about the bad things that will come. 1:12:29.080 --> 1:12:31.870 So, she wrote an article, and this is interesting, it was in 1:12:31.870 --> 1:12:33.620 Harvard Magazine. 1:12:33.620 --> 1:12:37.360 And that's a magazine that I suspect none of you read. 1:12:37.360 --> 1:12:40.510 Anyone read Harvard Magazine? 1:12:40.510 --> 1:12:43.760 It's the Harvard alumni magazine. 1:12:43.760 --> 1:12:47.500 It goes out to all graduates of Harvard. 1:12:47.500 --> 1:12:50.670 So, you don't read it, and you probably will never read it. 1:12:50.670 --> 1:12:55.450 You will be a reader of the Yale Alumni Magazine, which 1:12:55.450 --> 1:12:59.350 will start arriving in your doorstep after you graduate. 1:12:59.350 --> 1:13:05.470 And it will also include your obituary in the next century 1:13:05.470 --> 1:13:07.540 when that comes. 1:13:07.540 --> 1:13:10.780 But the Harvard alumni magazine published this 1:13:10.780 --> 1:13:14.980 wonderful article about Elizabeth, describing all of 1:13:14.980 --> 1:13:19.850 the abuses that happen in lending in the United States. 1:13:19.850 --> 1:13:21.630 I don't know how I ended up reading it. 1:13:21.630 --> 1:13:24.880 I think it was just such a nicely written piece that it 1:13:24.880 --> 1:13:26.680 just became one of their success stories. 1:13:26.680 --> 1:13:30.580 Most people don't read that magazine, but I read it, and a 1:13:30.580 --> 1:13:31.760 lot of people have read it. 1:13:31.760 --> 1:13:35.940 And she was so successful in convincing the public -- this 1:13:35.940 --> 1:13:39.690 is just two years -- or 2008, three years ago -- 1:13:39.690 --> 1:13:44.460 she was so successful that she got a Consumer Financial 1:13:44.460 --> 1:13:49.140 Protection Bureau inserted into the Dodd-Frank bill. 1:13:49.140 --> 1:13:54.430 And we now have a regulator, a new regulator, that's supposed 1:13:54.430 --> 1:14:00.180 to stomp on these usurious practices. 1:14:00.180 --> 1:14:02.750 It's kind of an inspirational story, but the downside of it 1:14:02.750 --> 1:14:05.720 is, she got too carried away criticizing the lending 1:14:05.720 --> 1:14:08.010 industry in that nice article. 1:14:08.010 --> 1:14:12.380 And it makes them sound worse than they really are, and so 1:14:12.380 --> 1:14:17.260 Obama could not appoint her to head the Consumer Financial 1:14:17.260 --> 1:14:20.600 Protection Bureau, because it would be too politically 1:14:20.600 --> 1:14:21.320 controversial. 1:14:21.320 --> 1:14:26.240 So, she is now the person trying to find someone to head 1:14:26.240 --> 1:14:28.190 her bureau. 1:14:28.190 --> 1:14:30.720 But I think that this is just another step, and it's 1:14:30.720 --> 1:14:32.960 happening in Europe and in other places. 1:14:32.960 --> 1:14:36.060 The financial crisis has made us more aware of 1:14:36.060 --> 1:14:38.160 bad financial practices. 1:14:38.160 --> 1:14:40.640 And so, usury is again on our minds. 1:14:40.640 --> 1:14:44.900 Usury is abusive lending that's taken without concern 1:14:44.900 --> 1:14:47.220 for the person who's borrowing. 1:14:47.220 --> 1:14:50.280 And I think what it means to me is that -- 1:14:50.280 --> 1:14:52.140 we'll come back to talk about regulation in 1:14:52.140 --> 1:14:53.190 another lecture -- 1:14:53.190 --> 1:14:56.520 but that the original Irving Fisher story and von 1:14:56.520 --> 1:14:59.190 Boehm-Bawerk story about interest was right. 1:14:59.190 --> 1:15:02.110 And even vacation loans, especially 1:15:02.110 --> 1:15:04.190 honeymoon loans, are right. 1:15:04.190 --> 1:15:08.810 But we need government regulation to prevent abuses. 1:15:08.810 --> 1:15:12.280 And we do still have abuses in the lending process. 1:15:12.280 --> 1:15:15.710 So, I'll stop with that and I'll see you on Monday.