WEBVTT 00:01.670 --> 00:05.160 Professor Robert Shiller: Before I begin, 00:05.159 --> 00:09.469 I just wanted to say that I was very--I found last period's 00:09.466 --> 00:13.026 lecture with David Swensen very interesting. 00:13.030 --> 00:18.910 Also, I liked being serenaded by New Blue, which is a first 00:18.911 --> 00:20.941 experience for me. 00:20.940 --> 00:26.530 Swensen--He gave, I thought, a very interesting 00:26.529 --> 00:29.469 talk. I've heard him talk before but 00:29.474 --> 00:31.224 it's always interesting. 00:31.220 --> 00:34.710 He really emphasized diversification. 00:34.710 --> 00:41.110 But, I don't know what you were thinking, we got a 28% portfolio 00:41.109 --> 00:43.039 return last year. 00:43.040 --> 00:46.020 There's something else going on besides diversification; 00:46.020 --> 00:49.220 diversification means we get the average return. 00:49.220 --> 00:52.380 And I was glad that you asked questions at the end. 00:52.380 --> 00:57.470 Some of your questions seemed to draw out other things that he 00:57.468 --> 01:02.308 doesn't plan to talk about, like what he really did to make 01:02.305 --> 01:05.265 money. One thing was that he said that 01:05.265 --> 01:08.825 they shorted the Internet stocks in the late 1990s. 01:08.829 --> 01:13.029 That's a brilliant market timing device that--I think 01:13.029 --> 01:17.549 enlightened people thought that those prices were getting 01:17.552 --> 01:22.562 high--and also made some play on credit spreads and now on real 01:22.560 --> 01:24.630 estate, he said. 01:24.630 --> 01:27.560 How does he do it? 01:27.560 --> 01:33.620 Again, it's my theory that there's no--you can't entirely 01:33.619 --> 01:39.569 be taught, but partly though I think that he does it, 01:39.569 --> 01:44.089 as do other good portfolio managers, by just keeping a very 01:44.089 --> 01:47.979 broad base of knowledge and listening to people and 01:47.984 --> 01:52.114 collecting information and watching the big trends and 01:52.114 --> 01:54.144 thinking about them. 01:54.140 --> 01:59.260 One of, I think, Swensen's best talents is he's 01:59.256 --> 02:04.816 a good listener and he incorporates basic facts and 02:04.818 --> 02:09.098 acts on them. You might have--it would be 02:09.095 --> 02:13.245 incorrect, I think, in listening to what he said 02:13.247 --> 02:18.717 and conclude that he just says diversify because he's obviously 02:18.724 --> 02:22.704 done something very different from that. 02:22.699 --> 02:26.099 By the way, I have another speaker who told me that he 02:26.101 --> 02:30.211 would like to talk to our class and I hope we can work it out. 02:30.210 --> 02:34.810 His name is Carl Icahn, who is one of the biggest Wall 02:34.808 --> 02:40.188 Street--powerful and enlightened people on Wall Street--who can 02:40.187 --> 02:45.307 also maybe tell us something about how he makes money or how 02:45.306 --> 02:48.166 he makes it a better world. 02:48.169 --> 02:51.609 The problem is that he has a--these people have very tight 02:51.607 --> 02:55.107 schedules and he's involved in various takeovers and things 02:55.105 --> 02:59.535 right now. He said he could do it if we 02:59.541 --> 03:07.111 could arrange to meet after 3:00 p.m., so I'm going to--on a 03:07.109 --> 03:13.009 Monday or a Wednesday, perhaps at 3:00 p.m. 03:13.010 --> 03:17.230 or later. He said--his assistant said it 03:17.227 --> 03:21.267 might even be 7:00 p.m., so that's the way he works. 03:21.270 --> 03:24.580 I don't think he gets up at 9:00 a.m., apparently. 03:24.580 --> 03:28.780 So, I take that that's all right with you--that you can 03:28.781 --> 03:32.051 come to a special section of this class. 03:32.050 --> 03:35.080 We would have to see if we can arrange that. 03:35.080 --> 03:39.090 Again, I don't guarantee that it will happen because the 03:39.086 --> 03:43.306 reality is, someone who is involved in as many things as he 03:43.310 --> 03:45.860 is--it's going to be something. 03:45.860 --> 03:53.550 We do have Stephen Schwarzman coming February 22^(nd) and we 03:53.547 --> 03:59.017 have Andrew Redleaf coming March 5^(th), 03:59.020 --> 04:07.970 so we have a really strong set of outside speakers this year. 04:07.969 --> 04:11.369 Again, the mid-term exam is Monday; 04:11.370 --> 04:14.530 sorry that I misstated that last week. 04:14.530 --> 04:18.250 You've already seen last year's mid-term and it's going to look 04:18.250 --> 04:19.330 a lot like that. 04:19.330 --> 04:25.940 04:25.939 --> 04:33.069 We're talking today about interest rates and bonds. 04:33.069 --> 04:36.509 Interest rates are an old, old thing. 04:36.509 --> 04:40.919 They go back to ancient times, but I'm going to talk about 04:40.923 --> 04:45.413 some of our modern institutions and I'm going to talk first 04:45.414 --> 04:47.354 about discount bonds. 04:47.350 --> 04:51.650 This is a little bit more of a technical lecture, 04:51.654 --> 04:55.514 but I find it just as interesting myself. 04:55.509 --> 05:01.739 We're talking about discount bonds, and then coupon-carrying 05:01.742 --> 05:08.292 bonds, and then talk about the term structure of interest rates 05:08.292 --> 05:11.992 and why we have interest rates. 05:11.990 --> 05:19.390 I think that's my Blackberry beeping. 05:19.389 --> 05:22.109 I'm trying not to live in too electronic a world. 05:22.110 --> 05:24.690 That's the way it is these days. 05:24.690 --> 05:30.830 05:30.830 --> 05:35.120 It's giving its last gasp. 05:35.120 --> 05:38.460 Then finally, talk about inflation index 05:38.455 --> 05:48.725 bonds. The first thing is a discount 05:48.726 --> 05:56.246 bond. It's the most simple--or often 05:56.245 --> 06:06.205 called a bill--a discount bond does not pay interest; 06:06.210 --> 06:08.750 it's sold at a discount. 06:08.750 --> 06:16.310 You have the principle, which is the amount owed, 06:16.310 --> 06:24.350 which is, let's say it's $100, that will be paid to you at 06:24.347 --> 06:30.117 some date in the future, specified in the contract. 06:30.120 --> 06:35.290 And nothing, you would just get $100. 06:35.290 --> 06:39.440 Effectively, you get interest from this 06:39.435 --> 06:45.975 because it's sold at a discount, so the price that you pay is 06:45.980 --> 06:50.780 equal to one hundred minus the discount. 06:50.780 --> 06:55.950 06:55.949 --> 06:59.949 You wouldn't buy this bond at par because--at par, 06:59.949 --> 07:04.929 meaning at $100--because then you wouldn't get any interest on 07:04.928 --> 07:09.968 it. So you buy it at a discount and 07:09.965 --> 07:18.895 the return you get is of course a hundred minus--the return you 07:18.896 --> 07:22.206 get is the discount. 07:22.210 --> 07:26.890 The U.S. Government is a big issuer of 07:26.889 --> 07:30.629 discount bonds and they're called Treasury bills. 07:30.629 --> 07:35.589 I have them up on the screen here. 07:35.590 --> 07:37.760 This is from a U.S. 07:37.759 --> 07:43.819 Government website called treasurydirect.gov and you can 07:43.816 --> 07:47.666 get on and access it at any time. 07:47.670 --> 07:50.600 It is showing--since the U.S. 07:50.600 --> 07:55.490 Government issues these bonds, it's showing its data on these 07:55.488 --> 07:59.868 bonds. The bonds are auctioned off on 07:59.867 --> 08:06.947 regular dates and you cannot participate in the auction; 08:06.950 --> 08:08.510 I assume you can't. 08:08.509 --> 08:12.169 You'd have to be an authorized participant, but if you become 08:12.168 --> 08:15.338 an institution you can get authorized to trade in the 08:15.338 --> 08:17.678 auction. These are the dates; 08:17.680 --> 08:22.420 the latest auction was February 14^(th). 08:22.420 --> 08:27.190 I guess that was yesterday, right? 08:27.189 --> 08:33.289 The term means it was a sixty-day Treasury bill; 08:33.289 --> 08:38.919 that means it pays not $100, it would start at $10,000. 08:38.919 --> 08:43.169 Treasury bills--maybe you have to realize there's a distinction 08:43.165 --> 08:46.105 between savings bonds and Treasury bills. 08:46.110 --> 08:49.890 Treasury bills are for serious investors and so they don't come 08:49.894 --> 08:51.424 in small denominations. 08:51.420 --> 08:55.260 The U.S. Government also issues small 08:55.261 --> 09:01.541 denomination debt to individuals to help them called savings 09:01.544 --> 09:06.234 bonds, but we aren't talking about those. 09:06.230 --> 09:11.650 At the February 14^(th) auction, Treasury bills 09:11.646 --> 09:18.826 were--sixty-day treasury bills were sold and the auction price 09:18.829 --> 09:23.569 is given. Well, here's the price of the 09:23.566 --> 09:26.926 bill. The issue date was today, 09:26.932 --> 09:32.012 February 15^(th), and they mature in what should 09:32.012 --> 09:36.662 be exactly sixty days--on April 15^(th). 09:36.660 --> 09:42.880 09:42.879 --> 09:47.009 If you want to buy one you would pay this price. 09:47.009 --> 09:49.479 This number, CUSIP number, 09:49.476 --> 09:53.716 is a number that identifies any security. 09:53.720 --> 09:56.880 It's like you have a social security number or other ID 09:56.881 --> 10:00.571 number, which positively--there might be another person with the 10:00.570 --> 10:03.550 same name as you, God forbid, but you at least 10:03.553 --> 10:06.443 have your own number, which is guaranteed to be 10:06.435 --> 10:09.705 unique to you. So every security has an 10:09.714 --> 10:13.224 identical CUSIP, which identifies it. 10:13.220 --> 10:21.280 I want to start by explaining the numbers here. 10:21.280 --> 10:26.640 10:26.639 --> 10:29.519 How did they get--how do these numbers interrelate? 10:29.520 --> 10:34.910 10:34.909 --> 10:40.119 Well, the discount rate is sort of the--you notice there are two 10:40.116 --> 10:44.826 different interest rates here and you might be confused by 10:44.826 --> 10:48.356 them. The discount rate that is shown 10:48.360 --> 10:53.850 is the number that you plug into a formula to get the price. 10:53.850 --> 10:59.880 What really matters to you as an investor is how much you have 10:59.884 --> 11:03.944 to pay today to get $100 in sixty days. 11:03.940 --> 11:09.450 So, how do we get the price from the discount rate? 11:09.450 --> 11:16.590 Well, there's a formula that's been used by bond traders for 11:16.587 --> 11:23.117 hundreds of years and it's a traditional expression, 11:23.120 --> 11:27.760 which goes from the discount rate to the price. 11:27.759 --> 11:33.829 In this case, price is $99.58 and what does 11:33.830 --> 11:41.680 that equal? It equals 2.51--that's the 11:41.681 --> 11:55.691 discount rate that you see up there--well, (2.510 x 60)/360. 11:55.690 --> 12:01.620 As you know, the maturity is 60-days and, 12:01.623 --> 12:07.713 as you know, there are about 360 days in a 12:07.705 --> 12:10.705 year. By tradition, 12:10.713 --> 12:17.023 they divide by 360, not 365, and so you understand 12:17.019 --> 12:23.969 that dealers of Treasury bills tend to "discounts." 12:23.970 --> 12:27.840 It's like a language, a language of finance. 12:27.840 --> 12:34.820 So what everybody knows is that the discount is converted into a 12:34.821 --> 12:38.591 price according to this formula. 12:38.590 --> 12:43.480 You might ask, well is this an approximate 12:43.477 --> 12:46.337 formula? No, it's an exact formula. 12:46.340 --> 12:49.940 Then you say, well why didn't they divide by 12:49.940 --> 12:54.210 365, because I know there are 365 days in a year? 12:54.210 --> 12:59.390 The answer is--this goes way back--it's an old tradition and 12:59.387 --> 13:02.807 they used to have to do this by hand. 13:02.809 --> 13:07.299 They had to divide by hand and so they didn't like the number 13:07.301 --> 13:11.121 365, so they thought, let's just round it to 360. 13:11.120 --> 13:13.910 As long as everybody knows that's what we're doing, 13:13.909 --> 13:16.029 what difference does it make, right? 13:16.029 --> 13:18.759 That's what you're supposed to know. 13:18.759 --> 13:21.799 If your dealer quotes you a discount rate of 2.51%, 13:21.802 --> 13:25.272 you know how to convert that into the price and that's all 13:25.270 --> 13:28.980 that matters--all that really matters is the price you have to 13:28.981 --> 13:33.571 pay. They also have something up 13:33.567 --> 13:38.427 here called the investment rate. 13:38.430 --> 13:40.470 Yes? Student: I'm sorry, 13:40.468 --> 13:43.498 I don't understand since the left hand side of your equation 13:43.504 --> 13:45.464 does not equal the right hand side, 13:45.460 --> 13:46.200 isn't that discount, not price? 13:46.200 --> 13:50.630 Professor Robert Shiller: I'm sorry, 13:50.627 --> 13:56.317 glad you--that's the difference between 1 and 99.58. 13:56.320 --> 14:03.640 Yes, thank you--between 100 and 99.58. 14:03.640 --> 14:23.820 14:23.820 --> 14:25.470 Are you okay now? 14:25.470 --> 14:29.530 I'm sorry I made a--now the thing is, to convert that 14:29.525 --> 14:33.345 into--what is this other--there's another interest 14:33.347 --> 14:36.777 rate up here called the investment rate. 14:36.779 --> 14:41.739 Well, that's supposed to be your percentage return on an 14:41.744 --> 14:43.464 annualized basis. 14:43.460 --> 14:46.990 Remember, this thing only runs for sixty days and you could 14:46.985 --> 14:50.605 compute your sixty-day return, but people like to compare 14:50.611 --> 14:53.781 annual returns--once again, a tradition we have. 14:53.779 --> 14:56.849 Now, there's nothing special about annual--that's the time it 14:56.847 --> 14:58.787 take the Earth to go around the sun, 14:58.789 --> 15:02.149 but it doesn't have any relevance to finance--but we are 15:02.146 --> 15:04.096 just accustomed to using that. 15:04.100 --> 15:09.400 What we're going to do, however, is take account of 15:09.401 --> 15:16.321 another problem. That is, you might think that 15:16.319 --> 15:27.029 this quantity here is my return but you have to actually divide 15:27.028 --> 15:32.218 it by the price, which is less than a hundred, 15:32.220 --> 15:35.750 to get a return. You're not putting in $100 to 15:35.748 --> 15:39.508 this investment; you're putting in $99.58 for 15:39.510 --> 15:43.790 the investment and you're getting out the difference 15:43.793 --> 15:46.063 between $100 and $99.58. 15:46.059 --> 15:54.569 So, that is not--your return is actually higher than 2.51% on an 15:54.572 --> 15:57.142 annualized basis. 15:57.139 --> 16:01.529 What we do--I'll show you how they got their number. 16:01.530 --> 16:06.840 16:06.840 --> 16:15.740 2.563%, which is the number you see under investment rate, 16:15.744 --> 16:24.964 is equal to 1/(.9958 – 1), corrected for the number of 16:24.961 --> 16:27.931 days in a year. 16:27.930 --> 16:33.400 16:33.400 --> 16:35.690 How do we do that correction? 16:35.690 --> 16:41.780 When I first tried this, I thought, fine I'll multiply 16:41.782 --> 16:47.072 by 365/60, but I forgot this is a leap year. 16:47.070 --> 16:53.840 So, times 366/60. 16:53.840 --> 17:03.360 So, that's how you go from the discount rate to the investment 17:03.357 --> 17:06.087 rate. Do you understand why we had to 17:06.085 --> 17:08.725 do this? The investment rate is telling 17:08.733 --> 17:13.223 you how much money you're really making on an annualized basis, 17:13.223 --> 17:14.893 so it's very simple. 17:14.890 --> 17:24.290 I put in .9958 for every dollar I got out, so my appreciation of 17:24.288 --> 17:27.568 my money is 1/.9958. 17:27.569 --> 17:30.689 Subtract that by $1, which is what I put in, 17:30.687 --> 17:35.107 and that's how much money I made as a fraction of a dollar. 17:35.109 --> 17:40.239 All I have to do then is correct that for the number of 17:40.242 --> 17:43.952 days in a year, so that's what I did. 17:43.950 --> 17:49.180 That's how we go from the discount rate to the investment 17:49.176 --> 17:51.256 rate. Now you might ask, 17:51.256 --> 17:55.456 well if we did 360 here, why don't we just do 360 over 17:55.456 --> 17:57.686 here? Well, it's one of the mysteries 17:57.692 --> 18:00.012 of Wall Street. They like to--when they're 18:00.006 --> 18:03.266 computing the investment yield, they want to be completely 18:03.265 --> 18:05.605 honest and not use any rules of thumb. 18:05.609 --> 18:08.749 So you have to understand that it's 360 a year because that's 18:08.752 --> 18:12.002 just a convention and everybody knows that it's just the way we 18:11.999 --> 18:14.929 quote prices. Rather than say $99.58, 18:14.926 --> 18:20.146 we just quote the 2.51 and everybody knows how to convert. 18:20.150 --> 18:22.640 When you ask for the investment rate, you want to know the 18:22.637 --> 18:25.077 truth--how much am I really getting--so they don't monkey 18:25.081 --> 18:26.841 around here. Also, they don't have to 18:26.843 --> 18:29.243 actually--in the old days, they didn't actually have to 18:29.236 --> 18:30.606 compute the investment rate. 18:30.609 --> 18:33.789 If you were talking to your broker--if you go really old 18:33.787 --> 18:36.847 days, you'd send a boy running over to your broker. 18:36.850 --> 18:39.860 They didn't have telephones; they used to have runners. 18:39.859 --> 18:43.619 The boy would go say, we're offering to pay a 18:43.624 --> 18:48.674 discount rate of 2.51--that was the formula--and then anyone 18:48.672 --> 18:52.892 could do these calculations; they knew what it meant. 18:52.890 --> 18:58.530 This calculation wasn't done very frequently; 18:58.529 --> 19:01.719 that's just if you had one of the satisfactions of knowing how 19:01.722 --> 19:03.242 much money you were making. 19:03.240 --> 19:12.780 19:12.779 --> 19:15.609 I think we pretty much explained--there's another thing 19:15.610 --> 19:17.550 I want to say about Treasury bills. 19:17.549 --> 19:21.949 I used to have up here a page--I used to take--instead of 19:21.946 --> 19:24.926 Treasury Direct, which is a website, 19:24.930 --> 19:27.990 I used to get a clipping from The Wall Street Journal 19:27.992 --> 19:30.952 that showed much the same information that you see on this 19:30.950 --> 19:32.990 chart. But, it showed additional 19:32.986 --> 19:36.136 information that you won't find on Treasury Direct; 19:36.140 --> 19:40.020 it showed bid and ask for dealers. 19:40.019 --> 19:43.439 Now, you have to understand that the Treasury has these 19:43.444 --> 19:45.414 auctions only on these dates. 19:45.410 --> 19:48.760 On February 14^(th), they only sold sixty-day ones, 19:48.756 --> 19:52.406 nothing else. On February 11^(th) they sold 19:52.410 --> 19:56.250 only thirteen-week ones and nothing else. 19:56.250 --> 20:01.310 What if you want to buy a Treasury bill on some other day? 20:01.309 --> 20:04.699 Well, you can go to Treasury Direct as an individual and buy 20:04.700 --> 20:07.110 a Treasury bill, but it may not be the best 20:07.113 --> 20:10.453 place to buy. What you normally do is you go 20:10.453 --> 20:14.633 to a dealer and a dealer is someone, a professional, 20:14.630 --> 20:18.640 who participated in the auction and bought these up to 20:18.638 --> 20:22.418 accumulate an inventory to then sell off to you, 20:22.420 --> 20:24.070 the customer. So normally, 20:24.068 --> 20:27.718 you don't deal with Treasury Direct, you deal with a dealer. 20:27.720 --> 20:31.930 The Wall Street Journal calls around to the dealer, 20:31.930 --> 20:36.290 which has an inventory of all these maturities and asks them 20:36.289 --> 20:38.209 for their bid and ask. 20:38.210 --> 20:43.280 And a dealer--what a dealer does is it maintains an 20:43.283 --> 20:45.923 inventory of, in this case, 20:45.921 --> 20:52.011 Treasury bills and then it stands ready to buy and sell. 20:52.009 --> 20:55.899 So, the bid price is the--they don't do it in terms of price, 20:55.900 --> 20:59.210 they do it in terms of discount--so the bid discount 20:59.207 --> 21:02.187 rate--there would be two numbers for each. 21:02.190 --> 21:05.670 One is the bid, which is what they'll pay you 21:05.667 --> 21:09.617 for a Treasury bill if you want to sell to them. 21:09.619 --> 21:15.319 The ask is what you have to pay them through this formula. 21:15.319 --> 21:23.839 The formula is--I could write it this way: price equals one 21:23.843 --> 21:26.933 hundred minus this. 21:26.930 --> 21:32.870 Normally, when you have a dealer, the dealer has a--when 21:32.869 --> 21:37.949 we talk in terms of price the dealer has an ask, 21:37.945 --> 21:41.505 which is higher than the bid. 21:41.509 --> 21:44.609 If you go to an antique dealer--maybe you're familiar or 21:44.612 --> 21:47.832 maybe you've done this if you've bought furniture for some 21:47.827 --> 21:49.347 apartment or something. 21:49.349 --> 21:54.139 The dealer will charge a higher price for you to buy the 21:54.140 --> 21:59.450 furniture than will give to you to purchase the furniture from 21:59.453 --> 22:01.633 you; that's how the dealer makes a 22:01.628 --> 22:04.298 difference. The difference between bid and 22:04.301 --> 22:08.491 ask is the profit for the dealer and the bid-ask spread is the 22:08.492 --> 22:10.212 profit for the dealer. 22:10.210 --> 22:14.520 You can see these--you can see the bid and ask in The Wall 22:14.521 --> 22:16.031 Street Journal. 22:16.029 --> 22:19.829 It's interesting to look at it because you note that the 22:19.825 --> 22:22.995 bid-ask spread, which is the difference between 22:22.999 --> 22:25.689 the bid and the ask for the dealer, 22:25.690 --> 22:30.210 is narrower in the more liquid securities and some of the 22:30.205 --> 22:35.035 securities that are small and unimportant have a wide bid-ask 22:35.043 --> 22:37.553 spread. That means that it's harder to 22:37.545 --> 22:40.235 make a market for it, so the dealer wants to charge 22:40.239 --> 22:45.129 more. This doesn't show this here. 22:45.130 --> 22:48.160 Unfortunately, The Wall Street Journal 22:48.161 --> 22:51.951 stopped carrying this and I thought--it's an interesting 22:51.951 --> 22:53.951 story about what goes on. 22:53.950 --> 22:58.910 The Wall Street Journal is the most influential 22:58.912 --> 23:04.342 financial publication in this country but it has been going 23:04.343 --> 23:09.683 through financial difficulties with the Internet age. 23:09.680 --> 23:14.960 In the last five years, the stock in Dow Jones Company 23:14.958 --> 23:17.048 has fallen by half. 23:17.050 --> 23:18.810 What's happening? 23:18.809 --> 23:22.699 Well, there are many factors, but one important factor is, 23:22.699 --> 23:26.589 the rise of the Internet has competed with--people used to 23:26.588 --> 23:29.998 buy The Wall Street Journal to get data like 23:29.999 --> 23:32.229 this. You see how I completely 23:32.225 --> 23:35.415 bypassed The Wall Street Journal and I went to 23:35.422 --> 23:38.842 Treasury Direct? There are a million websites 23:38.842 --> 23:43.832 that give away financial data so The Wall Street Journal 23:43.829 --> 23:45.839 was not doing as well. 23:45.839 --> 23:49.569 Do you know what happened finally? 23:49.570 --> 23:56.190 I'll give this as an aside; they reduced the size of the 23:56.192 --> 23:58.992 newspaper in 2005. 23:58.990 --> 24:01.550 It used to be a big, broad sheet and they made it 24:01.554 --> 24:04.444 smaller in 2005 and they started--they keep cutting out 24:04.439 --> 24:06.629 data. There's less and less data in 24:06.631 --> 24:08.521 The Wall Street Journal. 24:08.519 --> 24:10.429 It used to be this big, thick thing and you would go 24:10.432 --> 24:12.572 there everyday to look up--and everything was in there. 24:12.569 --> 24:17.169 But now, the Web is competing with it, so they're scaling down 24:17.170 --> 24:20.640 the size of the paper and trying to survive. 24:20.640 --> 24:25.140 So, they created Wall Street Journal Online, 24:25.135 --> 24:29.175 which is WSJ.com, and they were trying to make 24:29.181 --> 24:32.451 money off of that, but people weren't willing to 24:32.447 --> 24:34.207 pay for it. You know how it is on the Web? 24:34.210 --> 24:38.600 You can get so much for free, why should I pay for WSJ.com? 24:38.599 --> 24:42.849 That wasn't working well, so last year--about one year 24:42.853 --> 24:46.383 ago--they announced, wallstreetjournal.com is 24:46.384 --> 24:51.364 absolutely free and we're going to give away all the data, 24:51.359 --> 24:54.099 basically all the data that used to be in the newspaper, 24:54.102 --> 24:57.222 free to anyone. I thought that was great. 24:57.220 --> 25:00.510 Now we can all get The Wall Street Journal without 25:00.509 --> 25:02.979 paying for it. There's some problem with that; 25:02.980 --> 25:06.980 it's not economic, so let's not be too jubilant. 25:06.980 --> 25:11.110 What ended up happening is, you know the news, 25:11.110 --> 25:16.250 Rupert Murdoch bought The Wall Street Journal last 25:16.250 --> 25:22.030 fall and he announced that Wall Street Journal--WSJ.com--will no 25:22.032 --> 25:26.042 longer be free. So, this is the reality of the 25:26.043 --> 25:29.493 world. I thought it was interesting to 25:29.492 --> 25:33.412 look at Rupert Murdoch--this is finance. 25:33.410 --> 25:36.010 This may sound like an aside, but this is all finance. 25:36.009 --> 25:39.349 Rupert Murdoch, you may have heard of him, 25:39.352 --> 25:44.242 is a huge newspaper baron who buys up newspapers all over the 25:44.244 --> 25:46.804 world. It's interesting, 25:46.798 --> 25:52.318 he's been at it--he's continuing what his father did. 25:52.319 --> 25:55.219 To become the biggest publishing monolith in the 25:55.215 --> 25:58.535 world, it takes maybe a hundred years, so his father in 25:58.541 --> 26:01.191 Australia started buying up newspapers. 26:01.190 --> 26:06.430 His father was born in 1886 and now Rupert Murdoch is 26:06.430 --> 26:10.410 continuing. Rupert Murdoch is in his 70s 26:10.413 --> 26:13.663 and he's still buying newspapers. 26:13.660 --> 26:17.900 He kind of makes them survive and NewsCorp doubled its 26:17.895 --> 26:21.485 price--that's his company--doubled in the last 26:21.491 --> 26:23.491 five years. You can see, 26:23.492 --> 26:27.302 this is how the unseen rule of finance--The Wall Street 26:27.302 --> 26:30.582 Journal is a venerable newspaper and source of 26:30.577 --> 26:34.337 information about finance, but it's not making money. 26:34.339 --> 26:37.139 The world is changing and The Wall Street Journal 26:37.137 --> 26:38.547 is flagging. So NewsCorp, 26:38.551 --> 26:42.121 whose price doubled when The Wall Street Journal's fell 26:42.117 --> 26:44.957 in half, eats up and The Wall Street 26:44.958 --> 26:48.548 Journal is gobbled up by the bigger company. 26:48.549 --> 26:51.659 You can see why stock prices matter. 26:51.660 --> 26:55.870 The Newscorp's rising stock price was a sign that Rupert 26:55.874 --> 27:00.014 Murdoch had some idea how to make money and The Wall 27:00.011 --> 27:03.461 Street Journal was not doing as well, 27:03.460 --> 27:04.870 so it got gobbled up. 27:04.869 --> 27:08.239 The question is, what will happen to The Wall 27:08.244 --> 27:10.044 Street Journal now? 27:10.040 --> 27:16.430 Well, they have to make money; that's the real world. 27:16.430 --> 27:19.640 So Rupert Murdoch tends to bring papers around. 27:19.640 --> 27:23.360 I'm just going to go a little bit further on--Rupert Murdoch 27:23.357 --> 27:26.507 bought The Times of London in 1981--that was 27:26.508 --> 27:28.208 twenty-seven years ago. 27:28.210 --> 27:31.650 The Times of London is one of the most venerable 27:31.653 --> 27:35.163 newspapers in the world and it was losing money fast; 27:35.160 --> 27:38.950 it might have disappeared if Murdoch hadn't taken over. 27:38.950 --> 27:43.380 But, Murdoch turned it around and it's still around. 27:43.380 --> 27:45.010 They turned it into a tabloid. 27:45.009 --> 27:48.549 It was the most dignified newspaper in the world and he 27:48.547 --> 27:51.227 kind of decided that, in order to survive, 27:51.233 --> 27:54.643 they had to get a little bit more down to earth. 27:54.640 --> 27:57.950 So, they reduced the size, so it looks like one of 27:57.948 --> 28:01.728 those--like New York Daily News newspapers now. 28:01.730 --> 28:03.990 It's still a great newspaper. 28:03.990 --> 28:07.720 He added celebrity gossip too, which The London 28:07.721 --> 28:10.321 Times would never do in the past. 28:10.320 --> 28:12.090 But you go to do it, right? 28:12.089 --> 28:15.439 That's the thing about the real world and finance is very much 28:15.444 --> 28:16.714 about the real world. 28:16.710 --> 28:20.510 Murdoch claims he will not alter the editorial content of 28:20.510 --> 28:22.750 The Wall Street Journal. 28:22.750 --> 28:25.590 The thing that we have seen him doing is charging more, 28:25.585 --> 28:27.575 but I guess we've got to allow that. 28:27.579 --> 28:30.839 So we may feel annoyed that we now have to pay to get our 28:30.836 --> 28:32.926 Wall Street Journal Online. 28:32.930 --> 28:37.650 In the long run, we want The Wall Street 28:37.650 --> 28:43.720 Journal and so I guess that--we just have to accept 28:43.718 --> 28:46.398 that. If you want to find--by the 28:46.404 --> 28:50.194 way, if you want to read The Wall Street Journal online 28:50.185 --> 28:52.475 at Yale, you can do it no problem. 28:52.480 --> 28:55.450 You go to ABI Inform, which is one of the things that 28:55.449 --> 28:58.249 Yale subscribes to, on your laptop and it puts you 28:58.247 --> 29:01.557 right into the text of The Wall Street Journal. 29:01.559 --> 29:03.889 But it doesn't put you, as far as I can tell, 29:03.889 --> 29:06.059 into Wall Street Journal Online. 29:06.059 --> 29:10.769 We have other--lots of data sources--that Yale subscribes to 29:10.768 --> 29:14.118 and there are lots of free data sources, 29:14.119 --> 29:16.849 but Wall Street Journal Online is not free. 29:16.849 --> 29:21.909 Anyway, I want to talk--you understand now about discount 29:21.907 --> 29:24.057 bonds? It's pretty simple, right? 29:24.059 --> 29:27.309 I just wanted to get the pricing formula. 29:27.309 --> 29:30.419 The critical thing about a discount bond is it pays no 29:30.415 --> 29:33.745 interest. Treasury bills in the United 29:33.750 --> 29:37.210 States are limited to one year out; 29:37.210 --> 29:38.860 well, that's the name of it. 29:38.859 --> 29:44.779 We call an instrument of the U.S. 29:44.779 --> 29:49.629 Treasury with a maturity less than or equal to one year--we 29:49.626 --> 29:54.636 call that a bill--and they used to be the only discount bonds 29:54.639 --> 29:56.139 issued by the U.S. 29:56.143 --> 29:59.923 Government. Now, they also have longer 29:59.915 --> 30:05.065 maturity, called Treasury strips, but let me move to the 30:05.067 --> 30:07.907 other. So we have--U.S. 30:07.910 --> 30:13.430 Government issues bills and that's less than or equal to one 30:13.427 --> 30:16.417 year and they pay no interest. 30:16.420 --> 30:21.160 They also have government-issued notes and 30:21.161 --> 30:27.061 that's from one to ten years and bonds--this is just 30:27.058 --> 30:35.288 jargon--these are ten or more, well actually more than ten. 30:35.289 --> 30:42.169 I'll show you from Treasury Direct--I have notes--this 30:42.173 --> 30:45.943 should be greater than ten. 30:45.940 --> 30:54.770 These are the recent auctions of the Treasury of notes. 30:54.769 --> 30:58.929 Now, these are different from bills, as I emphasized, 30:58.930 --> 31:01.170 because they pay interest. 31:01.170 --> 31:03.320 They carry what's called a coupon. 31:03.320 --> 31:12.940 And then we have the bonds. 31:12.940 --> 31:15.570 You see there aren't as many of these issued. 31:15.569 --> 31:18.399 We issue a lot of–there are a lot of auctions of 31:18.402 --> 31:21.612 Treasury bills and there are comparatively fewer of bonds. 31:21.610 --> 31:27.660 31:27.660 --> 31:33.730 So, let's talk about a bond. 31:33.730 --> 31:41.030 A bond differs from a bill in that it carries what's called a 31:41.025 --> 31:47.465 coupon, which I will denote by the letter C, 31:47.470 --> 31:56.650 and it has a principal, which it pays out at the 31:56.645 --> 32:00.935 end--of one hundred. 32:00.940 --> 32:05.270 Of course, there would be larger denominations than $100, 32:05.273 --> 32:08.683 but by tradition, we speak of them as if they 32:08.677 --> 32:11.847 were bonds that you paid $100 to get. 32:11.849 --> 32:21.319 Now, another Wall Street tradition is that bonds pay a 32:21.321 --> 32:28.891 coupon; they pay C/2 every six 32:28.894 --> 32:30.544 months. 32:30.540 --> 32:35.850 32:35.849 --> 32:38.479 The coupon is expressed as an annual amount; 32:38.480 --> 32:41.060 you get half of it every six months. 32:41.059 --> 32:45.609 The reason they call them coupons is that, 32:45.612 --> 32:50.722 in the old days, you used to actually--when you 32:50.721 --> 32:54.541 bought a bond, there would be a piece of paper 32:54.542 --> 32:57.842 and the piece of paper would have attached to it a lot of 32:57.835 --> 33:00.065 little coupons that you would clip. 33:00.069 --> 33:04.049 If it was a twenty-year bond, there would be forty coupons, 33:04.052 --> 33:08.172 one for each six-month period, and each one would have a date 33:08.173 --> 33:10.123 on it. What you used to do is, 33:10.119 --> 33:13.399 every six months you'd pull out your bonds and you'd clip the 33:13.403 --> 33:17.433 coupons with a pair of scissors; you take them to a bank and 33:17.425 --> 33:20.775 they would give you cash for your coupons. 33:20.779 --> 33:24.839 So, we still call them coupons, but now we don't do it--we do 33:24.844 --> 33:26.474 things electronically. 33:26.470 --> 33:28.370 You don't have to clip coupons anymore. 33:28.369 --> 33:32.169 If you want to see bonds as they used to look, 33:32.165 --> 33:36.205 with their coupons, there are a number of them at 33:36.213 --> 33:40.943 the International Center for Finance down the street here 33:40.936 --> 33:44.306 with their coupons still attached. 33:44.309 --> 33:48.059 So they've got a lot of--Will Goetzmann and Geert Rouwenhorst 33:48.061 --> 33:51.881 are collectors of old bonds and they've got lots of bonds with 33:51.876 --> 33:53.936 their coupons still attached. 33:53.940 --> 33:56.460 You know what that means when they're framed there on the wall 33:56.461 --> 33:57.951 with their coupons still attached? 33:57.950 --> 34:01.110 It means the company went bankrupt and never paid; 34:01.109 --> 34:03.869 otherwise, the coupons would have been clipped. 34:03.869 --> 34:07.759 It's actually--our International Center for Finance 34:07.761 --> 34:11.031 is sort of a museum for defaulted bonds. 34:11.030 --> 34:14.490 The ones that are beautiful for framing are the ones that 34:14.488 --> 34:17.018 failed, so you can see all the coupons. 34:17.019 --> 34:19.919 Some of them have some of the coupons clipped and then they 34:19.920 --> 34:22.670 stop and you know that it was bad news when they stopped 34:22.670 --> 34:25.820 clipping them. We still call them coupons. 34:25.820 --> 34:32.030 If you have a bond with an interest rate of 4.375%--that's 34:32.031 --> 34:38.351 not an easy one to divide by two--but you would get half of 34:38.352 --> 34:42.822 that every six months until maturity. 34:42.820 --> 34:49.860 We have to ask then, how do we get the price and the 34:49.863 --> 34:52.353 yield from this? 34:52.350 --> 34:55.490 34:55.489 --> 34:58.429 What we do is we take the interest rate, 34:58.427 --> 35:02.567 which I'll call r, and plug it into a formula, 35:02.570 --> 35:11.640 which I didn't actually do the arithmetic to check--to check 35:11.643 --> 35:19.253 their number. The price is just the present 35:19.252 --> 35:28.762 value of the coupons at the interest rate r, 35:28.760 --> 35:36.140 so the price of a bond is the present discounted value of 35:36.144 --> 35:45.024 coupons and principal, at rate r. 35:45.020 --> 35:48.970 35:48.969 --> 35:51.799 Now, you have to understand that when you buy a bond, 35:51.799 --> 35:55.279 if you buy it at issue, you get the first coupon in six 35:55.283 --> 35:59.193 months, the second coupon in one year, the third coupon in 35:59.188 --> 36:03.268 eighteen months, and the last coupon you get at 36:03.269 --> 36:05.029 the maturity date. 36:05.030 --> 36:08.710 So that means--what is the stream of payments? 36:08.710 --> 36:14.440 You get C/2 in six months, C/2 again in a 36:14.440 --> 36:19.110 year, C/2 again in eighteen months, 36:19.110 --> 36:26.900 and that continues until the last date--the maturity 36:26.903 --> 36:31.643 date--when you get 100 + C/2. 36:31.639 --> 36:38.399 The price is just the present value of that stream, 36:38.401 --> 36:43.001 discounted at the interest rate. 36:43.000 --> 37:03.370 The formula can also be written and expanded out--P = 37:03.370 --> 37:20.610 (c/2) x [(1/(r/2)--which is the 37:20.606 --> 37:34.456 consol formula, if this were applied to an 37:34.459 --> 37:45.309 infinite stream-- - 1/(1+(r/2))^(2T) x 37:45.306 --> 37:57.806 1/(r/2)]. Let me make sure I've got this 37:57.811 --> 38:07.981 right-- +100 (1/(1+(r/2))^(2T). 38:07.980 --> 38:11.870 This should be obvious--if I did that right--this should be 38:11.868 --> 38:16.158 obvious from what you learned about in present value formulas. 38:16.159 --> 38:21.369 If you had a perpetuity, which paid C/2 forever, 38:21.371 --> 38:26.391 you already know from the perpetuity formula that the 38:26.390 --> 38:31.600 value of that would be C/2 divided by r/2 38:31.602 --> 38:35.562 if r/2 is the discount rate. 38:35.559 --> 38:42.549 It's not forever because it terminates after 2T periods of 38:42.551 --> 38:45.741 six-month interval each. 38:45.739 --> 38:51.759 You want to subtract off the value of a perpetuity that 38:51.761 --> 38:56.111 starts after 2T, six-month intervals, 38:56.110 --> 39:02.770 so this is the present value of the perpetuity that starts after 39:02.771 --> 39:05.521 2T, six-month intervals. 39:05.519 --> 39:09.909 Then you want to add the present value of the principal 39:09.908 --> 39:11.938 and that's the formula. 39:11.940 --> 39:17.830 That's another conventional formula that goes from interest 39:17.830 --> 39:21.080 rate to price of the security. 39:21.080 --> 39:39.310 39:39.309 --> 39:45.099 Now, I want to talk about the term structure of interest rates 39:45.098 --> 39:48.038 and that's my next plot here. 39:48.039 --> 39:53.859 That's the term structure as of now on the chart. 39:53.860 --> 40:04.930 We've identified the prices and yields of bonds of various 40:04.926 --> 40:11.096 maturities. How do the prices and yields 40:11.099 --> 40:15.269 look at various points in time? 40:15.269 --> 40:18.929 So, I've got here a term structure; 40:18.929 --> 40:26.909 well, the term structure is the plot of yield-to-maturity 40:26.911 --> 40:30.761 against time-to-maturity. 40:30.760 --> 40:35.180 This is January of this year, before the Fed cut interest 40:35.181 --> 40:38.341 rates, and this is the term structure. 40:38.340 --> 40:43.110 I've got the Federal Funds Rate--it's the shortest interest 40:43.105 --> 40:47.865 rate, an overnight rate--it was at 4% at that time and then 40:47.871 --> 40:50.091 there was a sharp drop. 40:50.090 --> 40:53.610 The three-month Treasury bill rate is shown there--it was much 40:53.608 --> 40:55.048 lower--it was under 3%. 40:55.050 --> 41:00.160 Then the--so the term structure was downward-sloping until about 41:00.159 --> 41:04.539 two and a half years and then it was upward sloping. 41:04.539 --> 41:08.089 The interesting question from the standpoint of economic 41:08.085 --> 41:11.045 theory is, why did it have that funny shape? 41:11.050 --> 41:19.060 I want to compare it with other examples of the term structure 41:19.064 --> 41:23.244 recently. This is the term structure just 41:23.244 --> 41:27.924 a short while ago--of December 2006--very different. 41:27.920 --> 41:33.160 The Federal Funds Rate was 5.5% and then the whole term 41:33.156 --> 41:37.516 structure--all the way--almost all the way. 41:37.519 --> 41:41.819 Well, there's this funny glitch here between three-month and 41:41.823 --> 41:45.473 one-year, but then it just continued to decline. 41:45.469 --> 41:48.949 That's a strongly downward-sloping term structure. 41:48.949 --> 41:53.399 This is another example, not so long ago--this is 41:53.397 --> 41:57.017 December 2003. Now, the term structure was 41:57.023 --> 42:00.123 pretty much upward-sloping everywhere. 42:00.119 --> 42:03.509 At that time, the Fed had cut the Federal 42:03.510 --> 42:07.580 Funds Rate to 1%, we had very low short rates. 42:07.579 --> 42:12.259 And the three-month Treasury bill rate was about the same, 42:12.262 --> 42:14.382 at 1%. Going further out, 42:14.382 --> 42:17.392 the term structure just kept rising. 42:17.389 --> 42:21.349 It's one of the questions of economics--what determines the 42:21.349 --> 42:24.059 term structure? You have to understand that 42:24.064 --> 42:25.854 it's determined in the market. 42:25.849 --> 42:30.579 The Fed has these auctions but it auctions them off at what 42:30.580 --> 42:34.980 price the public will pay, so the Fed doesn't determine 42:34.984 --> 42:36.864 the term structure. 42:36.860 --> 42:39.900 Neither do the dealers determine the term structure; 42:39.900 --> 42:43.510 the dealers have to buy and sell at prices that are in the 42:43.510 --> 42:45.730 market. It has to stay relevant to the 42:45.726 --> 42:49.066 market, so nobody really knows where these interest rates come 42:49.074 --> 42:51.274 from because no one person sets them. 42:51.269 --> 42:54.539 If you're a dealer, you've got to keep your bid-ask 42:54.544 --> 42:57.254 at market; otherwise, you'll get only one 42:57.253 --> 42:58.923 side or the other, right? 42:58.920 --> 43:03.140 You'll be selling too cheaply or you'll be buying too dearly. 43:03.139 --> 43:05.569 You've got to do it so you're right in the middle, 43:05.567 --> 43:07.447 so that the market is in the middle. 43:07.449 --> 43:10.099 Nobody really sees the reason for this; 43:10.099 --> 43:16.009 it's all a question of theory, so we have to think a little 43:16.012 --> 43:17.952 bit about theory. 43:17.949 --> 43:23.789 The term structure is one of the most interesting things in 43:23.791 --> 43:29.231 economics because it shows the price of time at various 43:29.229 --> 43:34.869 maturities. In 2003, time was almost free 43:34.867 --> 43:37.427 out three months. 43:37.429 --> 43:40.809 It didn't--if you needed more time to get some business done 43:40.812 --> 43:43.792 you'd have to borrow, but you'd only have to pay 1% a 43:43.793 --> 43:46.593 year. That would be like a quarter of 43:46.590 --> 43:49.900 1% to postpone your payment by another year; 43:49.900 --> 43:51.700 so time was really cheap. 43:51.699 --> 43:55.699 But if you wanted to postpone it over seven years or so, 43:55.695 --> 43:58.015 time got a lot more expensive. 43:58.019 --> 44:02.109 Why is this and why is the price of time changing? 44:02.110 --> 44:10.310 One thing to do is to go back and ask, what really are the 44:10.310 --> 44:13.620 reasons for interest? 44:13.619 --> 44:22.359 I wanted to talk about the theory of interest as presented 44:22.360 --> 44:31.410 by Professor Irving Fisher at Yale, who is famous for having 44:31.406 --> 44:37.456 exposited that. I imagine he did it at this 44:37.459 --> 44:43.849 very blackboard because, as I said, he had his office in 44:43.854 --> 44:49.324 this building and he didn't die until 1940s, 44:49.320 --> 44:51.680 so he must have been--this building was--this room goes 44:51.679 --> 44:52.509 back to the '30s. 44:52.510 --> 44:56.870 He had a diagram, which illustrated what is the 44:56.873 --> 45:02.283 ultimate cause of interest, and it helps us to think about 45:02.279 --> 45:08.539 this diagram whenever we try to understand the term structure. 45:08.539 --> 45:17.819 What his diagram--this is the famous Irving Fisher 45:17.823 --> 45:26.353 diagram--depicted, there's only one period; 45:26.349 --> 45:32.019 there's today on this axis and tomorrow–well, 45:32.016 --> 45:37.906 I shouldn't say tomorrow, that suggests one day--next 45:37.909 --> 45:40.629 period on this axis. 45:40.630 --> 45:46.840 Let's say it's one year and I'm going to actually plot on this 45:46.838 --> 45:50.398 axis a person's income this year. 45:50.400 --> 45:59.720 I should say income today on this axis and on this, 45:59.723 --> 46:03.643 income next period. 46:03.639 --> 46:08.659 So for each person, there is a point representing 46:08.659 --> 46:13.259 my income today and my income next period. 46:13.260 --> 46:15.590 Let's assume that I know what I'm earning next year; 46:15.590 --> 46:17.950 there is actually uncertainty about it. 46:17.949 --> 46:24.119 If I draw this down this--this point is this year's income down 46:24.116 --> 46:28.986 here and this point here is next year's income; 46:28.990 --> 46:33.970 I'll use Y for income. 46:33.969 --> 46:37.779 This is Y today and this is Y next period. 46:37.780 --> 46:43.060 A person has a budget constraint if the person can 46:43.058 --> 46:47.258 borrow and lend at the interest rate. 46:47.260 --> 46:55.970 The budget constraint is a straight line through this point 46:55.966 --> 47:00.616 with a slope of (1+r). 47:00.620 --> 47:01.970 I'll try to draw this line. 47:01.970 --> 47:06.770 47:06.770 --> 47:08.310 That should be a straight line. 47:08.309 --> 47:10.889 It doesn't look that straight because I was running out of 47:10.890 --> 47:14.140 room up here. You see, that's a straight line. 47:14.139 --> 47:25.009 This point here then is the present value of your income; 47:25.010 --> 47:31.720 it's (Y _today + Y _next 47:31.718 --> 47:36.058 period) / (1 + r). 47:36.060 --> 47:40.450 What's this point up here? 47:40.449 --> 47:47.939 This point up here is the terminal value of my income, 47:47.939 --> 47:56.839 so the upper point is (Y _today *(1 + r) 47:56.842 --> 48:01.932 + Y _next year. 48:01.929 --> 48:05.529 In an ideal world, where you can borrow and lend 48:05.532 --> 48:09.752 freely, an individual could choose consumption along any 48:09.747 --> 48:11.507 point on this line. 48:11.510 --> 48:15.180 I could consume all of my income--if I borrow against my 48:15.182 --> 48:18.192 future income, I could--there's a problem here 48:18.187 --> 48:21.327 of starvation. If I consume it all this year, 48:21.333 --> 48:22.633 I will be starving. 48:22.630 --> 48:25.420 I don't see how I can earn income next year but, 48:25.420 --> 48:28.210 in principle, that's what Irving Fisher said. 48:28.210 --> 48:31.100 Well, I could just not consume anything this year and I could 48:31.104 --> 48:33.714 wait until next year and consume the terminal value. 48:33.710 --> 48:37.420 I would take my income this year, invest it at the interest 48:37.422 --> 48:41.262 rate, and it would turn into Y today times (1 + R) and 48:41.262 --> 48:44.952 then I get income next year; so I could consume all that. 48:44.949 --> 48:47.909 I can consume at any point along that line as well. 48:47.909 --> 48:50.939 I could consume at today's income, or I could consume here, 48:50.935 --> 48:52.235 or I consume down here. 48:52.239 --> 48:55.359 If I consume less than my income today, 48:55.360 --> 49:00.040 I'm saving and my consumption would be lower this year. 49:00.040 --> 49:02.680 Am I doing that right? 49:02.679 --> 49:06.919 No, if I'm saving this year my consumption would be less than 49:06.922 --> 49:11.022 my income, so my consumption might be here and I would then 49:11.023 --> 49:12.723 have more next year. 49:12.719 --> 49:18.959 Each individual reaches a decision--each individual has an 49:18.964 --> 49:25.104 income point and decides how much to consume based on the 49:25.099 --> 49:27.509 budget constraint. 49:27.510 --> 49:32.210 Now, the interest rate in Irving Fisher's world has to 49:32.213 --> 49:36.653 equate supply and demand in the market for debt. 49:36.650 --> 49:42.090 Each person who wants to borrow has to be met by somebody else 49:42.093 --> 49:46.203 who wants to lend, so the interest rate that we 49:46.198 --> 49:49.588 have in society is the compromise. 49:49.590 --> 49:55.520 It's the interest rate that clears the market for loans and 49:55.521 --> 50:01.351 that interest rate determines the market interest rate. 50:01.349 --> 50:06.249 Nobody can see the interest rate--why the interest rate's at 50:06.250 --> 50:10.570 the level it is in the market--because nobody can see 50:10.570 --> 50:16.110 all these individuals; but that's why the interest 50:16.110 --> 50:21.620 rate gets determined and is in equilibrium. 50:21.619 --> 50:24.829 Why the interest rate clears--it's a mysterious 50:24.830 --> 50:28.460 phenomenon, because it's a market phenomenon and each 50:28.458 --> 50:32.718 person only sees his or her own contribution to the market and 50:32.715 --> 50:34.595 not the whole market. 50:34.599 --> 50:38.929 Irving Fisher also drew on the curve a production possibility 50:38.926 --> 50:42.816 frontier for society, which he made downward-curved. 50:42.820 --> 50:48.050 This is production possibility frontier and that is a 50:48.049 --> 50:54.279 curve--you've seen these before in economics--that says how the 50:54.284 --> 51:00.224 production of our society can produce different combinations 51:00.217 --> 51:04.237 of income this year and next year. 51:04.239 --> 51:07.789 If there were no credit markets, everyone would have to 51:07.794 --> 51:10.694 be on the production possibility frontier; 51:10.690 --> 51:12.260 there would be no other choice. 51:12.260 --> 51:16.540 But if we have credit markets, then people can individually 51:16.537 --> 51:20.957 choose to be off the production possibility frontier and at a 51:20.961 --> 51:24.871 higher level of consumption than otherwise would. 51:24.869 --> 51:29.319 You might have some people up here who are saving and other 51:29.324 --> 51:33.324 people down here who are dissaving and the production 51:33.318 --> 51:36.158 would be operating at the middle. 51:36.159 --> 51:42.369 So, that is Irving Fisher's diagram in a nutshell, 51:42.370 --> 51:50.610 but I think it's--so what does it say about the term structure? 51:50.610 --> 51:53.830 It says that at different horizons everything on this 51:53.833 --> 51:55.263 diagram is different. 51:55.260 --> 51:58.900 The production possibility frontier at different horizons 51:58.896 --> 52:00.516 is in different places. 52:00.519 --> 52:04.689 The budget constraint is going to have a different slope to it 52:04.687 --> 52:08.097 and preferences will be different over this horizon 52:08.102 --> 52:11.452 between consumption then and consumption now. 52:11.449 --> 52:15.499 So you--it doesn't--this theory doesn't say a whole lot about 52:15.502 --> 52:19.422 what the term structure will look like but it suggests that 52:19.419 --> 52:23.809 it's determined by the interplay of lots of economic factors. 52:23.810 --> 52:35.010 52:35.010 --> 52:39.370 I want to talk about a couple of other basic concepts in 52:39.371 --> 52:41.751 economics of interest rates. 52:41.750 --> 52:47.530 One of them is the forward rate and the other one is inflation 52:47.530 --> 52:49.900 indexed interest rates. 52:49.900 --> 52:57.680 Forward rates--I wrote a survey article years ago about the term 52:57.677 --> 53:05.447 structure of interest rates and I wanted to find out who was the 53:05.454 --> 53:10.644 originator of the term "forward rate." 53:10.639 --> 53:14.619 I asked my graduate student research assistant to research 53:14.617 --> 53:18.727 the whole literature and find out where did the word forward 53:18.734 --> 53:22.324 rate come from. My graduate student came back 53:22.318 --> 53:27.148 and said, it seems to have been Sir John Hicks in London in his 53:27.147 --> 53:30.727 1931--1939 book, A Value in Capital. 53:30.730 --> 53:38.370 53:38.370 --> 53:40.710 This is another aside. 53:40.710 --> 53:43.800 but I think it's motivational, and so I said, 53:43.798 --> 53:45.338 are you sure that J.R. 53:45.342 --> 53:48.292 Hicks invented the term "forward rate"? 53:48.290 --> 53:49.890 He said, how can I be sure? 53:49.889 --> 53:51.519 I mean, I've looked through everything; 53:51.519 --> 53:53.239 I can't find any earlier reference. 53:53.239 --> 53:55.979 And he said, I think it's J.R. 53:55.983 --> 53:58.403 Hicks. Then, I was talking it over 53:58.401 --> 54:02.161 with another graduate student and he said, well if you want to 54:02.156 --> 54:04.056 find out why don't you ask J.R. 54:04.064 --> 54:06.334 Hicks? And I said, wait a minute, 54:06.326 --> 54:07.906 is that guy still alive? 54:07.910 --> 54:09.690 He said, I think he is. 54:09.690 --> 54:13.880 I found out he was living in London--Lord Hicks; 54:13.880 --> 54:17.360 I guess he got knighted for his contribution. 54:17.360 --> 54:20.400 I wrote him a letter and I said, basically, 54:20.403 --> 54:22.653 did you invent forward rates? 54:22.650 --> 54:26.870 Then, I didn't get any response for like three months and then 54:26.872 --> 54:29.782 to my surprise I got a hand-written letter, 54:29.780 --> 54:32.480 in kind of a trembling handwriting; 54:32.480 --> 54:35.780 I still have it. I should--I can put it up on 54:35.784 --> 54:36.774 the screen actually. 54:36.769 --> 54:44.979 He said, my apologies--he was very polite and diplomatic. 54:44.980 --> 54:48.950 He said, my apologies for not answering your letter but my 54:48.948 --> 54:52.218 health is poor and--but it was a long letter. 54:52.219 --> 54:55.669 He said, I'm trying to remember where I got the idea and, 54:55.669 --> 54:59.119 he said, I think it probably came from some of our coffee 54:59.118 --> 55:02.628 hours at The London School of Economics in the 1920s. 55:02.630 --> 55:05.910 He said, we were discussing that, and then he said, 55:05.909 --> 55:09.849 I thought it was in a book that my wife and I translated from 55:09.845 --> 55:13.385 the Swedish in the 1930s but, he said, I've looked and it's 55:13.387 --> 55:15.487 not there. So he said, I guess maybe it is 55:15.487 --> 55:17.927 my idea--I was the first person to write it up. 55:17.929 --> 55:22.209 Then he died shortly thereafter, so I got to him just 55:22.207 --> 55:25.507 in time. I thought I would describe 55:25.512 --> 55:31.342 forward rates in terms of the coffee hour at The London School 55:31.336 --> 55:34.006 of Economics in the '20s. 55:34.010 --> 55:38.230 This is J.R. Hicks talking--so the year is 55:38.225 --> 55:44.385 1925--and we're talking about investing in discount bonds and 55:47.889 --> 55:54.939 Now suppose--the idea that Hicks invented is that they're, 55:54.940 --> 56:02.610 implicit in the term structure, there are future interest rates 56:02.609 --> 56:07.069 already quoted. I showed you the term structure. 56:07.070 --> 56:11.060 I showed you a one-year Treasury bill rate for right 56:11.056 --> 56:14.966 now--that's not right now, but you can see I have a 56:14.965 --> 56:18.635 one-year and a two-year Treasury bill rate. 56:18.639 --> 56:22.669 The idea of a forward rate is that, implicit in that term 56:22.665 --> 56:26.255 structure is also a quote for the one-year rate, 56:26.260 --> 56:29.060 one year hence, because if you look at the 56:29.062 --> 56:31.732 two-year rate, can't you infer back what 56:31.727 --> 56:34.937 interest rates are going to be in one year? 56:34.940 --> 56:39.600 Because the two-year rate is--you've got the one-year rate 56:39.604 --> 56:42.554 and the two rate, so between the two, 56:42.550 --> 56:45.230 what's left? The difference between those 56:45.225 --> 56:47.905 two somehow reflects what interest rates will be between 56:47.908 --> 56:50.378 one and two. What Hicks said--this is the 56:50.377 --> 56:54.157 coffee hour conversation at The London School of Economics--he 56:54.163 --> 56:57.873 said, it's right now 1925 but if you 56:57.870 --> 57:03.650 want to invest or borrow in 1926 I can do it for you. 57:03.650 --> 57:07.590 I can lock in the interest rate right now. 57:07.590 --> 57:15.830 So let's say, okay I expect--suppose I expect 57:21.070 --> 57:23.320 Here we are, sitting in 1925, 57:23.322 --> 57:25.572 and I want to, today in 1925, 57:25.574 --> 57:30.244 lock in the investment return that I will get when I invest 57:30.238 --> 57:32.328 that hundred pounds. 57:32.329 --> 57:38.979 So, what we want to do--this is what Hicks discovered--I can do 57:38.978 --> 57:43.158 the following transaction to lock in, 57:43.159 --> 57:49.649 in 1925, the interest rate between 1926 and 1927. 57:49.650 --> 57:56.110 Here we are sitting in 1925; I'm going to buy in '25 this 57:56.112 --> 58:03.172 amount of two-period bonds--two year-bonds--(1 + 58:11.870 --> 58:18.400 58:27.655 --> 58:30.685 to short how much? 58:30.690 --> 58:37.700 I'm going to short one one-period bond. 58:37.700 --> 58:45.720 58:45.719 --> 58:52.579 This is the number of bonds I have to buy and so let's analyze 58:52.582 --> 58:56.442 this. That's all I have to do and I 58:56.435 --> 59:00.025 have locked in the interest rate. 59:00.030 --> 59:04.330 r_1 is the yield on the one-period bond and 59:04.329 --> 59:08.629 r_2 is the yield on the two-period bond. 59:08.630 --> 59:12.510 The price of the two-period bond is 1/(1 + 59:17.992 --> 59:21.872 bond is 1/(1 + r_1). 59:21.869 --> 59:26.789 If I buy this amount of two-period bonds, 59:26.789 --> 59:30.109 how much does it cost me? 59:30.110 --> 59:33.770 It costs me 1/(1 + r_1). 59:33.769 --> 59:39.609 If I short the one-period bond it cancels out, 59:39.614 --> 59:44.684 so I've made no net purchase in 1925. 59:44.679 --> 59:49.589 I bought a number of two-period bonds such that the value of my 59:49.589 --> 59:53.629 purchase exactly equals the proceeds that I get from 59:53.627 --> 59:58.447 shorting the one period bond, so I've made a zero wealth 59:58.453 --> 1:00:01.623 transaction. It hasn't affected my 1:00:01.616 --> 1:00:05.236 portfolio--my cash position--at all. 1:00:05.239 --> 1:00:13.639 What happens then in--that's in 1925, so there's no cash flow at 1:00:13.639 --> 1:00:14.439 all. 1:00:14.440 --> 1:00:19.180 1:00:19.180 --> 1:00:22.490 In '26, what happens? 1:00:22.489 --> 1:00:25.799 Well, in '26, the--I've shorted the 1:00:25.802 --> 1:00:30.772 one-period bond and so I have to pay out one dollar, 1:00:30.770 --> 1:00:34.960 but that's exactly what I wanted to do. 1:00:34.960 --> 1:00:39.420 Remember, I said I'm doing this because I expect to have a 1:00:39.422 --> 1:00:43.962 hundred pounds--I said one dollar--I'm going to have to pay 1:00:43.962 --> 1:00:48.192 out a hundred pounds because this one-period bond, 1:00:48.190 --> 1:00:51.570 worth one hundred pounds principal, is coming due so I 1:00:51.570 --> 1:00:52.910 have to pay it out. 1:00:52.909 --> 1:00:55.499 That's what I wanted to do because I said I'd have a 1:00:55.499 --> 1:00:56.869 hundred pounds to invest. 1:00:56.869 --> 1:01:02.709 Nothing happens to the two-period bond because it just 1:01:02.714 --> 1:01:05.144 continues to mature. 1:01:05.139 --> 1:01:13.539 So 1926, I pay one hundred pounds. 1:01:13.540 --> 1:01:19.990 What happens in 1927? 1:01:19.989 --> 1:01:25.899 Now what happens is, I now get the maturity of this 1:01:25.902 --> 1:01:31.552 bond. What I get--I have purchased 1:01:31.552 --> 1:01:40.162 this number of bonds, so I'm going to get a hundred 1:01:40.164 --> 1:01:47.994 pounds times that amount there, the number of bonds--(1 + 1:01:52.409 --> 1:01:58.279 You can see that by doing this transaction I have locked in a 1:01:58.284 --> 1:02:01.324 return between 1926 and 1927. 1:02:01.320 --> 1:02:05.470 I did it in 1925, but I've got it set up so that 1:02:05.469 --> 1:02:11.119 I will pay a hundred pounds in 1926 and I'll get this in 1927. 1:02:11.119 --> 1:02:18.179 He calls the forward rate equal to (1 + 1:02:28.760 --> 1:02:32.060 This is Hicks's discovery. 1:02:32.059 --> 1:02:33.869 You might say, this should have been obvious 1:02:33.868 --> 1:02:36.348 to someone, but it had never been written up well before. 1:02:36.349 --> 1:02:39.079 What Hicks said is that in these term structures, 1:02:39.077 --> 1:02:42.027 you don't just have today's interest rates--this is a 1:02:42.032 --> 1:02:44.422 map–actually, I've just showed the 1:02:44.416 --> 1:02:47.586 one-period, he had one-period forward rate--but you could do 1:02:47.590 --> 1:02:50.760 it over any combination and you can get forward rates of any 1:02:50.764 --> 1:02:52.544 maturity at any future date. 1:02:52.539 --> 1:02:59.389 That's Hicks's insight and it comes back then to Hicks's book, 1:02:59.394 --> 1:03:03.444 Value and Capital, in 1939. 1:03:03.440 --> 1:03:07.870 He said that we shouldn't think that the--the simplest story of 1:03:07.865 --> 1:03:10.645 the term structure of interest rates, 1:03:10.650 --> 1:03:13.750 which he expounded there, is that forward rates equal 1:03:13.745 --> 1:03:15.705 expected future interest rates. 1:03:15.710 --> 1:03:19.560 That means, in the simplest--it's called the 1:03:19.555 --> 1:03:23.485 expectations theory of the term structure. 1:03:23.489 --> 1:03:27.439 It says that the forward rate, which you can compute from 1:03:27.442 --> 1:03:31.472 today's newspaper or from today's website--you can compute 1:03:31.465 --> 1:03:34.495 the forward rates for all future dates. 1:03:34.500 --> 1:03:38.090 What he says is those forward rates are what people think 1:03:38.085 --> 1:03:41.725 interest rates will be in the future and that's called the 1:03:41.734 --> 1:03:44.684 expectations theory of the term structure. 1:03:44.679 --> 1:03:47.089 Forward rates equal expected future spot rates. 1:03:47.090 --> 1:03:50.710 If you look at the December 2003, what's going on? 1:03:50.710 --> 1:03:54.940 It's very clear and that is the Fed had just cut interest rates 1:03:54.939 --> 1:03:58.349 to 1%--it was unusual--it was much talked about. 1:03:58.349 --> 1:04:02.639 People didn't expect that to hold and so people thought, 1:04:02.642 --> 1:04:06.702 well it's going to still be down at 1% maybe in three 1:04:06.701 --> 1:04:09.641 months. So, you can see the term 1:04:09.639 --> 1:04:14.839 structure doesn't go up between overnight and three months. 1:04:14.840 --> 1:04:17.780 But they are expecting that the Fed is eventually--and they were 1:04:17.784 --> 1:04:20.124 right of course in this case--the Fed is eventually 1:04:20.121 --> 1:04:21.291 going to raise rates. 1:04:21.289 --> 1:04:25.259 The upward-sloping term structure means that the forward 1:04:25.257 --> 1:04:27.347 rates are at higher levels. 1:04:27.349 --> 1:04:31.239 So, that's the expectations theory. 1:04:31.239 --> 1:04:41.699 Hicks also talked about another theory in his 1939 book, 1:04:41.697 --> 1:04:49.487 which is--there's the expectations theory, 1:04:49.493 --> 1:04:58.623 but there's also a liquidity premium theory. 1:04:58.620 --> 1:05:13.470 1:05:13.469 --> 1:05:20.619 This is the theory that there's risk in longer-term bonds, 1:05:20.620 --> 1:05:27.390 so there's a tendency for upward-sloping term structure 1:05:27.394 --> 1:05:31.664 even if expectations are flat. 1:05:31.660 --> 1:05:34.680 1:05:34.679 --> 1:05:41.319 So, according to the expectations theory augmented 1:05:41.318 --> 1:05:49.308 with liquidity preference--This strongly upward-sloping term 1:05:49.312 --> 1:05:55.682 structure in 2003 would reflect two things. 1:05:55.679 --> 1:05:59.829 One is that people expected interest rates to go up and, 1:05:59.831 --> 1:06:03.301 secondly, that interest rates–longer-term 1:06:03.303 --> 1:06:07.693 bonds--are riskier, so there's also another effect 1:06:07.687 --> 1:06:10.067 pushing interest rates up. 1:06:10.070 --> 1:06:14.600 The last thing I want to talk about is just--I'm running out 1:06:14.604 --> 1:06:18.454 of time here and I want to mention this before your 1:06:18.446 --> 1:06:22.806 mid-term exam, which is next Monday and covers 1:06:22.806 --> 1:06:27.316 everything through this lecture--something about 1:06:27.318 --> 1:06:30.388 inflation and interest rates. 1:06:30.389 --> 1:06:41.839 Inflation--we'll call that π--the inflation rate is 1:06:41.836 --> 1:06:44.446 π. So right now, 1:06:44.452 --> 1:06:47.882 it's something like 2% or it's a little bit higher last year, 1:06:47.881 --> 1:06:50.111 but maybe it'll be 2% going forward. 1:06:50.110 --> 1:06:57.950 The real interest rate, computed from nominal rates, 1:06:57.952 --> 1:07:06.562 is equal to one plus the nominal rate divided by one plus 1:07:06.563 --> 1:07:11.943 the inflation rate, so it corrects for inflation. 1:07:11.940 --> 1:07:16.480 If you have an interest rate--this is approximately 1:07:16.475 --> 1:07:21.555 equal to--one plus the real interest rate is equal to one 1:07:21.555 --> 1:07:26.545 plus the nominal interest rate, divided by one plus the rate of 1:07:26.553 --> 1:07:29.793 inflation. So we would say the real 1:07:29.785 --> 1:07:36.565 interest rate equals the nominal rate--approximately equals--the 1:07:36.572 --> 1:07:40.992 nominal rate minus the inflation rate. 1:07:40.990 --> 1:07:47.060 1:07:47.059 --> 1:07:50.299 If we have--right now, if we go back to our current 1:07:50.297 --> 1:07:53.467 term structure–well, this isn't complete. 1:07:53.469 --> 1:07:56.319 If you look at the current term structure, it's interesting. 1:07:56.320 --> 1:07:59.430 Look how--this is as of earlier this year; 1:07:59.429 --> 1:08:03.339 the Federal Funds Rate was at around 4% and it has this huge 1:08:03.335 --> 1:08:06.505 drop in the term structure and then it starts the 1:08:06.512 --> 1:08:08.752 upward-sloping. Why is that? 1:08:08.750 --> 1:08:11.970 That's because on the date that I got this term structure 1:08:11.971 --> 1:08:15.131 everybody knew the Fed was cutting rates and they got it 1:08:15.134 --> 1:08:17.964 exactly right. The Fed was cutting rates to 3%; 1:08:17.960 --> 1:08:20.760 they knew it was coming but not today. 1:08:20.760 --> 1:08:26.980 Right now, we have a Federal Funds Rate of about 3% and an 1:08:26.980 --> 1:08:33.310 inflation rate of around 3%, so right now the real interest 1:08:33.310 --> 1:08:35.820 rate is close to 0. 1:08:35.819 --> 1:08:41.669 Finally, I just want to say that we have also a kind of bond 1:08:41.673 --> 1:08:46.833 called an indexed bond, which is a bond whose coupons 1:08:46.832 --> 1:08:49.712 are indexed to inflation. 1:08:49.710 --> 1:08:54.610 With an indexed bond you don't have to do this calculation to 1:08:54.614 --> 1:08:56.254 get the real rate. 1:08:56.250 --> 1:09:00.350 The yield-to-maturity on an indexed bond is already in real 1:09:00.346 --> 1:09:04.086 terms because the coupons are indexed to inflation. 1:09:04.090 --> 1:09:10.470 In my final slide is a picture of the first indexed bond; 1:09:10.470 --> 1:09:15.500 this is issued by the State of Massachusetts--I actually own 1:09:15.497 --> 1:09:18.507 this bond. I bought it for $1,000 on a 1:09:18.510 --> 1:09:22.270 website because I was interested in indexed bonds. 1:09:22.270 --> 1:09:26.050 I could have brought it to class and showed it to you, 1:09:26.046 --> 1:09:29.966 but this was issued during the Revolutionary War to help 1:09:29.965 --> 1:09:33.265 finance the war. Now, what happened was the U.S. 1:09:33.270 --> 1:09:36.290 Government--or the Massachusetts Government--had 1:09:36.288 --> 1:09:39.948 created high inflation during the war and nobody wanted to 1:09:39.948 --> 1:09:43.478 lend money to it so they create here a price index. 1:09:43.479 --> 1:09:47.639 It says the price index contained this amount of beef, 1:09:47.637 --> 1:09:51.867 this amount of sheep wool, this amount of sole leather, 1:09:51.873 --> 1:09:56.153 and this amount of corn; that was the first consumer 1:09:56.149 --> 1:09:59.769 price index ever used for financial contracts. 1:09:59.770 --> 1:10:02.850 We now have something else called the Consumer Price Index. 1:10:02.850 --> 1:10:08.080 This bond was paid off, the U.S.–Massa 1:10:08.083 --> 1:10:13.563 chusetts--didn't fail to pay on it in 1784. 1:10:13.560 --> 1:10:21.450 But anyway, indexed bonds are about 15% of the U.S. 1:10:21.449 --> 1:10:23.749 national--I'm sorry, about 8% of the U.S. 1:10:23.750 --> 1:10:26.280 national debt--about 15% of the U.K. 1:10:26.279 --> 1:10:30.229 national debt--and they are very important but still a 1:10:30.226 --> 1:10:33.126 minority of all of our fixed incomes. 1:10:33.130 --> 1:10:39.060 That concludes this lecture and I won't be here on Monday, 1:10:39.064 --> 1:10:45.004 but we'll have our lecture in this classroom on Monday.