WEBVTT 00:00:00.090 --> 00:00:02.430 The following content is provided under a Creative 00:00:02.430 --> 00:00:03.820 Commons license. 00:00:03.820 --> 00:00:06.030 Your support will help MIT OpenCourseWare 00:00:06.030 --> 00:00:10.120 continue to offer high quality educational resources for free. 00:00:10.120 --> 00:00:12.690 To make a donation or to view additional materials 00:00:12.690 --> 00:00:16.620 from hundreds of MIT courses, visit MIT OpenCourseWare 00:00:16.620 --> 00:00:17.830 at ocw.mit.edu. 00:00:26.622 --> 00:00:28.830 ANDREW LO: Now, also, before I begin today's lecture, 00:00:28.830 --> 00:00:31.246 I want to comment a bit about what's going on in the news, 00:00:31.246 --> 00:00:36.990 because last time, on Monday, we said-- or I said-- 00:00:36.990 --> 00:00:39.045 that the Fed was going to cut rates. 00:00:39.045 --> 00:00:40.350 [LAUGHTER] 00:00:40.350 --> 00:00:44.880 And in fact, if you looked at the data on Monday 00:00:44.880 --> 00:00:47.580 and you looked at things like the Fed fund's future 00:00:47.580 --> 00:00:51.060 and other financial contracts, the market 00:00:51.060 --> 00:00:53.400 had priced in the fact that the Fed 00:00:53.400 --> 00:00:56.130 was going to cut at least 25 basis points, 00:00:56.130 --> 00:00:58.070 and actually a reasonable probability that it 00:00:58.070 --> 00:00:59.730 was going to cut 50. 00:00:59.730 --> 00:01:01.590 And of course, they did neither. 00:01:01.590 --> 00:01:03.960 They actually held rates steady. 00:01:03.960 --> 00:01:07.140 But they did do something. 00:01:07.140 --> 00:01:08.130 What did they do? 00:01:08.130 --> 00:01:09.150 Anybody know? 00:01:09.150 --> 00:01:09.828 Yeah. 00:01:09.828 --> 00:01:13.320 STUDENT: Extended [INAUDIBLE] 00:01:13.320 --> 00:01:15.340 ANDREW LO: How large a loan? 00:01:15.340 --> 00:01:20.520 $85 billion, which, even among friends, is a lot of money. 00:01:20.520 --> 00:01:22.230 [LAUGHTER] 00:01:22.230 --> 00:01:27.840 Now, this is yet again an extraordinary and unprecedented 00:01:27.840 --> 00:01:28.890 measure. 00:01:28.890 --> 00:01:32.820 We know that the Fed did backstop Bear Stearns. 00:01:32.820 --> 00:01:36.360 But the Fed didn't spend any direct money on Bear Stearns. 00:01:36.360 --> 00:01:39.210 They basically got JP Morgan to buy Bear Stearns 00:01:39.210 --> 00:01:41.700 and negotiated the deal. 00:01:41.700 --> 00:01:46.050 In this instance, the Fed is lending money to AIG, 00:01:46.050 --> 00:01:48.090 lending $85 billion. 00:01:48.090 --> 00:01:50.490 And AIG isn't even a bank. 00:01:50.490 --> 00:01:53.210 So what do you think is going on? 00:01:53.210 --> 00:01:54.716 Does that make sense? 00:01:54.716 --> 00:01:57.090 What does that tell you about what's going on in markets? 00:01:57.090 --> 00:02:00.480 The fact that everybody thought the Fed was gonna cut rates, 00:02:00.480 --> 00:02:01.620 and they didn't-- 00:02:01.620 --> 00:02:04.200 that shows a certain kind of restraint. 00:02:04.200 --> 00:02:05.910 In fact, I think it was in this class 00:02:05.910 --> 00:02:10.090 that somebody mentioned, well, rates are already down at 2%. 00:02:10.090 --> 00:02:11.490 How much more can they cut? 00:02:11.490 --> 00:02:13.622 I mean, if they cut 50 basis points, 00:02:13.622 --> 00:02:15.330 that leaves them very little flexibility. 00:02:15.330 --> 00:02:18.990 And also, if you think that the reason we are in this crisis 00:02:18.990 --> 00:02:22.620 is because borrowing has been so low for so long, that people 00:02:22.620 --> 00:02:24.990 have been going out making all these bad loans when they 00:02:24.990 --> 00:02:27.007 shouldn't be doing that to begin with, 00:02:27.007 --> 00:02:29.340 cutting rates is not going to really help that situation 00:02:29.340 --> 00:02:31.770 but can only encourage it. 00:02:31.770 --> 00:02:33.330 Nevertheless, there was a crisis. 00:02:33.330 --> 00:02:36.060 Certainly over the weekend, we had some very bad news. 00:02:36.060 --> 00:02:41.240 Lehman Brothers went under, and the Fed did what? 00:02:41.240 --> 00:02:42.230 Nothing. 00:02:42.230 --> 00:02:44.780 So if the Fed did nothing for Lehman, 00:02:44.780 --> 00:02:49.567 yet they extended an $85 billion loan for AIG, 00:02:49.567 --> 00:02:50.900 something's got to be different. 00:02:50.900 --> 00:02:51.200 Right? 00:02:51.200 --> 00:02:53.090 I mean, I guess you could see whether or not 00:02:53.090 --> 00:02:56.480 Ben Bernanke has a brother-in-law working at AIG, 00:02:56.480 --> 00:02:58.560 but I don't think that's it. 00:02:58.560 --> 00:02:59.253 Yeah. 00:02:59.253 --> 00:03:02.031 STUDENT: [? But today it was ?] reported that Barclays is 00:03:02.031 --> 00:03:04.320 actually going to go ahead and buy [? them. ?] So what 00:03:04.320 --> 00:03:04.820 changed-- 00:03:04.820 --> 00:03:06.980 ANDREW LO: Well, the announcement 00:03:06.980 --> 00:03:10.280 is that Barclays is buying some of the US operations of Lehman 00:03:10.280 --> 00:03:11.060 Brothers. 00:03:11.060 --> 00:03:14.510 They are cherry-picking the operations that they want. 00:03:14.510 --> 00:03:17.660 What Lehman tried to do over the weekend was broker a deal 00:03:17.660 --> 00:03:19.490 where Barclays would buy all of them, 00:03:19.490 --> 00:03:21.200 assume all their obligations, and allow 00:03:21.200 --> 00:03:24.450 them to keep on going as a going business concern. 00:03:24.450 --> 00:03:26.450 Barclays couldn't do that, because they couldn't 00:03:26.450 --> 00:03:28.670 get shareholder approval quickly enough, 00:03:28.670 --> 00:03:31.520 and also ostensibly because the Fed would not 00:03:31.520 --> 00:03:34.700 backstop any losses that Lehman had hidden in its books. 00:03:34.700 --> 00:03:36.890 And in a matter of 48 hours, it's, 00:03:36.890 --> 00:03:39.770 kind of, hard to figure out all the buried bodies 00:03:39.770 --> 00:03:42.770 in an organization as complex and as large as Lehman. 00:03:42.770 --> 00:03:47.120 But Barclays is going ahead and purchasing those units 00:03:47.120 --> 00:03:48.849 that they like, and there are many units 00:03:48.849 --> 00:03:51.140 at Lehman Brothers that are extraordinarily profitable, 00:03:51.140 --> 00:03:53.667 very good businesses with excellent people. 00:03:53.667 --> 00:03:55.250 So Barclays is going ahead with those. 00:03:55.250 --> 00:03:57.800 And by the way, there are all sorts of other sharks 00:03:57.800 --> 00:04:00.320 that are swimming around Lehman, cherry-picking various 00:04:00.320 --> 00:04:01.310 different groups. 00:04:01.310 --> 00:04:04.160 This is part of the problem with these this kind 00:04:04.160 --> 00:04:05.150 of financial distress. 00:04:05.150 --> 00:04:07.985 We're going to actually get to this at about lecture 18. 00:04:07.985 --> 00:04:09.860 We're going to talk about financial distress, 00:04:09.860 --> 00:04:11.943 and I'm going to bring you back to Lehman Brothers 00:04:11.943 --> 00:04:14.300 and ask you to think about the problems 00:04:14.300 --> 00:04:15.470 that this company faces. 00:04:15.470 --> 00:04:16.700 Because think about it. 00:04:16.700 --> 00:04:19.902 Now that it's been announced that Lehman is liquidating-- 00:04:19.902 --> 00:04:21.110 well, let me put it this way. 00:04:21.110 --> 00:04:22.550 Suppose you were working at Lehman Brothers, 00:04:22.550 --> 00:04:24.080 suppose that you've been there 15 years, 00:04:24.080 --> 00:04:25.455 and suppose that you were running 00:04:25.455 --> 00:04:28.389 one of the most successful proprietary trading groups 00:04:28.389 --> 00:04:29.180 at Lehman Brothers. 00:04:29.180 --> 00:04:32.630 And now, this news comes up, and it's a surprise to you. 00:04:32.630 --> 00:04:34.070 What is your first reaction? 00:04:34.070 --> 00:04:35.490 What are you going to do? 00:04:35.490 --> 00:04:35.990 Yeah? 00:04:35.990 --> 00:04:36.830 STUDENT: [INAUDIBLE] 00:04:36.830 --> 00:04:37.340 ANDREW LO: Right. 00:04:37.340 --> 00:04:38.480 That's certainly one thing. 00:04:38.480 --> 00:04:40.771 You're going to take a look at what your positions are. 00:04:40.771 --> 00:04:42.560 And then, after you establish that you're 00:04:42.560 --> 00:04:44.512 OK in terms of your trading positions, 00:04:44.512 --> 00:04:46.220 what's the next thing you're going to do? 00:04:46.220 --> 00:04:47.950 What are you gonna start thinking about? 00:04:47.950 --> 00:04:48.100 Yeah? 00:04:48.100 --> 00:04:49.430 STUDENT: Start bringing your resume? 00:04:49.430 --> 00:04:49.940 ANDREW LO: Exactly. 00:04:49.940 --> 00:04:51.560 You're going to start looking around. 00:04:51.560 --> 00:04:54.350 So you're going to talk to lots of other people about, maybe, 00:04:54.350 --> 00:04:56.379 moving your entire group of 15 people 00:04:56.379 --> 00:04:57.920 that you've hand-picked and developed 00:04:57.920 --> 00:04:58.954 over the last 15 years. 00:04:58.954 --> 00:05:00.620 And you're gonna start talking all sorts 00:05:00.620 --> 00:05:03.500 of other counter-parties to move your entire group. 00:05:03.500 --> 00:05:07.100 And now, Barclays decides to buy Lehman, the operations 00:05:07.100 --> 00:05:09.390 that you're a part of. 00:05:09.390 --> 00:05:11.640 But there's no slavery in the United States, 00:05:11.640 --> 00:05:13.800 at least not since the 1800s, which 00:05:13.800 --> 00:05:16.350 means that if you want to walk, you can. 00:05:16.350 --> 00:05:17.670 So if Lehman buys-- 00:05:17.670 --> 00:05:21.690 if Barclays buys Lehman and buys the group that you're in, 00:05:21.690 --> 00:05:24.210 and you're one of the most profitable parts of that, 00:05:24.210 --> 00:05:25.830 you don't have to stay. 00:05:25.830 --> 00:05:28.550 So in addition to paying for Lehman, 00:05:28.550 --> 00:05:30.300 Barclays is also gonna have to talk to you 00:05:30.300 --> 00:05:32.175 and get you to stay, which means that they're 00:05:32.175 --> 00:05:34.140 going to have to pay you an extra bonus and all 00:05:34.140 --> 00:05:35.790 of your people bonuses to stay. 00:05:35.790 --> 00:05:38.430 So now, the price of having to keep Lehman 00:05:38.430 --> 00:05:41.520 together has just gone up dramatically, 00:05:41.520 --> 00:05:44.580 because you've got to keep all of the talent, 00:05:44.580 --> 00:05:46.050 and it's very hard to do that. 00:05:46.050 --> 00:05:48.510 So the fact that Lehman is in trouble 00:05:48.510 --> 00:05:51.120 has caused all sorts of problems and will 00:05:51.120 --> 00:05:54.510 create additional amounts of frictions and payments 00:05:54.510 --> 00:05:56.400 that otherwise wouldn't have had to be. 00:05:56.400 --> 00:05:58.650 So I want you to keep that in the back of your minds-- 00:05:58.650 --> 00:05:59.983 the costs of financial distress. 00:05:59.983 --> 00:06:03.910 We're going to come back to that in, about, 10 lectures. 00:06:03.910 --> 00:06:06.210 OK so-- yeah, question? 00:06:06.210 --> 00:06:09.210 STUDENT: I heard a [? quote ?] with regards to the Fed action, 00:06:09.210 --> 00:06:11.560 that the Fed decided that the problem is not 00:06:11.560 --> 00:06:13.870 the cost of money but the supply of money. 00:06:13.870 --> 00:06:17.460 So they're going to infuse capital into the market. 00:06:17.460 --> 00:06:20.866 Is that just referring to the AIG 85 billion, 00:06:20.866 --> 00:06:23.520 or is there some other way that they're infusing capital? 00:06:23.520 --> 00:06:23.760 ANDREW LO: No. 00:06:23.760 --> 00:06:25.051 Well, that's certainly one way. 00:06:25.051 --> 00:06:28.350 But the other way is that they are allowing the other banks 00:06:28.350 --> 00:06:30.730 to borrow from them at a lower rate. 00:06:30.730 --> 00:06:33.060 So the discount window that typically banks 00:06:33.060 --> 00:06:34.890 go to borrow from the Fed-- 00:06:34.890 --> 00:06:37.260 they're making more money available in that way. 00:06:37.260 --> 00:06:39.870 And other central banks are doing the same thing-- 00:06:39.870 --> 00:06:41.880 injecting money into the system in order 00:06:41.880 --> 00:06:43.322 to calm the fears of individuals. 00:06:43.322 --> 00:06:45.780 STUDENT: Does that lower the effect of [? interest rate? ?] 00:06:45.780 --> 00:06:47.250 ANDREW LO: Well, we're going to see that in a minute. 00:06:47.250 --> 00:06:48.600 We're going to actually-- one of the things 00:06:48.600 --> 00:06:50.850 I want to talk about today is, exactly what do we 00:06:50.850 --> 00:06:52.500 see from market prices? 00:06:52.500 --> 00:06:55.560 Now, on Monday, I claimed that market prices was telling us, 00:06:55.560 --> 00:06:56.940 there's going to be a Fed cut. 00:06:56.940 --> 00:06:59.280 Clearly, it was wrong. 00:06:59.280 --> 00:07:02.280 Now, that's a very good lesson, because what 00:07:02.280 --> 00:07:05.267 this is telling us is that market prices have information, 00:07:05.267 --> 00:07:07.600 but as I told you last time, they're not a crystal ball. 00:07:07.600 --> 00:07:10.210 They're not perfect, and so they can be wrong. 00:07:10.210 --> 00:07:14.130 Apparently-- and this is now very speculative. 00:07:14.130 --> 00:07:16.800 Apparently, the Fed decided, as you pointed out, 00:07:16.800 --> 00:07:21.810 that it's not the availability of-- or rather the cost 00:07:21.810 --> 00:07:22.330 of funds. 00:07:22.330 --> 00:07:24.390 That's not what's important, but rather the availability. 00:07:24.390 --> 00:07:26.520 In other words, they're worried about a credit 00:07:26.520 --> 00:07:29.340 crisis, a crisis of liquidity. 00:07:29.340 --> 00:07:33.600 And AIG is a very important player in that respect-- 00:07:33.600 --> 00:07:35.910 apparently, much more so than Lehman. 00:07:35.910 --> 00:07:38.400 Because Fed didn't do anything to try to keep Lehman 00:07:38.400 --> 00:07:40.940 from going under, but an $85 billion 00:07:40.940 --> 00:07:45.330 loan was what they decided was appropriate for AIG. 00:07:45.330 --> 00:07:47.070 The reason for that-- 00:07:47.070 --> 00:07:48.510 the ostensible reason. 00:07:48.510 --> 00:07:50.310 Who knows what the real reasons may be? 00:07:50.310 --> 00:07:54.660 But the reasons that we think this happened 00:07:54.660 --> 00:07:59.250 is that AIG provides enormous amounts of insurance 00:07:59.250 --> 00:08:03.090 to a variety of other players in the credit markets. 00:08:03.090 --> 00:08:05.790 And if they go under, if they decide 00:08:05.790 --> 00:08:08.820 that they can't make good on those insurance claims, 00:08:08.820 --> 00:08:11.970 what happens is that those investors that 00:08:11.970 --> 00:08:15.450 are holding the paper that is backed 00:08:15.450 --> 00:08:20.580 by subprime assets and that are insured by AIG-- 00:08:20.580 --> 00:08:23.100 once the insurance disappears, they 00:08:23.100 --> 00:08:27.090 are obligated, a number of them, to sell those pieces of paper. 00:08:27.090 --> 00:08:28.920 If you're a pension fund, you are 00:08:28.920 --> 00:08:32.190 obligated to hold only investment grade assets. 00:08:32.190 --> 00:08:34.873 If it turns out that for any reason 00:08:34.873 --> 00:08:36.914 those assets become lower than investment grade-- 00:08:36.914 --> 00:08:39.122 and we're going to talk about this at 4 o'clock today 00:08:39.122 --> 00:08:39.960 at that proseminar. 00:08:39.960 --> 00:08:43.140 If it falls below investment grade, by law, 00:08:43.140 --> 00:08:47.669 you are obligated to get rid of those assets. 00:08:47.669 --> 00:08:49.710 Now, what do you think would happen to the market 00:08:49.710 --> 00:08:53.201 if everybody all at once decided to get rid of those assets? 00:08:53.201 --> 00:08:55.812 STUDENT: [INAUDIBLE] 00:08:55.812 --> 00:08:56.520 ANDREW LO: Right. 00:08:56.520 --> 00:08:58.890 And then, there'd be a mass panic. 00:08:58.890 --> 00:08:59.390 Right. 00:08:59.390 --> 00:09:00.745 STUDENT: I just have-- there's something 00:09:00.745 --> 00:09:02.348 simple that I don't understand. 00:09:02.348 --> 00:09:06.300 How can the interest rate go below the inflation rate? 00:09:06.300 --> 00:09:08.130 ANDREW LO: Well, it's not supposed to 00:09:08.130 --> 00:09:10.210 for any extended period of time. 00:09:10.210 --> 00:09:12.420 But for any short period of time, it certainly can. 00:09:12.420 --> 00:09:14.592 And what it says is that the real rate is negative 00:09:14.592 --> 00:09:16.050 or that the economy is contracting. 00:09:16.050 --> 00:09:18.496 STUDENT: So like right now, $1 a year from now 00:09:18.496 --> 00:09:20.490 is more valuable than it [? would be ?] today. 00:09:20.490 --> 00:09:21.420 Right? 00:09:21.420 --> 00:09:24.400 ANDREW LO: Well, if you take inflation into account, 00:09:24.400 --> 00:09:27.534 yes, in real terms, not in nominal terms. 00:09:27.534 --> 00:09:29.700 You can never have a negative nominal interest rate. 00:09:29.700 --> 00:09:30.450 Right? 00:09:30.450 --> 00:09:33.342 Unless, you know, somebody is burning dollar bills. 00:09:33.342 --> 00:09:34.800 But let me let me hold off on that, 00:09:34.800 --> 00:09:36.800 because I want to actually-- that brings us back 00:09:36.800 --> 00:09:38.454 to the end of last lecture. 00:09:38.454 --> 00:09:39.870 What I want to do today is, I want 00:09:39.870 --> 00:09:44.220 to talk about information specifically contained 00:09:44.220 --> 00:09:45.020 in interest rates. 00:09:45.020 --> 00:09:46.644 And we're going to actually take a look 00:09:46.644 --> 00:09:48.579 at what the short-term interest rate is. 00:09:48.579 --> 00:09:50.120 I think you'll be, kind of, surprised 00:09:50.120 --> 00:09:54.110 to see what the three-month T-bill rate is, as of today. 00:09:54.110 --> 00:09:57.300 Anybody know what it is? 00:09:57.300 --> 00:09:58.770 You've seen it? 00:09:58.770 --> 00:10:00.240 2%? 00:10:00.240 --> 00:10:01.210 No. 00:10:01.210 --> 00:10:01.710 No. 00:10:01.710 --> 00:10:03.180 It's lower. 00:10:03.180 --> 00:10:04.729 STUDENT: [INAUDIBLE] 00:10:04.729 --> 00:10:05.520 ANDREW LO: Let me-- 00:10:05.520 --> 00:10:06.644 we'll see in just a minute. 00:10:12.880 --> 00:10:15.430 Let me start today's lecture by going back 00:10:15.430 --> 00:10:19.010 to where we left off last time. 00:10:19.010 --> 00:10:22.000 Last time, we talked about the pricing of pure discount bonds, 00:10:22.000 --> 00:10:25.460 bonds that pay only principal at the end 00:10:25.460 --> 00:10:27.630 and no intermediate coupon payments. 00:10:27.630 --> 00:10:29.830 And we saw that the price today is simply 00:10:29.830 --> 00:10:32.950 equal to the face value or principal 00:10:32.950 --> 00:10:36.580 at the end of the maturity date, and then discounted back 00:10:36.580 --> 00:10:38.800 using the interest rate. 00:10:38.800 --> 00:10:40.930 And I pointed out at the end of last lecture 00:10:40.930 --> 00:10:44.020 that the interest rate can differ, 00:10:44.020 --> 00:10:45.370 depending on the horizon. 00:10:45.370 --> 00:10:47.500 So a one-year interest rate is not 00:10:47.500 --> 00:10:49.180 the same as a five-year interest rate, 00:10:49.180 --> 00:10:53.530 because the market has different expectations about how 00:10:53.530 --> 00:10:56.230 the economy will do and what the appropriate borrowing 00:10:56.230 --> 00:11:00.250 rate or the time rate of preference might be. 00:11:00.250 --> 00:11:03.430 So in fact, for every horizon-- 00:11:03.430 --> 00:11:06.100 one year, two years, three years, five years-- 00:11:06.100 --> 00:11:08.170 we have a different interest rate. 00:11:08.170 --> 00:11:10.750 It doesn't have to be different, but in general, it 00:11:10.750 --> 00:11:12.580 does tend to be different. 00:11:12.580 --> 00:11:16.690 How do we find out what these interest rates are? 00:11:16.690 --> 00:11:17.320 Yeah. 00:11:17.320 --> 00:11:18.220 STUDENT: The market. 00:11:18.220 --> 00:11:19.011 ANDREW LO: Exactly. 00:11:19.011 --> 00:11:19.630 The market. 00:11:19.630 --> 00:11:23.030 The way to do it is not to think about interest rates at all, 00:11:23.030 --> 00:11:25.570 but rather to auction off pieces of paper that 00:11:25.570 --> 00:11:30.310 pay $1,000 in a year, $1,000 in two years, 00:11:30.310 --> 00:11:32.500 $1,000 in three years, and so on. 00:11:32.500 --> 00:11:34.600 And we auction off each of these pieces of paper 00:11:34.600 --> 00:11:38.710 and see what the prices we fetch are, for those pieces of paper. 00:11:38.710 --> 00:11:40.720 Once we have the price and once we 00:11:40.720 --> 00:11:43.240 know the face value of $1,000, we 00:11:43.240 --> 00:11:45.550 can back out the interest rate. 00:11:45.550 --> 00:11:49.300 We can solve for the interest rate, r. 00:11:49.300 --> 00:11:51.050 So that's how we get the rates. 00:11:51.050 --> 00:11:53.672 And what I want to do today is to explicate 00:11:53.672 --> 00:11:54.880 what those rates really mean. 00:11:54.880 --> 00:11:57.250 I want to show you how to read the entrails 00:11:57.250 --> 00:12:01.150 and see that these rates contain enormous amounts of information 00:12:01.150 --> 00:12:02.290 about the future. 00:12:02.290 --> 00:12:04.460 Not all of that information is good. 00:12:04.460 --> 00:12:07.180 So sometimes, it's misleading and incorrect, 00:12:07.180 --> 00:12:11.330 but it's always useful in one form or another. 00:12:11.330 --> 00:12:14.080 Now, to do that, I want to develop 00:12:14.080 --> 00:12:15.940 a little bit of new notation and get 00:12:15.940 --> 00:12:19.720 you to think, yet again, differently about the evolution 00:12:19.720 --> 00:12:23.280 of interest rates over time. 00:12:23.280 --> 00:12:26.070 I'm going to define what's called a spot 00:12:26.070 --> 00:12:32.070 rate as the rate of interest between today 00:12:32.070 --> 00:12:34.470 and some other point in time. 00:12:34.470 --> 00:12:38.220 And I'm going to talk about future spot rates 00:12:38.220 --> 00:12:41.610 as the interest rates between some future date, 00:12:41.610 --> 00:12:45.510 and then another date even beyond that. 00:12:45.510 --> 00:12:51.450 So to be explicit, I wanted to find new notation called 00:12:51.450 --> 00:12:58.320 capital R. Uppercase R is meant to convey a one-year spot 00:12:58.320 --> 00:13:02.940 rate of interest at a particular point in time, t. 00:13:02.940 --> 00:13:03.810 OK? 00:13:03.810 --> 00:13:08.250 So capital R1 denotes the spot rate 00:13:08.250 --> 00:13:11.610 of interest between today and next year. 00:13:11.610 --> 00:13:16.080 Capital R3 denotes the spot rate of interest 00:13:16.080 --> 00:13:20.220 between years 2 and 3. 00:13:20.220 --> 00:13:24.360 And capital Rt denotes the one year spot rate 00:13:24.360 --> 00:13:27.690 between dates t minus 1 and t. 00:13:27.690 --> 00:13:28.380 OK? 00:13:28.380 --> 00:13:32.520 So these capital R's are always one-year rates, 00:13:32.520 --> 00:13:37.380 unlike the little r's, which can denote multi-year rates, 00:13:37.380 --> 00:13:40.020 depending on the application. 00:13:40.020 --> 00:13:44.640 Now, there's a reason I wanted to find these big R's. 00:13:44.640 --> 00:13:50.640 It turns out that if I have a pure discount bond that 00:13:50.640 --> 00:13:56.910 pays off at year t, then I can use the one-year spot rates 00:13:56.910 --> 00:13:59.660 to compute today's price. 00:13:59.660 --> 00:14:00.420 Right? 00:14:00.420 --> 00:14:03.610 The one-year spot rate, when you accumulate 00:14:03.610 --> 00:14:06.480 that, when you multiply them together, 00:14:06.480 --> 00:14:09.840 will give you the accumulated interest 00:14:09.840 --> 00:14:12.910 over this entire t-year period. 00:14:12.910 --> 00:14:16.980 So if I want to discount face value, F, 00:14:16.980 --> 00:14:19.770 and bring it back to year zero, I 00:14:19.770 --> 00:14:23.100 can just assume that there exists one rate. 00:14:23.100 --> 00:14:25.690 Or I can say, you know what? 00:14:25.690 --> 00:14:29.760 If there are multiple rates that differ year by year, 00:14:29.760 --> 00:14:33.210 I can use those individual rates. 00:14:33.210 --> 00:14:35.580 So I get that first equation. 00:14:35.580 --> 00:14:37.080 Now, we don't observe them. 00:14:37.080 --> 00:14:42.320 So this is a pure fiction, in terms of what I'm writing down. 00:14:42.320 --> 00:14:44.000 It's a theory. 00:14:44.000 --> 00:14:47.240 So I'm not telling you that we know what those big R's are. 00:14:47.240 --> 00:14:51.710 But I know that they exist, and whatever they are, 00:14:51.710 --> 00:14:56.320 this is what the price of the bond ought to be today. 00:14:56.320 --> 00:14:58.750 Any questions about that? 00:14:58.750 --> 00:14:59.920 OK. 00:14:59.920 --> 00:15:04.330 Now, what I do observe is the price and F. Those things, 00:15:04.330 --> 00:15:09.460 I get from the marketplace and the contract for these bonds. 00:15:09.460 --> 00:15:15.880 Therefore, it turns out that as a very simple identity, 00:15:15.880 --> 00:15:20.000 this expression, this little r-- 00:15:20.000 --> 00:15:23.630 which-- I'm adding some more complicated notation 00:15:23.630 --> 00:15:27.410 to indicate when I begin and when I end in terms 00:15:27.410 --> 00:15:28.910 of my horizon-- 00:15:28.910 --> 00:15:33.320 I can simply define this little r as being equal 00:15:33.320 --> 00:15:36.770 to the geometric average of these big R's. 00:15:36.770 --> 00:15:39.061 It's really just terminology at this point. 00:15:39.061 --> 00:15:39.560 Right? 00:15:39.560 --> 00:15:42.500 I'm simply saying that in reality, we 00:15:42.500 --> 00:15:47.910 have one-year interest rates that may change over time. 00:15:47.910 --> 00:15:50.190 And I know that the price of the bond today 00:15:50.190 --> 00:15:53.700 is equal to the future course of one-year interest rates 00:15:53.700 --> 00:15:56.652 as discounts over that period. 00:15:56.652 --> 00:15:58.110 When I use those as discount rates, 00:15:58.110 --> 00:16:01.500 I bring back the value F, and I get today's price. 00:16:01.500 --> 00:16:05.460 I can just as well write that chain of one-year interest 00:16:05.460 --> 00:16:08.820 rates as a single number, raised to the t-th power. 00:16:08.820 --> 00:16:11.010 I can always do that. 00:16:11.010 --> 00:16:15.330 You can think of this little r as an average, 00:16:15.330 --> 00:16:18.540 a geometric average, of the big R's. 00:16:18.540 --> 00:16:19.590 Right? 00:16:19.590 --> 00:16:22.860 So the strict definition is going to be-- 00:16:22.860 --> 00:16:27.810 little r is going to be the t-th root of the product, 00:16:27.810 --> 00:16:29.530 and then minus 1. 00:16:29.530 --> 00:16:31.530 That's what the little r is. 00:16:31.530 --> 00:16:32.520 All right? 00:16:32.520 --> 00:16:34.835 You take that product, and you raise that to the 1 00:16:34.835 --> 00:16:38.790 over t-th power or take the t-th root, 00:16:38.790 --> 00:16:41.574 and then subtract 1 from that-- that's what my little r is. 00:16:41.574 --> 00:16:43.240 Now, why am I going through all of this? 00:16:43.240 --> 00:16:45.630 It's because I want to show you that 00:16:45.630 --> 00:16:49.830 from a theoretical perspective, the little r, which 00:16:49.830 --> 00:16:53.380 we can observe, contains information 00:16:53.380 --> 00:16:55.270 about the future course of interest rates. 00:16:57.800 --> 00:17:02.120 Within the little r are all the big R's-- 00:17:02.120 --> 00:17:06.079 at least today's expectations of what those big R's are 00:17:06.079 --> 00:17:08.440 going to be. 00:17:08.440 --> 00:17:15.480 So it turns out that if we look into the little r's, we 00:17:15.480 --> 00:17:18.030 can actually develop insight about what's 00:17:18.030 --> 00:17:21.760 going to be happening next year, five years from now, 00:17:21.760 --> 00:17:23.387 30 years from now. 00:17:23.387 --> 00:17:25.470 Now, let me give you an example, just to make sure 00:17:25.470 --> 00:17:28.290 that we understand the mechanism by which these little r's 00:17:28.290 --> 00:17:31.710 and big R's are determined. 00:17:31.710 --> 00:17:36.630 Here's a set of prices of strips. 00:17:36.630 --> 00:17:40.590 These are treasury securities, issued by the US government. 00:17:40.590 --> 00:17:46.830 And then, a third party buys them, takes the coupons, 00:17:46.830 --> 00:17:49.560 creates separate securities, and sells 00:17:49.560 --> 00:17:52.080 those separate securities, each one of which 00:17:52.080 --> 00:17:53.820 is one of these coupons. 00:17:53.820 --> 00:17:56.670 So from our perspective, they look like pure discount bonds. 00:17:56.670 --> 00:17:59.340 There's no intermediate coupon payments 00:17:59.340 --> 00:18:01.620 for each one of these strips, and the maturity 00:18:01.620 --> 00:18:04.170 is three months, six months, one year, two years, 00:18:04.170 --> 00:18:05.580 up to 30 years. 00:18:05.580 --> 00:18:06.910 OK? 00:18:06.910 --> 00:18:08.210 And those are the prices. 00:18:08.210 --> 00:18:12.340 So a three-month strip is currently priced-- 00:18:12.340 --> 00:18:18.130 as of August the 1st, 2001, it was priced at a little bit less 00:18:18.130 --> 00:18:21.250 than the dollar. 00:18:21.250 --> 00:18:26.350 So how do we figure out what the little r is, associated 00:18:26.350 --> 00:18:27.750 with those various prices? 00:18:27.750 --> 00:18:29.110 Well, let's take an example. 00:18:29.110 --> 00:18:35.050 The five-year strip is priced at, about, $0.80 to the dollar. 00:18:35.050 --> 00:18:35.920 OK? 00:18:35.920 --> 00:18:39.280 So the price is 0.797, and that's 00:18:39.280 --> 00:18:43.180 equal to $1 paid five years later. 00:18:43.180 --> 00:18:46.930 So therefore, it's $1 discounted back five years. 00:18:46.930 --> 00:18:50.590 So I'm gonna use my little r, and the zero comma five 00:18:50.590 --> 00:18:54.610 indicates that it's today's spot rate for borrowing 00:18:54.610 --> 00:18:57.400 over a five-year horizon. 00:18:57.400 --> 00:19:00.040 And it turns out that when I solve for that, 00:19:00.040 --> 00:19:02.980 I get a number that's 4.64%. 00:19:02.980 --> 00:19:07.480 That's the rate of return, the cost of capital, 00:19:07.480 --> 00:19:12.640 the yield of that five period horizon. 00:19:16.480 --> 00:19:18.770 Any questions about this? 00:19:18.770 --> 00:19:19.800 Yeah. 00:19:19.800 --> 00:19:22.350 STUDENT: How do we do it, maybe, if it was one that 00:19:22.350 --> 00:19:24.039 was less than a year's horizon? 00:19:24.039 --> 00:19:26.080 ANDREW LO: So if it's less than a year's horizon, 00:19:26.080 --> 00:19:28.254 then you basically have to go the other way, 00:19:28.254 --> 00:19:29.170 in terms of the power. 00:19:29.170 --> 00:19:29.875 Right? 00:19:29.875 --> 00:19:31.180 STUDENT: [? 1 over 1/2. ?] 00:19:31.180 --> 00:19:32.170 ANDREW LO: Yeah. 00:19:32.170 --> 00:19:33.340 Exactly. 00:19:33.340 --> 00:19:33.900 That's right. 00:19:33.900 --> 00:19:35.200 Yeah, that's it. 00:19:35.200 --> 00:19:40.050 It's just a shorter time horizon than a year. 00:19:40.050 --> 00:19:43.900 Now, suppose that we observe a bunch of these 00:19:43.900 --> 00:19:45.400 as we do with the strips. 00:19:45.400 --> 00:19:47.830 So in other words, you've got a five-year rate, 00:19:47.830 --> 00:19:50.080 you've got a 10-year rate, you've got a two-year rate, 00:19:50.080 --> 00:19:51.500 and so on. 00:19:51.500 --> 00:19:53.270 What does that tell us about the future? 00:19:53.270 --> 00:19:56.360 Well, let's write down the big R's. 00:19:56.360 --> 00:19:59.480 Even though we don't see them, we know that somehow, 00:19:59.480 --> 00:20:01.430 implicitly, they're there. 00:20:01.430 --> 00:20:04.790 So what are the relationships between the little 00:20:04.790 --> 00:20:07.070 r's and the big R's? 00:20:07.070 --> 00:20:10.070 Well, you'll see something really neat emerge out of this. 00:20:10.070 --> 00:20:13.790 We'll start with a one-year strip. 00:20:13.790 --> 00:20:17.220 With a one-year strip, the little r and the big R 00:20:17.220 --> 00:20:20.700 are the same, because it's only one year. 00:20:20.700 --> 00:20:23.450 So there's a one-year big R, a one-year little r, 00:20:23.450 --> 00:20:26.420 and when you work out the math, they're 00:20:26.420 --> 00:20:29.060 actually equal to each other. 00:20:29.060 --> 00:20:32.150 But now, when you go with two years, three years, and t 00:20:32.150 --> 00:20:37.110 years, it gets a little bit more complicated. 00:20:37.110 --> 00:20:39.390 Take a look at what happens if you 00:20:39.390 --> 00:20:44.780 take the price of the one-year, and you divide that 00:20:44.780 --> 00:20:47.570 into the price of the two-year. 00:20:50.510 --> 00:20:54.050 These two securities-- the one-year and the two-year-- 00:20:54.050 --> 00:20:56.360 they have the same F, the same face value. 00:20:56.360 --> 00:20:58.147 They pay $1,000 at maturity. 00:20:58.147 --> 00:21:00.230 But one of them goes for one year, and one of them 00:21:00.230 --> 00:21:01.021 goes for two years. 00:21:01.021 --> 00:21:04.910 What happens when you take P 0,1, 00:21:04.910 --> 00:21:07.700 and you divide that by P 0,2? 00:21:07.700 --> 00:21:11.140 By the way, both of those prices exist today. 00:21:11.140 --> 00:21:11.980 Right? 00:21:11.980 --> 00:21:15.040 For example, if you take a look at the strips, 00:21:15.040 --> 00:21:18.880 the price of P 0,1 is 0.967. 00:21:18.880 --> 00:21:23.330 The price of P 0,2 is 0.927. 00:21:23.330 --> 00:21:28.730 If I take the price of 1 divided by the price of 2, 00:21:28.730 --> 00:21:29.550 what do I get? 00:21:29.550 --> 00:21:30.050 Yeah. 00:21:30.050 --> 00:21:31.299 STUDENT: [INAUDIBLE] 00:21:31.299 --> 00:21:32.090 ANDREW LO: Exactly. 00:21:32.090 --> 00:21:34.930 I get 1 plus R2. 00:21:34.930 --> 00:21:39.880 And so if I subtract 1 from that, I get R2. 00:21:39.880 --> 00:21:41.340 So let's just go back. 00:21:41.340 --> 00:21:43.980 I don't have a calculator with me, but I'm sure all of you do. 00:21:43.980 --> 00:21:46.010 Somebody do that division for me, will you? 00:21:46.010 --> 00:21:50.070 Can you take 0.967 and divide that by 0.927? 00:21:50.070 --> 00:21:52.990 What do you get? 00:21:52.990 --> 00:21:58.090 0.967 divided by 0.927. 00:21:58.090 --> 00:21:58.765 What's that? 00:21:58.765 --> 00:21:59.920 STUDENT: 1.04. 00:21:59.920 --> 00:22:02.630 ANDREW LO: 1.04-- and then, subtract 1 from that. 00:22:02.630 --> 00:22:03.990 4%. 00:22:03.990 --> 00:22:07.660 Actually, can you give me a few more digits of accuracy? 00:22:07.660 --> 00:22:08.520 STUDENT: [INAUDIBLE] 00:22:08.520 --> 00:22:09.478 ANDREW LO: What's that? 00:22:09.478 --> 00:22:10.810 STUDENT: 4.314. 00:22:10.810 --> 00:22:14.070 ANDREW LO: 4.314. 00:22:14.070 --> 00:22:20.370 So it turns out that in year 0, where 00:22:20.370 --> 00:22:23.610 we have all of these prices, we actually 00:22:23.610 --> 00:22:28.050 have a forecast for what big R2 is. 00:22:28.050 --> 00:22:31.200 Big R2 in this case is the borrowing cost 00:22:31.200 --> 00:22:33.060 between year 1 and year 2. 00:22:35.670 --> 00:22:38.070 But we're sitting at year 0. 00:22:38.070 --> 00:22:41.460 So implicit in the price of a two-year bond and a one-year 00:22:41.460 --> 00:22:42.090 bond-- 00:22:42.090 --> 00:22:47.250 implicit in that is a forecast of what the price is going 00:22:47.250 --> 00:22:49.110 to be, what the yield is going to be, 00:22:49.110 --> 00:22:50.610 or what the borrowing costs is going 00:22:50.610 --> 00:22:53.220 to be between years 1 and 2. 00:22:53.220 --> 00:22:56.900 In this case, 4.3% or so. 00:22:56.900 --> 00:23:02.330 And that's a really important observation. 00:23:02.330 --> 00:23:09.380 If you plot these little r's on a graph as a function of time, 00:23:09.380 --> 00:23:15.680 you actually get a sense of where the future big R's are 00:23:15.680 --> 00:23:17.490 going to lie. 00:23:17.490 --> 00:23:21.960 This plot, a plot of the r's as a function of time, 00:23:21.960 --> 00:23:25.320 is known as the term structure of interest rates or the yield 00:23:25.320 --> 00:23:30.540 curve, and it gives you a sense of where future interest 00:23:30.540 --> 00:23:32.160 rates are going to go. 00:23:32.160 --> 00:23:36.450 If the curve is upward-sloping, it says that as you go out 00:23:36.450 --> 00:23:41.310 into longer maturities, your average yield, 00:23:41.310 --> 00:23:44.990 the geometric average of all the big R's-- 00:23:44.990 --> 00:23:47.790 it's getting bigger as time grows, 00:23:47.790 --> 00:23:49.920 as the time horizon grows. 00:23:49.920 --> 00:23:53.400 If it's downward-sloping, it suggests 00:23:53.400 --> 00:23:58.830 that future interest rates, future big R's, are declining. 00:23:58.830 --> 00:24:01.440 I want to show you what the yield curve looks like today. 00:24:01.440 --> 00:24:05.730 Now, it turns out that we don't have a yield curve of strips 00:24:05.730 --> 00:24:08.850 as readily available as a yield curve that includes 00:24:08.850 --> 00:24:09.660 coupon payments. 00:24:09.660 --> 00:24:12.384 So I'm going to come back to the distinction 00:24:12.384 --> 00:24:13.300 a little bit later on. 00:24:13.300 --> 00:24:15.270 We haven't talked about coupon bonds yet, 00:24:15.270 --> 00:24:17.580 but I just want to show you what the yield curve is. 00:24:17.580 --> 00:24:20.280 So I'm on the Bloomberg website. 00:24:20.280 --> 00:24:22.470 This is publicly available, so I don't have 00:24:22.470 --> 00:24:24.110 a particular license for it. 00:24:24.110 --> 00:24:25.690 It's the public version. 00:24:25.690 --> 00:24:27.990 And if you click on market data, and then click 00:24:27.990 --> 00:24:31.240 on rates and bonds, you're going to get this page right here. 00:24:31.240 --> 00:24:34.380 So these are the different US treasury securities, 00:24:34.380 --> 00:24:35.790 the different horizons. 00:24:35.790 --> 00:24:36.870 These are the coupons. 00:24:36.870 --> 00:24:39.525 For less than a year, there are no coupon payments, 00:24:39.525 --> 00:24:41.610 so these are pure discount bonds. 00:24:41.610 --> 00:24:47.950 And there's the graph. 00:24:47.950 --> 00:24:49.870 That's it. 00:24:49.870 --> 00:24:54.910 That graph-- the green line is showing you the future course 00:24:54.910 --> 00:24:57.070 of interest rates. 00:24:57.070 --> 00:24:58.990 It's extremely low today. 00:24:58.990 --> 00:25:01.210 The scale is on the left-hand access. 00:25:01.210 --> 00:25:05.050 And by the way, these are in percent. 00:25:05.050 --> 00:25:12.610 So where we are today, for a three-month rate, 00:25:12.610 --> 00:25:14.740 is close to zero. 00:25:14.740 --> 00:25:17.560 It's actually three basis points, 00:25:17.560 --> 00:25:22.201 three basis points for a three-month T-bill. 00:25:22.201 --> 00:25:23.200 What does that tell you? 00:25:26.450 --> 00:25:32.686 What's the relationship between price and the little r? 00:25:32.686 --> 00:25:33.614 Yeah? 00:25:33.614 --> 00:25:37.362 STUDENT: [INAUDIBLE] 00:25:37.362 --> 00:25:39.040 ANDREW LO: Well, that's right. 00:25:39.040 --> 00:25:43.120 But how does that yield get so low? 00:25:43.120 --> 00:25:43.824 Yes? 00:25:43.824 --> 00:25:45.995 STUDENT: Because the price is extremely high. 00:25:45.995 --> 00:25:47.620 ANDREW LO: The price is extremely high. 00:25:47.620 --> 00:25:48.161 That's right. 00:25:48.161 --> 00:25:51.490 Price is equal to the three-month pay-out divided 00:25:51.490 --> 00:25:52.880 by 1 plus little r. 00:25:52.880 --> 00:25:56.830 If little r ends up being really, really tiny, 00:25:56.830 --> 00:26:00.670 it's only because the price is really high. 00:26:00.670 --> 00:26:01.840 Why would the price be high? 00:26:04.600 --> 00:26:06.870 STUDENT: Because US treasuries are the safe thing 00:26:06.870 --> 00:26:08.270 to own right now. 00:26:08.270 --> 00:26:10.920 ANDREW LO: At least, that's what many people think, exactly. 00:26:10.920 --> 00:26:14.460 There is a really strong flight to liquidity going on 00:26:14.460 --> 00:26:16.310 in markets, as of today. 00:26:16.310 --> 00:26:18.060 And how do you know that it's as of today? 00:26:18.060 --> 00:26:19.500 Well, take a look at the difference 00:26:19.500 --> 00:26:21.291 between the green line and the orange line. 00:26:21.291 --> 00:26:23.800 The orange line was what it was yesterday. 00:26:23.800 --> 00:26:25.100 You see, there's a difference. 00:26:25.100 --> 00:26:27.490 There's a noticeable difference on the short end that 00:26:27.490 --> 00:26:30.400 means a lot of people are out there buying treasury bills 00:26:30.400 --> 00:26:33.700 now, probably as we speak. 00:26:33.700 --> 00:26:37.300 Maybe you ought to go and buy some treasury bills. 00:26:37.300 --> 00:26:38.830 People are scared. 00:26:38.830 --> 00:26:40.930 And they're scared because of all the things 00:26:40.930 --> 00:26:43.990 that are going on in the news, and this is exactly what 00:26:43.990 --> 00:26:46.970 the Fed is trying to stave off. 00:26:46.970 --> 00:26:48.790 So you're absolutely right. 00:26:48.790 --> 00:26:51.250 The Fed is not worried about the cost of borrowing. 00:26:51.250 --> 00:26:52.930 They're worried about whether or not 00:26:52.930 --> 00:26:55.690 there's money out there to be able to calm 00:26:55.690 --> 00:26:59.410 the fears of market participants. 00:26:59.410 --> 00:27:00.126 Yeah? 00:27:00.126 --> 00:27:02.606 STUDENT: [INAUDIBLE] two days ago 00:27:02.606 --> 00:27:05.416 to today, [INAUDIBLE] probably the Fed didn't cut the interest 00:27:05.416 --> 00:27:07.070 rate once [INAUDIBLE]. 00:27:07.070 --> 00:27:10.500 They [INAUDIBLE]. 00:27:10.500 --> 00:27:11.500 ANDREW LO: That's right. 00:27:11.500 --> 00:27:14.470 They might have to, so that expectation actually 00:27:14.470 --> 00:27:15.970 is built into these prices. 00:27:15.970 --> 00:27:18.820 The market recognizes that, and they're worried. 00:27:18.820 --> 00:27:20.520 But think about that. 00:27:20.520 --> 00:27:23.020 If the Fed has said that they're going to be cutting rates-- 00:27:23.020 --> 00:27:26.310 possibly cutting rates in the future, and yet, 00:27:26.310 --> 00:27:30.270 the rate stays relatively high going forward, 00:27:30.270 --> 00:27:33.210 and rates go down today, what that's 00:27:33.210 --> 00:27:36.120 telling you is that the market is being driven by a panic 00:27:36.120 --> 00:27:37.360 reaction. 00:27:37.360 --> 00:27:39.480 Now, rates are going to go up. 00:27:39.480 --> 00:27:44.460 So the fact that you see the market determining a yield 00:27:44.460 --> 00:27:46.080 curve that's upward-sloping-- that's 00:27:46.080 --> 00:27:48.330 telling you that people expect that rates 00:27:48.330 --> 00:27:50.580 are going to go up, that rates have to go up, 00:27:50.580 --> 00:27:52.300 for one of two reasons. 00:27:52.300 --> 00:27:55.410 And in fact, you can take a look at the steepness of the yield 00:27:55.410 --> 00:27:58.800 curve as telling you what the market's expectations are 00:27:58.800 --> 00:28:00.690 for how quickly rates are going to go up 00:28:00.690 --> 00:28:02.770 and where they're going to go up. 00:28:02.770 --> 00:28:06.090 So you have to look at the x-axis a little bit 00:28:06.090 --> 00:28:07.150 differently. 00:28:07.150 --> 00:28:08.947 These are denominated in years, so this 00:28:08.947 --> 00:28:11.280 is three months, six months, one year, two, three, four, 00:28:11.280 --> 00:28:13.140 five, up to 10-- 00:28:13.140 --> 00:28:14.760 then, 15, 20, and 30. 00:28:14.760 --> 00:28:17.490 So these are long-term rates. 00:28:17.490 --> 00:28:21.930 And you can see that the yield curve really goes up sharply 00:28:21.930 --> 00:28:23.680 after the first three months. 00:28:23.680 --> 00:28:26.260 There's a big increase in the slope, 00:28:26.260 --> 00:28:29.370 and then it becomes a little bit more gradual. 00:28:29.370 --> 00:28:34.980 That's a sign of a short-term flight to quality or flight 00:28:34.980 --> 00:28:36.060 to liquidity. 00:28:36.060 --> 00:28:38.640 But the market expects, over time 00:28:38.640 --> 00:28:42.840 as things calm down, that interest rates will go up, 00:28:42.840 --> 00:28:45.030 for one of two reasons. 00:28:45.030 --> 00:28:47.910 Either there are inflationary pressures and that 00:28:47.910 --> 00:28:50.370 will drive rates up, or there are 00:28:50.370 --> 00:28:52.500 going to be some economic consequences of what's 00:28:52.500 --> 00:28:54.750 happening today, and that will ultimately 00:28:54.750 --> 00:28:56.740 cause rates to go up. 00:28:56.740 --> 00:28:59.215 Yeah. 00:28:59.215 --> 00:29:02.680 STUDENT: What's happening to the interest rates 00:29:02.680 --> 00:29:04.660 outside of this case? 00:29:04.660 --> 00:29:10.408 Because I'm from Argentina, and when we have crises, 00:29:10.408 --> 00:29:13.930 like [? internal ?] interest rates go up, 00:29:13.930 --> 00:29:16.780 because the probability of default increases. 00:29:16.780 --> 00:29:20.240 And now, I see here, it's the other way around, 00:29:20.240 --> 00:29:23.400 because they are not considering it will be-- 00:29:23.400 --> 00:29:24.400 ANDREW LO: That's right. 00:29:24.400 --> 00:29:26.570 It depends on the nature of the crisis. 00:29:26.570 --> 00:29:30.520 So in certain countries where there is a financial crisis, 00:29:30.520 --> 00:29:33.730 the typical reaction of monetary authorities 00:29:33.730 --> 00:29:36.280 is to flood the market with cash, 00:29:36.280 --> 00:29:39.070 because that's their reaction to a liquidity crunch. 00:29:39.070 --> 00:29:42.310 They want to reduce the prospect of having a kind of run 00:29:42.310 --> 00:29:46.900 on the banks, so they'll flood the market with their currency. 00:29:46.900 --> 00:29:49.630 When you do that, you encourage inflation, 00:29:49.630 --> 00:29:53.320 and that's why interest rates go up in those kinds of economies. 00:29:53.320 --> 00:29:57.220 The US, for better or for worse, has shown a certain degree 00:29:57.220 --> 00:30:01.330 of monetary restraint over the years in that while they do 00:30:01.330 --> 00:30:05.260 certainly cut interest rates-- and Alan Greenspan was very 00:30:05.260 --> 00:30:09.850 active in this respect over the last 10 or 15 years-- 00:30:09.850 --> 00:30:12.100 the fact is that there has been more 00:30:12.100 --> 00:30:16.840 measured control of monetary policy in the United States. 00:30:16.840 --> 00:30:19.810 What that means is that this is a symptom more 00:30:19.810 --> 00:30:21.820 of a short-term cash crunch. 00:30:21.820 --> 00:30:23.980 People are just putting money in treasury bills 00:30:23.980 --> 00:30:27.430 for the short term without any expectation 00:30:27.430 --> 00:30:30.880 that the Fed is going to dramatically increase the money 00:30:30.880 --> 00:30:31.690 supply. 00:30:31.690 --> 00:30:33.190 If they did that, you would then see 00:30:33.190 --> 00:30:35.500 interest rates rise, because inflation would 00:30:35.500 --> 00:30:38.210 be much more of a problem. 00:30:38.210 --> 00:30:39.020 OK. 00:30:39.020 --> 00:30:39.740 Yes? 00:30:39.740 --> 00:30:43.534 STUDENT: [INAUDIBLE] European Central Bank? 00:30:43.534 --> 00:30:44.200 ANDREW LO: Yeah. 00:30:44.200 --> 00:30:49.740 STUDENT: --normally raises the interest rates [INAUDIBLE].. 00:30:49.740 --> 00:30:50.740 ANDREW LO: That's right. 00:30:50.740 --> 00:30:52.870 They do raise it, and that's one of the reasons why 00:30:52.870 --> 00:30:55.140 the Fed did not cut it. 00:30:55.140 --> 00:30:58.000 It's because they are concerned with inflation. 00:30:58.000 --> 00:31:00.100 And so if they ended up cutting interest rates, 00:31:00.100 --> 00:31:03.790 while that might stave off certain credit crunches, 00:31:03.790 --> 00:31:05.958 that would actually encourage inflation. 00:31:05.958 --> 00:31:08.398 STUDENT: So inflation does encourage higher interest 00:31:08.398 --> 00:31:10.840 rates, but what is the [? advantage ?] of it? 00:31:10.840 --> 00:31:12.390 ANDREW LO: Inflation causes-- 00:31:12.390 --> 00:31:16.210 so I see the confusion, and let me make a distinction. 00:31:16.210 --> 00:31:18.640 There are two different interest rates that are going on. 00:31:18.640 --> 00:31:20.240 There is the market rate of interest, 00:31:20.240 --> 00:31:21.560 which is what this is. 00:31:21.560 --> 00:31:25.670 And then, there is the Fed's stated federal funds rate, 00:31:25.670 --> 00:31:28.480 which is what it charges its other member 00:31:28.480 --> 00:31:30.070 banks for borrowing. 00:31:30.070 --> 00:31:34.120 The Fed is able to control what it charges to other banks. 00:31:34.120 --> 00:31:36.430 The Fed cannot control these rates. 00:31:36.430 --> 00:31:40.810 So the interest rates that you're thinking about, that-- 00:31:40.810 --> 00:31:43.420 for example, when the ECB raises rates, 00:31:43.420 --> 00:31:49.090 they do so, so as to discourage lots of borrowing and lending, 00:31:49.090 --> 00:31:53.500 and reduce the amount of money that's in circulation. 00:31:53.500 --> 00:31:56.350 And that decreases business activity, 00:31:56.350 --> 00:31:58.860 which then reduces the pressure on inflation. 00:31:58.860 --> 00:31:59.680 OK? 00:31:59.680 --> 00:32:02.240 So that's what they do in response, 00:32:02.240 --> 00:32:04.570 but they don't control the interest rate determined 00:32:04.570 --> 00:32:06.380 by the market for treasury bills. 00:32:06.380 --> 00:32:08.830 And in these interest rates, these 30-year rates, 00:32:08.830 --> 00:32:11.230 as opposed to overnight borrowing rates and Fed funds 00:32:11.230 --> 00:32:13.780 rates, these rates give you a sense 00:32:13.780 --> 00:32:17.260 of what the market is expecting over time. 00:32:17.260 --> 00:32:19.070 [? Megan, ?] do you have a question? 00:32:19.070 --> 00:32:25.440 STUDENT: [INAUDIBLE] As it cuts the interest rates, 00:32:25.440 --> 00:32:31.810 [INAUDIBLE] had an impact [INAUDIBLE] the actual banks 00:32:31.810 --> 00:32:43.570 that [? spread ?] over time [INAUDIBLE] to stave off that 00:32:43.570 --> 00:32:44.600 credit crunch-- 00:32:44.600 --> 00:32:45.850 ANDREW LO: Well, that's right. 00:32:45.850 --> 00:32:48.140 I think that when you think about the instruments 00:32:48.140 --> 00:32:52.220 that the Fed has for managing monetary policy, credit, 00:32:52.220 --> 00:32:55.540 and liquidity, it's actually pretty minimal. 00:32:55.540 --> 00:32:58.130 I mean, they have one variable. 00:32:58.130 --> 00:32:58.630 You know? 00:32:58.630 --> 00:33:02.575 Imagine flying a mirror plane and you get one control. 00:33:02.575 --> 00:33:03.450 You pick the control. 00:33:03.450 --> 00:33:06.280 You want to be able to control the wheels, or the ailerons, 00:33:06.280 --> 00:33:07.891 or the--? 00:33:07.891 --> 00:33:09.910 It's very, very hard to try to manage 00:33:09.910 --> 00:33:12.280 the economy with one variable. 00:33:12.280 --> 00:33:14.380 Now, the Fed has other policy instruments 00:33:14.380 --> 00:33:17.920 that are a little bit more complex, like the discount 00:33:17.920 --> 00:33:19.630 window, like moral suasion. 00:33:19.630 --> 00:33:21.250 The New York Fed can go to these banks 00:33:21.250 --> 00:33:22.680 and say, what are you guys doing? 00:33:22.680 --> 00:33:24.510 Are you nuts? 00:33:24.510 --> 00:33:29.080 But what's going on now is that because the crisis has reached 00:33:29.080 --> 00:33:31.990 such an extraordinary level, they're not 00:33:31.990 --> 00:33:33.250 worrying about interest rates. 00:33:33.250 --> 00:33:34.791 They're actually trying to figure out 00:33:34.791 --> 00:33:37.390 how to stave off some kind of mass panic. 00:33:37.390 --> 00:33:39.910 And so getting directly involved with AIG, 00:33:39.910 --> 00:33:42.910 getting in discussions with Bear Stearns and JP Morgan-- 00:33:42.910 --> 00:33:44.600 they really have no choice. 00:33:44.600 --> 00:33:49.390 And it's a signal of, sort of, how desperate times are. 00:33:49.390 --> 00:33:50.480 One last question? 00:33:50.480 --> 00:33:54.086 STUDENT: [INAUDIBLE] My understanding is first 00:33:54.086 --> 00:33:55.877 that the Fed is not a federal organization. 00:33:55.877 --> 00:33:58.118 It's made up of a number of banks, 00:33:58.118 --> 00:34:00.309 so that it's not a government entity, 00:34:00.309 --> 00:34:02.600 but the government has appointed representatives to it. 00:34:02.600 --> 00:34:04.790 And at the same time, where does the Fed 00:34:04.790 --> 00:34:06.380 get all their money from? 00:34:06.380 --> 00:34:08.830 ANDREW LO: Well, this is more of a question 00:34:08.830 --> 00:34:11.850 that you probably should be asking your macro instructor. 00:34:11.850 --> 00:34:14.560 I'm happy to answer it, but the macro folks 00:34:14.560 --> 00:34:17.290 may disagree with what I'm about to tell you. 00:34:17.290 --> 00:34:19.120 The Fed is a government organization. 00:34:19.120 --> 00:34:21.310 It's separate from the government in the sense 00:34:21.310 --> 00:34:24.340 that it's not a political organization, 00:34:24.340 --> 00:34:27.010 but it does have the full backing of the government, 00:34:27.010 --> 00:34:29.770 and it has powers granted to it as part 00:34:29.770 --> 00:34:34.060 of the various legal proposals that 00:34:34.060 --> 00:34:37.750 were developed to create the Federal Reserve system. 00:34:37.750 --> 00:34:39.520 Where does the Fed get its money from? 00:34:39.520 --> 00:34:41.350 It gets its money from the treasury. 00:34:41.350 --> 00:34:43.870 So the Fed can actually engage in what 00:34:43.870 --> 00:34:46.030 are called open market operations 00:34:46.030 --> 00:34:49.870 and can actually contract or expand money supply, 00:34:49.870 --> 00:34:53.199 based upon what the treasury will allow it to do 00:34:53.199 --> 00:34:55.630 or will work with it to do. 00:34:55.630 --> 00:34:57.490 And the Fed controls the borrowing rate 00:34:57.490 --> 00:35:01.780 among all of the member banks, and actually, all 00:35:01.780 --> 00:35:03.532 of the major banks are members. 00:35:03.532 --> 00:35:05.740 So it's not like you can start up your bank tomorrow. 00:35:05.740 --> 00:35:08.480 In order to start a bank and deal with the public, 00:35:08.480 --> 00:35:10.870 you need a bank charter, and the bank charter 00:35:10.870 --> 00:35:12.370 is issued by the government. 00:35:12.370 --> 00:35:14.020 And once you're part of that network, 00:35:14.020 --> 00:35:16.792 you are part of the Federal Reserve system. 00:35:16.792 --> 00:35:19.155 STUDENT: Aren't they losing money from, say, 00:35:19.155 --> 00:35:20.530 the fallout of these [? banks? ?] 00:35:20.530 --> 00:35:22.810 Aren't they, in essence, losing also themselves? 00:35:22.810 --> 00:35:25.760 ANDREW LO: Well, they're not trying to make money. 00:35:25.760 --> 00:35:27.610 That's not their objective. 00:35:27.610 --> 00:35:30.400 And if they're losing money, ultimately, it's 00:35:30.400 --> 00:35:32.080 not them that is losing money. 00:35:32.080 --> 00:35:33.580 It is-- who? 00:35:33.580 --> 00:35:34.564 STUDENT: [INAUDIBLE] 00:35:34.564 --> 00:35:35.230 ANDREW LO: Yeah. 00:35:35.230 --> 00:35:36.130 We're losing money. 00:35:36.130 --> 00:35:37.411 It's government-sponsored. 00:35:37.411 --> 00:35:39.160 So that's one of the reasons why, I think, 00:35:39.160 --> 00:35:42.544 the Fed has been so concerned about bailing out 00:35:42.544 --> 00:35:43.210 Lehman Brothers. 00:35:43.210 --> 00:35:46.690 And even the bailout of Bear Stearns, which did not 00:35:46.690 --> 00:35:49.690 necessarily cost them anything-- 00:35:49.690 --> 00:35:52.390 the fact that they were willing to provide this backstop 00:35:52.390 --> 00:35:54.520 guarantee in order to make the deal happen-- 00:35:54.520 --> 00:35:57.430 that implicit insurance is a cost 00:35:57.430 --> 00:35:59.230 that we ultimately end up paying. 00:35:59.230 --> 00:36:00.924 They got a huge amount of heat for that, 00:36:00.924 --> 00:36:03.340 and that's one of the reasons why they decided to back off 00:36:03.340 --> 00:36:04.589 from the Lehman Brothers deal. 00:36:04.589 --> 00:36:08.320 It's because they would have gotten huge, huge backlash 00:36:08.320 --> 00:36:10.130 from that kind of an event. 00:36:10.130 --> 00:36:12.340 Now, AIG-- the fact that they went and did 00:36:12.340 --> 00:36:14.380 something there tells you something 00:36:14.380 --> 00:36:16.930 about how important AIG is, or what 00:36:16.930 --> 00:36:21.160 repercussions might have come about if they had let AIG fail. 00:36:21.160 --> 00:36:22.930 So that says more, not about the Fed, 00:36:22.930 --> 00:36:25.090 but more about the situation with AIG 00:36:25.090 --> 00:36:27.460 and the specific financial transactions 00:36:27.460 --> 00:36:29.610 that they were engaged in. 00:36:29.610 --> 00:36:30.110 OK. 00:36:30.110 --> 00:36:31.280 Let me continue on. 00:36:31.280 --> 00:36:34.130 And sorry, I want to hold off questions for a little bit 00:36:34.130 --> 00:36:38.720 longer, but I do want to cover some additional material. 00:36:38.720 --> 00:36:40.550 So this is the expression that we just 00:36:40.550 --> 00:36:43.430 described for getting a sense of future interest rates. 00:36:43.430 --> 00:36:47.030 And we saw, given today's yield curve, 00:36:47.030 --> 00:36:49.310 that there is some sense that interest rates are 00:36:49.310 --> 00:36:50.660 going to rise. 00:36:50.660 --> 00:36:53.300 But it turns out that the yield curve contains 00:36:53.300 --> 00:36:56.870 all sorts of information, not just about one-year rates, 00:36:56.870 --> 00:37:00.530 but in fact, about multi-year rates. 00:37:00.530 --> 00:37:02.270 This is a clear example. 00:37:02.270 --> 00:37:04.190 This is one example. 00:37:04.190 --> 00:37:07.580 And it turns out that there's another example that 00:37:07.580 --> 00:37:09.950 makes this a little bit clearer, which is 00:37:09.950 --> 00:37:13.130 future rates and forward rates. 00:37:13.130 --> 00:37:15.560 These are all very confusing terminology, 00:37:15.560 --> 00:37:17.960 unless you sit down and read through it carefully, 00:37:17.960 --> 00:37:20.780 so I would encourage you all to do that after this lecture. 00:37:20.780 --> 00:37:22.730 There's a lot of notation in this lecture, 00:37:22.730 --> 00:37:25.010 but not a lot of conceptual challenges. 00:37:25.010 --> 00:37:26.690 Because all the conceptual challenges, 00:37:26.690 --> 00:37:29.570 we derived when we talked about net present value rules. 00:37:29.570 --> 00:37:32.900 So most of this is just lots of notation and terminology. 00:37:32.900 --> 00:37:35.700 So let me describe the terminology here. 00:37:35.700 --> 00:37:39.470 At date zero, if we focus on the price of a bond, 00:37:39.470 --> 00:37:41.670 that matures at time t minus 1. 00:37:41.670 --> 00:37:44.570 And at date zero, if we focus on the price of a bond that 00:37:44.570 --> 00:37:48.860 matures at day t, and we take the ratio of those two, 00:37:48.860 --> 00:37:53.480 then it turns out, we're getting an implicit forecast 00:37:53.480 --> 00:37:58.650 of the future one-year spot rate between t minus 1 and t. 00:37:58.650 --> 00:37:59.150 Right? 00:37:59.150 --> 00:38:02.370 That's just what we did with r2. 00:38:02.370 --> 00:38:05.580 So this is true in general, and there's 00:38:05.580 --> 00:38:09.390 a name for this forecast. 00:38:09.390 --> 00:38:13.800 It's called, today's forward rate 00:38:13.800 --> 00:38:18.090 between dates t minus 1 and t. 00:38:18.090 --> 00:38:23.040 It is a forecast of the future spot rate 00:38:23.040 --> 00:38:25.320 between dates t minus 1 and t. 00:38:25.320 --> 00:38:25.890 OK? 00:38:25.890 --> 00:38:28.230 We don't know what that spot rate is going to be, 00:38:28.230 --> 00:38:29.036 in general. 00:38:29.036 --> 00:38:31.410 We don't know what future interest rates are going to be. 00:38:31.410 --> 00:38:32.550 It's uncertain. 00:38:32.550 --> 00:38:35.760 But today, implicit in today's prices 00:38:35.760 --> 00:38:39.330 is a forecast of that unknown future, 00:38:39.330 --> 00:38:42.780 and we're going to call that forecast the forward rate. 00:38:45.370 --> 00:38:48.490 That is really meant to convey that it is a rate that we 00:38:48.490 --> 00:38:53.560 observe today, and it is meant to capture the market's best 00:38:53.560 --> 00:38:58.750 guess about what the future spot rate will be. 00:38:58.750 --> 00:39:00.670 OK? 00:39:00.670 --> 00:39:04.270 So this is, I know, a little bit confusing. 00:39:04.270 --> 00:39:07.030 And just to give you a summary of all the notation 00:39:07.030 --> 00:39:08.950 and terminology we've defined today-- 00:39:08.950 --> 00:39:11.200 we have a spot rate. 00:39:11.200 --> 00:39:14.860 A spot rate is the rate that you have to pay 00:39:14.860 --> 00:39:20.220 or that you will earn on the spot, for a period of time. 00:39:20.220 --> 00:39:23.980 So you've got the two-year spot rate today. 00:39:23.980 --> 00:39:27.520 You've also got future spot rates, which you 00:39:27.520 --> 00:39:30.070 don't know and don't observe. 00:39:30.070 --> 00:39:34.810 You also have a forward rate, which you do observe today. 00:39:34.810 --> 00:39:38.530 And the forward rate is a rate that applies 00:39:38.530 --> 00:39:41.560 over some period in the future. 00:39:41.560 --> 00:39:46.820 And it's today's best guess of what that future rate will be. 00:39:46.820 --> 00:39:52.130 Now, we can see the implicit forecasts 00:39:52.130 --> 00:39:55.970 that are in the yield curve. 00:39:55.970 --> 00:39:58.730 The one-year spot rate today also 00:39:58.730 --> 00:40:02.470 happens to be equal to the one-year forward rate. 00:40:02.470 --> 00:40:06.350 However, if you take a look at the two-year spot rate 00:40:06.350 --> 00:40:09.380 and compare that with the one-year spot rate, 00:40:09.380 --> 00:40:15.190 you can compute the one-year forward rate 00:40:15.190 --> 00:40:18.920 for borrowing between years 1 and 2. 00:40:18.920 --> 00:40:23.770 And similarly, if you compare the four-year spot rate 00:40:23.770 --> 00:40:25.810 with the three-year spot rate, you 00:40:25.810 --> 00:40:28.240 will be able to figure out what the forward rate is 00:40:28.240 --> 00:40:33.340 for borrowing one year between 3 and 4. 00:40:33.340 --> 00:40:35.282 OK? 00:40:35.282 --> 00:40:36.990 Now, you might think this is complicated. 00:40:36.990 --> 00:40:37.410 Believe me. 00:40:37.410 --> 00:40:39.243 It gets even more complicated when you think 00:40:39.243 --> 00:40:41.310 about multi-year forward rates. 00:40:41.310 --> 00:40:43.860 So suppose I asked you, what is the two-year borrowing 00:40:43.860 --> 00:40:46.770 rate, three years from now? 00:40:46.770 --> 00:40:50.010 Then, what you would do is to take a five-year bond 00:40:50.010 --> 00:40:52.440 and compare that to a three-year bond, 00:40:52.440 --> 00:40:56.520 and that would give you the two-year forward rate today, 00:40:56.520 --> 00:40:58.300 starting in year 3. 00:40:58.300 --> 00:40:59.370 OK? 00:40:59.370 --> 00:41:00.700 Lots of different rates. 00:41:00.700 --> 00:41:03.030 This is, again, why I've told you, every time you 00:41:03.030 --> 00:41:04.890 have a problem like this, draw a timeline. 00:41:04.890 --> 00:41:08.130 Otherwise, you're going to get hopelessly confused. 00:41:08.130 --> 00:41:11.580 Now, in general, you can define forward 00:41:11.580 --> 00:41:15.220 interest rates between any two points in time, between time t1 00:41:15.220 --> 00:41:16.710 and t2. 00:41:16.710 --> 00:41:21.120 And so the typical forward transaction 00:41:21.120 --> 00:41:25.590 is one where today, we agree to do a deal that 00:41:25.590 --> 00:41:28.530 starts at some point t1 in the future 00:41:28.530 --> 00:41:31.950 and concludes at some point t2 in the future. 00:41:31.950 --> 00:41:34.620 And that's known as a forward transaction. 00:41:34.620 --> 00:41:37.260 It's a transaction that we agree upon today, 00:41:37.260 --> 00:41:40.260 to engage in sometime in the future. 00:41:42.990 --> 00:41:44.700 Now, I want to work through an example, 00:41:44.700 --> 00:41:46.770 because this is a bit confusing. 00:41:46.770 --> 00:41:49.930 So let me show you how this might work, 00:41:49.930 --> 00:41:53.860 and why the whole idea of forward rates and future spot 00:41:53.860 --> 00:41:56.650 rates is so important. 00:41:56.650 --> 00:42:00.130 A practical example is that you are the chief financial officer 00:42:00.130 --> 00:42:03.100 of a multinational company based in the US, 00:42:03.100 --> 00:42:07.390 and you're going to get $10 million a year 00:42:07.390 --> 00:42:10.935 from now, from operations overseas. 00:42:10.935 --> 00:42:13.060 And it's going to come back in the form of dollars, 00:42:13.060 --> 00:42:14.643 but it's not going to come back today. 00:42:14.643 --> 00:42:17.480 It's going to come back exactly one year from today. 00:42:17.480 --> 00:42:21.104 Now, you've got to pay dividends two years from today. 00:42:21.104 --> 00:42:23.020 So you're going to use that money that's going 00:42:23.020 --> 00:42:25.070 to come in a year from now. 00:42:25.070 --> 00:42:29.790 And then, at the end of year 2, you're going to pay it out. 00:42:29.790 --> 00:42:32.580 And so you don't want to take that money next year 00:42:32.580 --> 00:42:33.870 and fool around with it. 00:42:33.870 --> 00:42:36.000 You don't know what interest rates are going to be. 00:42:36.000 --> 00:42:37.860 But what you'd like to be able to do 00:42:37.860 --> 00:42:43.020 is, today, lock in a rate of return between years 1 and 2. 00:42:43.020 --> 00:42:46.710 Because you know that you're going to need to get that money 00:42:46.710 --> 00:42:50.140 invested in year 1, and you'd like 00:42:50.140 --> 00:42:52.750 to be able to pay it out in year 2. 00:42:52.750 --> 00:42:54.274 And you want to do that all today. 00:42:54.274 --> 00:42:55.190 So how do you do that? 00:42:55.190 --> 00:42:57.490 Well, you go to the financial markets, 00:42:57.490 --> 00:42:59.177 and you look at the yield curve. 00:42:59.177 --> 00:43:00.760 And you see what the one-year rate is, 00:43:00.760 --> 00:43:02.140 and what the two-year rate is. 00:43:02.140 --> 00:43:05.620 And what you get from looking at the newspaper is, 00:43:05.620 --> 00:43:13.320 the one-year rate is 5%, and the two-year rate is 7%. 00:43:13.320 --> 00:43:16.050 Question-- is 7% a spot rate, forward rate, 00:43:16.050 --> 00:43:18.787 or future spot rate? 00:43:18.787 --> 00:43:19.620 STUDENT: [INAUDIBLE] 00:43:19.620 --> 00:43:22.147 ANDREW LO: It's a spot rate of what? 00:43:22.147 --> 00:43:22.980 STUDENT: [INAUDIBLE] 00:43:22.980 --> 00:43:23.771 ANDREW LO: Exactly. 00:43:23.771 --> 00:43:26.310 It is today's spot rate between now and two years from now. 00:43:26.310 --> 00:43:27.480 It's a two-year spot rate. 00:43:27.480 --> 00:43:28.470 Right. 00:43:28.470 --> 00:43:31.440 What you care about, though, for the example 00:43:31.440 --> 00:43:34.152 I just gave you, is what? 00:43:34.152 --> 00:43:36.130 STUDENT: [INAUDIBLE] 00:43:36.130 --> 00:43:37.000 ANDREW LO: Exactly. 00:43:37.000 --> 00:43:39.370 You care about the one-year spot rate in one year, 00:43:39.370 --> 00:43:42.460 the future one-year spot rate, which-- 00:43:42.460 --> 00:43:44.110 you don't know what it's going to be. 00:43:44.110 --> 00:43:45.430 That's uncertain. 00:43:45.430 --> 00:43:48.850 But you do have the-- 00:43:48.850 --> 00:43:51.571 what rate do you have today? 00:43:51.571 --> 00:43:52.570 The forward rate, right. 00:43:52.570 --> 00:43:53.440 You have a forward rate. 00:43:53.440 --> 00:43:55.190 Because you've got the two-year spot rate, 00:43:55.190 --> 00:43:57.080 and you've got the one-year spot rate. 00:43:57.080 --> 00:44:03.620 So when you compare the two, implicitly in those two rates 00:44:03.620 --> 00:44:05.780 is the forecast of the future one-year spot rate 00:44:05.780 --> 00:44:10.250 or today's forward rate between years 1 and 2. 00:44:10.250 --> 00:44:11.130 All right. 00:44:11.130 --> 00:44:12.890 Now, let's get to brass tacks. 00:44:12.890 --> 00:44:16.860 How do you go about locking in the rates between years 1 00:44:16.860 --> 00:44:18.680 and 2? 00:44:18.680 --> 00:44:24.620 Well, here's a really cool transaction that you can do. 00:44:24.620 --> 00:44:32.980 Today, borrow $9.524 million for a year. 00:44:32.980 --> 00:44:36.430 How do you know you can do that? 00:44:36.430 --> 00:44:38.059 STUDENT: [INAUDIBLE] 00:44:38.059 --> 00:44:38.850 ANDREW LO: Exactly. 00:44:38.850 --> 00:44:40.810 You've got the one-year interest rate at 5%. 00:44:40.810 --> 00:44:42.240 So if that's really a market rate, 00:44:42.240 --> 00:44:44.656 that means that you should be able to borrow at that rate. 00:44:44.656 --> 00:44:45.360 OK? 00:44:45.360 --> 00:44:49.330 So when you're borrowing money, what are you doing? 00:44:49.330 --> 00:44:52.914 You're-- are you buying a bond? 00:44:52.914 --> 00:44:53.830 You're selling a bond. 00:44:53.830 --> 00:44:54.890 You're issuing a bond. 00:44:54.890 --> 00:44:55.681 Right. 00:44:55.681 --> 00:44:56.180 OK. 00:44:56.180 --> 00:44:59.499 So you borrowed $9.52 million dollars today. 00:44:59.499 --> 00:45:01.040 Now, in a minute, I'll explain to you 00:45:01.040 --> 00:45:04.100 why that number is so weird. 00:45:04.100 --> 00:45:11.610 Then, after you get the money today, 00:45:11.610 --> 00:45:16.600 I'm going to ask you to put it into the two-year bond. 00:45:16.600 --> 00:45:24.030 So you got $9.52 million in cash, 00:45:24.030 --> 00:45:26.442 and you put it into a two-year bond. 00:45:26.442 --> 00:45:27.900 So let's take a look at what you've 00:45:27.900 --> 00:45:29.834 done with that transaction. 00:45:33.550 --> 00:45:37.880 The outcome looks like this. 00:45:37.880 --> 00:45:41.864 In year zero, you've borrowed 9.52, 00:45:41.864 --> 00:45:43.280 and then you've taken the proceeds 00:45:43.280 --> 00:45:47.780 and you've bought a bond at 9.52. 00:45:47.780 --> 00:45:54.060 So in fact, your net expenditures is nothing. 00:45:54.060 --> 00:45:55.890 You borrowed money, you took that money, 00:45:55.890 --> 00:45:57.140 and you bought something else. 00:45:57.140 --> 00:45:58.136 You've loaned it out. 00:45:58.136 --> 00:46:00.510 You borrowed money for one year, and you've loaned it out 00:46:00.510 --> 00:46:01.470 for two years. 00:46:01.470 --> 00:46:02.730 That's what you've done. 00:46:02.730 --> 00:46:05.190 So today, you actually have zero, 00:46:05.190 --> 00:46:08.910 in terms of your assets and liabilities. 00:46:08.910 --> 00:46:10.620 Now, let's see what happens next year. 00:46:10.620 --> 00:46:18.440 In one year's time, that 9.52 to magically turns into 10, 00:46:18.440 --> 00:46:23.810 but it's a negative 10, meaning you borrowed 9.52. 00:46:23.810 --> 00:46:26.750 You've got to pay back 9.52 with interest. 00:46:26.750 --> 00:46:28.840 How much interest? 00:46:28.840 --> 00:46:29.659 5%. 00:46:29.659 --> 00:46:30.700 That's the one-year rate. 00:46:30.700 --> 00:46:35.420 So now, you actually have to pay back $10 million. 00:46:35.420 --> 00:46:37.770 Well, it just so happens, you have $10 million. 00:46:37.770 --> 00:46:38.372 How? 00:46:38.372 --> 00:46:40.580 From the money that's coming in from your subsidiary, 00:46:40.580 --> 00:46:43.040 that repatriation amount of money. 00:46:43.040 --> 00:46:45.650 So you take that $10 million, you pay it back, 00:46:45.650 --> 00:46:48.450 and you're done with that part of your portfolio. 00:46:48.450 --> 00:46:49.670 What do you have left? 00:46:49.670 --> 00:46:54.700 What you have left is a bond that 00:46:54.700 --> 00:46:59.780 will pay you money in the year after that, between years 1 00:46:59.780 --> 00:47:01.070 and 2. 00:47:01.070 --> 00:47:03.080 And there you go. 00:47:03.080 --> 00:47:06.080 You get paid $10.9 million. 00:47:06.080 --> 00:47:09.140 You've done all of this transaction today. 00:47:09.140 --> 00:47:12.710 You've locked in the rates today. 00:47:12.710 --> 00:47:13.900 OK? 00:47:13.900 --> 00:47:14.400 Yeah? 00:47:14.400 --> 00:47:17.780 STUDENT: You locked in the one-year spot rate [INAUDIBLE]?? 00:47:17.780 --> 00:47:18.850 ANDREW LO: That's right. 00:47:18.850 --> 00:47:22.460 Well, you're locking in the forward rate, 00:47:22.460 --> 00:47:24.480 which is the forecast-- 00:47:24.480 --> 00:47:24.980 right. 00:47:24.980 --> 00:47:28.340 It's what the market expects the future one-year spot 00:47:28.340 --> 00:47:29.210 rate will be. 00:47:29.210 --> 00:47:31.550 Now, that's a good point that you bring up, 00:47:31.550 --> 00:47:36.540 which is, let's say that in year 1, 00:47:36.540 --> 00:47:39.270 it turns out that at that point in time, 00:47:39.270 --> 00:47:44.900 the one-year spot rate is 7%. 00:47:44.900 --> 00:47:46.340 Are you happy or are you sad? 00:47:50.380 --> 00:47:52.225 Some people say said, some people say happy. 00:47:56.250 --> 00:48:01.080 If the one-year spot rate one year from now is 7%, 00:48:01.080 --> 00:48:02.827 and you've done this deal already-- 00:48:02.827 --> 00:48:04.020 STUDENT: You're happy. 00:48:04.020 --> 00:48:05.020 ANDREW LO: You're happy. 00:48:05.020 --> 00:48:05.700 That's right. 00:48:05.700 --> 00:48:09.930 Because, what are you getting on your portfolio? 00:48:09.930 --> 00:48:10.950 9%. 00:48:10.950 --> 00:48:12.480 Now, wait a minute. 00:48:12.480 --> 00:48:13.860 How do you get 9%? 00:48:13.860 --> 00:48:16.020 I thought that I told you the two-year rate was 7%. 00:48:22.730 --> 00:48:25.595 I'm purposely confusing you, so I'm hoping it works. 00:48:25.595 --> 00:48:27.470 And then, I'm going to try to un-confuse you, 00:48:27.470 --> 00:48:30.590 and I hope that works, too. 00:48:30.590 --> 00:48:32.960 5% is the one-year spot rate. 00:48:32.960 --> 00:48:35.380 7% is the two-year spot rate. 00:48:35.380 --> 00:48:36.452 Yeah. 00:48:36.452 --> 00:48:38.992 STUDENT: [INAUDIBLE] 00:48:38.992 --> 00:48:39.700 ANDREW LO: Right. 00:48:39.700 --> 00:48:40.960 That's right. 00:48:40.960 --> 00:48:47.230 The rate between years 1 and 2 is around 9%. 00:48:47.230 --> 00:48:49.060 And the reason it's got to be that way 00:48:49.060 --> 00:48:52.280 is, the 7% that I told you-- 00:48:52.280 --> 00:48:53.239 that's a two-year rate. 00:48:53.239 --> 00:48:53.738 Right? 00:48:53.738 --> 00:48:55.190 That's the average of two years. 00:48:55.190 --> 00:48:57.570 But you know what the rate is the first year. 00:48:57.570 --> 00:48:59.550 The first year rate is 5%. 00:48:59.550 --> 00:49:02.300 So if something averages to 7% over 2 years, 00:49:02.300 --> 00:49:05.130 but the first year is 5, the second year 00:49:05.130 --> 00:49:06.410 has got to be greater than 7. 00:49:06.410 --> 00:49:09.950 Otherwise, the average can't be 7. 00:49:09.950 --> 00:49:11.870 In fact, the second year rate-- 00:49:11.870 --> 00:49:15.890 the one year rate between years 1 and 2 is around 9%. 00:49:15.890 --> 00:49:22.360 And so that's why if when you arrive at the end of year 1, 00:49:22.360 --> 00:49:24.250 ready to borrow for one more year, 00:49:24.250 --> 00:49:26.590 and you've already locked in a 9% rate, 00:49:26.590 --> 00:49:30.280 you are pretty happy that the rate at that time is 7. 00:49:30.280 --> 00:49:35.620 However, if I told you that the rate at that time was 15, 00:49:35.620 --> 00:49:37.740 you'll be kicking yourself, because you locked 00:49:37.740 --> 00:49:40.425 in a 9% rate, and yet it's 15%. 00:49:43.080 --> 00:49:46.440 So there's room for regret as well as celebration, 00:49:46.440 --> 00:49:48.310 depending on what the market is going to do. 00:49:48.310 --> 00:49:51.030 But the point is that in year zero, 00:49:51.030 --> 00:49:52.590 I don't know what it's going to be. 00:49:52.590 --> 00:49:54.390 And I'm not a hedge fund manager. 00:49:54.390 --> 00:49:55.200 I'm not a trader. 00:49:55.200 --> 00:49:55.784 I don't care-- 00:49:55.784 --> 00:49:57.949 I don't want to make a bet on future interest rates. 00:49:57.949 --> 00:49:59.790 I just want to get this problem solved. 00:49:59.790 --> 00:50:02.340 And right now, today, I can actually 00:50:02.340 --> 00:50:04.860 solve my problem of figuring out how 00:50:04.860 --> 00:50:07.650 to invest my money between years 1 and 2 00:50:07.650 --> 00:50:11.400 by doing this very simple transaction in open markets 00:50:11.400 --> 00:50:13.300 with market-determined interest rates. 00:50:13.300 --> 00:50:16.270 And I know, as long as the interest rates are not nuts, 00:50:16.270 --> 00:50:18.300 then I'm getting a reasonable deal. 00:50:18.300 --> 00:50:19.516 Yeah? 00:50:19.516 --> 00:50:22.530 STUDENT: This is one of the main [? things that you can do. ?] 00:50:22.530 --> 00:50:26.258 Could you please [INAUDIBLE] is it even similar in the same-- 00:50:26.258 --> 00:50:29.302 at the end of year 1, I get my 10 million, 00:50:29.302 --> 00:50:35.354 put it in [INAUDIBLE],, because it's pretty much [INAUDIBLE].. 00:50:35.354 --> 00:50:36.020 ANDREW LO: Yeah. 00:50:36.020 --> 00:50:37.395 But the problem is that you don't 00:50:37.395 --> 00:50:39.820 know what that one-year T-bill rate will be, 00:50:39.820 --> 00:50:42.950 whereas right now, you know that it's 9%. 00:50:42.950 --> 00:50:45.320 Right now, you know it's 9%, and it 00:50:45.320 --> 00:50:47.810 seems like a pretty good deal to go ahead and do it. 00:50:47.810 --> 00:50:51.530 If, however, you think that interest rates are going 00:50:51.530 --> 00:50:55.790 to go up much more than the market thinks, 00:50:55.790 --> 00:50:57.590 then you may want to wait. 00:50:57.590 --> 00:51:01.040 But now, you're becoming an interest rate speculator. 00:51:01.040 --> 00:51:02.390 You're taking a risk. 00:51:02.390 --> 00:51:05.570 And as a CFO, that's generally not your job and not 00:51:05.570 --> 00:51:06.631 your level of competency. 00:51:06.631 --> 00:51:07.130 Right? 00:51:07.130 --> 00:51:10.148 You're not there trying to forecast interest rates. 00:51:10.148 --> 00:51:11.146 Yeah? 00:51:11.146 --> 00:51:14.570 STUDENT: [INAUDIBLE] 00:51:14.570 --> 00:51:15.570 ANDREW LO: That's right. 00:51:15.570 --> 00:51:19.220 The 9.524 is the present value of $10 million today, 00:51:19.220 --> 00:51:20.900 at the rate of 5% interest. 00:51:23.900 --> 00:51:25.520 So the way that I did this-- 00:51:25.520 --> 00:51:28.010 and you know, this is a good illustration 00:51:28.010 --> 00:51:30.140 of what I've been telling you about finance 00:51:30.140 --> 00:51:31.730 not being a spectator sport. 00:51:31.730 --> 00:51:33.470 I suspect that all of you understand 00:51:33.470 --> 00:51:36.110 the lectures that I've given so far about present value, 00:51:36.110 --> 00:51:38.420 about time value of money, and the fact that you've got 00:51:38.420 --> 00:51:39.711 to use the right exchange rate. 00:51:39.711 --> 00:51:42.500 It all is pretty straightforward. 00:51:42.500 --> 00:51:45.890 But putting it into practice is not so easy, at least for me. 00:51:45.890 --> 00:51:48.320 I don't find this example so transparent. 00:51:48.320 --> 00:51:50.840 You have to actually spend some time thinking about it, 00:51:50.840 --> 00:51:52.370 thinking about where the money is coming from, 00:51:52.370 --> 00:51:54.080 where the money is going, how much money 00:51:54.080 --> 00:51:56.440 you have at any point in time. 00:51:56.440 --> 00:51:59.040 But when you work it out, it all makes sense. 00:51:59.040 --> 00:52:01.220 And so I would encourage all of you 00:52:01.220 --> 00:52:03.350 to spend some time working this out. 00:52:03.350 --> 00:52:05.021 OK, question? 00:52:05.021 --> 00:52:05.520 Yeah. 00:52:05.520 --> 00:52:12.940 STUDENT: [INAUDIBLE] 00:52:12.940 --> 00:52:14.380 ANDREW LO: Yes, there are ways you 00:52:14.380 --> 00:52:16.720 can engage in a forward contract, of course. 00:52:16.720 --> 00:52:18.460 So you don't have to do this. 00:52:18.460 --> 00:52:21.520 But the fact is doing this is so simple. 00:52:21.520 --> 00:52:22.720 Why not? 00:52:22.720 --> 00:52:25.960 And if it's simple, most likely, it'll be cheap. 00:52:25.960 --> 00:52:29.030 If it's complex, that's when you're going to pay for it. 00:52:29.030 --> 00:52:29.530 Right? 00:52:29.530 --> 00:52:32.590 So I'm happy to structure a derivative product for you. 00:52:32.590 --> 00:52:34.030 Let's call it a structured product 00:52:34.030 --> 00:52:35.571 that we trade over the counter, where 00:52:35.571 --> 00:52:38.440 I offer you a forward contract, one-year borrowing, 00:52:38.440 --> 00:52:40.660 with certain terms and privileges, and so on. 00:52:40.660 --> 00:52:42.521 And by the time we're done, I'm going 00:52:42.521 --> 00:52:44.770 to charge you a transaction fee of-- oh, I don't know, 00:52:44.770 --> 00:52:46.720 maybe 5%. 00:52:46.720 --> 00:52:49.990 Versus, you buy a two-year bond and a one-year bill, 00:52:49.990 --> 00:52:51.020 and you're done. 00:52:51.020 --> 00:52:51.520 Right? 00:52:51.520 --> 00:52:53.260 So that's the difference. 00:52:53.260 --> 00:52:56.450 It's really the ease with which you can implement the strategy. 00:52:56.450 --> 00:52:58.270 All of you right now, today-- 00:52:58.270 --> 00:52:59.410 all of you can do this. 00:52:59.410 --> 00:53:00.610 You can do this. 00:53:00.610 --> 00:53:02.500 You can actually trade in these markets. 00:53:02.500 --> 00:53:05.110 Set up a brokerage account, trade these treasury 00:53:05.110 --> 00:53:07.540 instruments, and do this yourself. 00:53:07.540 --> 00:53:09.100 In fact, you can do this online. 00:53:09.100 --> 00:53:11.660 So it's very, very simple. 00:53:11.660 --> 00:53:12.935 And-- yeah? 00:53:12.935 --> 00:53:15.790 STUDENT: [INAUDIBLE] $10 million? 00:53:15.790 --> 00:53:17.035 ANDREW LO: Oh, yeah. 00:53:17.035 --> 00:53:17.826 [STUDENTS LAUGHING] 00:53:17.826 --> 00:53:19.350 Well, that's the hard part. 00:53:19.350 --> 00:53:20.269 Yeah. 00:53:20.269 --> 00:53:22.060 There's an old Steve Martin joke that says, 00:53:22.060 --> 00:53:24.220 I'm going to show you how to make a million dollars 00:53:24.220 --> 00:53:25.420 and pay no taxes. 00:53:25.420 --> 00:53:27.910 First, get a million dollars. 00:53:27.910 --> 00:53:30.610 So yes, that's the hard part. 00:53:30.610 --> 00:53:32.140 OK. 00:53:32.140 --> 00:53:36.850 So now, this transaction today locks you 00:53:36.850 --> 00:53:40.720 into a 9% rate between years 1 and 2. 00:53:40.720 --> 00:53:42.490 And so going back to the question 00:53:42.490 --> 00:53:43.977 that [? Anan ?] raised, should you 00:53:43.977 --> 00:53:45.310 do this or should you just wait? 00:53:45.310 --> 00:53:47.380 Well, it depends. 00:53:47.380 --> 00:53:50.560 Do you feel lucky? 00:53:50.560 --> 00:53:53.210 Do you think you can do better than 9%? 00:53:53.210 --> 00:53:54.627 I mean, today, 9% looks wonderful, 00:53:54.627 --> 00:53:56.918 but that's not with the rate you're going to get today. 00:53:56.918 --> 00:53:58.840 In fact, if we go back to the Bloomberg site, 00:53:58.840 --> 00:54:00.940 you can see what kind of rate you would lock 00:54:00.940 --> 00:54:03.280 in today between years 1 and 2. 00:54:03.280 --> 00:54:06.390 And I promise you, it's nowhere near 9%. 00:54:06.390 --> 00:54:09.010 And so again, you might actually say-- 00:54:09.010 --> 00:54:11.620 in today's low interest rate environment, 00:54:11.620 --> 00:54:14.290 you might say, look, I think that inflation 00:54:14.290 --> 00:54:17.950 is going to heat up a great deal over the next year, 00:54:17.950 --> 00:54:23.470 and therefore what's implicit in today's forecast of future spot 00:54:23.470 --> 00:54:26.780 rates is lower than I think it ought to be. 00:54:26.780 --> 00:54:29.470 So I'm going to hold off. 00:54:29.470 --> 00:54:30.125 That's a bet. 00:54:30.125 --> 00:54:31.750 And so you're going to take some risks. 00:54:31.750 --> 00:54:32.431 That's all. 00:54:32.431 --> 00:54:34.930 And for those people who are good at taking risks like that, 00:54:34.930 --> 00:54:35.888 they end up doing well. 00:54:35.888 --> 00:54:38.830 For those who don't, they end up losing out 00:54:38.830 --> 00:54:41.789 on good opportunities. 00:54:41.789 --> 00:54:44.330 There's another example that I'd like you to look at and work 00:54:44.330 --> 00:54:45.260 through on your own. 00:54:45.260 --> 00:54:47.000 It's very similar to the first one, 00:54:47.000 --> 00:54:49.760 but it just gives you practice in thinking about timelines, 00:54:49.760 --> 00:54:52.190 moving money back and forth, and trying 00:54:52.190 --> 00:54:57.380 to understand how to structure the payoffs in order to satisfy 00:54:57.380 --> 00:54:59.370 certain consumption patterns. 00:54:59.370 --> 00:55:02.060 So if you look at this example and work it through, 00:55:02.060 --> 00:55:05.150 that will give you more practice on how to deal 00:55:05.150 --> 00:55:06.150 with these transactions. 00:55:09.430 --> 00:55:13.930 Now, if there are no more questions about pure discount 00:55:13.930 --> 00:55:17.740 bonds, I want to turn to the more general case of coupon 00:55:17.740 --> 00:55:18.350 bonds. 00:55:18.350 --> 00:55:21.730 These are bonds that pay off coupons. 00:55:21.730 --> 00:55:24.700 And really, the theory behind coupon bonds 00:55:24.700 --> 00:55:28.660 is virtually identical to that of discount bonds, in the sense 00:55:28.660 --> 00:55:32.780 that you can always look at a coupon bond 00:55:32.780 --> 00:55:35.480 as a package of discount bonds. 00:55:35.480 --> 00:55:36.850 Right? 00:55:36.850 --> 00:55:38.740 That's, sort of, the opposite of a strip. 00:55:38.740 --> 00:55:41.980 A strip takes a coupon bond and breaks it up 00:55:41.980 --> 00:55:45.310 into what look like little discount bonds. 00:55:45.310 --> 00:55:48.250 Well, if you think about what a coupon bond is, 00:55:48.250 --> 00:55:51.691 it's really just a collection of discount bonds 00:55:51.691 --> 00:55:52.690 at different maturities. 00:55:52.690 --> 00:55:55.210 That's the way to think about it. 00:55:55.210 --> 00:55:56.740 Here's a simple example. 00:55:56.740 --> 00:56:00.550 A three-year bond with a 5% coupon 00:56:00.550 --> 00:56:02.050 is going to look like this. 00:56:02.050 --> 00:56:05.721 It's going to pay 50, 50, and then 1,050. 00:56:05.721 --> 00:56:07.720 Now, as I mentioned, there are some coupon bonds 00:56:07.720 --> 00:56:09.730 that pay semiannually. 00:56:09.730 --> 00:56:12.730 So when they say that there's a coupon of 3%, 00:56:12.730 --> 00:56:14.980 it's 3% every six months. 00:56:14.980 --> 00:56:16.540 So you have to take that into account 00:56:16.540 --> 00:56:18.280 when you're computing the present values 00:56:18.280 --> 00:56:20.480 of these objects. 00:56:20.480 --> 00:56:21.310 How do we do it? 00:56:21.310 --> 00:56:25.660 Exactly the same way as we do for pure discount bonds. 00:56:25.660 --> 00:56:29.380 Take the coupons, each of them, and discount them back 00:56:29.380 --> 00:56:35.040 to the present, using either the big R's or the little r's. 00:56:35.040 --> 00:56:38.200 Either way, you ought to get the same answer, 00:56:38.200 --> 00:56:42.150 because the little r's are simply the geometric averages 00:56:42.150 --> 00:56:43.360 of the big R's. 00:56:43.360 --> 00:56:44.650 OK? 00:56:44.650 --> 00:56:48.390 However, instead of using the little r's 00:56:48.390 --> 00:56:53.890 for the different payments, coupon bonds 00:56:53.890 --> 00:57:01.680 are often quoted with a single number that is a yield. 00:57:01.680 --> 00:57:05.360 So the theoretically correct way to write the price 00:57:05.360 --> 00:57:06.910 is given up there. 00:57:06.910 --> 00:57:09.500 P0 is equal to C, all the coupons, 00:57:09.500 --> 00:57:12.350 divided by the appropriate big R's. 00:57:12.350 --> 00:57:15.320 Or we could replace every one of those big R's 00:57:15.320 --> 00:57:17.480 with the appropriate little r. 00:57:17.480 --> 00:57:21.590 By appropriate little r, I mean, little r 0,1, little r 0,2, 00:57:21.590 --> 00:57:23.750 too little r 0,3-- 00:57:23.750 --> 00:57:25.470 each of those. 00:57:25.470 --> 00:57:29.900 But we can also calculate an average 00:57:29.900 --> 00:57:34.130 of all of those little r's and just use one variable. 00:57:34.130 --> 00:57:36.590 And to simplify notation, I'm going to give it a completely 00:57:36.590 --> 00:57:43.670 different symbol, Y, and say, , what is that single number, Y, 00:57:43.670 --> 00:57:47.960 that will give me the price of the bond? 00:57:47.960 --> 00:57:52.970 And that Y is known as the particular bond's yield. 00:57:52.970 --> 00:57:56.870 It is the single interest rate which, 00:57:56.870 --> 00:58:00.110 if interest rates were constant throughout time, 00:58:00.110 --> 00:58:04.760 would make the present value of all the coupons and principal 00:58:04.760 --> 00:58:07.610 equal to the current price. 00:58:07.610 --> 00:58:10.560 So if you think about a mortgage, 00:58:10.560 --> 00:58:13.860 and you ask the question, if the mortgage rate 00:58:13.860 --> 00:58:20.430 is 5%, what is the value of the loan, 00:58:20.430 --> 00:58:24.590 that's exactly this expression right here. 00:58:24.590 --> 00:58:29.886 Now, obviously, when you get a fixed rate mortgage of 5.89%, 00:58:29.886 --> 00:58:31.760 you know that the interest rate is not really 00:58:31.760 --> 00:58:33.710 going to be 5.98% forever. 00:58:33.710 --> 00:58:35.840 The interest rate changes every year. 00:58:35.840 --> 00:58:41.750 But that 5.98% is an average of the 30-year period where 00:58:41.750 --> 00:58:44.360 you're going to be borrowing that mortgage money. 00:58:44.360 --> 00:58:48.590 So you can think of this coupon bond in exactly the same way. 00:58:48.590 --> 00:58:52.010 We quote this number Y as a yield. 00:58:52.010 --> 00:58:54.890 Sometimes, we talk about yield instead of prices. 00:58:54.890 --> 00:58:56.690 But the way that we figure out the yield 00:58:56.690 --> 00:58:59.330 is, we take this 30-year bond that 00:58:59.330 --> 00:59:02.840 pays 5% a year, we auction it off, 00:59:02.840 --> 00:59:04.940 and we figure out what the price is. 00:59:04.940 --> 00:59:07.470 Given the price, we can find the yield. 00:59:10.300 --> 00:59:13.850 Finding the yield is not so easy in this case, 00:59:13.850 --> 00:59:18.300 because in this case, unlike just taking a simple geometric 00:59:18.300 --> 00:59:21.750 average, which is what we did to calculate the little r's from 00:59:21.750 --> 00:59:22.530 the big R's-- 00:59:22.530 --> 00:59:26.830 in this case, in order to find the Y, 00:59:26.830 --> 00:59:30.760 we actually have to solve an equation that 00:59:30.760 --> 00:59:32.080 can be highly non-linear. 00:59:32.080 --> 00:59:34.480 In fact, it's a polynomial. 00:59:34.480 --> 00:59:38.230 It's a t-th order polynomial. 00:59:38.230 --> 00:59:41.350 And for those of you high school math team jocks, 00:59:41.350 --> 00:59:45.850 you'll remember that when you've got a t-th order 00:59:45.850 --> 00:59:49.930 polynomial, first of all, you have a lot of solutions. 00:59:49.930 --> 00:59:52.280 How many solutions do you typically have? 00:59:52.280 --> 00:59:53.500 t. 00:59:53.500 --> 00:59:57.250 And of those solutions, how many of them 00:59:57.250 --> 01:00:00.067 are guaranteed to be real numbers? 01:00:03.511 --> 01:00:04.010 Right. 01:00:04.010 --> 01:00:06.740 There's no guarantee that any of them are real. 01:00:06.740 --> 01:00:08.690 Now, you might ask, what do you mean by real? 01:00:08.690 --> 01:00:10.790 Well, if you're asking me, you don't need to know. 01:00:10.790 --> 01:00:13.400 [LAUGHTER] Don't-- don't. 01:00:13.400 --> 01:00:16.370 It means numbers that we encounter in reality. 01:00:16.370 --> 01:00:18.409 Let's put it that way. 01:00:18.409 --> 01:00:20.450 It turns out that there are numbers that actually 01:00:20.450 --> 01:00:22.310 don't exist in reality. 01:00:22.310 --> 01:00:24.170 They're called complex numbers. 01:00:24.170 --> 01:00:28.130 And they are quite complex, so I won't talk about them. 01:00:28.130 --> 01:00:30.004 But these kinds of equations-- 01:00:30.004 --> 01:00:31.670 it turns out that they're not guaranteed 01:00:31.670 --> 01:00:33.950 to even have real solutions. 01:00:33.950 --> 01:00:37.240 Now, it turns out that for bonds, 01:00:37.240 --> 01:00:39.640 where the coupon payments are all positive 01:00:39.640 --> 01:00:41.800 and the principle is all positive, 01:00:41.800 --> 01:00:43.500 it turns out in that very restrictive-- 01:00:43.500 --> 01:00:44.710 and the price is positive. 01:00:44.710 --> 01:00:49.300 It turns out in those cases, you actually do get a real number-- 01:00:49.300 --> 01:00:51.340 at least, one real number. 01:00:51.340 --> 01:00:52.900 The problem is that in some cases, 01:00:52.900 --> 01:00:54.520 you get multiple real numbers. 01:00:54.520 --> 01:00:57.280 And then, it's very, very hard to figure out which yield 01:00:57.280 --> 01:00:58.621 is the correct one to use. 01:00:58.621 --> 01:01:00.370 The only reason I'm telling you about this 01:01:00.370 --> 01:01:03.940 is because it turns out as a matter of convention, 01:01:03.940 --> 01:01:09.100 very often, people will quote these little Y yields when 01:01:09.100 --> 01:01:10.774 they talk about coupon bonds. 01:01:10.774 --> 01:01:12.190 But the way to think about that is 01:01:12.190 --> 01:01:13.660 to think about the price, which is 01:01:13.660 --> 01:01:16.780 the present value of the coupon payments as a present discount 01:01:16.780 --> 01:01:21.400 value of the interest that really applies between today 01:01:21.400 --> 01:01:22.810 and date t. 01:01:22.810 --> 01:01:25.360 In fact, in order to do this present value calculation, 01:01:25.360 --> 01:01:27.070 you need not just one interest rate. 01:01:27.070 --> 01:01:30.710 How many interest rates do you need? 01:01:30.710 --> 01:01:32.180 t, right? 01:01:32.180 --> 01:01:35.030 You're at year zero, and you've got payments 01:01:35.030 --> 01:01:37.520 for every single year between 1 and t. 01:01:37.520 --> 01:01:40.838 So you need interest rates that apply between 0 and 1, 0 01:01:40.838 --> 01:01:43.260 and 2, 0 and 3, and so on. 01:01:43.260 --> 01:01:46.440 You need t interest rates or exchange rates. 01:01:46.440 --> 01:01:46.940 Right? 01:01:46.940 --> 01:01:49.700 Or exchanges between different dates. 01:01:49.700 --> 01:01:52.850 But now, the yield is important because it 01:01:52.850 --> 01:01:57.170 allows us to quote the pseudo rate of return 01:01:57.170 --> 01:02:01.070 of this bond in a single number. 01:02:01.070 --> 01:02:06.860 And very often, people will plot the Y's as a function 01:02:06.860 --> 01:02:09.810 of the horizon of these bonds. 01:02:09.810 --> 01:02:12.200 So when I showed you that yield curve-- 01:02:12.200 --> 01:02:13.370 let me get that back. 01:02:16.870 --> 01:02:17.720 Whoops. 01:02:17.720 --> 01:02:18.470 I just had it. 01:02:23.440 --> 01:02:26.460 Let's take a look at this again. 01:02:26.460 --> 01:02:32.190 These treasury bonds from years 2 to years 30-- 01:02:32.190 --> 01:02:36.210 those have coupon payments, and those are the coupon rates. 01:02:36.210 --> 01:02:41.040 And they have prices, and they have yields. 01:02:41.040 --> 01:02:47.210 So what's plotted here is not the little r. 01:02:47.210 --> 01:02:50.870 It's the Y for the coupon bonds. 01:02:50.870 --> 01:02:53.990 And so the reason that they're not the same 01:02:53.990 --> 01:02:57.620 is because the yields, the little Y's, depend 01:02:57.620 --> 01:02:59.680 on the coupon payments. 01:02:59.680 --> 01:03:02.150 And really strictly speaking, we don't 01:03:02.150 --> 01:03:05.000 care about coupon payments when we look at time to maturity. 01:03:05.000 --> 01:03:06.749 We just want to know, what is the interest 01:03:06.749 --> 01:03:11.130 rate between 0 and 1, 0 and 2, 0 and 3, 0 and 5, and so on. 01:03:11.130 --> 01:03:13.670 But this is a reasonable proxy as long 01:03:13.670 --> 01:03:16.130 as the coupons don't look too crazy 01:03:16.130 --> 01:03:18.240 and are not too different from each other. 01:03:18.240 --> 01:03:20.369 And you can see that the coupons are all, sort of, 01:03:20.369 --> 01:03:21.410 in the same neighborhood. 01:03:21.410 --> 01:03:25.340 Some of them are 2.3% versus 4.5%, 01:03:25.340 --> 01:03:26.600 but they're not so different. 01:03:26.600 --> 01:03:32.630 So this gives us an indication of what the strip's yield 01:03:32.630 --> 01:03:33.750 curve would look like. 01:03:44.860 --> 01:03:47.950 Here's an example of the historical yield 01:03:47.950 --> 01:03:50.650 curve for US Treasury securities, 01:03:50.650 --> 01:03:53.560 and let me just show you a plot. 01:03:53.560 --> 01:03:55.720 They move around a lot. 01:03:55.720 --> 01:03:58.330 So these yield curves tell us something 01:03:58.330 --> 01:04:01.270 about the average interest rate across 01:04:01.270 --> 01:04:03.020 various different maturities. 01:04:03.020 --> 01:04:05.440 So if you look at the yellow line, 01:04:05.440 --> 01:04:10.490 that's a one-year yield over time. 01:04:10.490 --> 01:04:12.580 So this is not the yield curve anymore. 01:04:12.580 --> 01:04:15.250 This is a plot of the time series 01:04:15.250 --> 01:04:18.960 of one-year yields over time. 01:04:18.960 --> 01:04:24.360 And you can see that starting when the sample began in 1982, 01:04:24.360 --> 01:04:31.450 the one-year yield for US Treasury bills is 12%. 01:04:31.450 --> 01:04:34.450 12% back in 1982-- 01:04:34.450 --> 01:04:39.730 and there is a point at which one of the longer maturity 01:04:39.730 --> 01:04:44.410 instruments reaches a peak of 16% or 17%. 01:04:44.410 --> 01:04:48.040 Remember, I told you, I was looking to get a house 01:04:48.040 --> 01:04:50.560 and get a mortgage at 18%. 01:04:50.560 --> 01:04:54.320 That was a 30-year fixed rate back in the 1980s. 01:04:54.320 --> 01:04:58.450 So borrowing rates are very, very low 01:04:58.450 --> 01:05:01.360 by these historical standards. 01:05:01.360 --> 01:05:04.390 If borrowing rates are very low, what 01:05:04.390 --> 01:05:08.830 does that tell you about credit and about the amount of cash 01:05:08.830 --> 01:05:12.940 sloshing around in the economy? 01:05:12.940 --> 01:05:13.625 Yeah? 01:05:13.625 --> 01:05:14.960 STUDENT: [INAUDIBLE] 01:05:14.960 --> 01:05:16.960 ANDREW LO: Exactly-- lots and lots 01:05:16.960 --> 01:05:18.950 and lots of money available. 01:05:18.950 --> 01:05:20.560 So for those of you who are thinking 01:05:20.560 --> 01:05:22.582 about entrepreneurial ventures-- if you're 01:05:22.582 --> 01:05:24.040 thinking about raising capital, you 01:05:24.040 --> 01:05:27.040 might be depressed by what's going on in markets today. 01:05:27.040 --> 01:05:30.560 But look at the interest rate and ask yourself, 01:05:30.560 --> 01:05:35.010 gee, would I rather start a company today or back in 1982? 01:05:35.010 --> 01:05:36.970 There's a heck of a lot more money sloshing 01:05:36.970 --> 01:05:39.800 around the system today. 01:05:39.800 --> 01:05:42.670 In fact, a few years ago, I talked to a couple 01:05:42.670 --> 01:05:44.507 of MIT undergraduates. 01:05:44.507 --> 01:05:46.340 One of them came up and asked me whether I'd 01:05:46.340 --> 01:05:49.180 be willing to advise them on some internet company they 01:05:49.180 --> 01:05:50.680 wanted to start. 01:05:50.680 --> 01:05:53.414 And you know, I said, well, you know, where are you 01:05:53.414 --> 01:05:54.580 going to get your financing? 01:05:54.580 --> 01:05:55.770 And they said, oh, don't worry about that. 01:05:55.770 --> 01:05:57.460 We've already got it all set. 01:05:57.460 --> 01:06:00.310 You know, we've got 10 of us, and each of us 01:06:00.310 --> 01:06:04.660 is able to borrow $1,000 each on credit cards, 01:06:04.660 --> 01:06:10.810 and we each have 10 credit cards, so that's $100,000. 01:06:10.810 --> 01:06:12.990 And I'm saying, $100,000 on credit cards? 01:06:12.990 --> 01:06:15.620 I mean, you guys are going to be paying 18% a year 01:06:15.620 --> 01:06:16.750 or something on that. 01:06:16.750 --> 01:06:18.208 And they said, yeah, you know what? 01:06:18.208 --> 01:06:20.860 That's the cheapest venture financing you'll ever find. 01:06:20.860 --> 01:06:24.100 And they're right, because those are non-recourse loans. 01:06:24.100 --> 01:06:25.810 They don't take a piece of your company. 01:06:25.810 --> 01:06:29.096 And 18% for a venture is actually pretty attractive. 01:06:29.096 --> 01:06:30.970 Well, look at what the borrowing rate is now. 01:06:30.970 --> 01:06:33.257 Now, you can't borrow at this rate for ventures, 01:06:33.257 --> 01:06:35.590 but it indicates that there's a lot of credit out there, 01:06:35.590 --> 01:06:38.900 and there's still a lot of credit out there. 01:06:38.900 --> 01:06:40.810 In fact, the treasury and the Fed 01:06:40.810 --> 01:06:42.880 would argue there's too much credit out there. 01:06:42.880 --> 01:06:45.171 And that's why we're in the problems that we are today. 01:06:45.171 --> 01:06:46.300 Because too many people-- 01:06:46.300 --> 01:06:49.320 people that should not have been leveraging and borrowing 01:06:49.320 --> 01:06:50.680 have done so. 01:06:50.680 --> 01:06:54.490 And now, we're feeling the pains of a contraction. 01:06:54.490 --> 01:06:56.890 So this is the history of yield curves. 01:06:56.890 --> 01:07:01.090 And at a given point in time, we can take a look at yield curves 01:07:01.090 --> 01:07:03.580 and see how that curve changes day to day. 01:07:03.580 --> 01:07:06.770 I showed you today's yield curve, which is upward sloping. 01:07:06.770 --> 01:07:10.180 But you know, there was a period back in 2000 01:07:10.180 --> 01:07:13.390 where this yield curve was actually upward-sloping, 01:07:13.390 --> 01:07:17.250 and then downward-sloping. 01:07:17.250 --> 01:07:20.840 Why would the yield curve be downward-sloping? 01:07:20.840 --> 01:07:22.490 What that tells you is that there's 01:07:22.490 --> 01:07:26.480 an expectation of the market participants 01:07:26.480 --> 01:07:31.010 that interest rates in the long run have got to come down, 01:07:31.010 --> 01:07:33.740 and that there's going to be some kind of Fed policy 01:07:33.740 --> 01:07:37.430 shift possible within three years, five years, 10 years, 01:07:37.430 --> 01:07:40.650 that would make that more likely than not. 01:07:40.650 --> 01:07:44.240 So by looking at these yield curves over different dates, 01:07:44.240 --> 01:07:47.450 you can get a sense of how the market's expectations are 01:07:47.450 --> 01:07:52.260 of the future, which I think is a tremendous ability 01:07:52.260 --> 01:07:54.260 to actually look into the future-- at least look 01:07:54.260 --> 01:08:00.954 into the future as predicted by all the market participants. 01:08:00.954 --> 01:08:03.120 This is just that yield curve that I told you about. 01:08:03.120 --> 01:08:04.800 This is not in your notes, but I was 01:08:04.800 --> 01:08:06.716 able to copy that from Bloomberg this morning. 01:08:06.716 --> 01:08:08.940 You have that in the public website. 01:08:08.940 --> 01:08:15.090 And now, the next topic I want to take on-- very briefly, 01:08:15.090 --> 01:08:19.170 because there's a lot to be said about models of the yield 01:08:19.170 --> 01:08:21.960 curve, and I won't take up class time to do that. 01:08:21.960 --> 01:08:26.069 This is something that is a topic that's 01:08:26.069 --> 01:08:29.729 more significantly focused on in investments 01:08:29.729 --> 01:08:32.160 and in fixed-income securities. 01:08:32.160 --> 01:08:35.460 But one of the things that we'd like to be able to do 01:08:35.460 --> 01:08:39.300 is to try to model that term structure interest rates. 01:08:39.300 --> 01:08:41.189 Is there any logic that we can come up 01:08:41.189 --> 01:08:43.800 with that explains why the yield curve is 01:08:43.800 --> 01:08:47.939 upward-sloping or backward-bending or inverted? 01:08:47.939 --> 01:08:51.060 And it turns out that there are a number of theories 01:08:51.060 --> 01:08:53.340 that have come to be proposed. 01:08:53.340 --> 01:08:55.590 I'm not going to cover any of these in any depth, 01:08:55.590 --> 01:08:57.881 but I want to at least mention the names so that you'll 01:08:57.881 --> 01:09:00.569 know that there are theories out there that will tell you 01:09:00.569 --> 01:09:04.170 whether or not the yield curve should be so steeply sloped 01:09:04.170 --> 01:09:05.310 or not. 01:09:05.310 --> 01:09:07.735 There's something called the Expectations Hypothesis. 01:09:07.735 --> 01:09:09.359 There is something called the Liquidity 01:09:09.359 --> 01:09:10.620 Preference Hypothesis. 01:09:10.620 --> 01:09:13.859 There is a Preferred Habitat Model, Market Segmentation 01:09:13.859 --> 01:09:14.620 Model. 01:09:14.620 --> 01:09:17.609 And then, there are a whole slew of extraordinarily 01:09:17.609 --> 01:09:21.359 sophisticated and complex mathematical models, 01:09:21.359 --> 01:09:22.229 one of which-- 01:09:22.229 --> 01:09:23.812 and probably the best known of which-- 01:09:23.812 --> 01:09:27.660 was developed by our very own John Cox and Steve Ross. 01:09:27.660 --> 01:09:30.630 The Cox-Ingersoll-Ross model of the term structure 01:09:30.630 --> 01:09:34.170 of interest rates is probably the single best known yield 01:09:34.170 --> 01:09:35.260 curve model. 01:09:35.260 --> 01:09:36.930 It's a very complicated model, but it 01:09:36.930 --> 01:09:39.246 has some pretty significant implications 01:09:39.246 --> 01:09:40.620 for whether the yield curve ought 01:09:40.620 --> 01:09:42.540 to be upward-sloping or downward-sloping, 01:09:42.540 --> 01:09:45.390 or how it changes over time. 01:09:45.390 --> 01:09:49.200 I'll give you one example of what these theories are, 01:09:49.200 --> 01:09:51.090 and I won't spend much time on it, 01:09:51.090 --> 01:09:53.880 but I want to at least leave you with some intuition 01:09:53.880 --> 01:09:56.190 for how you would go about modeling it. 01:09:56.190 --> 01:10:04.630 So one model says that today's forward rates are in fact 01:10:04.630 --> 01:10:10.470 the best guess of what future spot rates are likely to be, 01:10:10.470 --> 01:10:14.100 and that's known as the Expectations Hypothesis. 01:10:14.100 --> 01:10:17.340 This hypothesis states that today's forward rate, which 01:10:17.340 --> 01:10:24.560 is what we do observe, is equal to the mathematical expectation 01:10:24.560 --> 01:10:30.210 today, of the future one-year spot rate. 01:10:30.210 --> 01:10:31.710 Now, you might say, well, that's not 01:10:31.710 --> 01:10:32.876 that's not much of a theory. 01:10:32.876 --> 01:10:34.420 I mean, what else could it be? 01:10:34.420 --> 01:10:37.200 Well, it turns out that there is another theory called 01:10:37.200 --> 01:10:40.320 the Preferred Liquidity Preference Theory that 01:10:40.320 --> 01:10:46.420 says that the longer the term of borrowing, 01:10:46.420 --> 01:10:50.200 the more you're going to have to pay a premium for people 01:10:50.200 --> 01:10:56.660 to lend to you, because people would prefer liquidity. 01:10:56.660 --> 01:11:00.710 So the longer you demand the borrowing 01:11:00.710 --> 01:11:04.880 for a greater period of time, the more you have to pay-- 01:11:04.880 --> 01:11:08.130 much more so than just linearly. 01:11:08.130 --> 01:11:11.210 So in particular, the Expectations Hypothesis 01:11:11.210 --> 01:11:14.020 suggests that the yield curve is flat. 01:11:14.020 --> 01:11:14.930 Right? 01:11:14.930 --> 01:11:18.810 There's no impact on borrowing for two years, three years, 01:11:18.810 --> 01:11:20.360 five years, 10 years. 01:11:20.360 --> 01:11:23.120 The future rate is just equal to-- 01:11:23.120 --> 01:11:28.110 today's forward rate is the expectation of the future. 01:11:28.110 --> 01:11:28.610 OK? 01:11:28.610 --> 01:11:30.410 It's a fair bet. 01:11:30.410 --> 01:11:32.480 Liquidity Preference says that the yield curve 01:11:32.480 --> 01:11:36.030 should be upward-sloping, because it's 01:11:36.030 --> 01:11:39.690 going to be more costly for you to borrow 01:11:39.690 --> 01:11:42.900 over a three-year period than a one-year period, simply 01:11:42.900 --> 01:11:46.920 because it's going to entail somebody 01:11:46.920 --> 01:11:49.637 giving up their money for a longer period of time. 01:11:49.637 --> 01:11:50.970 They're going to be less liquid. 01:11:50.970 --> 01:11:54.150 You're going to have to bribe them to be willing to give up 01:11:54.150 --> 01:11:56.810 that liquidity. 01:11:56.810 --> 01:11:59.960 That's the Liquidity Preference Theory. 01:11:59.960 --> 01:12:01.610 The Preferred Habitat Theory says, 01:12:01.610 --> 01:12:06.470 you know, there are preferred maturities that people have. 01:12:06.470 --> 01:12:08.120 And for those maturities, you're going 01:12:08.120 --> 01:12:11.930 to have different rates than for those that people don't prefer. 01:12:11.930 --> 01:12:14.060 So if you want a 30-year maturity-- 01:12:14.060 --> 01:12:16.504 and that's not preferred because it's too far off-- 01:12:16.504 --> 01:12:18.170 then you're gonna have to pay a premium. 01:12:18.170 --> 01:12:20.870 On the Other Hand, 10 years is a period 01:12:20.870 --> 01:12:23.840 that a number of pension funds prefer, 01:12:23.840 --> 01:12:27.480 so you may not have to pay as much for those preferred 01:12:27.480 --> 01:12:29.200 habitats. 01:12:29.200 --> 01:12:34.320 And to give you a sense of where academics is today, 01:12:34.320 --> 01:12:36.420 none of these models work. 01:12:36.420 --> 01:12:39.600 None of them can fully explain movements 01:12:39.600 --> 01:12:42.640 in the yield curve, which, by the way, 01:12:42.640 --> 01:12:44.670 is a wonderful opportunity for all of you. 01:12:44.670 --> 01:12:48.090 Because if you have a model that does work, 01:12:48.090 --> 01:12:50.490 then you can do extraordinarily well. 01:12:50.490 --> 01:12:54.030 You can turn very, very small forecast power 01:12:54.030 --> 01:12:56.680 into enormous amounts of wealth very, 01:12:56.680 --> 01:12:58.710 very quickly on Wall Street. 01:12:58.710 --> 01:13:00.384 Yes? 01:13:00.384 --> 01:13:09.667 STUDENT: [INAUDIBLE] 01:13:09.667 --> 01:13:10.500 ANDREW LO: Does he-- 01:13:10.500 --> 01:13:12.099 STUDENT: [INAUDIBLE] 01:13:12.099 --> 01:13:13.390 ANDREW LO: You can't patent it. 01:13:13.390 --> 01:13:13.889 Right. 01:13:13.889 --> 01:13:17.290 So does he get anything out of that besides notoriety? 01:13:17.290 --> 01:13:19.130 Well, that's a good question. 01:13:19.130 --> 01:13:22.030 The question has to do with, I guess, the difference 01:13:22.030 --> 01:13:26.020 between academic endeavors and business endeavors. 01:13:26.020 --> 01:13:27.880 As an academic, what you're trying to do 01:13:27.880 --> 01:13:30.430 is to make a name for yourself and to put out 01:13:30.430 --> 01:13:33.460 research ideas that will have an impact 01:13:33.460 --> 01:13:36.980 with your colleagues and the particular area that you're in. 01:13:36.980 --> 01:13:39.490 So if you're asking, did Professor Cox 01:13:39.490 --> 01:13:40.540 get rich off of this? 01:13:40.540 --> 01:13:43.180 The answer is, no, probably not. 01:13:43.180 --> 01:13:44.680 Neither did Black-Scholes, actually, 01:13:44.680 --> 01:13:46.930 when they published their Black-Scholes option pricing 01:13:46.930 --> 01:13:47.440 formula. 01:13:47.440 --> 01:13:49.648 That was the same year that the Chicago Board Options 01:13:49.648 --> 01:13:51.820 Exchange started trading, and everybody just 01:13:51.820 --> 01:13:54.750 used the option pricing formula almost from the very start. 01:13:54.750 --> 01:13:56.170 Did they make money off of that? 01:13:56.170 --> 01:13:57.622 No, they didn't. 01:13:57.622 --> 01:13:58.330 And you're right. 01:13:58.330 --> 01:13:59.620 You can't patent it. 01:13:59.620 --> 01:14:03.880 So very often, in financial firms, 01:14:03.880 --> 01:14:05.140 when they have good ideas-- 01:14:05.140 --> 01:14:06.700 so for example, I do believe there 01:14:06.700 --> 01:14:09.610 are term structure models out there that work reasonably 01:14:09.610 --> 01:14:10.410 well. 01:14:10.410 --> 01:14:11.620 They're not published. 01:14:11.620 --> 01:14:15.640 They're kept as the Coca-Colas of financial markets. 01:14:15.640 --> 01:14:16.990 They're trade secrets. 01:14:16.990 --> 01:14:19.540 And so if you go there to work and ultimately 01:14:19.540 --> 01:14:22.840 work with the right people, you will learn such trade secrets, 01:14:22.840 --> 01:14:25.600 which, by the way, is one of the reasons why when Barclays 01:14:25.600 --> 01:14:28.060 acquires Lehman and wants to keep all of these 01:14:28.060 --> 01:14:30.040 really, really terrific people together, 01:14:30.040 --> 01:14:32.270 they're going to have to offer premia to do that. 01:14:32.270 --> 01:14:35.230 And so that's part of the cost of financial distress 01:14:35.230 --> 01:14:37.210 when you disturb the status quo. 01:14:40.380 --> 01:14:44.860 That's a few models of the term structure of interest rates. 01:14:44.860 --> 01:14:49.140 And I want to talk about one last topic on coupon bonds 01:14:49.140 --> 01:14:52.980 before concluding this lecture. 01:14:52.980 --> 01:14:55.350 Next lecture on Monday, we're going to take up 01:14:55.350 --> 01:14:57.390 measures of interest rate risk. 01:14:57.390 --> 01:14:59.850 We're going to look explicitly at what happens when 01:14:59.850 --> 01:15:01.320 interest rates bounce around. 01:15:01.320 --> 01:15:04.080 Before we get to that, though, I want to talk about another way 01:15:04.080 --> 01:15:06.720 to value coupon bonds, and it's exactly the idea 01:15:06.720 --> 01:15:11.070 that I said before, of using pure discount bonds to do so. 01:15:11.070 --> 01:15:14.790 If I have a pure discount bond, I 01:15:14.790 --> 01:15:18.450 can use that to price coupon bonds by building up 01:15:18.450 --> 01:15:20.490 a package of discount bonds. 01:15:20.490 --> 01:15:22.920 The example of the strips is given here. 01:15:22.920 --> 01:15:25.740 You've got a three-year 5% bond, and it turns out 01:15:25.740 --> 01:15:28.560 that you can show that that three-year 5% bond is going 01:15:28.560 --> 01:15:33.060 to be identical to 50 one-year strips, 50 two-year strips, 01:15:33.060 --> 01:15:37.050 and 1050 three-year strips, each strip 01:15:37.050 --> 01:15:42.600 paying $1 in years 1, 2, and 3. 01:15:42.600 --> 01:15:43.950 Any question about that claim? 01:15:43.950 --> 01:15:46.950 Anybody want to argue with me that that's not true? 01:15:46.950 --> 01:15:48.840 It's pretty obvious, right? 01:15:48.840 --> 01:15:53.100 Well, this actually has a very dramatic implication, 01:15:53.100 --> 01:15:56.530 and let me tell you what that implication is. 01:15:56.530 --> 01:16:03.040 The implication is that the price of a three-year 5% bond 01:16:03.040 --> 01:16:08.660 better be equal to the cost of 50 one-year strips, 50 01:16:08.660 --> 01:16:12.100 two-year strips, and 1050 three-year strips. 01:16:12.100 --> 01:16:14.740 The price of this three-year bond 01:16:14.740 --> 01:16:18.220 better be equal to what it costs to put that portfolio of strips 01:16:18.220 --> 01:16:20.260 together today. 01:16:20.260 --> 01:16:23.000 Why? 01:16:23.000 --> 01:16:24.200 Why should it be equal? 01:16:24.200 --> 01:16:24.923 Yes. 01:16:24.923 --> 01:16:25.770 STUDENT: [INAUDIBLE] 01:16:25.770 --> 01:16:26.540 ANDREW LO: What is arbitrage? 01:16:26.540 --> 01:16:27.801 We haven't defined that. 01:16:27.801 --> 01:16:32.030 STUDENT: [INAUDIBLE] basically, if the prices are different, 01:16:32.030 --> 01:16:34.150 [INAUDIBLE] buy the one or sell the other, 01:16:34.150 --> 01:16:35.979 so they come together [INAUDIBLE].. 01:16:35.979 --> 01:16:36.770 ANDREW LO: Exactly. 01:16:36.770 --> 01:16:41.510 There is a way to make money if the price 01:16:41.510 --> 01:16:45.380 of that three-year bond is anything other than the cost 01:16:45.380 --> 01:16:47.540 of that package of strips. 01:16:47.540 --> 01:16:49.050 So let's do an example. 01:16:49.050 --> 01:16:51.560 Suppose that the price of a three-year bond 01:16:51.560 --> 01:16:54.800 is greater than the cost of the strips. 01:16:54.800 --> 01:16:56.900 Tell me what to do. 01:16:56.900 --> 01:16:57.510 Yeah? 01:16:57.510 --> 01:16:59.970 STUDENT: Buy those strips, package them into a bond, 01:16:59.970 --> 01:17:01.484 and then sell it. 01:17:01.484 --> 01:17:02.902 Sell the bond to the market. 01:17:02.902 --> 01:17:04.610 Just keep doing that over and over again. 01:17:04.610 --> 01:17:05.200 ANDREW LO: OK. 01:17:05.200 --> 01:17:07.450 So let's talk about this slowly. 01:17:07.450 --> 01:17:09.200 I first buy those strips. 01:17:09.200 --> 01:17:11.360 I buy the portfolio strips. 01:17:11.360 --> 01:17:13.810 And then, I take this bond that's 01:17:13.810 --> 01:17:18.130 trading in the open marketplace, and I sell it. 01:17:18.130 --> 01:17:20.860 How do I sell something I don't own? 01:17:20.860 --> 01:17:22.732 Short-sell it, yes. 01:17:22.732 --> 01:17:25.190 Short-selling, which you can read about and Brealey, Myers, 01:17:25.190 --> 01:17:29.390 and Allen, is when, if you don't own the security, 01:17:29.390 --> 01:17:32.910 you can borrow it from a broker, and then sell it, 01:17:32.910 --> 01:17:35.091 and you'll collect the money from selling it. 01:17:35.091 --> 01:17:36.590 Now, the broker, obviously, is going 01:17:36.590 --> 01:17:39.830 to want you to keep that money in that brokerage firm 01:17:39.830 --> 01:17:41.720 so that you don't run away with it. 01:17:41.720 --> 01:17:44.477 Because you've borrowed the security at some point, 01:17:44.477 --> 01:17:45.560 you've got to pay it back. 01:17:45.560 --> 01:17:47.018 You've got to return that security. 01:17:47.018 --> 01:17:47.870 Right? 01:17:47.870 --> 01:17:51.770 So the transaction is, you buy these strips, 01:17:51.770 --> 01:17:55.970 you short-sell the bond, and what have you done? 01:17:55.970 --> 01:17:59.370 Have you made money or lost money on day one? 01:17:59.370 --> 01:18:00.120 You've made money. 01:18:00.120 --> 01:18:00.619 Why? 01:18:00.619 --> 01:18:03.225 Because buying costs less than the amount of money 01:18:03.225 --> 01:18:04.100 you get from selling. 01:18:04.100 --> 01:18:05.850 And how do you know that? 01:18:05.850 --> 01:18:09.050 Because I just assumed that it's more expensive for you 01:18:09.050 --> 01:18:12.320 to get the three-year bond than the package of strips. 01:18:12.320 --> 01:18:15.410 So you've made money today, but you 01:18:15.410 --> 01:18:19.670 have no further obligations, because what you end up 01:18:19.670 --> 01:18:21.850 getting from the strips-- you've bought the strips, 01:18:21.850 --> 01:18:24.860 so you're going to get their coupons or their face value. 01:18:24.860 --> 01:18:28.850 You're going to use those to pay the coupons of the bonds 01:18:28.850 --> 01:18:31.450 that you sold. 01:18:31.450 --> 01:18:33.580 And therefore, you have no further obligations, 01:18:33.580 --> 01:18:36.190 but you have a pile of money in front of you. 01:18:36.190 --> 01:18:37.570 That's pretty cool. 01:18:37.570 --> 01:18:41.560 And if you do that a lot, that pile of money grows. 01:18:41.560 --> 01:18:45.089 So obviously, we know it's not easy to do that. 01:18:45.089 --> 01:18:46.630 And if it's not easy to do that, that 01:18:46.630 --> 01:18:50.200 means that our assumption that the bond was greater 01:18:50.200 --> 01:18:52.990 than the cost of the strips can't be true. 01:18:52.990 --> 01:18:55.180 If you reverse the logic, you get the same kind 01:18:55.180 --> 01:18:56.830 of argument in reverse. 01:18:56.830 --> 01:18:58.570 Therefore, the only thing that could be 01:18:58.570 --> 01:19:00.850 is that the prices are equal to each other. 01:19:00.850 --> 01:19:02.650 Next time, what we're going to do 01:19:02.650 --> 01:19:05.119 is show that a little bit of linear algebra 01:19:05.119 --> 01:19:06.910 is going to allow you to make tons of money 01:19:06.910 --> 01:19:08.770 by comparing all sorts of bonds and looking 01:19:08.770 --> 01:19:10.280 at these kinds of relationships. 01:19:10.280 --> 01:19:10.780 OK. 01:19:10.780 --> 01:19:14.460 I'll see you at 4:00, if you're interested.