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 --> 00:00:25.770 at ocw.mit.edu 00:00:25.770 --> 00:00:29.040 Let me begin by first asking whether there 00:00:29.040 --> 00:00:35.310 are any questions from last class, which was a week ago. 00:00:35.310 --> 00:00:37.470 Hope you had a good break. 00:00:37.470 --> 00:00:38.280 Any questions? 00:00:41.670 --> 00:00:42.220 OK. 00:00:42.220 --> 00:00:45.360 Before we begin today's topic-- question? 00:00:45.360 --> 00:00:46.157 AUDIENCE: No. 00:00:46.157 --> 00:00:46.740 ANDREW LO: No. 00:00:46.740 --> 00:00:51.150 Before we begin today's topic on arbitrage 00:00:51.150 --> 00:00:56.160 and the pricing of multiple fixed income securities, 00:00:56.160 --> 00:00:58.170 I want to just take a few moments 00:00:58.170 --> 00:01:01.200 to talk a bit about what's going on in financial markets, 00:01:01.200 --> 00:01:04.110 also to welcome the prospective students that we have 00:01:04.110 --> 00:01:06.960 sitting here in class today. 00:01:06.960 --> 00:01:11.370 So for once, over the weekend, unprecedented things 00:01:11.370 --> 00:01:12.580 didn't occur. 00:01:12.580 --> 00:01:15.690 And so I'm glad to report that we're still here. 00:01:15.690 --> 00:01:18.270 Financial markets are still around. 00:01:18.270 --> 00:01:22.050 And as you know, the government has proposed some measures 00:01:22.050 --> 00:01:25.890 to deal with this current financial crisis. 00:01:25.890 --> 00:01:28.140 And at this point, it's still unclear as 00:01:28.140 --> 00:01:29.920 to what they're proposing. 00:01:29.920 --> 00:01:32.910 But we can actually see from the data 00:01:32.910 --> 00:01:34.380 what the market's reaction is. 00:01:34.380 --> 00:01:36.910 Last time, remember, we looked at the yield curve 00:01:36.910 --> 00:01:40.170 and literally, it was just a week ago that the yield 00:01:40.170 --> 00:01:42.360 curve looked like this. 00:01:42.360 --> 00:01:44.850 Now remember that we focused on what 00:01:44.850 --> 00:01:47.260 happened at the very short end of the yield curve, 00:01:47.260 --> 00:01:49.170 which is three month Treasury bills. 00:01:49.170 --> 00:01:53.160 And last week when we looked at this graph, 00:01:53.160 --> 00:01:58.230 the yield was about three basis points for a three month 00:01:58.230 --> 00:01:59.130 Treasury bill. 00:01:59.130 --> 00:02:01.620 And we pointed out that that was telling us 00:02:01.620 --> 00:02:02.757 something about the market. 00:02:02.757 --> 00:02:05.340 In particular, it was telling us that the market is panicking. 00:02:05.340 --> 00:02:07.560 Yeah? 00:02:07.560 --> 00:02:10.530 AUDIENCE: So aren't we sort of in this whole situation 00:02:10.530 --> 00:02:13.946 because looking at the market grossly mispriced things? 00:02:13.946 --> 00:02:15.570 ANDREW LO: Well, I wouldn't say that it 00:02:15.570 --> 00:02:18.050 was looking at the market grossly mispriced things. 00:02:18.050 --> 00:02:22.406 AUDIENCE: The market obviously did not officially 00:02:22.406 --> 00:02:27.630 price this risk, which looking at the market a year 00:02:27.630 --> 00:02:31.095 and a half ago, we would have been, oh, here's 00:02:31.095 --> 00:02:33.570 this much risk, this criteria [INAUDIBLE]. 00:02:33.570 --> 00:02:36.060 It turned out to be right, totally right. 00:02:36.060 --> 00:02:38.250 ANDREW LO: Well, there are a number of things that 00:02:38.250 --> 00:02:39.750 are priced into a security. 00:02:39.750 --> 00:02:42.180 It's not just a risk, but it's also a reflection 00:02:42.180 --> 00:02:44.310 of supply and demand, right? 00:02:44.310 --> 00:02:46.560 So in other words, what's going on here-- the question 00:02:46.560 --> 00:02:49.050 that we want to answer from looking at the price 00:02:49.050 --> 00:02:51.930 is what do we know about what's going on in the marketplace 00:02:51.930 --> 00:02:52.800 based on that price. 00:02:52.800 --> 00:02:54.690 What is it telling us? 00:02:54.690 --> 00:02:57.330 The cost of borrowing over a three month period-- 00:02:57.330 --> 00:02:59.190 when it goes down to three basis points, 00:02:59.190 --> 00:03:02.250 that's telling you that the price of that security, 00:03:02.250 --> 00:03:05.565 the price of Treasury bills is extraordinarily high relative 00:03:05.565 --> 00:03:07.590 to historical standards. 00:03:07.590 --> 00:03:10.230 Now let's take a look at what happens 00:03:10.230 --> 00:03:12.630 more recently, in particular, today, 00:03:12.630 --> 00:03:16.200 if we go to any of these websites-- 00:03:16.200 --> 00:03:18.660 so in particular, let's go back to the Bloomberg site 00:03:18.660 --> 00:03:21.090 where we originally looked at this. 00:03:21.090 --> 00:03:23.310 First of all, this is now the yield curve. 00:03:23.310 --> 00:03:27.200 And it's hard to compare because I've 00:03:27.200 --> 00:03:29.820 got a different slide for last weeks. 00:03:29.820 --> 00:03:34.560 This is just yesterday's, the orange, not last week's. 00:03:34.560 --> 00:03:37.680 But the one thing you'll note is that at the very short end, now 00:03:37.680 --> 00:03:42.060 instead of three basis points, the three month Treasury 00:03:42.060 --> 00:03:45.250 is yielding 41 basis points. 00:03:45.250 --> 00:03:48.360 What does that tell you about the price? 00:03:48.360 --> 00:03:52.620 Now, so Treasury securities, short-term Treasury securities, 00:03:52.620 --> 00:03:55.740 have declined in price over the last week. 00:03:55.740 --> 00:04:00.852 And that's one sign that perhaps markets are not as panicked 00:04:00.852 --> 00:04:01.810 as they were last week. 00:04:01.810 --> 00:04:05.040 There isn't this mad rush to get into Treasury securities 00:04:05.040 --> 00:04:05.791 in the short term. 00:04:05.791 --> 00:04:07.623 All right, so short term means have gone up. 00:04:07.623 --> 00:04:08.296 Yeah. 00:04:08.296 --> 00:04:09.796 AUDIENCE: So would you say that this 00:04:09.796 --> 00:04:12.760 would be a lot about the psychology of [INAUDIBLE]. 00:04:12.760 --> 00:04:13.650 ANDREW LO: Yeah. 00:04:13.650 --> 00:04:18.060 AUDIENCE: So what I was wondering is when the fact-- 00:04:18.060 --> 00:04:20.810 it seemed like, as you said, there's a flight in liquidity 00:04:20.810 --> 00:04:21.780 last week. 00:04:21.780 --> 00:04:25.660 Now why was there such a huge movement, 00:04:25.660 --> 00:04:30.025 or what led to the price dropping so much when, I guess, 00:04:30.025 --> 00:04:33.043 it could be reasonably expected that the price would 00:04:33.043 --> 00:04:34.584 come back up and so people would just 00:04:34.584 --> 00:04:36.350 wait it out and take a shot. 00:04:36.350 --> 00:04:38.676 ANDREW LO: Which price are you talking about dropping? 00:04:38.676 --> 00:04:40.800 AUDIENCE: I should probably say the yield dropping. 00:04:40.800 --> 00:04:44.020 ANDREW LO: The yield dropping and the price going up. 00:04:44.020 --> 00:04:47.130 Well, so there are a number of factors at play, 00:04:47.130 --> 00:04:52.740 but the current perspective that most of us 00:04:52.740 --> 00:04:55.300 have in financial markets about last week-- 00:04:55.300 --> 00:04:56.670 and this is just perspective. 00:04:56.670 --> 00:04:59.820 Remember, last week is not that far away. 00:04:59.820 --> 00:05:02.070 What happened last week, by most accounts, 00:05:02.070 --> 00:05:05.370 is that there was a very significant rush 00:05:05.370 --> 00:05:07.400 to the exits by investors. 00:05:07.400 --> 00:05:11.400 By rushing to the exits, I mean getting out of risky securities 00:05:11.400 --> 00:05:13.800 and into safer securities. 00:05:13.800 --> 00:05:16.350 And at this point, it doesn't seem 00:05:16.350 --> 00:05:19.290 like there's much of a safe haven 00:05:19.290 --> 00:05:21.810 other than US Treasury securities, 00:05:21.810 --> 00:05:23.550 and in particular, short-term securities 00:05:23.550 --> 00:05:26.820 because you know you can get the money out over a relatively 00:05:26.820 --> 00:05:28.390 short period of time. 00:05:28.390 --> 00:05:31.170 So that's what the yield curve told us last week, 00:05:31.170 --> 00:05:35.670 that three basis points means that basically people didn't 00:05:35.670 --> 00:05:37.380 care about the yield. 00:05:37.380 --> 00:05:39.760 All they wanted to do was to get into US treasuries 00:05:39.760 --> 00:05:42.000 at almost any price. 00:05:42.000 --> 00:05:43.750 OK. 00:05:43.750 --> 00:05:45.610 This week it's different. 00:05:45.610 --> 00:05:50.800 In particular, not only has the short-term yield gone up, 00:05:50.800 --> 00:05:53.980 so now instead of three basis points, we're up to 41. 00:05:53.980 --> 00:05:56.740 But look at the long end of the yield curve. 00:05:56.740 --> 00:05:58.810 Before, the long end of the yield curve-- 00:05:58.810 --> 00:06:02.590 let me just go back and remind you what that looked like. 00:06:02.590 --> 00:06:10.080 At the 30 year, a week ago, the 30 year yield was 4%. 00:06:10.080 --> 00:06:13.870 Let's take a look at what it is today. 00:06:13.870 --> 00:06:18.750 It's now, the 30 year yield, 4.37. 00:06:18.750 --> 00:06:21.630 That's another big movement. 00:06:21.630 --> 00:06:22.500 Why is that? 00:06:22.500 --> 00:06:26.510 Why would the yield for the long-term bond go up? 00:06:26.510 --> 00:06:29.324 What is the market thinking today? 00:06:29.324 --> 00:06:32.008 AUDIENCE: They might be more worried about inflation. 00:06:32.008 --> 00:06:34.760 The government has promised $700 billion. 00:06:34.760 --> 00:06:37.470 ANDREW LO: OK, so inflation has now 00:06:37.470 --> 00:06:40.650 been incorporated, just over the last seven days. 00:06:40.650 --> 00:06:45.870 So question-- is this price correct 00:06:45.870 --> 00:06:48.270 or was last week's price correct? 00:06:48.270 --> 00:06:50.320 Getting to your point, I mean, what do we do? 00:06:50.320 --> 00:06:53.430 Is the short end of the yield curve appropriate today 00:06:53.430 --> 00:06:56.130 at 41 basis points, or was it really appropriate at three 00:06:56.130 --> 00:06:56.880 basis points? 00:06:59.490 --> 00:07:01.330 There's no answer to that question 00:07:01.330 --> 00:07:03.310 because there is no right answer. 00:07:03.310 --> 00:07:08.310 These prices are a reflection of the current expectations 00:07:08.310 --> 00:07:10.920 of all the market participants. 00:07:10.920 --> 00:07:13.290 Right or wrong, it really reflects 00:07:13.290 --> 00:07:17.430 the combined either wisdom or fear or greed 00:07:17.430 --> 00:07:18.910 of the marketplace. 00:07:18.910 --> 00:07:22.170 And so our approach is to try to understand what that is. 00:07:22.170 --> 00:07:25.140 We want to explicate the information that 00:07:25.140 --> 00:07:27.570 happens to be in prices, but you have 00:07:27.570 --> 00:07:31.290 to understand that these are the same imperfect kind of prices 00:07:31.290 --> 00:07:33.180 that we came up with on day one when you 00:07:33.180 --> 00:07:34.930 bid for that little package. 00:07:34.930 --> 00:07:37.980 And it turned out that you got lucky 00:07:37.980 --> 00:07:42.130 and got an iPod for whatever, $45. 00:07:42.130 --> 00:07:43.770 But it could've gone the other way. 00:07:43.770 --> 00:07:47.080 And in fact, , in the second class it did go the other way. 00:07:47.080 --> 00:07:50.550 So we won't talk about that. 00:07:50.550 --> 00:07:56.790 The prices reflect all aspects of the economy, the rational 00:07:56.790 --> 00:07:58.260 as well as the irrational. 00:07:58.260 --> 00:08:01.140 And so last week, was it irrational for people 00:08:01.140 --> 00:08:04.170 to pull their money out from all sorts of investments 00:08:04.170 --> 00:08:06.210 and put them into Treasury bills? 00:08:06.210 --> 00:08:08.700 Well this goes to the heart of why the Treasury acted 00:08:08.700 --> 00:08:12.510 so quickly, and why Chairman Bernanke has said that he wants 00:08:12.510 --> 00:08:14.160 to get a quick resolution. 00:08:14.160 --> 00:08:17.760 Something very significant happened last week. 00:08:17.760 --> 00:08:21.900 And I don't know how many of you really got wind of it. 00:08:21.900 --> 00:08:23.920 Certainly, the Treasury knew what was going on 00:08:23.920 --> 00:08:26.430 and the Fed did, but it wasn't really highlighted 00:08:26.430 --> 00:08:29.336 in the newspapers in the way that I 00:08:29.336 --> 00:08:30.960 would have thought it should have been, 00:08:30.960 --> 00:08:31.835 given the importance. 00:08:31.835 --> 00:08:33.640 Anybody know what I'm talking about? 00:08:33.640 --> 00:08:34.630 Yeah. 00:08:34.630 --> 00:08:37.360 AUDIENCE: Stopping the short sell-- 00:08:37.360 --> 00:08:39.370 ANDREW LO: Well, that was one piece of news. 00:08:39.370 --> 00:08:42.580 The SEC mandated that for a period of time, 00:08:42.580 --> 00:08:44.560 to be determined, we are not allowed 00:08:44.560 --> 00:08:46.900 to short sell financial stocks because they wanted 00:08:46.900 --> 00:08:49.170 to stop the kind of run that there 00:08:49.170 --> 00:08:50.784 has been on these securities. 00:08:50.784 --> 00:08:52.450 I'm going to come back and talk about it 00:08:52.450 --> 00:08:54.070 in the end of this lecture because we're going 00:08:54.070 --> 00:08:55.154 to talk about short sales. 00:08:55.154 --> 00:08:56.778 But that's not what I was referring to. 00:08:56.778 --> 00:08:59.280 That's certainly a concern, but that's not the major concern 00:08:59.280 --> 00:09:01.030 that I think the market was responding to. 00:09:01.030 --> 00:09:01.530 Yeah. 00:09:01.530 --> 00:09:04.690 AUDIENCE: Was it the $8 billion of redemption in money funds? 00:09:04.690 --> 00:09:05.830 ANDREW LO: That's right. 00:09:05.830 --> 00:09:07.570 Where was that coming from? 00:09:07.570 --> 00:09:09.880 What was going on with that? 00:09:09.880 --> 00:09:11.682 Why did that happen? 00:09:11.682 --> 00:09:13.666 AUDIENCE: Because people are losing confidence 00:09:13.666 --> 00:09:17.010 in the short-term debt securities 00:09:17.010 --> 00:09:18.330 to put in money market funds. 00:09:18.330 --> 00:09:19.705 ANDREW LO: And was there a reason 00:09:19.705 --> 00:09:21.540 for that loss of confidence? 00:09:21.540 --> 00:09:24.890 I mean, money funds, what does that have to do with mortgages 00:09:24.890 --> 00:09:27.810 and Lehman and Goldman? 00:09:27.810 --> 00:09:28.914 What's the connection? 00:09:28.914 --> 00:09:30.690 AUDIENCE: Well, I just think more of it 00:09:30.690 --> 00:09:33.739 was a psychological reaction than it was an actual-- 00:09:33.739 --> 00:09:36.030 ANDREW LO: Absolutely, it was a psychological reaction, 00:09:36.030 --> 00:09:37.770 but did something trigger that? 00:09:37.770 --> 00:09:40.590 Is that psychological reaction completely unreasonable? 00:09:40.590 --> 00:09:42.810 If your grandmother asked you what she should do now 00:09:42.810 --> 00:09:44.940 with her money market fund, should you 00:09:44.940 --> 00:09:49.350 tell her, don't worry about it, just stay the course 00:09:49.350 --> 00:09:51.420 and see what happens? 00:09:51.420 --> 00:09:54.930 Something happened last week that is related exactly 00:09:54.930 --> 00:09:55.514 to that issue. 00:09:55.514 --> 00:09:56.596 So you're on to something. 00:09:56.596 --> 00:09:57.360 What it that? 00:09:57.360 --> 00:09:57.860 Megan. 00:09:57.860 --> 00:10:02.300 AUDIENCE: Well, one of the major money funds broke the buck. 00:10:02.300 --> 00:10:03.780 ANDREW LO: Broke the buck, exactly. 00:10:03.780 --> 00:10:04.488 Which money fund? 00:10:04.488 --> 00:10:05.162 Do you remember? 00:10:05.162 --> 00:10:06.994 AUDIENCE: Lehman, no, no. 00:10:06.994 --> 00:10:08.160 ANDREW LO: The Reserve Fund. 00:10:08.160 --> 00:10:09.180 AUDIENCE: It's the Reserve. 00:10:09.180 --> 00:10:11.180 ANDREW LO: The Reserve Fund is one of the first, 00:10:11.180 --> 00:10:13.200 if not the first, money market funds. 00:10:13.200 --> 00:10:14.740 And what is a money market fund? 00:10:14.740 --> 00:10:15.780 Do we know what that is? 00:10:15.780 --> 00:10:17.975 You all know what that money market fund as? 00:10:17.975 --> 00:10:20.100 You all probably have money in a money market fund. 00:10:20.100 --> 00:10:22.950 Whether you know it or not. 00:10:22.950 --> 00:10:25.320 Money market fund is a fund that contains 00:10:25.320 --> 00:10:29.610 relatively short-term and supposedly riskless 00:10:29.610 --> 00:10:33.960 securities, like CDs, treasuries, 00:10:33.960 --> 00:10:37.170 and other kinds of very, very safe assets. 00:10:37.170 --> 00:10:39.744 And what does it mean to break the buck? 00:10:39.744 --> 00:10:43.188 AUDIENCE: That for every dollar that people invested 00:10:43.188 --> 00:10:47.124 in money market funds had invested what they would 00:10:47.124 --> 00:10:48.582 be able to redeem at that time. 00:10:48.582 --> 00:10:49.290 ANDREW LO: Right. 00:10:49.290 --> 00:10:51.102 AUDIENCE: --less than already spent. 00:10:51.102 --> 00:10:51.810 ANDREW LO: Right. 00:10:51.810 --> 00:10:55.470 Breaking the buck means that when you put in $1, 00:10:55.470 --> 00:10:59.730 money funds are supposed to be so safe that at the very least 00:10:59.730 --> 00:11:03.710 when you withdraw the money, you're going to get $1 back. 00:11:03.710 --> 00:11:07.670 Breaking the buck means that if you withdraw, 00:11:07.670 --> 00:11:11.990 there is a possibility that what you withdraw is less than $1. 00:11:11.990 --> 00:11:16.100 Now that's scary because think about a bank-- 00:11:16.100 --> 00:11:21.710 when you put your money into a checking account for a bank, 00:11:21.710 --> 00:11:23.750 you expect to get that money out, maybe 00:11:23.750 --> 00:11:26.870 not with a lot of interest, maybe even with no interest 00:11:26.870 --> 00:11:30.450 if things don't go well, but you expect to get what you put in. 00:11:30.450 --> 00:11:33.920 You expect to get the principal back, right? 00:11:33.920 --> 00:11:36.320 Well, money market funds are very much the same way. 00:11:36.320 --> 00:11:39.429 People use them as if they were checking accounts. 00:11:39.429 --> 00:11:40.970 In fact, there are money market funds 00:11:40.970 --> 00:11:43.280 where you can write checks on them, right? 00:11:43.280 --> 00:11:47.180 And so breaking the buck has been a major concern, 00:11:47.180 --> 00:11:52.070 not just among the money funds, but among regulators. 00:11:52.070 --> 00:11:57.770 Because if it turns out that retail investors, 00:11:57.770 --> 00:12:01.340 ordinary consumers are scared about what's 00:12:01.340 --> 00:12:05.510 going on with their money market accounts, 00:12:05.510 --> 00:12:09.060 they will do in mass what happened last week, 00:12:09.060 --> 00:12:11.720 which is pull out huge sums of money 00:12:11.720 --> 00:12:14.120 from these money market funds. 00:12:14.120 --> 00:12:17.330 And as I mentioned earlier, no business 00:12:17.330 --> 00:12:23.300 can sustain a massive withdrawal of all capital all at once. 00:12:23.300 --> 00:12:25.160 It's just not possible for a business 00:12:25.160 --> 00:12:27.260 to be able to be conducted in that manner. 00:12:27.260 --> 00:12:31.520 If that happens, we will see mass failures 00:12:31.520 --> 00:12:35.960 of financial institutions that will make the last four weeks 00:12:35.960 --> 00:12:38.840 look like the good old days. 00:12:38.840 --> 00:12:41.130 And that's what the Fed is concerned about. 00:12:41.130 --> 00:12:43.080 That's what the Treasury is concerned about. 00:12:43.080 --> 00:12:46.190 And so the hope is that the measures that they put in place 00:12:46.190 --> 00:12:48.290 will calm the fears of the public. 00:12:48.290 --> 00:12:50.030 That's the first order of business. 00:12:50.030 --> 00:12:53.870 It's calming the psychological kinds of effects 00:12:53.870 --> 00:12:57.380 that these headlines have produced. 00:12:57.380 --> 00:12:59.300 And so the hope is that once they 00:12:59.300 --> 00:13:00.770 put these measures in place, that 00:13:00.770 --> 00:13:02.510 will take care of the concerns. 00:13:02.510 --> 00:13:05.300 What they've done is to propose to guarantee money market 00:13:05.300 --> 00:13:10.250 funds the same way that the FDIC guarantees your banking 00:13:10.250 --> 00:13:11.160 accounts. 00:13:11.160 --> 00:13:13.790 And the way that the SIPC guarantees your brokerage 00:13:13.790 --> 00:13:14.522 accounts. 00:13:14.522 --> 00:13:16.730 And there are other measures that have been proposed. 00:13:16.730 --> 00:13:18.560 We won't have time to talk about them here, 00:13:18.560 --> 00:13:20.060 but over the next couple of weeks, 00:13:20.060 --> 00:13:21.830 the finance group at the Sloan School 00:13:21.830 --> 00:13:24.320 will be putting together some kind of a panel discussion 00:13:24.320 --> 00:13:26.190 that will focus exactly on these issues. 00:13:26.190 --> 00:13:27.860 So we'll let you know when that happens. 00:13:27.860 --> 00:13:31.670 And we'll take on these issues head on in that session. 00:13:31.670 --> 00:13:34.430 OK, but it looks like for the moment, at least 00:13:34.430 --> 00:13:38.120 from the yield curves that we saw, 00:13:38.120 --> 00:13:41.240 that things are actually quieting down. 00:13:41.240 --> 00:13:44.360 We'll see on a day by day basis. 00:13:44.360 --> 00:13:46.730 So this is obviously last week. 00:13:46.730 --> 00:13:48.805 This week, we have yields going up a little bit, 00:13:48.805 --> 00:13:50.180 so that suggests that there isn't 00:13:50.180 --> 00:13:51.910 the same kind of pressure. 00:13:51.910 --> 00:13:55.850 But every day is another day and with another set 00:13:55.850 --> 00:13:56.750 of revelations. 00:13:56.750 --> 00:13:59.540 So by looking at these pieces of information, 00:13:59.540 --> 00:14:02.420 we can actually glean what the market is thinking. 00:14:02.420 --> 00:14:03.920 Is it right? 00:14:03.920 --> 00:14:04.700 Of course not. 00:14:04.700 --> 00:14:07.190 All forecasts are by construction 00:14:07.190 --> 00:14:09.590 incorrect to some degree, but it's 00:14:09.590 --> 00:14:12.792 a window on exactly what's going on in the marketplace 00:14:12.792 --> 00:14:14.000 and what people are thinking. 00:14:14.000 --> 00:14:14.990 Yeah. 00:14:14.990 --> 00:14:17.465 AUDIENCE: Sorry, what's the connection between this money 00:14:17.465 --> 00:14:18.950 market issue and the yield curve? 00:14:18.950 --> 00:14:20.750 Could you make the connection again? 00:14:20.750 --> 00:14:21.250 I missed it. 00:14:21.250 --> 00:14:22.166 ANDREW LO: Yeah, sure. 00:14:22.166 --> 00:14:25.460 So the money market concern is that what 00:14:25.460 --> 00:14:29.870 people thought were safe, apparently is not 00:14:29.870 --> 00:14:31.574 as safe as people thought. 00:14:31.574 --> 00:14:33.740 And the Reserve Fund breaking the buck-- by the way, 00:14:33.740 --> 00:14:35.630 breaking the buck in that case meant 00:14:35.630 --> 00:14:38.870 that if you put in a dollar, when you withdrew, 00:14:38.870 --> 00:14:40.700 as of last week, you would have withdrawn 00:14:40.700 --> 00:14:45.500 $0.97 so you'd lost $0.03 to the dollar, which may not 00:14:45.500 --> 00:14:49.730 seem like much, but if you went to your Bank of America ATM 00:14:49.730 --> 00:14:51.290 and you did a withdrawal. 00:14:51.290 --> 00:14:54.770 And for every dollar you put in, you'd get $0.97 back, 00:14:54.770 --> 00:14:57.020 you'd be pretty ticked off, right? 00:14:57.020 --> 00:14:59.787 So it's something that is of great concern 00:14:59.787 --> 00:15:00.620 to retail investors. 00:15:00.620 --> 00:15:03.230 Anyway, so what happened last week was that-- 00:15:03.230 --> 00:15:06.590 actually the estimate, I think, is $90 billion. $90 billion 00:15:06.590 --> 00:15:11.070 of money came out of these funds in a week 00:15:11.070 --> 00:15:15.270 and were put into either cash in the mattress 00:15:15.270 --> 00:15:18.510 or were put into Treasury securities 00:15:18.510 --> 00:15:20.190 like the three month T-bills. 00:15:20.190 --> 00:15:22.710 That's what pushed the prices of those T-bills 00:15:22.710 --> 00:15:25.140 up and therefore depressed the yields. 00:15:25.140 --> 00:15:28.740 And now we're back to a somewhat more reasonable level. 00:15:28.740 --> 00:15:31.600 I say reasonable because having this kind of a short-term yield 00:15:31.600 --> 00:15:35.290 of 40 basis points by historical standards is still pretty low. 00:15:35.290 --> 00:15:39.240 So there are still many nervous investors out there 00:15:39.240 --> 00:15:41.370 that are trying to figure out what's going on 00:15:41.370 --> 00:15:43.828 and are waiting for the Treasury to come up with something. 00:15:43.828 --> 00:15:46.230 This is another reason why Chairman Bernanke said 00:15:46.230 --> 00:15:49.740 we have to act quickly because markets are not 00:15:49.740 --> 00:15:52.890 going to stand and wait for the Treasury or the Fed 00:15:52.890 --> 00:15:54.540 to do something. 00:15:54.540 --> 00:15:55.770 Markets will react. 00:15:55.770 --> 00:16:00.180 And if we wait too long, the fear of this breaking the buck 00:16:00.180 --> 00:16:02.010 could actually return. 00:16:02.010 --> 00:16:05.670 And then once you have a mass panic, 00:16:05.670 --> 00:16:07.230 it's very, very hard to stop that. 00:16:07.230 --> 00:16:12.450 Anybody who's ever seen one of these old animal kingdom type 00:16:12.450 --> 00:16:15.420 of movies about a stampede-- 00:16:15.420 --> 00:16:19.410 if you've got water buffalo stampeding, 00:16:19.410 --> 00:16:24.180 it's pretty hard to try to just say, oh, calm down, stop it. 00:16:24.180 --> 00:16:25.350 Slow down. 00:16:25.350 --> 00:16:28.839 You can't easily do that once it begins. 00:16:28.839 --> 00:16:30.630 So you've got to stop it before it actually 00:16:30.630 --> 00:16:31.950 gets to that critical point. 00:16:31.950 --> 00:16:34.860 And that's exactly what the government is trying to do. 00:16:34.860 --> 00:16:35.966 Yes. 00:16:35.966 --> 00:16:39.110 AUDIENCE: When you say that-- if you interpret these, 00:16:39.110 --> 00:16:42.632 like the prices went down so now there's less demand so it means 00:16:42.632 --> 00:16:43.730 people are more relaxed-- 00:16:43.730 --> 00:16:44.470 ANDREW LO: Yeah. 00:16:44.470 --> 00:16:47.780 AUDIENCE: What if you say, like, if the interest rate went up, 00:16:47.780 --> 00:16:50.551 it means they are considering the Treasury bills 00:16:50.551 --> 00:16:52.890 to be more risky or riskier? 00:16:52.890 --> 00:16:55.140 ANDREW LO: Well, remember that Treasury bills 00:16:55.140 --> 00:17:00.510 don't have any default risk, at least as far as we know. 00:17:00.510 --> 00:17:02.520 We have to be careful about stating. 00:17:02.520 --> 00:17:04.410 All these unprecedented things have happened. 00:17:04.410 --> 00:17:06.990 The reason that Treasury bills don't have any default risk 00:17:06.990 --> 00:17:09.660 is because what the Treasury security 00:17:09.660 --> 00:17:13.349 is an IOU from the government that says I owe you 00:17:13.349 --> 00:17:15.420 a certain number of US dollars. 00:17:15.420 --> 00:17:17.694 And because the Treasury owns the printing press, 00:17:17.694 --> 00:17:20.069 they can always print out more dollars to give it to you, 00:17:20.069 --> 00:17:22.380 as long as you're willing to take it. 00:17:22.380 --> 00:17:25.440 And at least from this graph, it seems like a lot of people 00:17:25.440 --> 00:17:26.589 are willing to take it. 00:17:26.589 --> 00:17:29.040 They really want Treasury bills right now. 00:17:29.040 --> 00:17:30.720 And they're happy with that. 00:17:30.720 --> 00:17:33.660 Maybe they're not happy with it, but that's 00:17:33.660 --> 00:17:36.452 the smallest of all the evils that they can think of in terms 00:17:36.452 --> 00:17:37.410 of putting their money. 00:17:37.410 --> 00:17:42.060 AUDIENCE: So decreasing the yield in Treasury bonds 00:17:42.060 --> 00:17:44.670 do not mean an increase in the default risk? 00:17:44.670 --> 00:17:45.750 ANDREW LO: We hope not. 00:17:45.750 --> 00:17:47.340 I mean, I guess it could be possible 00:17:47.340 --> 00:17:48.870 that people are betting that the United States is 00:17:48.870 --> 00:17:50.310 going to default in 30 years. 00:17:50.310 --> 00:17:53.370 But my sense is that what's more likely, given 00:17:53.370 --> 00:17:55.890 that these are default free in the sense 00:17:55.890 --> 00:17:57.160 that their nominal bonds-- 00:17:57.160 --> 00:17:59.490 so these bonds are going to be paid off 00:17:59.490 --> 00:18:01.320 in the little certificates called 00:18:01.320 --> 00:18:03.600 US dollars that the printing presses can always 00:18:03.600 --> 00:18:04.380 come up with. 00:18:04.380 --> 00:18:06.960 There's no risk that they can't print up more dollars. 00:18:06.960 --> 00:18:10.080 The risk is that $1 30 years from now 00:18:10.080 --> 00:18:12.084 isn't going to be worth as much as we 00:18:12.084 --> 00:18:13.500 thought it was going to be because 00:18:13.500 --> 00:18:15.420 of inflationary expectations. 00:18:15.420 --> 00:18:20.868 So as of today, that 30 year yield is not 4%, it's 4.37% 00:18:20.868 --> 00:18:26.730 and the 0.37 one could attribute to an inflationary expectation 00:18:26.730 --> 00:18:28.047 by the marketplace. 00:18:28.047 --> 00:18:30.760 AUDIENCE: Do you think that the short-term change in the yield 00:18:30.760 --> 00:18:32.676 has anything to do with the recent devaluation 00:18:32.676 --> 00:18:35.700 of the dollar against foreign currencies? 00:18:35.700 --> 00:18:38.730 ANDREW LO: It could be that because of that devaluation, 00:18:38.730 --> 00:18:40.560 dollars are cheaper and people are putting 00:18:40.560 --> 00:18:42.780 more money into US securities. 00:18:42.780 --> 00:18:43.990 That's also a possibility. 00:18:43.990 --> 00:18:46.800 But another way of putting that is that foreign investors 00:18:46.800 --> 00:18:50.280 are now finding treasuries more attractive for whatever reason. 00:18:50.280 --> 00:18:54.930 So yes, that's also part of that supply and demand story. 00:18:54.930 --> 00:18:55.960 OK, last question. 00:18:55.960 --> 00:18:56.645 Yeah. 00:18:56.645 --> 00:18:58.769 AUDIENCE: Historically, what is a reasonable yield? 00:18:58.769 --> 00:19:01.437 You mentioned that before, like [INAUDIBLE] or before all 00:19:01.437 --> 00:19:02.120 this time? 00:19:02.120 --> 00:19:06.890 ANDREW LO: Well, I'm glad you asked that question because we 00:19:06.890 --> 00:19:09.590 have a graph. 00:19:09.590 --> 00:19:14.220 These are the historical yields of the three month, six month, 00:19:14.220 --> 00:19:16.490 one year, two year, five year, 10 year, and 30 year 00:19:16.490 --> 00:19:24.200 from 1962 to I think it's 2004. 00:19:24.200 --> 00:19:27.140 And it depends on what flavor you're looking at. 00:19:27.140 --> 00:19:29.180 And it's kind of hard to read this graph because 00:19:29.180 --> 00:19:29.763 of the colors. 00:19:29.763 --> 00:19:33.270 But if you look at the dark blue line, 00:19:33.270 --> 00:19:35.310 they actually all move together pretty much. 00:19:35.310 --> 00:19:41.090 But at one point, that short-term yield was 4%. 00:19:41.090 --> 00:19:44.857 4% for a three month Treasury bill. 00:19:44.857 --> 00:19:46.440 Now these are all annualized remember, 00:19:46.440 --> 00:19:49.010 so 4% doesn't mean 4% over three months. 00:19:49.010 --> 00:19:51.410 It means 4% on an annualized basis, 00:19:51.410 --> 00:19:53.720 which is why 41 basis points-- 00:19:53.720 --> 00:19:55.970 that's an annualized yield-- 00:19:55.970 --> 00:19:59.600 for a three month loan just seems ridiculously 00:19:59.600 --> 00:20:03.640 small by historical standards. 00:20:03.640 --> 00:20:06.580 But when people are scared about not getting paid, 00:20:06.580 --> 00:20:09.130 that kind of fear, that psychological pressure 00:20:09.130 --> 00:20:10.822 can be overwhelming. 00:20:10.822 --> 00:20:12.280 And do you believe in these prices? 00:20:12.280 --> 00:20:13.220 Does it make sense? 00:20:13.220 --> 00:20:16.600 Well, that I'm hoping to get you not 00:20:16.600 --> 00:20:19.600 to ask the question in that way, but rather to ask 00:20:19.600 --> 00:20:21.460 the question, given market prices and what 00:20:21.460 --> 00:20:25.310 I know about it, what can I interpret from what's going on 00:20:25.310 --> 00:20:27.400 and how does that affect me in terms 00:20:27.400 --> 00:20:29.990 of the financial decisions that I want to make. 00:20:29.990 --> 00:20:33.700 So if you are thinking about pricing other securities based 00:20:33.700 --> 00:20:36.610 upon these kinds of numbers, you need 00:20:36.610 --> 00:20:38.200 to ask yourself whether you believe 00:20:38.200 --> 00:20:40.720 the numbers make sense or are they 00:20:40.720 --> 00:20:42.910 just completely out of whack. 00:20:42.910 --> 00:20:45.100 And the only way to do that is to understand what 00:20:45.100 --> 00:20:47.090 the basis is for these numbers. 00:20:47.090 --> 00:20:48.940 So that's where we're going next in trying 00:20:48.940 --> 00:20:51.425 to understand how to measure the various different 00:20:51.425 --> 00:20:53.800 characteristics of these numbers to get a sense of what's 00:20:53.800 --> 00:20:55.070 reasonable and what's not. 00:20:55.070 --> 00:20:55.570 Question. 00:20:55.570 --> 00:20:56.695 AUDIENCE: I had a question. 00:20:56.695 --> 00:20:59.538 I was wondering, those sort of funds, Treasury bills, 00:20:59.538 --> 00:21:03.258 [INAUDIBLE], is that really individual people buying 00:21:03.258 --> 00:21:05.738 the Treasury bills or is it more hedge funds and that sort 00:21:05.738 --> 00:21:09.210 of thing that are systematically hedging the risk against other 00:21:09.210 --> 00:21:11.470 securities they have that are-- 00:21:11.470 --> 00:21:13.760 ANDREW LO: Well, obviously, it's very difficult 00:21:13.760 --> 00:21:16.520 to tell because we don't see who's making the purchases 00:21:16.520 --> 00:21:20.690 and sales, but we can tell from certain mutual funds 00:21:20.690 --> 00:21:23.240 and other money market flows that it 00:21:23.240 --> 00:21:26.030 seems like most of the flows last week came 00:21:26.030 --> 00:21:30.110 not from hedge funds, but rather from retail investors that 00:21:30.110 --> 00:21:32.840 were taking their money out of these money market accounts 00:21:32.840 --> 00:21:36.440 and then putting them into certain mutual funds that 00:21:36.440 --> 00:21:40.790 buy only Treasury securities, as well as Treasury securities 00:21:40.790 --> 00:21:41.570 directly. 00:21:41.570 --> 00:21:45.950 All of you can actually purchase Treasury securities directly. 00:21:45.950 --> 00:21:48.710 There is a website called TreasuryDirect.gov 00:21:48.710 --> 00:21:51.950 and you can give them your credit card 00:21:51.950 --> 00:21:54.560 and register as a user and actually 00:21:54.560 --> 00:21:58.770 participate in Treasury auctions and buy Treasury securities. 00:21:58.770 --> 00:22:00.650 So it was a combination of those. 00:22:00.650 --> 00:22:03.290 But it really seemed like it was the retail sector, 00:22:03.290 --> 00:22:06.140 not institutions, not sophisticated hedge 00:22:06.140 --> 00:22:09.230 funds that we're trying to do some kind of complex arbitrage. 00:22:09.230 --> 00:22:11.810 It was just investors saying, I'm really scared, 00:22:11.810 --> 00:22:14.720 I want to put my money into something that's real 00:22:14.720 --> 00:22:16.620 and that will be there. 00:22:16.620 --> 00:22:18.980 And so short-term treasuries seemed like an answer. 00:22:18.980 --> 00:22:22.610 And as we saw from last week, gold was the other answer. 00:22:22.610 --> 00:22:24.650 It's not an answer that I would propose 00:22:24.650 --> 00:22:27.890 for the typical investor because gold prices are quite volatile. 00:22:27.890 --> 00:22:30.770 And so you have to be very careful 00:22:30.770 --> 00:22:32.990 when you make an investment in that security 00:22:32.990 --> 00:22:35.240 or in that particular asset. 00:22:35.240 --> 00:22:38.540 But it is something that reflects the state of panic 00:22:38.540 --> 00:22:39.952 of the marketplace. 00:22:39.952 --> 00:22:42.410 And by the way, I'm telling you something that you probably 00:22:42.410 --> 00:22:44.720 already know in the sense that-- 00:22:44.720 --> 00:22:47.720 my guess is that deep down inside, all of you 00:22:47.720 --> 00:22:49.280 are feeling stressed out, right? 00:22:49.280 --> 00:22:50.990 I mean, you're probably stressed out 00:22:50.990 --> 00:22:53.510 about things like what does this mean for the job market, 00:22:53.510 --> 00:22:56.690 for career prospects, and so on. 00:22:56.690 --> 00:22:59.720 I would urge you all to take a deep breath 00:22:59.720 --> 00:23:03.350 and not get panicked about that because, as I said, 00:23:03.350 --> 00:23:07.310 this is the kind of dislocation that, while very 00:23:07.310 --> 00:23:09.920 traumatic for market participants today 00:23:09.920 --> 00:23:12.380 and for those on the losing end, there 00:23:12.380 --> 00:23:15.200 are as many opportunities created 00:23:15.200 --> 00:23:18.060 as there are taken away. 00:23:18.060 --> 00:23:20.870 And so my guess is that in a year's time, 00:23:20.870 --> 00:23:23.670 the job market is going to look extraordinarily attractive, 00:23:23.670 --> 00:23:26.000 particularly for those individuals that 00:23:26.000 --> 00:23:31.110 are trained in the science and art of financial analysis. 00:23:31.110 --> 00:23:33.740 So you're all going to be very well equipped for that, 00:23:33.740 --> 00:23:35.540 even though you may not feel that way 00:23:35.540 --> 00:23:38.100 right now because of what's going on in the marketplace. 00:23:38.100 --> 00:23:40.910 So I wouldn't panic certainly. 00:23:40.910 --> 00:23:43.160 And by the way, you can see the opportunities 00:23:43.160 --> 00:23:44.600 that are already being created. 00:23:44.600 --> 00:23:48.740 Warren Buffett just spent $5 billion 00:23:48.740 --> 00:23:50.734 purchasing a stake in Goldman Sachs. 00:23:50.734 --> 00:23:53.150 And we're going to talk about that in a couple of lectures 00:23:53.150 --> 00:23:54.740 when we do common stock because I 00:23:54.740 --> 00:24:01.040 want to use it as an example of getting a good deal in markets. 00:24:01.040 --> 00:24:04.460 I mean, first of all, Warren Buffett given the success he's 00:24:04.460 --> 00:24:08.030 enjoyed as an investor, you know that when he plunks down 00:24:08.030 --> 00:24:10.580 $5 billion in cash, he's probably 00:24:10.580 --> 00:24:14.060 doing it for a good reason, not out of charity. 00:24:14.060 --> 00:24:17.330 And by the way, Goldman raised another $5 billion 00:24:17.330 --> 00:24:19.820 from additional rights issues. 00:24:19.820 --> 00:24:23.210 That's $10 billion of capital that they 00:24:23.210 --> 00:24:26.390 raised relatively quickly. 00:24:26.390 --> 00:24:29.150 Also Nomura is in the negotiations 00:24:29.150 --> 00:24:32.150 to purchase certain assets of Lehman Brothers. 00:24:32.150 --> 00:24:34.640 Lehman has a terrific franchise and has 00:24:34.640 --> 00:24:38.390 some very significant operations in Asia, as well as in the US. 00:24:38.390 --> 00:24:40.747 And it's a very smart move on Nomura's part 00:24:40.747 --> 00:24:41.830 to take advantage of that. 00:24:41.830 --> 00:24:43.190 So these are the kind of opportunities 00:24:43.190 --> 00:24:43.939 I'm talking about. 00:24:43.939 --> 00:24:46.220 And when Nomura buys Lehman, they're 00:24:46.220 --> 00:24:47.930 going to have to hire people in order 00:24:47.930 --> 00:24:50.060 to run the operations because you 00:24:50.060 --> 00:24:52.880 can bet that the whole dislocation ended up 00:24:52.880 --> 00:24:57.230 shaking loose a number of very talented professionals 00:24:57.230 --> 00:24:59.090 from those organizations. 00:24:59.090 --> 00:25:00.560 So they got to hire. 00:25:00.560 --> 00:25:03.230 It's going to mean the next two or three months, 00:25:03.230 --> 00:25:05.360 there may be some difficulties in getting 00:25:05.360 --> 00:25:07.610 the attention of these organizations 00:25:07.610 --> 00:25:10.580 because they're in the midst of trying to figure out exactly 00:25:10.580 --> 00:25:14.050 what kind of organization they are going to have 00:25:14.050 --> 00:25:15.530 when all the dust settles. 00:25:15.530 --> 00:25:17.270 But there are plenty of opportunities 00:25:17.270 --> 00:25:20.360 that are being created today, including, by the way, 00:25:20.360 --> 00:25:22.130 the opportunity for the US government 00:25:22.130 --> 00:25:24.724 to take advantage of all of these distressed assets. 00:25:24.724 --> 00:25:27.140 So one of the things that you should be careful about when 00:25:27.140 --> 00:25:29.510 you read that there's a $700 billion 00:25:29.510 --> 00:25:32.690 bailout, that is somewhat misleading in the sense 00:25:32.690 --> 00:25:35.210 that, first of all, we don't really know at this point 00:25:35.210 --> 00:25:38.660 exactly what the $700 billion will be for, 00:25:38.660 --> 00:25:40.730 how it will be used, or how it's dispersed, 00:25:40.730 --> 00:25:42.920 or is it really $700 billion. 00:25:42.920 --> 00:25:44.960 A lot of it depends upon how the money is spent 00:25:44.960 --> 00:25:47.040 and also what happens to housing markets. 00:25:47.040 --> 00:25:48.950 There is a scenario that I can imagine 00:25:48.950 --> 00:25:54.150 where the actual amount expended is either zero or negative. 00:25:54.150 --> 00:25:56.600 In other words, the government actually makes money 00:25:56.600 --> 00:25:59.420 from the current state of the markets because they 00:25:59.420 --> 00:26:03.410 can buy assets very cheaply, hold onto them forever 00:26:03.410 --> 00:26:07.470 until they pay off, and then gain the kind of profit 00:26:07.470 --> 00:26:11.340 that the original financial engineers were expecting 00:26:11.340 --> 00:26:14.490 but could not take advantage of because of this liquidity 00:26:14.490 --> 00:26:15.120 crunch. 00:26:15.120 --> 00:26:17.460 So we'll talk about that over the next few lectures 00:26:17.460 --> 00:26:19.650 because we're going to develop some techniques to be 00:26:19.650 --> 00:26:24.300 able to illustrate how these kind of arbitrage strategies 00:26:24.300 --> 00:26:24.960 work. 00:26:24.960 --> 00:26:26.006 Yeah. 00:26:26.006 --> 00:26:28.810 AUDIENCE: Thinking about Nomura, is it more certain 00:26:28.810 --> 00:26:31.190 that it's going to happen or are there many plans 00:26:31.190 --> 00:26:33.050 that are trying to buy the [INAUDIBLE]. 00:26:33.050 --> 00:26:35.370 ANDREW LO: Well, certainly there are a number of banks. 00:26:35.370 --> 00:26:37.080 I wouldn't say many, simply because there 00:26:37.080 --> 00:26:39.660 aren't that many banks that are well capitalized enough 00:26:39.660 --> 00:26:43.410 to be able to take on a large unit of a business 00:26:43.410 --> 00:26:44.730 as big as Lehman Brothers. 00:26:44.730 --> 00:26:48.090 So Nomura is one of a handful of banks that are engaged, 00:26:48.090 --> 00:26:51.775 but they seem to be the front runner at this point. 00:26:51.775 --> 00:26:53.275 AUDIENCE: Generally, what I've heard 00:26:53.275 --> 00:26:56.897 kind of from the Asian analyst in Lehman 00:26:56.897 --> 00:26:59.230 that I had spoken to is that it's quite likely that that 00:26:59.230 --> 00:27:01.302 might be not be true as well because we 00:27:01.302 --> 00:27:03.402 find a lot of [INAUDIBLE]. 00:27:03.402 --> 00:27:04.750 ANDREW LO: Oh, absolutely. 00:27:04.750 --> 00:27:06.940 There are a number of issues that will come up 00:27:06.940 --> 00:27:07.930 in any kind of a deal. 00:27:07.930 --> 00:27:09.430 And so you don't know whether or not 00:27:09.430 --> 00:27:12.096 something is going to go through until it actually goes through. 00:27:12.096 --> 00:27:14.800 The same thing could be said for what happened 00:27:14.800 --> 00:27:19.270 with Merrill Lynch, with AIG. 00:27:19.270 --> 00:27:21.910 All of these deals are sort of put together 00:27:21.910 --> 00:27:23.270 at the last minute. 00:27:23.270 --> 00:27:25.870 And either they get consummated or there's 00:27:25.870 --> 00:27:28.040 some hitch at the end that makes it difficult. 00:27:28.040 --> 00:27:30.100 So yeah, I mean, with a grain of salt, 00:27:30.100 --> 00:27:32.260 you should take all of these news reports. 00:27:32.260 --> 00:27:34.400 And literally until the deal is signed, 00:27:34.400 --> 00:27:36.400 you will not know whether or not something's on. 00:27:36.400 --> 00:27:40.480 But the point I'm illustrating is that these assets are not 00:27:40.480 --> 00:27:41.500 completely worthless. 00:27:41.500 --> 00:27:44.560 What's happened is a very significant liquidity crunch 00:27:44.560 --> 00:27:45.820 and panic. 00:27:45.820 --> 00:27:47.980 When that happens, the pricing of all these assets 00:27:47.980 --> 00:27:49.340 becomes questionable. 00:27:49.340 --> 00:27:49.960 OK. 00:27:49.960 --> 00:27:51.350 We're going to actually see an example of that. 00:27:51.350 --> 00:27:54.040 So if you wouldn't mind, let me put that off for a few minutes. 00:27:54.040 --> 00:27:56.123 And then if you have further questions about this, 00:27:56.123 --> 00:27:57.610 we can come back to it. 00:27:57.610 --> 00:28:01.840 Let me start-- so this is lecture six. 00:28:01.840 --> 00:28:03.850 And what I want to do is to start 00:28:03.850 --> 00:28:07.360 where we ended last time, which was a discussion of coupon 00:28:07.360 --> 00:28:10.300 bonds and how you price coupon bonds simply 00:28:10.300 --> 00:28:15.520 as a package or a portfolio of pure discount bonds. 00:28:15.520 --> 00:28:19.480 Underlying this approach to pricing coupon bonds 00:28:19.480 --> 00:28:22.420 is a very important principle. 00:28:22.420 --> 00:28:24.460 That's a principle that was given 00:28:24.460 --> 00:28:26.590 to you in the very first day of class 00:28:26.590 --> 00:28:28.900 where we talked about the six fundamental principles 00:28:28.900 --> 00:28:30.820 of financial markets. 00:28:30.820 --> 00:28:33.290 And it's the principle of the law of one price. 00:28:33.290 --> 00:28:35.890 So what I want to do today is to focus on that 00:28:35.890 --> 00:28:37.690 and talk about the law of one price 00:28:37.690 --> 00:28:42.430 and what it means for things like arbitrage, leverage, 00:28:42.430 --> 00:28:46.030 short selling, and relative pricing. 00:28:46.030 --> 00:28:48.582 Those are the key concepts we're going to cover today. 00:28:48.582 --> 00:28:50.290 So let me talk about the law of one price 00:28:50.290 --> 00:28:52.000 and remind you all what it is. 00:28:52.000 --> 00:28:53.270 It's a very simple idea. 00:28:53.270 --> 00:28:56.290 It's so simple that you might think it's obvious, 00:28:56.290 --> 00:29:01.060 but it's got some very, very dramatic implications. 00:29:01.060 --> 00:29:09.430 The law of one price says that two identical cash flows must 00:29:09.430 --> 00:29:13.800 have the same market price. 00:29:13.800 --> 00:29:14.300 OK. 00:29:14.300 --> 00:29:15.091 Let me repeat that. 00:29:15.091 --> 00:29:21.090 Two identical cash flows must have the same price. 00:29:21.090 --> 00:29:24.930 Now remember that when we think of an asset. 00:29:24.930 --> 00:29:27.540 We think of an asset as just the sequence of cash flows. 00:29:27.540 --> 00:29:29.480 That's what an asset is. 00:29:29.480 --> 00:29:33.810 So all I'm saying is that when you have two identical assets, 00:29:33.810 --> 00:29:36.460 they have to have the same price. 00:29:36.460 --> 00:29:39.250 That's not a very controversial statement. 00:29:39.250 --> 00:29:43.720 And this principle is one of the most important ideas 00:29:43.720 --> 00:29:45.250 in all of modern finance because it 00:29:45.250 --> 00:29:48.890 leads to the pricing of all sorts of securities, 00:29:48.890 --> 00:29:51.520 including all the derivatives that have ever 00:29:51.520 --> 00:29:53.320 been priced on Wall Street. 00:29:53.320 --> 00:29:56.340 They use this idea of the law of one price, OK. 00:29:56.340 --> 00:29:56.840 Yeah. 00:29:56.840 --> 00:29:58.798 AUDIENCE: But wouldn't you have to qualify that 00:29:58.798 --> 00:30:00.500 by saying it's at equilibrium? 00:30:00.500 --> 00:30:02.620 ANDREW LO: No, no. 00:30:02.620 --> 00:30:05.110 I don't have to qualify that at all. 00:30:05.110 --> 00:30:06.880 First, because this is a free country 00:30:06.880 --> 00:30:09.700 and I don't have to do anything I don't want to do. 00:30:09.700 --> 00:30:12.940 But more importantly, it's because I 00:30:12.940 --> 00:30:16.780 don't want to restrict it to an equilibrium. 00:30:16.780 --> 00:30:21.190 By equilibrium, you mean when supply equals demand, right? 00:30:21.190 --> 00:30:23.140 I don't care about supply and demand. 00:30:23.140 --> 00:30:26.380 Supply may very well not equal demand. 00:30:26.380 --> 00:30:28.460 That's OK with me. 00:30:28.460 --> 00:30:32.690 This principle of the law of one price, that two identical cash 00:30:32.690 --> 00:30:34.820 flows have to have the same market 00:30:34.820 --> 00:30:39.020 price, the only assumption that I need in order for that law 00:30:39.020 --> 00:30:44.720 to be true is that people prefer more money to less money. 00:30:44.720 --> 00:30:46.570 And it's not even people. 00:30:46.570 --> 00:30:49.730 I just need one person in the economy that prefers 00:30:49.730 --> 00:30:51.440 more money to less money. 00:30:51.440 --> 00:30:56.460 And I'm happy to volunteer for that position, OK? 00:30:56.460 --> 00:30:57.340 Why is that? 00:30:57.340 --> 00:31:03.810 It's because if that law is violated, if you can show me 00:31:03.810 --> 00:31:08.270 two identical cash flows that sell for different market 00:31:08.270 --> 00:31:13.460 prices, first of all, tell nobody but me about it. 00:31:13.460 --> 00:31:20.270 What I'm going to do is I'm going to buy the cheaper asset, 00:31:20.270 --> 00:31:24.530 I'm going to sell the more expensive asset. 00:31:24.530 --> 00:31:28.370 So as of today, I make money, right, 00:31:28.370 --> 00:31:31.550 because I bought the cheap, I sold the more expensive. 00:31:31.550 --> 00:31:35.060 That difference is positive for me. 00:31:35.060 --> 00:31:38.010 And then I argue that from that point on, 00:31:38.010 --> 00:31:41.960 I have no further risk and, in fact, no further obligations. 00:31:41.960 --> 00:31:45.710 I can just forget about the deal and take my money and spend it. 00:31:45.710 --> 00:31:46.400 Why? 00:31:46.400 --> 00:31:50.460 Because I've bought and sold identical cash flows. 00:31:50.460 --> 00:31:52.610 So from that point on in the future, 00:31:52.610 --> 00:31:56.450 all the cash flows cancel out. 00:31:56.450 --> 00:31:58.140 So I'm done. 00:31:58.140 --> 00:32:05.174 That's called an arbitrage, or more technically, a free lunch. 00:32:05.174 --> 00:32:07.090 I've been able to create money out of nothing. 00:32:07.090 --> 00:32:09.420 It doesn't assume supply equals demand. 00:32:09.420 --> 00:32:13.020 It doesn't assume any kind of mathematical formula 00:32:13.020 --> 00:32:14.940 for any kind of instrument. 00:32:14.940 --> 00:32:18.480 All it assumes is that more people 00:32:18.480 --> 00:32:21.330 prefer more money to less. 00:32:21.330 --> 00:32:23.580 AUDIENCE: So that means so that day when you auctioned 00:32:23.580 --> 00:32:25.860 the iPhone, then the only difference 00:32:25.860 --> 00:32:28.600 between an open package and the concealed packaged 00:32:28.600 --> 00:32:31.960 was that in one case you basically did not 00:32:31.960 --> 00:32:33.072 give enough information. 00:32:33.072 --> 00:32:33.780 ANDREW LO: Right. 00:32:33.780 --> 00:32:36.879 AUDIENCE: And it wasn't reaching a fair value and so-- 00:32:36.879 --> 00:32:38.920 ANDREW LO: Well, wait, wait, wait, wait a minute. 00:32:38.920 --> 00:32:42.059 Well, when you say fair value, that's a loaded term. 00:32:42.059 --> 00:32:43.350 What do you mean by fair value? 00:32:43.350 --> 00:32:46.380 It was a fair value, given all the information 00:32:46.380 --> 00:32:47.310 that the market had. 00:32:47.310 --> 00:32:49.726 AUDIENCE: But it's not because [INAUDIBLE] of that object. 00:32:49.726 --> 00:32:51.750 When the person buys objects that's packaged, 00:32:51.750 --> 00:32:54.076 once they open it, they'll know that the cash 00:32:54.076 --> 00:32:58.542 flow of that object is the same as if it were not packaged. 00:32:58.542 --> 00:33:00.355 And they're going to read the [INAUDIBLE], 00:33:00.355 --> 00:33:01.230 as we just mentioned. 00:33:01.230 --> 00:33:02.220 ANDREW LO: That's right, but don't you 00:33:02.220 --> 00:33:04.530 think there's a difference between the package wrapped 00:33:04.530 --> 00:33:06.047 and the package unwrapped? 00:33:06.047 --> 00:33:07.380 AUDIENCE: Yeah, one of them is-- 00:33:07.380 --> 00:33:08.915 I mean, it's just like a factory which 00:33:08.915 --> 00:33:11.090 will produce the same stuff but is valued at the market 00:33:11.090 --> 00:33:12.530 at a lower price than what it would be-- 00:33:12.530 --> 00:33:14.370 ANDREW LO: Right, but if one factory didn't tell you 00:33:14.370 --> 00:33:16.440 how it produced it and another factory did. 00:33:16.440 --> 00:33:18.740 You think that they would sell for the same price? 00:33:18.740 --> 00:33:21.031 AUDIENCE: The factories wouldn't, but their future cash 00:33:21.031 --> 00:33:23.100 flow into revenue could be the same. 00:33:23.100 --> 00:33:25.990 ANDREW LO: Only if it turns out that, as a matter of fact, 00:33:25.990 --> 00:33:27.300 it is identical. 00:33:27.300 --> 00:33:29.760 But you don't know that ahead of time. 00:33:29.760 --> 00:33:33.640 You can only price something with the information you have, 00:33:33.640 --> 00:33:34.380 OK. 00:33:34.380 --> 00:33:37.020 So when I say two cash flows are identical, 00:33:37.020 --> 00:33:40.620 I'm saying that we acknowledge that the cash 00:33:40.620 --> 00:33:43.140 flows are, in fact, identical. 00:33:43.140 --> 00:33:45.690 And we know that they're identical. 00:33:45.690 --> 00:33:48.350 If I put two packages upfront in the room, one is an iPod 00:33:48.350 --> 00:33:51.780 and the other one is wrapped so it looks like an iPod. 00:33:51.780 --> 00:33:54.450 It's got the same shape, the same dimensions, 00:33:54.450 --> 00:33:56.590 but it's wrapped. 00:33:56.590 --> 00:33:58.600 Would you say that they're identical? 00:33:58.600 --> 00:34:00.610 You can't know that. 00:34:00.610 --> 00:34:04.180 If you knew that, then you would price it accordingly. 00:34:04.180 --> 00:34:06.280 By the way, that gives you a very important piece 00:34:06.280 --> 00:34:07.880 of information. 00:34:07.880 --> 00:34:09.580 Suppose that I did that experiment, I 00:34:09.580 --> 00:34:14.272 had the iPod that was clearly unwrapped and it was an iPod. 00:34:14.272 --> 00:34:15.730 And then I had another package that 00:34:15.730 --> 00:34:19.449 was the identical dimension but it was wrapped, OK. 00:34:19.449 --> 00:34:25.179 And I auctioned them off and it became clear initially 00:34:25.179 --> 00:34:31.050 that the two were priced at about the same. 00:34:31.050 --> 00:34:34.500 Well, if you saw that, you would then 00:34:34.500 --> 00:34:39.710 know that it was quite likely that what 00:34:39.710 --> 00:34:41.719 was in the wrapped package was the same as what 00:34:41.719 --> 00:34:43.514 was in the unwrapped package, right? 00:34:43.514 --> 00:34:45.139 But the only reason you would know that 00:34:45.139 --> 00:34:47.810 is because somebody in the audience 00:34:47.810 --> 00:34:50.310 apparently bid the same price. 00:34:50.310 --> 00:34:52.190 Now why would they do that? 00:34:52.190 --> 00:34:56.389 Either they're knuckleheads or they know something 00:34:56.389 --> 00:34:57.590 that you don't know. 00:34:57.590 --> 00:34:59.390 And now that you looked at the price, 00:34:59.390 --> 00:35:03.030 you actually learn something about what's in there. 00:35:03.030 --> 00:35:08.330 So what matters for pricing is what the entire market knows, 00:35:08.330 --> 00:35:11.690 not just what you know, but what the entire market knows. 00:35:11.690 --> 00:35:13.290 Now going back to this arbitrage, 00:35:13.290 --> 00:35:15.290 let's not worry about informational asymmetries. 00:35:15.290 --> 00:35:18.740 So let's assume that we all know exactly what there is to know, 00:35:18.740 --> 00:35:22.090 which is that these two securities have the same cash 00:35:22.090 --> 00:35:22.850 flow. 00:35:22.850 --> 00:35:24.800 If they have the same cash flow, they've 00:35:24.800 --> 00:35:26.180 got to have the same price. 00:35:26.180 --> 00:35:29.340 And that's exactly what we saw last time with this example. 00:35:29.340 --> 00:35:31.940 Same cash flows and therefore, they 00:35:31.940 --> 00:35:33.470 have to have the same price. 00:35:33.470 --> 00:35:36.320 If they don't have the same price, then instead 00:35:36.320 --> 00:35:41.090 of feeling upset and despondent that somehow finance theory is 00:35:41.090 --> 00:35:44.900 in question, the most exciting thing for a finance professor 00:35:44.900 --> 00:35:48.040 is to see that this theory breaks down, 00:35:48.040 --> 00:35:52.320 because then we actually can go transact in the marketplace 00:35:52.320 --> 00:35:53.670 and make money. 00:35:53.670 --> 00:35:55.440 So if the law of one price fails, 00:35:55.440 --> 00:35:59.430 instead of calling me up and complaining about it, 00:35:59.430 --> 00:36:01.170 you should call me up and tell me 00:36:01.170 --> 00:36:03.390 what it is so I can take advantage of it, all right? 00:36:03.390 --> 00:36:05.040 It's a great thing. 00:36:05.040 --> 00:36:07.050 And here's the example. 00:36:07.050 --> 00:36:10.710 This price of a coupon bond is got 00:36:10.710 --> 00:36:15.810 to be equal to the prices of the discount bonds multiplied 00:36:15.810 --> 00:36:19.800 by the number of bonds you need in order to yield 00:36:19.800 --> 00:36:22.660 an identical cash flow. 00:36:22.660 --> 00:36:23.770 OK. 00:36:23.770 --> 00:36:25.829 Now if you have an identical cash flow, 00:36:25.829 --> 00:36:28.120 the left-hand side has to equal to the right-hand side. 00:36:28.120 --> 00:36:31.810 If it doesn't, if the price of the left-hand side 00:36:31.810 --> 00:36:35.020 is greater than the prices of the right-hand side, 00:36:35.020 --> 00:36:38.350 then you should feel very happy because what you're going to do 00:36:38.350 --> 00:36:39.112 is to make money. 00:36:39.112 --> 00:36:40.820 Now how much money are you going to make? 00:36:40.820 --> 00:36:41.980 Well, let's see. 00:36:41.980 --> 00:36:43.900 What you're going to do is you're going 00:36:43.900 --> 00:36:45.640 to buy the right-hand side. 00:36:45.640 --> 00:36:47.880 You're going to buy those bonds and you're 00:36:47.880 --> 00:36:51.700 gonna sell the left-hand side bond, so what you make 00:36:51.700 --> 00:36:53.590 is that difference, right? 00:36:53.590 --> 00:36:55.447 Because you're buying, you're spending 00:36:55.447 --> 00:36:56.530 a certain amount of money. 00:36:56.530 --> 00:36:58.540 That's the right-hand amount of money. 00:36:58.540 --> 00:37:01.780 And the left-hand side is what you're going to get. 00:37:01.780 --> 00:37:04.840 And so you're actually going to be 00:37:04.840 --> 00:37:08.050 able to make that difference. 00:37:08.050 --> 00:37:10.080 But here's the key. 00:37:10.080 --> 00:37:14.280 When you make that difference, it's not a risky investment. 00:37:14.280 --> 00:37:17.400 There is no risk. 00:37:17.400 --> 00:37:20.550 By the way, how much money did you have to spend? 00:37:20.550 --> 00:37:23.400 How much of your own personal wealth 00:37:23.400 --> 00:37:27.285 did you have to commit to this trade? 00:37:27.285 --> 00:37:28.789 AUDIENCE: Just the risk. 00:37:28.789 --> 00:37:29.830 ANDREW LO: Just the risk? 00:37:29.830 --> 00:37:31.266 What risk? 00:37:31.266 --> 00:37:33.266 AUDIENCE: The difference between them the moment 00:37:33.266 --> 00:37:34.220 they can buy and sell. 00:37:34.220 --> 00:37:35.969 ANDREW LO: Did you have to spend that? 00:37:35.969 --> 00:37:37.260 AUDIENCE: You can guarantee it. 00:37:37.260 --> 00:37:38.840 ANDREW LO: That's money that you get, 00:37:38.840 --> 00:37:40.520 not that you have to spend. 00:37:40.520 --> 00:37:42.770 Is there any money that comes out of your pocket 00:37:42.770 --> 00:37:44.480 to do this trade? 00:37:44.480 --> 00:37:48.350 No, because what you are buying is actually 00:37:48.350 --> 00:37:50.510 financed by what you sold. 00:37:50.510 --> 00:37:53.480 And then on top of that, you have a little extra leftover, 00:37:53.480 --> 00:37:54.960 OK? 00:37:54.960 --> 00:37:57.800 So this is like one of these infomercials at two o'clock 00:37:57.800 --> 00:37:59.780 in the morning, real estate, how to make 00:37:59.780 --> 00:38:02.450 a million dollars in real estate with no money down, right? 00:38:02.450 --> 00:38:04.424 You've put no money down. 00:38:04.424 --> 00:38:06.590 You haven't spent any money because what you've done 00:38:06.590 --> 00:38:09.110 is you've sold the bond and you've 00:38:09.110 --> 00:38:11.030 gotten this amount of cash. 00:38:11.030 --> 00:38:14.330 With that cash, you can buy these bonds 00:38:14.330 --> 00:38:17.450 and how do you know you have money left over? 00:38:17.450 --> 00:38:19.970 By assumption, I'm assuming that this price 00:38:19.970 --> 00:38:21.890 is greater than that price. 00:38:21.890 --> 00:38:23.990 So now you have money left over. 00:38:23.990 --> 00:38:25.640 You've put no money down. 00:38:25.640 --> 00:38:27.380 You have cash in the pocket. 00:38:27.380 --> 00:38:28.400 You have no risk. 00:38:28.400 --> 00:38:31.880 You have no obligations because all the future cash flows 00:38:31.880 --> 00:38:36.530 that you owe are financed completely by the bonds 00:38:36.530 --> 00:38:37.760 that you bought. 00:38:37.760 --> 00:38:41.040 One for one, dollar for dollar, it matches. 00:38:41.040 --> 00:38:45.020 So literally, as of today, you walk away from this transaction 00:38:45.020 --> 00:38:46.940 a richer individual. 00:38:46.940 --> 00:38:47.575 Yeah. 00:38:47.575 --> 00:38:49.449 AUDIENCE: Professor, isn't, like, by the time 00:38:49.449 --> 00:38:51.850 that you recognize a an arbitrage opportunity, 00:38:51.850 --> 00:38:53.280 it corrects itself? 00:38:53.280 --> 00:38:55.990 ANDREW LO: Well, let me get back to that. 00:38:55.990 --> 00:38:57.730 That's an interesting point. 00:38:57.730 --> 00:38:59.960 The question is, can these things really exist, 00:38:59.960 --> 00:39:03.100 because once they do, it's almost too 00:39:03.100 --> 00:39:04.795 late because they're gone. 00:39:04.795 --> 00:39:07.765 AUDIENCE: And then follow-up, is it just my imagination 00:39:07.765 --> 00:39:11.240 or do arbitrage desks exist in financial firms today? 00:39:11.240 --> 00:39:13.260 ANDREW LO: Arbitrage desks absolutely 00:39:13.260 --> 00:39:15.600 exist in financial firms. 00:39:15.600 --> 00:39:20.520 And what they do is look for this stuff all day long. 00:39:20.520 --> 00:39:22.050 That's what they do. 00:39:22.050 --> 00:39:25.860 And so is it true that by the time you identify, it's gone? 00:39:25.860 --> 00:39:29.940 Well, it's true if you're a finance academic, as well 00:39:29.940 --> 00:39:33.420 as a retail investor. 00:39:33.420 --> 00:39:36.270 But you guys, you're going to go out in the job market 00:39:36.270 --> 00:39:40.020 and you get to be hired by some of these arbitrage desks. 00:39:40.020 --> 00:39:41.850 So you're going to be doing this. 00:39:41.850 --> 00:39:44.430 In fact, you're going to be doing something 00:39:44.430 --> 00:39:45.750 quite a bit more complicated. 00:39:45.750 --> 00:39:47.119 I'll get to that in one minute. 00:39:47.119 --> 00:39:48.660 Before I do that, I want to make sure 00:39:48.660 --> 00:39:50.618 that everybody is with me about this arbitrage. 00:39:50.618 --> 00:39:51.331 Yes. 00:39:51.331 --> 00:39:53.215 AUDIENCE: Is there any assumption 00:39:53.215 --> 00:39:55.570 that there is no transaction cost? 00:39:55.570 --> 00:39:56.860 ANDREW LO: Very good point. 00:39:56.860 --> 00:39:59.710 Yes, in this context, there's an assumption 00:39:59.710 --> 00:40:03.610 that you can buy and sell freely with no transactions cost. 00:40:03.610 --> 00:40:06.250 Obviously, in the real world, there are transactions cost. 00:40:06.250 --> 00:40:08.207 You've got to stick those in and figure out 00:40:08.207 --> 00:40:10.540 whether you can still make money with transactions cost. 00:40:10.540 --> 00:40:16.850 Now one form of transactions cost is not a numerical cost, 00:40:16.850 --> 00:40:18.980 but it's a friction. 00:40:18.980 --> 00:40:21.590 What do you have to be able to do in order 00:40:21.590 --> 00:40:25.370 to do this transaction? 00:40:25.370 --> 00:40:29.240 What financial operation do you need in order 00:40:29.240 --> 00:40:30.831 to be able to get this deal done? 00:40:30.831 --> 00:40:31.330 Yeah. 00:40:31.330 --> 00:40:32.656 AUDIENCE: Well, you have to be able to short sell. 00:40:32.656 --> 00:40:34.230 ANDREW LO: Short sell, right. 00:40:34.230 --> 00:40:36.400 Remember we talked about short selling last time. 00:40:36.400 --> 00:40:39.590 That's selling something you don't own. 00:40:39.590 --> 00:40:43.130 So you have to borrow the bond from somebody 00:40:43.130 --> 00:40:46.720 and then sell it and get those proceeds. 00:40:46.720 --> 00:40:52.410 What if it were the case that somebody imposed a constraint 00:40:52.410 --> 00:40:54.660 that you can't short sell? 00:40:54.660 --> 00:40:57.450 Who would ever do that? 00:40:57.450 --> 00:41:00.596 Well, we've seen what happens in the marketplace that 00:41:00.596 --> 00:41:02.220 can generate that kind of a constraint. 00:41:02.220 --> 00:41:03.540 What happens if you can't short sell? 00:41:03.540 --> 00:41:04.039 Yeah. 00:41:04.039 --> 00:41:05.840 AUDIENCE: You need to upfront the cost. 00:41:05.840 --> 00:41:06.325 ANDREW LO: What's that? 00:41:06.325 --> 00:41:08.520 AUDIENCE: You need to put up the cost of the original security. 00:41:08.520 --> 00:41:10.920 ANDREW LO: Well, in fact, yes, you need to put up the cost, 00:41:10.920 --> 00:41:13.045 but it really defeats the purpose because if you're 00:41:13.045 --> 00:41:16.155 going to buy the bond and then sell the bond, 00:41:16.155 --> 00:41:18.630 you've not really done anything, right? 00:41:18.630 --> 00:41:22.050 This arbitrage argument relies on the fact 00:41:22.050 --> 00:41:24.330 that you can sell something you don't 00:41:24.330 --> 00:41:28.560 own by borrowing and shorting it and getting the proceeds, 00:41:28.560 --> 00:41:31.410 and then giving it back to the person you borrowed whenever 00:41:31.410 --> 00:41:34.580 they want, OK? 00:41:34.580 --> 00:41:37.370 If I don't allow you to short sell, 00:41:37.370 --> 00:41:40.360 this argument doesn't work anymore. 00:41:40.360 --> 00:41:44.410 And what that means is that this pricing relationship, 00:41:44.410 --> 00:41:48.630 this left-hand side has to equal the right-hand side, 00:41:48.630 --> 00:41:51.920 that relationship goes out the window. 00:41:51.920 --> 00:41:54.770 For the next several weeks and possibly several months, 00:41:54.770 --> 00:41:57.410 finance theory is going to be on vacation 00:41:57.410 --> 00:42:00.260 because the government has suspended short sales 00:42:00.260 --> 00:42:02.430 for certain securities. 00:42:02.430 --> 00:42:05.360 And so the kind of force of markets 00:42:05.360 --> 00:42:09.890 that drive prices towards not an equilibrium, but a pricing 00:42:09.890 --> 00:42:12.890 relationship that does not depend on equilibrium, 00:42:12.890 --> 00:42:15.719 but depends on the law of one price, 00:42:15.719 --> 00:42:17.760 that goes out the window if you can't short sell. 00:42:17.760 --> 00:42:19.600 Yeah, Megan. 00:42:19.600 --> 00:42:21.099 AUDIENCE: I guess I'm just wondering 00:42:21.099 --> 00:42:25.352 why the Treasury, just looking for insight on this, why 00:42:25.352 --> 00:42:27.435 the Treasury wouldn't just make the short interest 00:42:27.435 --> 00:42:32.075 on those short sales so high that it was almost prohibitive, 00:42:32.075 --> 00:42:35.540 but people who really wanted to short sell would, 00:42:35.540 --> 00:42:38.015 these instruments to hedge portfolios, 00:42:38.015 --> 00:42:40.010 could do that if they wanted to pay that. 00:42:40.010 --> 00:42:42.320 ANDREW LO: You know, that's a fantastic alternative. 00:42:42.320 --> 00:42:43.520 I think that would have been far better. 00:42:43.520 --> 00:42:44.840 You're absolutely right. 00:42:44.840 --> 00:42:46.970 Increase the cost of short selling 00:42:46.970 --> 00:42:48.470 by raising borrowing costs. 00:42:48.470 --> 00:42:51.450 By the way, when you short sell, as we said last time, 00:42:51.450 --> 00:42:52.460 it's not free. 00:42:52.460 --> 00:42:54.770 People aren't going to lend you the security for free. 00:42:54.770 --> 00:42:56.540 They're going to charge you for it. 00:42:56.540 --> 00:43:02.420 So what if instead of forbidding it altogether, 00:43:02.420 --> 00:43:06.050 why not just triple the cost or quadruple the cost? 00:43:06.050 --> 00:43:10.570 Therefore, only people who really, really need to do it 00:43:10.570 --> 00:43:11.749 will do it. 00:43:11.749 --> 00:43:13.790 The problem with that is more of a political one. 00:43:13.790 --> 00:43:17.570 The political problem is that we want these evildoers, 00:43:17.570 --> 00:43:20.270 these short sellers that are driving 00:43:20.270 --> 00:43:22.430 the prices of financial securities 00:43:22.430 --> 00:43:25.610 to stop their bad activities. 00:43:25.610 --> 00:43:28.700 And so what we're going to do is to mandate by law 00:43:28.700 --> 00:43:30.850 that they can't do that. 00:43:30.850 --> 00:43:34.040 Now, that may be a reasonable thing 00:43:34.040 --> 00:43:36.620 from a political perspective, but it's not a reasonable thing 00:43:36.620 --> 00:43:38.960 from an economic perspective, because what it does 00:43:38.960 --> 00:43:42.050 is it disrupts relationships like this, pricing 00:43:42.050 --> 00:43:43.650 relationships like this. 00:43:43.650 --> 00:43:44.150 Yeah. 00:43:44.150 --> 00:43:47.036 AUDIENCE: Can you actually change the borrowing costs 00:43:47.036 --> 00:43:50.561 for a few types of security [INAUDIBLE] 00:43:50.561 --> 00:43:54.980 by selling the short [INAUDIBLE] and shorting [INAUDIBLE] 00:43:54.980 --> 00:43:57.435 the interest rate [INAUDIBLE]. 00:43:57.435 --> 00:43:59.940 ANDREW LO: Well, if you're the government 00:43:59.940 --> 00:44:01.620 and you're in a time of crisis, it 00:44:01.620 --> 00:44:04.930 seems like you can do anything you want. 00:44:04.930 --> 00:44:07.920 So I mean practically, yes, you can say, 00:44:07.920 --> 00:44:11.160 for all financial stocks that are on this list, 00:44:11.160 --> 00:44:15.240 we will now charge an extra high rate of interest 00:44:15.240 --> 00:44:16.530 for borrowing those stocks. 00:44:16.530 --> 00:44:21.030 And, in fact, there exists a mechanism even before this rule 00:44:21.030 --> 00:44:24.960 was put in place that for certain stocks that are quote 00:44:24.960 --> 00:44:27.930 "hard-to-borrow"-- that's a technical term that Wall Street 00:44:27.930 --> 00:44:29.790 firms, brokerage firms use. 00:44:29.790 --> 00:44:31.800 Securities that are hard-to-borrow 00:44:31.800 --> 00:44:34.170 means that they're very actively traded 00:44:34.170 --> 00:44:36.660 and it's very hard to find a counterparty that's 00:44:36.660 --> 00:44:39.270 willing to let you borrow it from them. 00:44:39.270 --> 00:44:41.550 The hard-to-borrow stocks typically 00:44:41.550 --> 00:44:43.200 are lent out at a premium. 00:44:43.200 --> 00:44:45.270 So they are charged higher prices 00:44:45.270 --> 00:44:47.640 for those that are very, very popular. 00:44:47.640 --> 00:44:50.910 And by simply eliminating short sells, 00:44:50.910 --> 00:44:53.070 you basically make those costs infinite. 00:44:53.070 --> 00:44:54.510 That's exactly what's going on. 00:44:54.510 --> 00:44:57.510 So would it have been better to make them finite, but bigger? 00:44:57.510 --> 00:44:59.920 That would have been better than what they did, 00:44:59.920 --> 00:45:03.270 which is making it infinite, but from the purely financial 00:45:03.270 --> 00:45:05.610 markets perspective, it would be best 00:45:05.610 --> 00:45:08.040 if there were no restrictions and no transactions cost 00:45:08.040 --> 00:45:08.700 at all. 00:45:08.700 --> 00:45:11.530 Obviously, transactions costs are inevitable. 00:45:11.530 --> 00:45:14.400 So when you price these relationships, 00:45:14.400 --> 00:45:20.250 the equality is going to be up to transactions cost. 00:45:20.250 --> 00:45:22.266 There might be a little bit of a wedge 00:45:22.266 --> 00:45:24.390 between the left-hand side and the right-hand side, 00:45:24.390 --> 00:45:28.440 but the difference will have to be small enough 00:45:28.440 --> 00:45:31.590 that apart from transactions costs, 00:45:31.590 --> 00:45:34.230 they are not significantly different. 00:45:34.230 --> 00:45:34.730 Yeah. 00:45:34.730 --> 00:45:36.614 AUDIENCE: Could it be that they also 00:45:36.614 --> 00:45:39.060 stopped the shorting because of some illegal transactions 00:45:39.060 --> 00:45:41.660 or inside information? 00:45:41.660 --> 00:45:43.740 ANDREW LO: Well, if it were illegal transactions, 00:45:43.740 --> 00:45:45.330 the way they should have done it was to prosecute 00:45:45.330 --> 00:45:47.790 the illegal parties, as opposed to stopping short sales 00:45:47.790 --> 00:45:49.057 for everybody, right? 00:45:49.057 --> 00:45:50.640 That would be a far more effective way 00:45:50.640 --> 00:45:52.098 of dealing with illegal activities. 00:45:52.098 --> 00:45:54.270 That's not what they were concerned about primarily. 00:45:54.270 --> 00:45:58.080 The SEC has an enforcement division whose sole job 00:45:58.080 --> 00:46:00.960 it is to check on all the kind of transactions that 00:46:00.960 --> 00:46:02.730 may have occurred to see whether or not 00:46:02.730 --> 00:46:04.851 there's any kind of illegal activity going on. 00:46:04.851 --> 00:46:07.350 It wasn't the illegal activity that prompted the short sales 00:46:07.350 --> 00:46:07.850 restriction. 00:46:07.850 --> 00:46:11.280 It was really the concern that financial firms 00:46:11.280 --> 00:46:13.770 were being pounded by short sellers that 00:46:13.770 --> 00:46:15.780 were betting on them failing. 00:46:15.780 --> 00:46:19.440 And the more pressure that they impose on the stock price 00:46:19.440 --> 00:46:21.720 going down, down, down, the more likely 00:46:21.720 --> 00:46:24.090 it is that people would lose confidence and then 00:46:24.090 --> 00:46:26.460 all of a sudden stop doing business with it. 00:46:26.460 --> 00:46:29.190 In many ways, that's what happened with Bear Stearns. 00:46:29.190 --> 00:46:31.250 At least from the historical record, 00:46:31.250 --> 00:46:33.000 it seems like what happened was that there 00:46:33.000 --> 00:46:36.330 was a rumor that Bear Stearns was not going to be solvent, 00:46:36.330 --> 00:46:39.120 even though they didn't have any particular pressure 00:46:39.120 --> 00:46:42.720 to pay certain debts at that point in time. 00:46:42.720 --> 00:46:45.930 And somehow that rumor grew into general fear 00:46:45.930 --> 00:46:48.707 and the short sellers got in and started shorting the stock. 00:46:48.707 --> 00:46:50.790 The stock price went down, people looked and said, 00:46:50.790 --> 00:46:52.248 oh my god, the stock is going down, 00:46:52.248 --> 00:46:54.546 I'd better take my business elsewhere. 00:46:54.546 --> 00:46:55.920 And everybody started doing that, 00:46:55.920 --> 00:46:57.150 and once everybody started doing that, 00:46:57.150 --> 00:46:59.070 the firm began having great difficulties 00:46:59.070 --> 00:47:00.520 in maintaining a business. 00:47:00.520 --> 00:47:01.191 Yeah. 00:47:01.191 --> 00:47:04.200 AUDIENCE: Even the days that short selling is not allowed, 00:47:04.200 --> 00:47:06.560 then the investors who own the more expensive-- 00:47:06.560 --> 00:47:07.560 ANDREW LO: That's right. 00:47:07.560 --> 00:47:09.794 AUDIENCE: --asset are going to sell them because they 00:47:09.794 --> 00:47:11.544 don't think if they don't sell this today, 00:47:11.544 --> 00:47:12.540 I'm buying the right-hand-- 00:47:12.540 --> 00:47:14.123 ANDREW LO: That's right, that's right. 00:47:14.123 --> 00:47:18.661 AUDIENCE: So again, you do the [INAUDIBLE]. 00:47:18.661 --> 00:47:20.160 ANDREW LO: That's a very good point. 00:47:20.160 --> 00:47:21.030 Let me repeat it. 00:47:21.030 --> 00:47:24.900 The point is that even if you're not allowed to short sell, 00:47:24.900 --> 00:47:27.930 then the folks who own the left-hand side, who 00:47:27.930 --> 00:47:30.910 own the coupon bond, they can say, hey, 00:47:30.910 --> 00:47:36.120 my coupon bond is worth 110, but I can get the exact same payoff 00:47:36.120 --> 00:47:38.340 by buying a bunch of pure discount bonds. 00:47:38.340 --> 00:47:41.430 And it's only cost me 100 to buy them. 00:47:41.430 --> 00:47:43.500 I'm going to sell my coupon bought at 110 00:47:43.500 --> 00:47:46.530 and I'm going to buy $100 worth of these this discount bonds 00:47:46.530 --> 00:47:48.750 and I just made $10. 00:47:48.750 --> 00:47:52.260 Now that can happen as long as two things occur. 00:47:52.260 --> 00:47:57.600 One, the person who owns the bond knows about this. 00:47:57.600 --> 00:48:00.900 And two, they actually want to take the trouble 00:48:00.900 --> 00:48:04.731 to do the trade or they're able to do the trade. 00:48:04.731 --> 00:48:06.480 The problem is that most of the folks that 00:48:06.480 --> 00:48:08.700 bought the bond on the left-hand side 00:48:08.700 --> 00:48:12.420 are pension funds that are not in the business of doing 00:48:12.420 --> 00:48:14.940 this kind of arbitrage transactions. 00:48:14.940 --> 00:48:16.260 So they're trying to do that. 00:48:16.260 --> 00:48:20.220 All they want to do is they've got a bunch of pension plan 00:48:20.220 --> 00:48:20.820 participants. 00:48:20.820 --> 00:48:22.380 They need to pay out their benefits. 00:48:22.380 --> 00:48:23.550 They've got contributions. 00:48:23.550 --> 00:48:25.250 They just want to match assets to liabilities. 00:48:25.250 --> 00:48:27.750 They're not in the business of doing this kind of high speed 00:48:27.750 --> 00:48:29.520 transaction. 00:48:29.520 --> 00:48:32.460 So what that means is that you're still right, 00:48:32.460 --> 00:48:36.280 that if they realize this relationship is there, 00:48:36.280 --> 00:48:40.000 and they are in a position to do the trades, 00:48:40.000 --> 00:48:41.890 they will sometimes. 00:48:41.890 --> 00:48:46.140 And then that will force prices closer, 00:48:46.140 --> 00:48:49.620 but it's not going to be the same kind of numerical identity 00:48:49.620 --> 00:48:53.520 that has to hold when you've got greedy people like myself 00:48:53.520 --> 00:48:55.620 trying to do the trades and being 00:48:55.620 --> 00:48:59.046 able to do the trades at a moment's notice. 00:48:59.046 --> 00:49:00.990 AUDIENCE: I'm especially more interested 00:49:00.990 --> 00:49:02.934 about if these players are big enough 00:49:02.934 --> 00:49:06.102 in the financial markets, then it will correct 00:49:06.102 --> 00:49:07.310 and it could get out of that. 00:49:07.310 --> 00:49:08.450 ANDREW LO: Exactly, right. 00:49:08.450 --> 00:49:10.520 There are all sorts of additional complexities 00:49:10.520 --> 00:49:13.320 of being able to do the trade that as a pension plan, 00:49:13.320 --> 00:49:15.590 you're not even allowed to do, never mind whether you 00:49:15.590 --> 00:49:16.839 want to do them or not. 00:49:16.839 --> 00:49:18.380 So these are the kind of restrictions 00:49:18.380 --> 00:49:21.530 that would present this gap. 00:49:21.530 --> 00:49:23.970 But let's for now assume that there's no gap. 00:49:23.970 --> 00:49:25.970 We're going to assume that there's no frictions. 00:49:25.970 --> 00:49:28.340 We're going to assume that there's no short sales 00:49:28.340 --> 00:49:29.630 prohibitions. 00:49:29.630 --> 00:49:31.700 And when that happens, this pricing relationship 00:49:31.700 --> 00:49:32.607 has to hold. 00:49:32.607 --> 00:49:33.440 Now I promised you-- 00:49:33.440 --> 00:49:35.315 I want to show you something more complicated 00:49:35.315 --> 00:49:37.700 that all of you may do when you get out 00:49:37.700 --> 00:49:41.180 of here, and that's this. 00:49:41.180 --> 00:49:44.780 Instead of looking at just one bond, what 00:49:44.780 --> 00:49:48.750 if we looked at a whole bunch of coupon bonds? 00:49:48.750 --> 00:49:53.200 Now, let's take a look using this pricing 00:49:53.200 --> 00:49:57.720 that's based on the law of one price and basic greed. 00:49:57.720 --> 00:50:01.650 We've got n bonds here, one through n, 00:50:01.650 --> 00:50:06.660 and each has its own coupon, whatever that is. 00:50:06.660 --> 00:50:09.810 I'm just going to use notation to write down 00:50:09.810 --> 00:50:13.440 that each bond has its own particular coupon, right? 00:50:13.440 --> 00:50:15.600 So you've got a 3% 10 year bond. 00:50:15.600 --> 00:50:18.250 You've got a 4% 30 year bond. 00:50:18.250 --> 00:50:21.660 You may have 5 and 1/2% five year bond. 00:50:21.660 --> 00:50:25.650 So some of these coupons may be zero 00:50:25.650 --> 00:50:28.260 because capital T I'm going to assume 00:50:28.260 --> 00:50:31.260 is the most extreme 30 year period, right? 00:50:31.260 --> 00:50:33.426 So a five year bond would have coupons 00:50:33.426 --> 00:50:34.800 for the first five years and then 00:50:34.800 --> 00:50:37.170 for all of the coupon payments after that, I'm 00:50:37.170 --> 00:50:40.500 going to have zero, zero, zero, zero, zero, right? 00:50:40.500 --> 00:50:47.990 So this should hearken back to your high school algebra days, 00:50:47.990 --> 00:50:52.070 where you have multiple equations 00:50:52.070 --> 00:50:55.340 with multiple unknowns. 00:50:55.340 --> 00:50:57.889 Now what's unknown here in these equations? 00:50:57.889 --> 00:50:58.805 What are the unknowns? 00:51:02.880 --> 00:51:06.370 Well, you observe the prices, right, from the marketplace, 00:51:06.370 --> 00:51:09.199 so the left-hand side is not unknown. 00:51:09.199 --> 00:51:10.490 What about the right-hand side? 00:51:10.490 --> 00:51:11.782 What are the unknowns? 00:51:11.782 --> 00:51:13.490 What do you observe, what are the knowns? 00:51:13.490 --> 00:51:14.114 How about that? 00:51:14.114 --> 00:51:15.850 Let's start with that. 00:51:15.850 --> 00:51:16.480 Yeah. 00:51:16.480 --> 00:51:16.960 AUDIENCE: The coupons. 00:51:16.960 --> 00:51:18.209 ANDREW LO: The coupons, right. 00:51:18.209 --> 00:51:23.530 If I tell you that I've got a 30 year 4 and 1/2% bond, 00:51:23.530 --> 00:51:26.623 you know what the coupon is going to be, right? 00:51:26.623 --> 00:51:28.590 AUDIENCE: Because we don't know the yield. 00:51:28.590 --> 00:51:29.326 ANDREW LO: What's that? 00:51:29.326 --> 00:51:30.159 AUDIENCE: The yield. 00:51:30.159 --> 00:51:33.960 ANDREW LO: The yield is what we don't know. 00:51:33.960 --> 00:51:34.460 All right. 00:51:34.460 --> 00:51:38.500 That we either get from the marketplace or we 00:51:38.500 --> 00:51:41.800 can try to solve it from these prices. 00:51:41.800 --> 00:51:45.910 But how many different yields do we need in order 00:51:45.910 --> 00:51:47.130 to price each bond? 00:51:49.810 --> 00:51:51.100 These are T year bonds. 00:51:51.100 --> 00:51:51.941 How many yields? 00:51:51.941 --> 00:51:52.440 AUDIENCE: T. 00:51:52.440 --> 00:51:57.070 ANDREW LO: Yeah, we need T yields, one for each year. 00:51:57.070 --> 00:52:01.290 We have T yields in these equations 00:52:01.290 --> 00:52:04.230 and they're the same across the different bonds, right? 00:52:04.230 --> 00:52:08.040 Because we're using the same pure discount 00:52:08.040 --> 00:52:13.340 bonds to replicate each of these coupon bonds. 00:52:13.340 --> 00:52:14.690 I've got T unknowns. 00:52:14.690 --> 00:52:16.960 How many equations do I have? 00:52:16.960 --> 00:52:17.750 AUDIENCE: n. 00:52:17.750 --> 00:52:19.790 ANDREW LO: n bonds, right? 00:52:19.790 --> 00:52:26.630 Now, on any given day, you might have 200 to 300 bonds 00:52:26.630 --> 00:52:27.350 that are trading. 00:52:30.060 --> 00:52:34.680 But you've only got 30 unknowns. 00:52:34.680 --> 00:52:40.290 So let's think back to your high school algebra or college 00:52:40.290 --> 00:52:42.390 linear algebra days. 00:52:42.390 --> 00:52:49.300 If you've got 200 equations and 30 unknowns, 00:52:49.300 --> 00:52:50.730 how many solutions do you have? 00:52:54.490 --> 00:52:56.830 Well, let's get simpler. 00:52:56.830 --> 00:53:00.484 Suppose you had two equations and two unknowns. 00:53:00.484 --> 00:53:01.650 AUDIENCE: Just one solution. 00:53:01.650 --> 00:53:03.025 ANDREW LO: You have one solution, 00:53:03.025 --> 00:53:05.190 assuming certain kind of conditions 00:53:05.190 --> 00:53:07.950 that hold like invertability, which we're going to talk about 00:53:07.950 --> 00:53:08.820 in a minute. 00:53:08.820 --> 00:53:11.600 Two equations, two unknowns. 00:53:11.600 --> 00:53:13.610 You have one solution. 00:53:13.610 --> 00:53:17.890 How about one equation and two unknowns. 00:53:17.890 --> 00:53:21.640 How many solutions? 00:53:21.640 --> 00:53:22.910 Infinite. 00:53:22.910 --> 00:53:25.540 OK, that's right, because you've got that extra degree 00:53:25.540 --> 00:53:26.380 of freedom, right? 00:53:26.380 --> 00:53:28.130 There's lots of different solutions. 00:53:28.130 --> 00:53:33.570 What about three equations and two unknowns. 00:53:33.570 --> 00:53:37.390 Now how many solutions do you have? 00:53:37.390 --> 00:53:37.939 Yeah. 00:53:37.939 --> 00:53:39.980 AUDIENCE: Because it's linear, you only have one. 00:53:39.980 --> 00:53:41.600 ANDREW LO: It's linear. 00:53:41.600 --> 00:53:43.030 Are you guaranteed to have one? 00:53:43.030 --> 00:53:44.560 AUDIENCE: You might have zero. 00:53:44.560 --> 00:53:46.580 ANDREW LO: You might have zero. 00:53:46.580 --> 00:53:52.470 What are the conditions under which you would have one? 00:53:52.470 --> 00:53:54.318 AUDIENCE: If the solution of two equations 00:53:54.318 --> 00:53:55.710 applied for the third one. 00:53:55.710 --> 00:53:56.690 ANDREW LO: Right. 00:53:56.690 --> 00:53:58.900 There is a possibility you have one solution 00:53:58.900 --> 00:54:01.050 if the solution of the two equations 00:54:01.050 --> 00:54:04.060 actually applies to the third. 00:54:04.060 --> 00:54:06.107 Do you remember under what condition-- 00:54:06.107 --> 00:54:06.940 AUDIENCE: Exhausted. 00:54:06.940 --> 00:54:07.939 ANDREW LO: --that, what? 00:54:07.939 --> 00:54:09.076 AUDIENCE: Exhausted. 00:54:09.076 --> 00:54:09.951 ANDREW LO: Exhausted? 00:54:09.951 --> 00:54:12.890 That's not quite the term that mathematicians use. 00:54:12.890 --> 00:54:16.910 There's something called linear dependence. 00:54:16.910 --> 00:54:19.040 That's a very complicated word that 00:54:19.040 --> 00:54:20.960 describes the fact that if you have these two 00:54:20.960 --> 00:54:24.350 equations and two unknowns, and you have one solution, 00:54:24.350 --> 00:54:27.650 you can just take an average of those two, a combination 00:54:27.650 --> 00:54:29.630 of those two, and you'll get the third one. 00:54:29.630 --> 00:54:35.320 You can actually replicate the third equation from those two. 00:54:35.320 --> 00:54:37.940 What happens if you don't? 00:54:37.940 --> 00:54:41.410 What happens if you cannot take combinations of the first two 00:54:41.410 --> 00:54:44.050 equations to get the third? 00:54:44.050 --> 00:54:45.101 What does that mean? 00:54:45.101 --> 00:54:46.905 AUDIENCE: One of the numbers is wrong. 00:54:46.905 --> 00:54:48.589 ANDREW LO: One of the numbers is wrong. 00:54:48.589 --> 00:54:49.630 What do you mean by that? 00:54:52.420 --> 00:54:55.210 AUDIENCE: It just couldn't be-- it can't be a solution. 00:54:55.210 --> 00:54:57.130 ANDREW LO: It can't be a solution. 00:54:57.130 --> 00:54:59.350 OK, now this is getting really interesting 00:54:59.350 --> 00:55:01.330 because on the one hand, you're probably 00:55:01.330 --> 00:55:04.300 getting confused about what any of this has to do with money. 00:55:04.300 --> 00:55:05.716 In a minute, I'm going to tell you 00:55:05.716 --> 00:55:08.980 it has everything to do with money, as you might expect. 00:55:08.980 --> 00:55:10.914 If we've got two equations and two unknowns, 00:55:10.914 --> 00:55:12.580 and we have one solution, that basically 00:55:12.580 --> 00:55:16.780 says that there are two yields, a one year yield and a two year 00:55:16.780 --> 00:55:21.540 yield that is able to price both bonds. 00:55:21.540 --> 00:55:24.120 And that better be the case because we're 00:55:24.120 --> 00:55:27.690 going to use these two yields to replicate the bonds. 00:55:27.690 --> 00:55:31.780 And so this kind of a relationship has to hold. 00:55:31.780 --> 00:55:37.930 Now if we add a third bond, if we add a third bond, 00:55:37.930 --> 00:55:41.500 and those same two yields that worked for the first two bonds, 00:55:41.500 --> 00:55:48.020 they don't work for the third bond, something's wrong, right? 00:55:48.020 --> 00:55:52.200 It means that this third bond, its price 00:55:52.200 --> 00:55:57.295 does not satisfy the relationship between those two 00:55:57.295 --> 00:55:57.795 yields. 00:56:00.650 --> 00:56:04.700 That's evidence of a mispricing. 00:56:04.700 --> 00:56:06.680 Something is wrong. 00:56:06.680 --> 00:56:09.170 But in this case, what's wrong is 00:56:09.170 --> 00:56:11.930 that there's something mispriced between those two 00:56:11.930 --> 00:56:16.140 bonds and the third. 00:56:16.140 --> 00:56:18.080 So when you run into a situation like that-- 00:56:18.080 --> 00:56:20.538 and we're going to give you an example in the problem set-- 00:56:20.538 --> 00:56:23.090 when you come across that, what that means is 00:56:23.090 --> 00:56:28.280 you should be extremely excited, as opposed to depressed 00:56:28.280 --> 00:56:31.190 in math class, you know, gee, there's no solution. 00:56:31.190 --> 00:56:33.800 In finance, what no solution means 00:56:33.800 --> 00:56:35.450 is that there is a transaction. 00:56:35.450 --> 00:56:39.290 There exists a linear combination of the first two 00:56:39.290 --> 00:56:46.700 bonds and the third that A, costs you no money down; B, 00:56:46.700 --> 00:56:49.700 will generate cash flow today; C, 00:56:49.700 --> 00:56:54.280 will require no future payments of any sort, so it's riskless. 00:56:54.280 --> 00:56:55.630 It is a free lunch. 00:56:55.630 --> 00:56:57.219 It is an arbitrage. 00:56:57.219 --> 00:56:59.260 Now that's with three equations and two unknowns. 00:56:59.260 --> 00:57:00.610 Anybody can do that, right? 00:57:00.610 --> 00:57:02.330 That's easy. 00:57:02.330 --> 00:57:05.560 What if it were 200 equations and 30 unknowns? 00:57:05.560 --> 00:57:07.129 Now, not so easy. 00:57:07.129 --> 00:57:09.670 Now you actually have to know something about linear algebra. 00:57:09.670 --> 00:57:13.210 Now the whole notion of what an invertible matrix is, 00:57:13.210 --> 00:57:16.420 what the eigenvalues are, all the kind of infrastructure 00:57:16.420 --> 00:57:19.210 that you can build for understanding this 00:57:19.210 --> 00:57:22.330 becomes relevant as a quant trading 00:57:22.330 --> 00:57:25.280 on a proprietary trading desk. 00:57:25.280 --> 00:57:29.360 In the 1970s, a number of MIT graduates 00:57:29.360 --> 00:57:32.044 were hired by Salomon Brothers. 00:57:32.044 --> 00:57:34.210 They knew very little about fixed income securities. 00:57:34.210 --> 00:57:38.050 They knew the basics, which is what was taught here, 00:57:38.050 --> 00:57:41.830 but they didn't know much about market realities in practice. 00:57:41.830 --> 00:57:45.310 And so when they went to solve their three equations and two 00:57:45.310 --> 00:57:51.040 unknowns, they observed inconsistencies. 00:57:51.040 --> 00:57:53.590 And they didn't do three equations and two unknowns, 00:57:53.590 --> 00:57:56.800 they did 200 equations and 30 unknowns. 00:57:56.800 --> 00:58:00.400 And in the 1970s, that was not easy to do because we didn't 00:58:00.400 --> 00:58:02.740 have PCs, we didn't have Excel. 00:58:02.740 --> 00:58:05.830 We didn't have a lot of the tools that we have today. 00:58:05.830 --> 00:58:09.790 And what they did was they took these simultaneous linear 00:58:09.790 --> 00:58:11.154 equations. 00:58:11.154 --> 00:58:12.320 This is high school algebra. 00:58:12.320 --> 00:58:15.700 Even back then it was high school algebra, OK? 00:58:15.700 --> 00:58:19.840 And they just cranked through and looked for mispricing, 00:58:19.840 --> 00:58:21.640 looked for no solutions. 00:58:21.640 --> 00:58:25.460 And they found a lot of cases with no solutions. 00:58:25.460 --> 00:58:29.780 In one of the years during the 1970s or 80s, 00:58:29.780 --> 00:58:37.220 one of these MIT grads was paid an annual bonus of $22 million 00:58:37.220 --> 00:58:40.890 for doing this, for solving simultaneous linear equations. 00:58:40.890 --> 00:58:42.200 So this is an extraor-- 00:58:42.200 --> 00:58:45.290 and if that was what he got paid, 00:58:45.290 --> 00:58:48.170 you imagine what he generated for Salomon Brothers. 00:58:48.170 --> 00:58:51.140 It was a lot more than $22 million. 00:58:51.140 --> 00:58:56.450 This activity is known as fixed income arbitrage. 00:58:56.450 --> 00:58:58.000 There are many other versions of it, 00:58:58.000 --> 00:58:59.850 but this is the plain vanilla version. 00:58:59.850 --> 00:59:02.030 And by the way, the plain vanilla version, 00:59:02.030 --> 00:59:06.590 it still works in the sense that occasionally, 00:59:06.590 --> 00:59:09.970 if you're quick enough and you have the right tools, 00:59:09.970 --> 00:59:13.669 you can identify mispricings and take advantage of them quickly. 00:59:13.669 --> 00:59:15.710 It doesn't last long, so you're absolutely right. 00:59:15.710 --> 00:59:17.620 It doesn't last long. 00:59:17.620 --> 00:59:19.370 But the person who gets paid is the person 00:59:19.370 --> 00:59:22.310 who can do this the fastest and is 00:59:22.310 --> 00:59:26.390 able to understand the interrelationships 00:59:26.390 --> 00:59:27.732 among the securities. 00:59:27.732 --> 00:59:29.690 And you can understand now why retail investors 00:59:29.690 --> 00:59:33.080 have no chance of doing this kind of thing on their own. 00:59:33.080 --> 00:59:36.650 This is something you definitely don't want to try at home, OK? 00:59:36.650 --> 00:59:39.830 I know you guys have MATLAB and you can do matrix inversions, 00:59:39.830 --> 00:59:43.100 but there are lots of other frictions, 00:59:43.100 --> 00:59:45.620 transactions costs, and imperfections that you have 00:59:45.620 --> 00:59:47.600 to build into this analysis. 00:59:47.600 --> 00:59:50.900 But once you do, all sorts of interesting things 00:59:50.900 --> 00:59:52.460 start popping out. 00:59:52.460 --> 00:59:53.637 All right, question, yeah. 00:59:53.637 --> 00:59:55.220 AUDIENCE: Can you give a couple reason 00:59:55.220 --> 00:59:56.060 why this does still exist? 00:59:56.060 --> 00:59:58.518 Like, why hasn't the arms race between everyone narrowed it 00:59:58.518 --> 01:00:00.797 down to basic efficiency? 01:00:00.797 --> 01:00:02.630 ANDREW LO: Well, it's actually much narrower 01:00:02.630 --> 01:00:03.900 now than it used to be. 01:00:03.900 --> 01:00:06.000 So in fact, the market has gotten much, 01:00:06.000 --> 01:00:07.830 much more competitive. 01:00:07.830 --> 01:00:09.870 But it's not down to zero precisely 01:00:09.870 --> 01:00:12.780 because there are frictions and other aspects. 01:00:12.780 --> 01:00:14.970 For example, some of these bonds, 01:00:14.970 --> 01:00:18.180 they have weird features, like they're callable. 01:00:18.180 --> 01:00:21.600 Or in some cases, they may have certain types 01:00:21.600 --> 01:00:27.900 of other requirements and market institutional imperfections 01:00:27.900 --> 01:00:30.000 that require you to build in those constraints 01:00:30.000 --> 01:00:31.590 when you do the analysis. 01:00:31.590 --> 01:00:34.470 And so it's really about who has the better model. 01:00:34.470 --> 01:00:36.240 And frankly there's an arms race that's 01:00:36.240 --> 01:00:38.400 been going on for the last three decades 01:00:38.400 --> 01:00:40.830 as to who has the fastest computers. 01:00:40.830 --> 01:00:42.870 The first supercomputer that was ever 01:00:42.870 --> 01:00:45.000 installed on Wall Street, a Cray-2, 01:00:45.000 --> 01:00:47.460 was installed at Salomon Brothers 01:00:47.460 --> 01:00:51.520 doing simultaneous linear equations, among other things. 01:00:51.520 --> 01:00:55.860 And so this is where technology has played a really big role 01:00:55.860 --> 01:00:58.730 in the developments of market prices. 01:00:58.730 --> 01:01:00.510 Another question? 01:01:00.510 --> 01:01:08.380 OK, so this very, very simple idea, and again, it is simple, 01:01:08.380 --> 01:01:11.110 has all sorts of important ramifications for the pricing 01:01:11.110 --> 01:01:14.050 of bonds and other securities. 01:01:14.050 --> 01:01:18.280 What that tells us is that market prices have 01:01:18.280 --> 01:01:21.680 all sorts of information that are incorporated into it. 01:01:21.680 --> 01:01:23.680 And one of the things that we want to understand 01:01:23.680 --> 01:01:26.020 is how to interpret that information. 01:01:26.020 --> 01:01:28.750 In particular, the first thing I want to do 01:01:28.750 --> 01:01:31.164 is to understand the risks, all right, 01:01:31.164 --> 01:01:33.580 because we talked about the fact that some of these market 01:01:33.580 --> 01:01:36.580 prices may have missed the risks that were 01:01:36.580 --> 01:01:38.930 implicit in some of the trades. 01:01:38.930 --> 01:01:42.610 And so the question is why and how do we measure 01:01:42.610 --> 01:01:45.740 the risk of a bond portfolio. 01:01:45.740 --> 01:01:48.130 So what I want to do is to now look 01:01:48.130 --> 01:01:51.550 at the market price of a bond in terms 01:01:51.550 --> 01:01:56.770 of a function that has inputs and the price is the output. 01:01:56.770 --> 01:01:58.540 And I want to ask the question, what kind 01:01:58.540 --> 01:02:02.260 of fluctuation in the input will yield fluctuation 01:02:02.260 --> 01:02:02.870 in the output? 01:02:02.870 --> 01:02:04.870 You know, we now know how to price these things. 01:02:04.870 --> 01:02:07.660 We now know how the relationships must work 01:02:07.660 --> 01:02:10.500 from a present value approach. 01:02:10.500 --> 01:02:13.030 And now what I want to do is to ask whether we 01:02:13.030 --> 01:02:15.100 can measure the sensitivity. 01:02:15.100 --> 01:02:19.030 So one way to do it is to just graph 01:02:19.030 --> 01:02:22.127 the price of a bond as a function of its yield. 01:02:22.127 --> 01:02:24.460 And we know that there's an inverse relationship, right? 01:02:24.460 --> 01:02:27.740 Just like we saw with treasuries this week versus last week, 01:02:27.740 --> 01:02:28.240 right? 01:02:28.240 --> 01:02:30.730 Last week it was a big run on treasuries, lots of people 01:02:30.730 --> 01:02:31.900 wanted to get into them. 01:02:31.900 --> 01:02:34.150 Price goes up, yield goes down. 01:02:34.150 --> 01:02:38.050 And this week, less pressure, so we have yield going up 01:02:38.050 --> 01:02:40.180 and the prices coming down. 01:02:40.180 --> 01:02:45.620 That provides us with one kind of measure of risk. 01:02:45.620 --> 01:02:48.100 So the kind of measure I'm talking about 01:02:48.100 --> 01:02:52.090 is the slope of this line. 01:02:52.090 --> 01:02:55.300 The instantaneous slope that tells us 01:02:55.300 --> 01:02:57.430 for a bit of a tweak in interest rates 01:02:57.430 --> 01:03:00.550 or yield, what does that do to the market price? 01:03:00.550 --> 01:03:03.130 Because obviously when you're an investor, 01:03:03.130 --> 01:03:05.350 you're focusing on the price, right? 01:03:05.350 --> 01:03:07.720 Yield is a convenient way of summarizing 01:03:07.720 --> 01:03:10.232 the properties of a bond, but ultimately 01:03:10.232 --> 01:03:12.190 what you care about in your portfolio is price. 01:03:12.190 --> 01:03:15.160 And so the question is for a move in the interest rate, what 01:03:15.160 --> 01:03:16.840 does that do to the price? 01:03:16.840 --> 01:03:19.270 Well, it turns out that there is one way 01:03:19.270 --> 01:03:23.710 to get at that that is somewhat more intuitive than just 01:03:23.710 --> 01:03:25.450 looking at this kind of fluctuation. 01:03:25.450 --> 01:03:30.220 It's called duration and it's named after a person Macaulay 01:03:30.220 --> 01:03:33.340 who first proposed it as a way of measuring 01:03:33.340 --> 01:03:36.130 how risky a bond is. 01:03:36.130 --> 01:03:42.470 What Macaulay noted was that the longer the maturity of a bond, 01:03:42.470 --> 01:03:48.890 the more sensitive is the bond price to the yield. 01:03:48.890 --> 01:03:52.670 So for example, a 30 year bond, when you move the interest rate 01:03:52.670 --> 01:03:56.810 by one basis point, will have a much, much larger price 01:03:56.810 --> 01:04:00.650 fluctuation than a three month bond, right? 01:04:00.650 --> 01:04:01.250 Why is that? 01:04:01.250 --> 01:04:05.000 Anybody give me some intuition for why that should be? 01:04:05.000 --> 01:04:06.530 Why that makes sense? 01:04:06.530 --> 01:04:08.780 Why should a longer maturity bond 01:04:08.780 --> 01:04:11.260 be more sensitive to changes in yield? 01:04:11.260 --> 01:04:12.000 Yeah, Ken. 01:04:12.000 --> 01:04:13.970 AUDIENCE: Because you're hanging on, 01:04:13.970 --> 01:04:15.746 because the cash is tied up longer. 01:04:15.746 --> 01:04:16.620 ANDREW LO: Yeah, and? 01:04:16.620 --> 01:04:20.330 AUDIENCE: And because the risk-- 01:04:20.330 --> 01:04:22.193 because the opportunity cost essentially 01:04:22.193 --> 01:04:25.139 of having that money tied up for that long means 01:04:25.139 --> 01:04:29.060 you can't spend it on all these other things over those 30 01:04:29.060 --> 01:04:29.560 years. 01:04:29.560 --> 01:04:30.560 ANDREW LO: That's right. 01:04:30.560 --> 01:04:32.900 You're investing for a longer period of time 01:04:32.900 --> 01:04:35.050 so, in fact, the opportunity costs, 01:04:35.050 --> 01:04:37.570 as measured by the foregone interest, 01:04:37.570 --> 01:04:39.220 is going to be much larger. 01:04:39.220 --> 01:04:43.150 In other words, the discount rate that you use, 01:04:43.150 --> 01:04:47.650 this one plus r, you've raised that to the 30th power, 01:04:47.650 --> 01:04:51.100 not to the 1/4 power, and so something that's 01:04:51.100 --> 01:04:54.590 raised to the 30th power in the denominator, 01:04:54.590 --> 01:04:58.510 it has a much larger impact when you perturb that denominator 01:04:58.510 --> 01:05:04.200 by a little bit, because you're actually increasing that power. 01:05:04.200 --> 01:05:07.980 You're increasing that quantity by that 30th power. 01:05:07.980 --> 01:05:09.940 Well, so if that's the case, if it's 01:05:09.940 --> 01:05:13.780 the case that the longer the maturity, the more at risk 01:05:13.780 --> 01:05:17.890 you are per basis point of interest rate fluctuation, 01:05:17.890 --> 01:05:22.960 then why don't we just measure the average duration 01:05:22.960 --> 01:05:24.190 of the bond? 01:05:24.190 --> 01:05:26.980 By average duration, I mean how long does the bond 01:05:26.980 --> 01:05:30.760 last when you weighed it by the coupon payments 01:05:30.760 --> 01:05:32.210 that it pays you? 01:05:32.210 --> 01:05:35.170 So for a pure discount bond, the duration is simple. 01:05:35.170 --> 01:05:37.180 It's just the maturity date, right? 01:05:37.180 --> 01:05:41.560 If you've got a 30 year strip that pays you $1 in 30 years, 01:05:41.560 --> 01:05:44.170 the duration of that bond is just 30 years. 01:05:44.170 --> 01:05:46.930 But what if you had a coupon bond that paid you 01:05:46.930 --> 01:05:49.240 coupons all along the way? 01:05:49.240 --> 01:05:52.240 Well, then, you should take a weighted average of the 30 01:05:52.240 --> 01:05:54.610 years and give some weight to the early years 01:05:54.610 --> 01:05:57.340 too, because the early years are years where 01:05:57.340 --> 01:05:59.140 you're going to receive cash. 01:05:59.140 --> 01:06:00.970 And therefore, interest rate fluctuations 01:06:00.970 --> 01:06:04.850 are going to affect the value of those cash flows. 01:06:04.850 --> 01:06:08.770 So the weighted average term to maturity 01:06:08.770 --> 01:06:16.500 is simply equal to the sum of the date, 1, 2, 3, 4, 5, 6, 01:06:16.500 --> 01:06:21.420 7, multiplied by a weight factor that sums to one. 01:06:21.420 --> 01:06:26.280 And let's just use, as a weight factor, 01:06:26.280 --> 01:06:32.850 the proportion of present value of cash flow on that date. 01:06:35.560 --> 01:06:39.900 So if you take the weighted average 01:06:39.900 --> 01:06:44.220 where you take the weights as the present value of the coupon 01:06:44.220 --> 01:06:46.110 divided by the present value of the bond, 01:06:46.110 --> 01:06:49.080 those weights certainly sum to one. 01:06:49.080 --> 01:06:52.210 And then you're weighting that by the date, 01:06:52.210 --> 01:06:57.030 the year that you get paid, that number will give you what's 01:06:57.030 --> 01:07:01.920 called Macaulay duration. 01:07:01.920 --> 01:07:07.260 So it turns out that the reason that Macaulay duration is 01:07:07.260 --> 01:07:11.910 interesting is that when you take a look at bond prices 01:07:11.910 --> 01:07:16.440 and you ask the question, for a certain percentage change, 01:07:16.440 --> 01:07:18.990 a certain basis point change in the interest rate, what 01:07:18.990 --> 01:07:22.620 does that do to the bond price as a percentage 01:07:22.620 --> 01:07:24.180 of its current price? 01:07:24.180 --> 01:07:26.670 So this is the sensitivity. 01:07:26.670 --> 01:07:29.760 It turns out that you can show that that's actually 01:07:29.760 --> 01:07:34.380 the negative of the Macaulay duration divided 01:07:34.380 --> 01:07:38.170 by one plus the bond yield. 01:07:38.170 --> 01:07:43.020 So this is a long way of stating that the duration gives you 01:07:43.020 --> 01:07:45.360 a measure of how sensitive the bond 01:07:45.360 --> 01:07:49.860 price is to changes in yield. 01:07:49.860 --> 01:07:54.060 The longer the duration, the more sensitive 01:07:54.060 --> 01:07:56.790 the bond is to changes in yield. 01:07:56.790 --> 01:08:00.540 And duration now just means a weighted average 01:08:00.540 --> 01:08:05.670 of all of the payout dates that a bond will have. 01:08:05.670 --> 01:08:09.060 If a bond pays a lot of its cash up front 01:08:09.060 --> 01:08:12.820 and very little in later periods, 01:08:12.820 --> 01:08:15.865 is the duration high or low? 01:08:15.865 --> 01:08:16.695 AUDIENCE: Low. 01:08:16.695 --> 01:08:17.529 ANDREW LO: Low. 01:08:17.529 --> 01:08:19.840 And so if a duration is low what that says 01:08:19.840 --> 01:08:21.970 is that there's not a lot of sensitivity 01:08:21.970 --> 01:08:25.240 to changes in yield on the bond price itself. 01:08:25.240 --> 01:08:27.340 If on the other hand, all of your payment 01:08:27.340 --> 01:08:30.370 is out in the future, way out in the future, that's 01:08:30.370 --> 01:08:34.149 going to make it very interest rate sensitive. 01:08:34.149 --> 01:08:37.930 And the negative number here indicates 01:08:37.930 --> 01:08:42.340 that there's an inverse relationship between price 01:08:42.340 --> 01:08:43.330 and yield. 01:08:43.330 --> 01:08:48.279 So when bond investors look at a particular portfolio of bonds, 01:08:48.279 --> 01:08:51.021 and this is key, they look at a portfolio of bonds 01:08:51.021 --> 01:08:53.229 because that's what they're going to be investing in. 01:08:53.229 --> 01:08:55.720 When you put your money in a money market fund 01:08:55.720 --> 01:08:59.319 or in a bond fund, medium term, long term, 01:08:59.319 --> 01:09:01.210 you're not putting it in one bond, 01:09:01.210 --> 01:09:04.029 you're putting it in a whole set of bonds. 01:09:04.029 --> 01:09:07.300 Your natural question is, how sensitive 01:09:07.300 --> 01:09:11.020 is that portfolio to changes in interest rates? 01:09:11.020 --> 01:09:15.490 And the answer is it's related to the duration. 01:09:15.490 --> 01:09:17.740 And so if I told you that this portfolio has 01:09:17.740 --> 01:09:21.200 a duration of five and 1/2 years, 01:09:21.200 --> 01:09:23.590 that will give you some intuition for how sensitive 01:09:23.590 --> 01:09:26.649 or how risky that portfolio is. 01:09:26.649 --> 01:09:29.410 So duration is a measure that I've defined for a bond, 01:09:29.410 --> 01:09:32.200 but you can define it for a portfolio of bonds, 01:09:32.200 --> 01:09:36.649 simply by taking the cash flows at every period 01:09:36.649 --> 01:09:39.729 and then computing a weighted average where the weights are 01:09:39.729 --> 01:09:42.460 the present value of those cash flows as a function 01:09:42.460 --> 01:09:45.710 of the entire portfolio. 01:09:45.710 --> 01:09:50.870 OK, so here's an example where I've got a four year Treasury 01:09:50.870 --> 01:09:56.810 note with a face value of $100, 7% coupon selling at a $103.50, 01:09:56.810 --> 01:10:00.620 which yields 6%. 01:10:00.620 --> 01:10:03.320 That's the yield, that's the why that 01:10:03.320 --> 01:10:08.090 makes this 103.5 equal to the present value of all 01:10:08.090 --> 01:10:11.926 of those coupon payments plus the return of principal. 01:10:14.630 --> 01:10:18.620 And so here what I've done is to calculate for you 01:10:18.620 --> 01:10:23.210 the cash flows of the bond, the present value of those cash 01:10:23.210 --> 01:10:29.510 flows, and then the respective product of t 01:10:29.510 --> 01:10:32.130 times the present value of cash flows. 01:10:32.130 --> 01:10:36.200 So you can actually compute for yourself that duration number. 01:10:36.200 --> 01:10:41.560 And you can get a sense of exactly what that is. 01:10:41.560 --> 01:10:46.660 So the duration is about 7.13 years. 01:10:46.660 --> 01:10:49.180 So duration is a measurement that 01:10:49.180 --> 01:10:52.570 is in units of years or half year units. 01:10:52.570 --> 01:10:55.840 Sorry, 7.13 half year units. 01:10:55.840 --> 01:11:01.760 And the modified duration is going to be given by 6.92. 01:11:01.760 --> 01:11:05.360 Price risk at a yield of 3% therefore 01:11:05.360 --> 01:11:09.830 is going to be given by just this expression right here. 01:11:09.830 --> 01:11:12.080 What that says is that if the yield moves up 01:11:12.080 --> 01:11:15.920 by 1/10 of a percent or 10 basis points, 01:11:15.920 --> 01:11:19.820 the bond price is going to decrease by 68 basis points. 01:11:19.820 --> 01:11:23.390 That will give you a sense of how exposed you are. 01:11:23.390 --> 01:11:25.580 If you have very long duration portfolios, 01:11:25.580 --> 01:11:28.190 that means that you're going to be in for a wild ride 01:11:28.190 --> 01:11:31.050 as interest rates swing around a lot. 01:11:31.050 --> 01:11:33.740 And if you're willing to take on that risk, that's great, 01:11:33.740 --> 01:11:37.670 but you're going to be at least compensated for that. 01:11:41.270 --> 01:11:47.520 Macaulay duration, you can compute it in this way. 01:11:47.520 --> 01:11:50.350 For intra-year coupons, that's a very straightforward 01:11:50.350 --> 01:11:51.170 calculation. 01:11:51.170 --> 01:11:53.260 So you want to make sure you know how to do that. 01:11:53.260 --> 01:11:55.900 You simply just use the usual discounting 01:11:55.900 --> 01:12:01.060 and dividing the yield by the appropriate payment periods. 01:12:01.060 --> 01:12:05.740 And now the last concept that I want to cover today 01:12:05.740 --> 01:12:09.100 is convexity. 01:12:09.100 --> 01:12:14.380 Convexity is another measure of risk. 01:12:14.380 --> 01:12:16.210 It's the second derivative. 01:12:16.210 --> 01:12:24.870 What it measures is how the sensitivity itself changes. 01:12:24.870 --> 01:12:28.380 And it turns out that convexity, as a measure, 01:12:28.380 --> 01:12:33.750 gives you sort of a higher order approximation both to the price 01:12:33.750 --> 01:12:36.330 of the bond, as well as how the bond 01:12:36.330 --> 01:12:40.150 is going to move with respect to interest rates. 01:12:40.150 --> 01:12:42.460 So let me just show you what the derivation is. 01:12:42.460 --> 01:12:45.560 It's pretty straightforward, but if you have any questions, 01:12:45.560 --> 01:12:48.440 I'm happy to discuss it. 01:12:48.440 --> 01:12:51.910 You take the price of a bond and you take the second derivative 01:12:51.910 --> 01:12:54.504 with respect to the yield. 01:12:54.504 --> 01:12:55.920 What you're going to get out of it 01:12:55.920 --> 01:13:00.010 is an expression that looks like this. 01:13:00.010 --> 01:13:03.420 Now that expression in and of itself 01:13:03.420 --> 01:13:06.300 has relatively little intuition. 01:13:06.300 --> 01:13:11.340 But let me just write down the percentage change 01:13:11.340 --> 01:13:15.660 in the first derivative as v sub m, 01:13:15.660 --> 01:13:20.010 and then I'm going to show you an interesting relationship. 01:13:20.010 --> 01:13:23.910 For those of you who remember your high school calculus 01:13:23.910 --> 01:13:25.920 or college calculus class, you'll 01:13:25.920 --> 01:13:28.750 remember there's something called a Taylor approximation, 01:13:28.750 --> 01:13:29.250 right? 01:13:29.250 --> 01:13:30.600 Taylor series. 01:13:30.600 --> 01:13:34.020 This is a method of approximating nonlinear 01:13:34.020 --> 01:13:38.070 relationships using polynomials, powers 01:13:38.070 --> 01:13:40.470 of the variables in question. 01:13:40.470 --> 01:13:44.094 If you took the bond price as a function of the yield, 01:13:44.094 --> 01:13:46.260 it's a nonlinear function, of course, because you've 01:13:46.260 --> 01:13:50.120 got that discounting going on. 01:13:50.120 --> 01:13:52.030 Then you can ask the question, how 01:13:52.030 --> 01:13:55.960 can I approximate the bond price as a function of the yield 01:13:55.960 --> 01:14:02.680 if I'm willing to take a couple of terms of the approximation? 01:14:02.680 --> 01:14:06.370 And when you do that, you get what 01:14:06.370 --> 01:14:07.970 may look like an awful expression, 01:14:07.970 --> 01:14:11.740 but actually it's quite beautiful in its own right. 01:14:11.740 --> 01:14:15.790 What this says is that the price of the bond at a new interest 01:14:15.790 --> 01:14:22.150 rate, at a new yield, if the yield changes, then 01:14:22.150 --> 01:14:26.530 price of the bond at the new interest rate 01:14:26.530 --> 01:14:28.720 is going to be equal to the price of the bond 01:14:28.720 --> 01:14:30.790 at the old interest rate, multiplied 01:14:30.790 --> 01:14:34.240 by a factor of something or other. 01:14:34.240 --> 01:14:36.850 And that factor is going to be given 01:14:36.850 --> 01:14:43.600 by one minus a term that's a linear function of the yield, 01:14:43.600 --> 01:14:48.730 plus another term that is a quadratic function 01:14:48.730 --> 01:14:51.045 of the change in the yield. 01:14:51.045 --> 01:14:52.420 So this is what I mean when I say 01:14:52.420 --> 01:14:56.140 this is a second order approximation to the pricing 01:14:56.140 --> 01:14:58.060 relationship. 01:14:58.060 --> 01:15:02.710 And this basically gives us a way 01:15:02.710 --> 01:15:06.010 to figure out when yields move, what does that 01:15:06.010 --> 01:15:08.400 do to my portfolio. 01:15:08.400 --> 01:15:09.900 Now you might be thinking, gee, this 01:15:09.900 --> 01:15:12.840 is an awful long way to go to try to figure that out. 01:15:12.840 --> 01:15:15.450 Can't we just use an Excel spreadsheet 01:15:15.450 --> 01:15:18.660 and then move the interest rate and then recalculate and see 01:15:18.660 --> 01:15:20.340 what that does? 01:15:20.340 --> 01:15:24.290 Today, you can, but in the 1970s, you couldn't. 01:15:24.290 --> 01:15:25.860 You didn't have that ability. 01:15:25.860 --> 01:15:29.400 So much of this framework was developed in the 1970s 01:15:29.400 --> 01:15:34.410 because people wanted to have easy ways of not only pricing 01:15:34.410 --> 01:15:38.730 bonds, but figuring out what the risk of their positions 01:15:38.730 --> 01:15:40.650 were as bond traders. 01:15:40.650 --> 01:15:42.636 And to do that quickly is very difficult. 01:15:42.636 --> 01:15:44.010 You remember the story I told you 01:15:44.010 --> 01:15:47.340 about when I got a mortgage 20 years ago 01:15:47.340 --> 01:15:50.879 and the bank loan officer just could not figure out 01:15:50.879 --> 01:15:52.170 what my mortgage payments were. 01:15:52.170 --> 01:15:54.932 She had to go look for a book and try to thumb through what 01:15:54.932 --> 01:15:55.890 those calculations are. 01:15:55.890 --> 01:15:58.470 Well, imagine if you're a bond trader trading literally 01:15:58.470 --> 01:16:00.210 every minute of the day, and there 01:16:00.210 --> 01:16:04.020 was bond trading going on in the 1970s, believe it or not. 01:16:04.020 --> 01:16:06.330 You have to figure out these pricing relationships. 01:16:06.330 --> 01:16:07.900 And it was not so easy. 01:16:07.900 --> 01:16:11.250 So a number of mathematicians came up 01:16:11.250 --> 01:16:13.570 with these kind of relationships for bond prices. 01:16:13.570 --> 01:16:15.060 In fact, it's funny. 01:16:15.060 --> 01:16:16.830 Bond pricing is actually quite a bit more 01:16:16.830 --> 01:16:20.040 of a mathematical art than equity pricing 01:16:20.040 --> 01:16:21.480 simply because with a bond, there 01:16:21.480 --> 01:16:23.140 aren't that many moving parts. 01:16:23.140 --> 01:16:26.460 And so they aren't subject to mathematical analysis 01:16:26.460 --> 01:16:29.280 like this, whereas with stock prices, 01:16:29.280 --> 01:16:32.130 since there are so many factors impinging on it, 01:16:32.130 --> 01:16:34.560 the actual tools that we use are quite a bit 01:16:34.560 --> 01:16:38.730 less complex, at least from a historical perspective. 01:16:38.730 --> 01:16:41.670 So the purpose of this is really just 01:16:41.670 --> 01:16:45.840 to approximate the risk of a bond portfolio. 01:16:45.840 --> 01:16:47.790 You want to know when you change yields what 01:16:47.790 --> 01:16:49.290 that does to the portfolio. 01:16:49.290 --> 01:16:52.050 And you also want to know if the yield changes 01:16:52.050 --> 01:16:55.660 in volatility, what does that do to the portfolio. 01:16:55.660 --> 01:16:58.080 So this first term here, this term 01:16:58.080 --> 01:17:01.470 tells you about shifts in the interest rate. 01:17:01.470 --> 01:17:05.400 What this term does is tell you about fluctuations 01:17:05.400 --> 01:17:08.730 or volatility of interest rates. 01:17:08.730 --> 01:17:10.650 And it turns out that volatility has 01:17:10.650 --> 01:17:15.330 an impact on bond portfolios, as does changes 01:17:15.330 --> 01:17:18.570 in the level of interest rates. 01:17:18.570 --> 01:17:20.160 Just looking at this, can anybody 01:17:20.160 --> 01:17:25.500 tell me off the top of their head what direction this goes? 01:17:25.500 --> 01:17:29.540 In other words, if you are holding a bond and interest 01:17:29.540 --> 01:17:35.230 rates rise, we know that bond prices will fall. 01:17:35.230 --> 01:17:37.450 But what if the volatility of interest rates 01:17:37.450 --> 01:17:40.930 rise, as they have over the last few weeks? 01:17:40.930 --> 01:17:43.330 Yields have bounced around a lot more 01:17:43.330 --> 01:17:44.920 lately than they have in the past. 01:17:44.920 --> 01:17:46.758 What does that do to a bond? 01:17:49.150 --> 01:17:51.150 Does it make it more valuable and less valuable? 01:17:51.150 --> 01:17:53.440 Let's put it that way. 01:17:53.440 --> 01:17:54.360 How do you know? 01:17:54.360 --> 01:17:56.010 Less, more? 01:17:56.010 --> 01:17:57.960 We have some volatility here. 01:18:01.300 --> 01:18:03.880 Take a look at that expression. 01:18:03.880 --> 01:18:08.980 v sub m is going to be the second derivative, 01:18:08.980 --> 01:18:11.530 and then you've got a term there that's going 01:18:11.530 --> 01:18:17.200 to be the change in the yield squared. 01:18:17.200 --> 01:18:20.350 If the change in the yield squared goes up, 01:18:20.350 --> 01:18:24.240 other things equal, and other things are never equal, 01:18:24.240 --> 01:18:28.500 but economists like to say other things equal, 01:18:28.500 --> 01:18:33.120 it actually makes bonds more valuable. 01:18:33.120 --> 01:18:38.050 In this respect, owning a bond actually is sort of 01:18:38.050 --> 01:18:39.619 like owning an option. 01:18:39.619 --> 01:18:41.160 Now you don't know about options yet. 01:18:41.160 --> 01:18:43.580 We're going to come to in a few lectures. 01:18:43.580 --> 01:18:47.650 But it turns out that having an option when volatility goes up 01:18:47.650 --> 01:18:49.690 can be very valuable. 01:18:49.690 --> 01:18:53.020 And similarly for bonds, bonds have 01:18:53.020 --> 01:18:55.120 option-like characteristics. 01:18:55.120 --> 01:18:58.090 And we see that here with this approximation. 01:18:58.090 --> 01:19:02.530 That second term will actually yield some actual value 01:19:02.530 --> 01:19:04.420 when volatility goes up. 01:19:04.420 --> 01:19:06.280 Now I do a numerical example here 01:19:06.280 --> 01:19:08.860 that I'd like you to look through on your own 01:19:08.860 --> 01:19:13.720 where I compute for you both the first and second terms 01:19:13.720 --> 01:19:15.280 of that approximation. 01:19:15.280 --> 01:19:19.180 And you can actually see how good the approximation is. 01:19:19.180 --> 01:19:21.730 So I'd like you to take a look at that, make sure 01:19:21.730 --> 01:19:23.920 you understand it, and next time, 01:19:23.920 --> 01:19:26.830 be happy to answer questions about this. 01:19:26.830 --> 01:19:29.110 What we're going to cover on Monday 01:19:29.110 --> 01:19:33.550 is risky debt, which of course is directly related to what's 01:19:33.550 --> 01:19:35.410 going on in markets today. 01:19:35.410 --> 01:19:40.210 And so I'd like you to read up on that in the textbook. 01:19:40.210 --> 01:19:42.130 And when we come back on Monday, we're 01:19:42.130 --> 01:19:45.130 going to talk about debt ratings and possibly 01:19:45.130 --> 01:19:49.980 what went wrong with all of these subprime securities.