1 00:00:00,090 --> 00:00:02,430 The following content is provided under a Creative 2 00:00:02,430 --> 00:00:03,820 Commons license. 3 00:00:03,820 --> 00:00:06,030 Your support will help MIT OpenCourseWare 4 00:00:06,030 --> 00:00:10,120 continue to offer high quality educational resources for free. 5 00:00:10,120 --> 00:00:12,690 To make a donation or to view additional materials 6 00:00:12,690 --> 00:00:16,620 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:16,620 --> 00:00:25,770 at ocw.mit.edu 8 00:00:25,770 --> 00:00:29,040 Let me begin by first asking whether there 9 00:00:29,040 --> 00:00:35,310 are any questions from last class, which was a week ago. 10 00:00:35,310 --> 00:00:37,470 Hope you had a good break. 11 00:00:37,470 --> 00:00:38,280 Any questions? 12 00:00:41,670 --> 00:00:42,220 OK. 13 00:00:42,220 --> 00:00:45,360 Before we begin today's topic-- question? 14 00:00:45,360 --> 00:00:46,157 AUDIENCE: No. 15 00:00:46,157 --> 00:00:46,740 ANDREW LO: No. 16 00:00:46,740 --> 00:00:51,150 Before we begin today's topic on arbitrage 17 00:00:51,150 --> 00:00:56,160 and the pricing of multiple fixed income securities, 18 00:00:56,160 --> 00:00:58,170 I want to just take a few moments 19 00:00:58,170 --> 00:01:01,200 to talk a bit about what's going on in financial markets, 20 00:01:01,200 --> 00:01:04,110 also to welcome the prospective students that we have 21 00:01:04,110 --> 00:01:06,960 sitting here in class today. 22 00:01:06,960 --> 00:01:11,370 So for once, over the weekend, unprecedented things 23 00:01:11,370 --> 00:01:12,580 didn't occur. 24 00:01:12,580 --> 00:01:15,690 And so I'm glad to report that we're still here. 25 00:01:15,690 --> 00:01:18,270 Financial markets are still around. 26 00:01:18,270 --> 00:01:22,050 And as you know, the government has proposed some measures 27 00:01:22,050 --> 00:01:25,890 to deal with this current financial crisis. 28 00:01:25,890 --> 00:01:28,140 And at this point, it's still unclear as 29 00:01:28,140 --> 00:01:29,920 to what they're proposing. 30 00:01:29,920 --> 00:01:32,910 But we can actually see from the data 31 00:01:32,910 --> 00:01:34,380 what the market's reaction is. 32 00:01:34,380 --> 00:01:36,910 Last time, remember, we looked at the yield curve 33 00:01:36,910 --> 00:01:40,170 and literally, it was just a week ago that the yield 34 00:01:40,170 --> 00:01:42,360 curve looked like this. 35 00:01:42,360 --> 00:01:44,850 Now remember that we focused on what 36 00:01:44,850 --> 00:01:47,260 happened at the very short end of the yield curve, 37 00:01:47,260 --> 00:01:49,170 which is three month Treasury bills. 38 00:01:49,170 --> 00:01:53,160 And last week when we looked at this graph, 39 00:01:53,160 --> 00:01:58,230 the yield was about three basis points for a three month 40 00:01:58,230 --> 00:01:59,130 Treasury bill. 41 00:01:59,130 --> 00:02:01,620 And we pointed out that that was telling us 42 00:02:01,620 --> 00:02:02,757 something about the market. 43 00:02:02,757 --> 00:02:05,340 In particular, it was telling us that the market is panicking. 44 00:02:05,340 --> 00:02:07,560 Yeah? 45 00:02:07,560 --> 00:02:10,530 AUDIENCE: So aren't we sort of in this whole situation 46 00:02:10,530 --> 00:02:13,946 because looking at the market grossly mispriced things? 47 00:02:13,946 --> 00:02:15,570 ANDREW LO: Well, I wouldn't say that it 48 00:02:15,570 --> 00:02:18,050 was looking at the market grossly mispriced things. 49 00:02:18,050 --> 00:02:22,406 AUDIENCE: The market obviously did not officially 50 00:02:22,406 --> 00:02:27,630 price this risk, which looking at the market a year 51 00:02:27,630 --> 00:02:31,095 and a half ago, we would have been, oh, here's 52 00:02:31,095 --> 00:02:33,570 this much risk, this criteria [INAUDIBLE]. 53 00:02:33,570 --> 00:02:36,060 It turned out to be right, totally right. 54 00:02:36,060 --> 00:02:38,250 ANDREW LO: Well, there are a number of things that 55 00:02:38,250 --> 00:02:39,750 are priced into a security. 56 00:02:39,750 --> 00:02:42,180 It's not just a risk, but it's also a reflection 57 00:02:42,180 --> 00:02:44,310 of supply and demand, right? 58 00:02:44,310 --> 00:02:46,560 So in other words, what's going on here-- the question 59 00:02:46,560 --> 00:02:49,050 that we want to answer from looking at the price 60 00:02:49,050 --> 00:02:51,930 is what do we know about what's going on in the marketplace 61 00:02:51,930 --> 00:02:52,800 based on that price. 62 00:02:52,800 --> 00:02:54,690 What is it telling us? 63 00:02:54,690 --> 00:02:57,330 The cost of borrowing over a three month period-- 64 00:02:57,330 --> 00:02:59,190 when it goes down to three basis points, 65 00:02:59,190 --> 00:03:02,250 that's telling you that the price of that security, 66 00:03:02,250 --> 00:03:05,565 the price of Treasury bills is extraordinarily high relative 67 00:03:05,565 --> 00:03:07,590 to historical standards. 68 00:03:07,590 --> 00:03:10,230 Now let's take a look at what happens 69 00:03:10,230 --> 00:03:12,630 more recently, in particular, today, 70 00:03:12,630 --> 00:03:16,200 if we go to any of these websites-- 71 00:03:16,200 --> 00:03:18,660 so in particular, let's go back to the Bloomberg site 72 00:03:18,660 --> 00:03:21,090 where we originally looked at this. 73 00:03:21,090 --> 00:03:23,310 First of all, this is now the yield curve. 74 00:03:23,310 --> 00:03:27,200 And it's hard to compare because I've 75 00:03:27,200 --> 00:03:29,820 got a different slide for last weeks. 76 00:03:29,820 --> 00:03:34,560 This is just yesterday's, the orange, not last week's. 77 00:03:34,560 --> 00:03:37,680 But the one thing you'll note is that at the very short end, now 78 00:03:37,680 --> 00:03:42,060 instead of three basis points, the three month Treasury 79 00:03:42,060 --> 00:03:45,250 is yielding 41 basis points. 80 00:03:45,250 --> 00:03:48,360 What does that tell you about the price? 81 00:03:48,360 --> 00:03:52,620 Now, so Treasury securities, short-term Treasury securities, 82 00:03:52,620 --> 00:03:55,740 have declined in price over the last week. 83 00:03:55,740 --> 00:04:00,852 And that's one sign that perhaps markets are not as panicked 84 00:04:00,852 --> 00:04:01,810 as they were last week. 85 00:04:01,810 --> 00:04:05,040 There isn't this mad rush to get into Treasury securities 86 00:04:05,040 --> 00:04:05,791 in the short term. 87 00:04:05,791 --> 00:04:07,623 All right, so short term means have gone up. 88 00:04:07,623 --> 00:04:08,296 Yeah. 89 00:04:08,296 --> 00:04:09,796 AUDIENCE: So would you say that this 90 00:04:09,796 --> 00:04:12,760 would be a lot about the psychology of [INAUDIBLE]. 91 00:04:12,760 --> 00:04:13,650 ANDREW LO: Yeah. 92 00:04:13,650 --> 00:04:18,060 AUDIENCE: So what I was wondering is when the fact-- 93 00:04:18,060 --> 00:04:20,810 it seemed like, as you said, there's a flight in liquidity 94 00:04:20,810 --> 00:04:21,780 last week. 95 00:04:21,780 --> 00:04:25,660 Now why was there such a huge movement, 96 00:04:25,660 --> 00:04:30,025 or what led to the price dropping so much when, I guess, 97 00:04:30,025 --> 00:04:33,043 it could be reasonably expected that the price would 98 00:04:33,043 --> 00:04:34,584 come back up and so people would just 99 00:04:34,584 --> 00:04:36,350 wait it out and take a shot. 100 00:04:36,350 --> 00:04:38,676 ANDREW LO: Which price are you talking about dropping? 101 00:04:38,676 --> 00:04:40,800 AUDIENCE: I should probably say the yield dropping. 102 00:04:40,800 --> 00:04:44,020 ANDREW LO: The yield dropping and the price going up. 103 00:04:44,020 --> 00:04:47,130 Well, so there are a number of factors at play, 104 00:04:47,130 --> 00:04:52,740 but the current perspective that most of us 105 00:04:52,740 --> 00:04:55,300 have in financial markets about last week-- 106 00:04:55,300 --> 00:04:56,670 and this is just perspective. 107 00:04:56,670 --> 00:04:59,820 Remember, last week is not that far away. 108 00:04:59,820 --> 00:05:02,070 What happened last week, by most accounts, 109 00:05:02,070 --> 00:05:05,370 is that there was a very significant rush 110 00:05:05,370 --> 00:05:07,400 to the exits by investors. 111 00:05:07,400 --> 00:05:11,400 By rushing to the exits, I mean getting out of risky securities 112 00:05:11,400 --> 00:05:13,800 and into safer securities. 113 00:05:13,800 --> 00:05:16,350 And at this point, it doesn't seem 114 00:05:16,350 --> 00:05:19,290 like there's much of a safe haven 115 00:05:19,290 --> 00:05:21,810 other than US Treasury securities, 116 00:05:21,810 --> 00:05:23,550 and in particular, short-term securities 117 00:05:23,550 --> 00:05:26,820 because you know you can get the money out over a relatively 118 00:05:26,820 --> 00:05:28,390 short period of time. 119 00:05:28,390 --> 00:05:31,170 So that's what the yield curve told us last week, 120 00:05:31,170 --> 00:05:35,670 that three basis points means that basically people didn't 121 00:05:35,670 --> 00:05:37,380 care about the yield. 122 00:05:37,380 --> 00:05:39,760 All they wanted to do was to get into US treasuries 123 00:05:39,760 --> 00:05:42,000 at almost any price. 124 00:05:42,000 --> 00:05:43,750 OK. 125 00:05:43,750 --> 00:05:45,610 This week it's different. 126 00:05:45,610 --> 00:05:50,800 In particular, not only has the short-term yield gone up, 127 00:05:50,800 --> 00:05:53,980 so now instead of three basis points, we're up to 41. 128 00:05:53,980 --> 00:05:56,740 But look at the long end of the yield curve. 129 00:05:56,740 --> 00:05:58,810 Before, the long end of the yield curve-- 130 00:05:58,810 --> 00:06:02,590 let me just go back and remind you what that looked like. 131 00:06:02,590 --> 00:06:10,080 At the 30 year, a week ago, the 30 year yield was 4%. 132 00:06:10,080 --> 00:06:13,870 Let's take a look at what it is today. 133 00:06:13,870 --> 00:06:18,750 It's now, the 30 year yield, 4.37. 134 00:06:18,750 --> 00:06:21,630 That's another big movement. 135 00:06:21,630 --> 00:06:22,500 Why is that? 136 00:06:22,500 --> 00:06:26,510 Why would the yield for the long-term bond go up? 137 00:06:26,510 --> 00:06:29,324 What is the market thinking today? 138 00:06:29,324 --> 00:06:32,008 AUDIENCE: They might be more worried about inflation. 139 00:06:32,008 --> 00:06:34,760 The government has promised $700 billion. 140 00:06:34,760 --> 00:06:37,470 ANDREW LO: OK, so inflation has now 141 00:06:37,470 --> 00:06:40,650 been incorporated, just over the last seven days. 142 00:06:40,650 --> 00:06:45,870 So question-- is this price correct 143 00:06:45,870 --> 00:06:48,270 or was last week's price correct? 144 00:06:48,270 --> 00:06:50,320 Getting to your point, I mean, what do we do? 145 00:06:50,320 --> 00:06:53,430 Is the short end of the yield curve appropriate today 146 00:06:53,430 --> 00:06:56,130 at 41 basis points, or was it really appropriate at three 147 00:06:56,130 --> 00:06:56,880 basis points? 148 00:06:59,490 --> 00:07:01,330 There's no answer to that question 149 00:07:01,330 --> 00:07:03,310 because there is no right answer. 150 00:07:03,310 --> 00:07:08,310 These prices are a reflection of the current expectations 151 00:07:08,310 --> 00:07:10,920 of all the market participants. 152 00:07:10,920 --> 00:07:13,290 Right or wrong, it really reflects 153 00:07:13,290 --> 00:07:17,430 the combined either wisdom or fear or greed 154 00:07:17,430 --> 00:07:18,910 of the marketplace. 155 00:07:18,910 --> 00:07:22,170 And so our approach is to try to understand what that is. 156 00:07:22,170 --> 00:07:25,140 We want to explicate the information that 157 00:07:25,140 --> 00:07:27,570 happens to be in prices, but you have 158 00:07:27,570 --> 00:07:31,290 to understand that these are the same imperfect kind of prices 159 00:07:31,290 --> 00:07:33,180 that we came up with on day one when you 160 00:07:33,180 --> 00:07:34,930 bid for that little package. 161 00:07:34,930 --> 00:07:37,980 And it turned out that you got lucky 162 00:07:37,980 --> 00:07:42,130 and got an iPod for whatever, $45. 163 00:07:42,130 --> 00:07:43,770 But it could've gone the other way. 164 00:07:43,770 --> 00:07:47,080 And in fact, , in the second class it did go the other way. 165 00:07:47,080 --> 00:07:50,550 So we won't talk about that. 166 00:07:50,550 --> 00:07:56,790 The prices reflect all aspects of the economy, the rational 167 00:07:56,790 --> 00:07:58,260 as well as the irrational. 168 00:07:58,260 --> 00:08:01,140 And so last week, was it irrational for people 169 00:08:01,140 --> 00:08:04,170 to pull their money out from all sorts of investments 170 00:08:04,170 --> 00:08:06,210 and put them into Treasury bills? 171 00:08:06,210 --> 00:08:08,700 Well this goes to the heart of why the Treasury acted 172 00:08:08,700 --> 00:08:12,510 so quickly, and why Chairman Bernanke has said that he wants 173 00:08:12,510 --> 00:08:14,160 to get a quick resolution. 174 00:08:14,160 --> 00:08:17,760 Something very significant happened last week. 175 00:08:17,760 --> 00:08:21,900 And I don't know how many of you really got wind of it. 176 00:08:21,900 --> 00:08:23,920 Certainly, the Treasury knew what was going on 177 00:08:23,920 --> 00:08:26,430 and the Fed did, but it wasn't really highlighted 178 00:08:26,430 --> 00:08:29,336 in the newspapers in the way that I 179 00:08:29,336 --> 00:08:30,960 would have thought it should have been, 180 00:08:30,960 --> 00:08:31,835 given the importance. 181 00:08:31,835 --> 00:08:33,640 Anybody know what I'm talking about? 182 00:08:33,640 --> 00:08:34,630 Yeah. 183 00:08:34,630 --> 00:08:37,360 AUDIENCE: Stopping the short sell-- 184 00:08:37,360 --> 00:08:39,370 ANDREW LO: Well, that was one piece of news. 185 00:08:39,370 --> 00:08:42,580 The SEC mandated that for a period of time, 186 00:08:42,580 --> 00:08:44,560 to be determined, we are not allowed 187 00:08:44,560 --> 00:08:46,900 to short sell financial stocks because they wanted 188 00:08:46,900 --> 00:08:49,170 to stop the kind of run that there 189 00:08:49,170 --> 00:08:50,784 has been on these securities. 190 00:08:50,784 --> 00:08:52,450 I'm going to come back and talk about it 191 00:08:52,450 --> 00:08:54,070 in the end of this lecture because we're going 192 00:08:54,070 --> 00:08:55,154 to talk about short sales. 193 00:08:55,154 --> 00:08:56,778 But that's not what I was referring to. 194 00:08:56,778 --> 00:08:59,280 That's certainly a concern, but that's not the major concern 195 00:08:59,280 --> 00:09:01,030 that I think the market was responding to. 196 00:09:01,030 --> 00:09:01,530 Yeah. 197 00:09:01,530 --> 00:09:04,690 AUDIENCE: Was it the $8 billion of redemption in money funds? 198 00:09:04,690 --> 00:09:05,830 ANDREW LO: That's right. 199 00:09:05,830 --> 00:09:07,570 Where was that coming from? 200 00:09:07,570 --> 00:09:09,880 What was going on with that? 201 00:09:09,880 --> 00:09:11,682 Why did that happen? 202 00:09:11,682 --> 00:09:13,666 AUDIENCE: Because people are losing confidence 203 00:09:13,666 --> 00:09:17,010 in the short-term debt securities 204 00:09:17,010 --> 00:09:18,330 to put in money market funds. 205 00:09:18,330 --> 00:09:19,705 ANDREW LO: And was there a reason 206 00:09:19,705 --> 00:09:21,540 for that loss of confidence? 207 00:09:21,540 --> 00:09:24,890 I mean, money funds, what does that have to do with mortgages 208 00:09:24,890 --> 00:09:27,810 and Lehman and Goldman? 209 00:09:27,810 --> 00:09:28,914 What's the connection? 210 00:09:28,914 --> 00:09:30,690 AUDIENCE: Well, I just think more of it 211 00:09:30,690 --> 00:09:33,739 was a psychological reaction than it was an actual-- 212 00:09:33,739 --> 00:09:36,030 ANDREW LO: Absolutely, it was a psychological reaction, 213 00:09:36,030 --> 00:09:37,770 but did something trigger that? 214 00:09:37,770 --> 00:09:40,590 Is that psychological reaction completely unreasonable? 215 00:09:40,590 --> 00:09:42,810 If your grandmother asked you what she should do now 216 00:09:42,810 --> 00:09:44,940 with her money market fund, should you 217 00:09:44,940 --> 00:09:49,350 tell her, don't worry about it, just stay the course 218 00:09:49,350 --> 00:09:51,420 and see what happens? 219 00:09:51,420 --> 00:09:54,930 Something happened last week that is related exactly 220 00:09:54,930 --> 00:09:55,514 to that issue. 221 00:09:55,514 --> 00:09:56,596 So you're on to something. 222 00:09:56,596 --> 00:09:57,360 What it that? 223 00:09:57,360 --> 00:09:57,860 Megan. 224 00:09:57,860 --> 00:10:02,300 AUDIENCE: Well, one of the major money funds broke the buck. 225 00:10:02,300 --> 00:10:03,780 ANDREW LO: Broke the buck, exactly. 226 00:10:03,780 --> 00:10:04,488 Which money fund? 227 00:10:04,488 --> 00:10:05,162 Do you remember? 228 00:10:05,162 --> 00:10:06,994 AUDIENCE: Lehman, no, no. 229 00:10:06,994 --> 00:10:08,160 ANDREW LO: The Reserve Fund. 230 00:10:08,160 --> 00:10:09,180 AUDIENCE: It's the Reserve. 231 00:10:09,180 --> 00:10:11,180 ANDREW LO: The Reserve Fund is one of the first, 232 00:10:11,180 --> 00:10:13,200 if not the first, money market funds. 233 00:10:13,200 --> 00:10:14,740 And what is a money market fund? 234 00:10:14,740 --> 00:10:15,780 Do we know what that is? 235 00:10:15,780 --> 00:10:17,975 You all know what that money market fund as? 236 00:10:17,975 --> 00:10:20,100 You all probably have money in a money market fund. 237 00:10:20,100 --> 00:10:22,950 Whether you know it or not. 238 00:10:22,950 --> 00:10:25,320 Money market fund is a fund that contains 239 00:10:25,320 --> 00:10:29,610 relatively short-term and supposedly riskless 240 00:10:29,610 --> 00:10:33,960 securities, like CDs, treasuries, 241 00:10:33,960 --> 00:10:37,170 and other kinds of very, very safe assets. 242 00:10:37,170 --> 00:10:39,744 And what does it mean to break the buck? 243 00:10:39,744 --> 00:10:43,188 AUDIENCE: That for every dollar that people invested 244 00:10:43,188 --> 00:10:47,124 in money market funds had invested what they would 245 00:10:47,124 --> 00:10:48,582 be able to redeem at that time. 246 00:10:48,582 --> 00:10:49,290 ANDREW LO: Right. 247 00:10:49,290 --> 00:10:51,102 AUDIENCE: --less than already spent. 248 00:10:51,102 --> 00:10:51,810 ANDREW LO: Right. 249 00:10:51,810 --> 00:10:55,470 Breaking the buck means that when you put in $1, 250 00:10:55,470 --> 00:10:59,730 money funds are supposed to be so safe that at the very least 251 00:10:59,730 --> 00:11:03,710 when you withdraw the money, you're going to get $1 back. 252 00:11:03,710 --> 00:11:07,670 Breaking the buck means that if you withdraw, 253 00:11:07,670 --> 00:11:11,990 there is a possibility that what you withdraw is less than $1. 254 00:11:11,990 --> 00:11:16,100 Now that's scary because think about a bank-- 255 00:11:16,100 --> 00:11:21,710 when you put your money into a checking account for a bank, 256 00:11:21,710 --> 00:11:23,750 you expect to get that money out, maybe 257 00:11:23,750 --> 00:11:26,870 not with a lot of interest, maybe even with no interest 258 00:11:26,870 --> 00:11:30,450 if things don't go well, but you expect to get what you put in. 259 00:11:30,450 --> 00:11:33,920 You expect to get the principal back, right? 260 00:11:33,920 --> 00:11:36,320 Well, money market funds are very much the same way. 261 00:11:36,320 --> 00:11:39,429 People use them as if they were checking accounts. 262 00:11:39,429 --> 00:11:40,970 In fact, there are money market funds 263 00:11:40,970 --> 00:11:43,280 where you can write checks on them, right? 264 00:11:43,280 --> 00:11:47,180 And so breaking the buck has been a major concern, 265 00:11:47,180 --> 00:11:52,070 not just among the money funds, but among regulators. 266 00:11:52,070 --> 00:11:57,770 Because if it turns out that retail investors, 267 00:11:57,770 --> 00:12:01,340 ordinary consumers are scared about what's 268 00:12:01,340 --> 00:12:05,510 going on with their money market accounts, 269 00:12:05,510 --> 00:12:09,060 they will do in mass what happened last week, 270 00:12:09,060 --> 00:12:11,720 which is pull out huge sums of money 271 00:12:11,720 --> 00:12:14,120 from these money market funds. 272 00:12:14,120 --> 00:12:17,330 And as I mentioned earlier, no business 273 00:12:17,330 --> 00:12:23,300 can sustain a massive withdrawal of all capital all at once. 274 00:12:23,300 --> 00:12:25,160 It's just not possible for a business 275 00:12:25,160 --> 00:12:27,260 to be able to be conducted in that manner. 276 00:12:27,260 --> 00:12:31,520 If that happens, we will see mass failures 277 00:12:31,520 --> 00:12:35,960 of financial institutions that will make the last four weeks 278 00:12:35,960 --> 00:12:38,840 look like the good old days. 279 00:12:38,840 --> 00:12:41,130 And that's what the Fed is concerned about. 280 00:12:41,130 --> 00:12:43,080 That's what the Treasury is concerned about. 281 00:12:43,080 --> 00:12:46,190 And so the hope is that the measures that they put in place 282 00:12:46,190 --> 00:12:48,290 will calm the fears of the public. 283 00:12:48,290 --> 00:12:50,030 That's the first order of business. 284 00:12:50,030 --> 00:12:53,870 It's calming the psychological kinds of effects 285 00:12:53,870 --> 00:12:57,380 that these headlines have produced. 286 00:12:57,380 --> 00:12:59,300 And so the hope is that once they 287 00:12:59,300 --> 00:13:00,770 put these measures in place, that 288 00:13:00,770 --> 00:13:02,510 will take care of the concerns. 289 00:13:02,510 --> 00:13:05,300 What they've done is to propose to guarantee money market 290 00:13:05,300 --> 00:13:10,250 funds the same way that the FDIC guarantees your banking 291 00:13:10,250 --> 00:13:11,160 accounts. 292 00:13:11,160 --> 00:13:13,790 And the way that the SIPC guarantees your brokerage 293 00:13:13,790 --> 00:13:14,522 accounts. 294 00:13:14,522 --> 00:13:16,730 And there are other measures that have been proposed. 295 00:13:16,730 --> 00:13:18,560 We won't have time to talk about them here, 296 00:13:18,560 --> 00:13:20,060 but over the next couple of weeks, 297 00:13:20,060 --> 00:13:21,830 the finance group at the Sloan School 298 00:13:21,830 --> 00:13:24,320 will be putting together some kind of a panel discussion 299 00:13:24,320 --> 00:13:26,190 that will focus exactly on these issues. 300 00:13:26,190 --> 00:13:27,860 So we'll let you know when that happens. 301 00:13:27,860 --> 00:13:31,670 And we'll take on these issues head on in that session. 302 00:13:31,670 --> 00:13:34,430 OK, but it looks like for the moment, at least 303 00:13:34,430 --> 00:13:38,120 from the yield curves that we saw, 304 00:13:38,120 --> 00:13:41,240 that things are actually quieting down. 305 00:13:41,240 --> 00:13:44,360 We'll see on a day by day basis. 306 00:13:44,360 --> 00:13:46,730 So this is obviously last week. 307 00:13:46,730 --> 00:13:48,805 This week, we have yields going up a little bit, 308 00:13:48,805 --> 00:13:50,180 so that suggests that there isn't 309 00:13:50,180 --> 00:13:51,910 the same kind of pressure. 310 00:13:51,910 --> 00:13:55,850 But every day is another day and with another set 311 00:13:55,850 --> 00:13:56,750 of revelations. 312 00:13:56,750 --> 00:13:59,540 So by looking at these pieces of information, 313 00:13:59,540 --> 00:14:02,420 we can actually glean what the market is thinking. 314 00:14:02,420 --> 00:14:03,920 Is it right? 315 00:14:03,920 --> 00:14:04,700 Of course not. 316 00:14:04,700 --> 00:14:07,190 All forecasts are by construction 317 00:14:07,190 --> 00:14:09,590 incorrect to some degree, but it's 318 00:14:09,590 --> 00:14:12,792 a window on exactly what's going on in the marketplace 319 00:14:12,792 --> 00:14:14,000 and what people are thinking. 320 00:14:14,000 --> 00:14:14,990 Yeah. 321 00:14:14,990 --> 00:14:17,465 AUDIENCE: Sorry, what's the connection between this money 322 00:14:17,465 --> 00:14:18,950 market issue and the yield curve? 323 00:14:18,950 --> 00:14:20,750 Could you make the connection again? 324 00:14:20,750 --> 00:14:21,250 I missed it. 325 00:14:21,250 --> 00:14:22,166 ANDREW LO: Yeah, sure. 326 00:14:22,166 --> 00:14:25,460 So the money market concern is that what 327 00:14:25,460 --> 00:14:29,870 people thought were safe, apparently is not 328 00:14:29,870 --> 00:14:31,574 as safe as people thought. 329 00:14:31,574 --> 00:14:33,740 And the Reserve Fund breaking the buck-- by the way, 330 00:14:33,740 --> 00:14:35,630 breaking the buck in that case meant 331 00:14:35,630 --> 00:14:38,870 that if you put in a dollar, when you withdrew, 332 00:14:38,870 --> 00:14:40,700 as of last week, you would have withdrawn 333 00:14:40,700 --> 00:14:45,500 $0.97 so you'd lost $0.03 to the dollar, which may not 334 00:14:45,500 --> 00:14:49,730 seem like much, but if you went to your Bank of America ATM 335 00:14:49,730 --> 00:14:51,290 and you did a withdrawal. 336 00:14:51,290 --> 00:14:54,770 And for every dollar you put in, you'd get $0.97 back, 337 00:14:54,770 --> 00:14:57,020 you'd be pretty ticked off, right? 338 00:14:57,020 --> 00:14:59,787 So it's something that is of great concern 339 00:14:59,787 --> 00:15:00,620 to retail investors. 340 00:15:00,620 --> 00:15:03,230 Anyway, so what happened last week was that-- 341 00:15:03,230 --> 00:15:06,590 actually the estimate, I think, is $90 billion. $90 billion 342 00:15:06,590 --> 00:15:11,070 of money came out of these funds in a week 343 00:15:11,070 --> 00:15:15,270 and were put into either cash in the mattress 344 00:15:15,270 --> 00:15:18,510 or were put into Treasury securities 345 00:15:18,510 --> 00:15:20,190 like the three month T-bills. 346 00:15:20,190 --> 00:15:22,710 That's what pushed the prices of those T-bills 347 00:15:22,710 --> 00:15:25,140 up and therefore depressed the yields. 348 00:15:25,140 --> 00:15:28,740 And now we're back to a somewhat more reasonable level. 349 00:15:28,740 --> 00:15:31,600 I say reasonable because having this kind of a short-term yield 350 00:15:31,600 --> 00:15:35,290 of 40 basis points by historical standards is still pretty low. 351 00:15:35,290 --> 00:15:39,240 So there are still many nervous investors out there 352 00:15:39,240 --> 00:15:41,370 that are trying to figure out what's going on 353 00:15:41,370 --> 00:15:43,828 and are waiting for the Treasury to come up with something. 354 00:15:43,828 --> 00:15:46,230 This is another reason why Chairman Bernanke said 355 00:15:46,230 --> 00:15:49,740 we have to act quickly because markets are not 356 00:15:49,740 --> 00:15:52,890 going to stand and wait for the Treasury or the Fed 357 00:15:52,890 --> 00:15:54,540 to do something. 358 00:15:54,540 --> 00:15:55,770 Markets will react. 359 00:15:55,770 --> 00:16:00,180 And if we wait too long, the fear of this breaking the buck 360 00:16:00,180 --> 00:16:02,010 could actually return. 361 00:16:02,010 --> 00:16:05,670 And then once you have a mass panic, 362 00:16:05,670 --> 00:16:07,230 it's very, very hard to stop that. 363 00:16:07,230 --> 00:16:12,450 Anybody who's ever seen one of these old animal kingdom type 364 00:16:12,450 --> 00:16:15,420 of movies about a stampede-- 365 00:16:15,420 --> 00:16:19,410 if you've got water buffalo stampeding, 366 00:16:19,410 --> 00:16:24,180 it's pretty hard to try to just say, oh, calm down, stop it. 367 00:16:24,180 --> 00:16:25,350 Slow down. 368 00:16:25,350 --> 00:16:28,839 You can't easily do that once it begins. 369 00:16:28,839 --> 00:16:30,630 So you've got to stop it before it actually 370 00:16:30,630 --> 00:16:31,950 gets to that critical point. 371 00:16:31,950 --> 00:16:34,860 And that's exactly what the government is trying to do. 372 00:16:34,860 --> 00:16:35,966 Yes. 373 00:16:35,966 --> 00:16:39,110 AUDIENCE: When you say that-- if you interpret these, 374 00:16:39,110 --> 00:16:42,632 like the prices went down so now there's less demand so it means 375 00:16:42,632 --> 00:16:43,730 people are more relaxed-- 376 00:16:43,730 --> 00:16:44,470 ANDREW LO: Yeah. 377 00:16:44,470 --> 00:16:47,780 AUDIENCE: What if you say, like, if the interest rate went up, 378 00:16:47,780 --> 00:16:50,551 it means they are considering the Treasury bills 379 00:16:50,551 --> 00:16:52,890 to be more risky or riskier? 380 00:16:52,890 --> 00:16:55,140 ANDREW LO: Well, remember that Treasury bills 381 00:16:55,140 --> 00:17:00,510 don't have any default risk, at least as far as we know. 382 00:17:00,510 --> 00:17:02,520 We have to be careful about stating. 383 00:17:02,520 --> 00:17:04,410 All these unprecedented things have happened. 384 00:17:04,410 --> 00:17:06,990 The reason that Treasury bills don't have any default risk 385 00:17:06,990 --> 00:17:09,660 is because what the Treasury security 386 00:17:09,660 --> 00:17:13,349 is an IOU from the government that says I owe you 387 00:17:13,349 --> 00:17:15,420 a certain number of US dollars. 388 00:17:15,420 --> 00:17:17,694 And because the Treasury owns the printing press, 389 00:17:17,694 --> 00:17:20,069 they can always print out more dollars to give it to you, 390 00:17:20,069 --> 00:17:22,380 as long as you're willing to take it. 391 00:17:22,380 --> 00:17:25,440 And at least from this graph, it seems like a lot of people 392 00:17:25,440 --> 00:17:26,589 are willing to take it. 393 00:17:26,589 --> 00:17:29,040 They really want Treasury bills right now. 394 00:17:29,040 --> 00:17:30,720 And they're happy with that. 395 00:17:30,720 --> 00:17:33,660 Maybe they're not happy with it, but that's 396 00:17:33,660 --> 00:17:36,452 the smallest of all the evils that they can think of in terms 397 00:17:36,452 --> 00:17:37,410 of putting their money. 398 00:17:37,410 --> 00:17:42,060 AUDIENCE: So decreasing the yield in Treasury bonds 399 00:17:42,060 --> 00:17:44,670 do not mean an increase in the default risk? 400 00:17:44,670 --> 00:17:45,750 ANDREW LO: We hope not. 401 00:17:45,750 --> 00:17:47,340 I mean, I guess it could be possible 402 00:17:47,340 --> 00:17:48,870 that people are betting that the United States is 403 00:17:48,870 --> 00:17:50,310 going to default in 30 years. 404 00:17:50,310 --> 00:17:53,370 But my sense is that what's more likely, given 405 00:17:53,370 --> 00:17:55,890 that these are default free in the sense 406 00:17:55,890 --> 00:17:57,160 that their nominal bonds-- 407 00:17:57,160 --> 00:17:59,490 so these bonds are going to be paid off 408 00:17:59,490 --> 00:18:01,320 in the little certificates called 409 00:18:01,320 --> 00:18:03,600 US dollars that the printing presses can always 410 00:18:03,600 --> 00:18:04,380 come up with. 411 00:18:04,380 --> 00:18:06,960 There's no risk that they can't print up more dollars. 412 00:18:06,960 --> 00:18:10,080 The risk is that $1 30 years from now 413 00:18:10,080 --> 00:18:12,084 isn't going to be worth as much as we 414 00:18:12,084 --> 00:18:13,500 thought it was going to be because 415 00:18:13,500 --> 00:18:15,420 of inflationary expectations. 416 00:18:15,420 --> 00:18:20,868 So as of today, that 30 year yield is not 4%, it's 4.37% 417 00:18:20,868 --> 00:18:26,730 and the 0.37 one could attribute to an inflationary expectation 418 00:18:26,730 --> 00:18:28,047 by the marketplace. 419 00:18:28,047 --> 00:18:30,760 AUDIENCE: Do you think that the short-term change in the yield 420 00:18:30,760 --> 00:18:32,676 has anything to do with the recent devaluation 421 00:18:32,676 --> 00:18:35,700 of the dollar against foreign currencies? 422 00:18:35,700 --> 00:18:38,730 ANDREW LO: It could be that because of that devaluation, 423 00:18:38,730 --> 00:18:40,560 dollars are cheaper and people are putting 424 00:18:40,560 --> 00:18:42,780 more money into US securities. 425 00:18:42,780 --> 00:18:43,990 That's also a possibility. 426 00:18:43,990 --> 00:18:46,800 But another way of putting that is that foreign investors 427 00:18:46,800 --> 00:18:50,280 are now finding treasuries more attractive for whatever reason. 428 00:18:50,280 --> 00:18:54,930 So yes, that's also part of that supply and demand story. 429 00:18:54,930 --> 00:18:55,960 OK, last question. 430 00:18:55,960 --> 00:18:56,645 Yeah. 431 00:18:56,645 --> 00:18:58,769 AUDIENCE: Historically, what is a reasonable yield? 432 00:18:58,769 --> 00:19:01,437 You mentioned that before, like [INAUDIBLE] or before all 433 00:19:01,437 --> 00:19:02,120 this time? 434 00:19:02,120 --> 00:19:06,890 ANDREW LO: Well, I'm glad you asked that question because we 435 00:19:06,890 --> 00:19:09,590 have a graph. 436 00:19:09,590 --> 00:19:14,220 These are the historical yields of the three month, six month, 437 00:19:14,220 --> 00:19:16,490 one year, two year, five year, 10 year, and 30 year 438 00:19:16,490 --> 00:19:24,200 from 1962 to I think it's 2004. 439 00:19:24,200 --> 00:19:27,140 And it depends on what flavor you're looking at. 440 00:19:27,140 --> 00:19:29,180 And it's kind of hard to read this graph because 441 00:19:29,180 --> 00:19:29,763 of the colors. 442 00:19:29,763 --> 00:19:33,270 But if you look at the dark blue line, 443 00:19:33,270 --> 00:19:35,310 they actually all move together pretty much. 444 00:19:35,310 --> 00:19:41,090 But at one point, that short-term yield was 4%. 445 00:19:41,090 --> 00:19:44,857 4% for a three month Treasury bill. 446 00:19:44,857 --> 00:19:46,440 Now these are all annualized remember, 447 00:19:46,440 --> 00:19:49,010 so 4% doesn't mean 4% over three months. 448 00:19:49,010 --> 00:19:51,410 It means 4% on an annualized basis, 449 00:19:51,410 --> 00:19:53,720 which is why 41 basis points-- 450 00:19:53,720 --> 00:19:55,970 that's an annualized yield-- 451 00:19:55,970 --> 00:19:59,600 for a three month loan just seems ridiculously 452 00:19:59,600 --> 00:20:03,640 small by historical standards. 453 00:20:03,640 --> 00:20:06,580 But when people are scared about not getting paid, 454 00:20:06,580 --> 00:20:09,130 that kind of fear, that psychological pressure 455 00:20:09,130 --> 00:20:10,822 can be overwhelming. 456 00:20:10,822 --> 00:20:12,280 And do you believe in these prices? 457 00:20:12,280 --> 00:20:13,220 Does it make sense? 458 00:20:13,220 --> 00:20:16,600 Well, that I'm hoping to get you not 459 00:20:16,600 --> 00:20:19,600 to ask the question in that way, but rather to ask 460 00:20:19,600 --> 00:20:21,460 the question, given market prices and what 461 00:20:21,460 --> 00:20:25,310 I know about it, what can I interpret from what's going on 462 00:20:25,310 --> 00:20:27,400 and how does that affect me in terms 463 00:20:27,400 --> 00:20:29,990 of the financial decisions that I want to make. 464 00:20:29,990 --> 00:20:33,700 So if you are thinking about pricing other securities based 465 00:20:33,700 --> 00:20:36,610 upon these kinds of numbers, you need 466 00:20:36,610 --> 00:20:38,200 to ask yourself whether you believe 467 00:20:38,200 --> 00:20:40,720 the numbers make sense or are they 468 00:20:40,720 --> 00:20:42,910 just completely out of whack. 469 00:20:42,910 --> 00:20:45,100 And the only way to do that is to understand what 470 00:20:45,100 --> 00:20:47,090 the basis is for these numbers. 471 00:20:47,090 --> 00:20:48,940 So that's where we're going next in trying 472 00:20:48,940 --> 00:20:51,425 to understand how to measure the various different 473 00:20:51,425 --> 00:20:53,800 characteristics of these numbers to get a sense of what's 474 00:20:53,800 --> 00:20:55,070 reasonable and what's not. 475 00:20:55,070 --> 00:20:55,570 Question. 476 00:20:55,570 --> 00:20:56,695 AUDIENCE: I had a question. 477 00:20:56,695 --> 00:20:59,538 I was wondering, those sort of funds, Treasury bills, 478 00:20:59,538 --> 00:21:03,258 [INAUDIBLE], is that really individual people buying 479 00:21:03,258 --> 00:21:05,738 the Treasury bills or is it more hedge funds and that sort 480 00:21:05,738 --> 00:21:09,210 of thing that are systematically hedging the risk against other 481 00:21:09,210 --> 00:21:11,470 securities they have that are-- 482 00:21:11,470 --> 00:21:13,760 ANDREW LO: Well, obviously, it's very difficult 483 00:21:13,760 --> 00:21:16,520 to tell because we don't see who's making the purchases 484 00:21:16,520 --> 00:21:20,690 and sales, but we can tell from certain mutual funds 485 00:21:20,690 --> 00:21:23,240 and other money market flows that it 486 00:21:23,240 --> 00:21:26,030 seems like most of the flows last week came 487 00:21:26,030 --> 00:21:30,110 not from hedge funds, but rather from retail investors that 488 00:21:30,110 --> 00:21:32,840 were taking their money out of these money market accounts 489 00:21:32,840 --> 00:21:36,440 and then putting them into certain mutual funds that 490 00:21:36,440 --> 00:21:40,790 buy only Treasury securities, as well as Treasury securities 491 00:21:40,790 --> 00:21:41,570 directly. 492 00:21:41,570 --> 00:21:45,950 All of you can actually purchase Treasury securities directly. 493 00:21:45,950 --> 00:21:48,710 There is a website called TreasuryDirect.gov 494 00:21:48,710 --> 00:21:51,950 and you can give them your credit card 495 00:21:51,950 --> 00:21:54,560 and register as a user and actually 496 00:21:54,560 --> 00:21:58,770 participate in Treasury auctions and buy Treasury securities. 497 00:21:58,770 --> 00:22:00,650 So it was a combination of those. 498 00:22:00,650 --> 00:22:03,290 But it really seemed like it was the retail sector, 499 00:22:03,290 --> 00:22:06,140 not institutions, not sophisticated hedge 500 00:22:06,140 --> 00:22:09,230 funds that we're trying to do some kind of complex arbitrage. 501 00:22:09,230 --> 00:22:11,810 It was just investors saying, I'm really scared, 502 00:22:11,810 --> 00:22:14,720 I want to put my money into something that's real 503 00:22:14,720 --> 00:22:16,620 and that will be there. 504 00:22:16,620 --> 00:22:18,980 And so short-term treasuries seemed like an answer. 505 00:22:18,980 --> 00:22:22,610 And as we saw from last week, gold was the other answer. 506 00:22:22,610 --> 00:22:24,650 It's not an answer that I would propose 507 00:22:24,650 --> 00:22:27,890 for the typical investor because gold prices are quite volatile. 508 00:22:27,890 --> 00:22:30,770 And so you have to be very careful 509 00:22:30,770 --> 00:22:32,990 when you make an investment in that security 510 00:22:32,990 --> 00:22:35,240 or in that particular asset. 511 00:22:35,240 --> 00:22:38,540 But it is something that reflects the state of panic 512 00:22:38,540 --> 00:22:39,952 of the marketplace. 513 00:22:39,952 --> 00:22:42,410 And by the way, I'm telling you something that you probably 514 00:22:42,410 --> 00:22:44,720 already know in the sense that-- 515 00:22:44,720 --> 00:22:47,720 my guess is that deep down inside, all of you 516 00:22:47,720 --> 00:22:49,280 are feeling stressed out, right? 517 00:22:49,280 --> 00:22:50,990 I mean, you're probably stressed out 518 00:22:50,990 --> 00:22:53,510 about things like what does this mean for the job market, 519 00:22:53,510 --> 00:22:56,690 for career prospects, and so on. 520 00:22:56,690 --> 00:22:59,720 I would urge you all to take a deep breath 521 00:22:59,720 --> 00:23:03,350 and not get panicked about that because, as I said, 522 00:23:03,350 --> 00:23:07,310 this is the kind of dislocation that, while very 523 00:23:07,310 --> 00:23:09,920 traumatic for market participants today 524 00:23:09,920 --> 00:23:12,380 and for those on the losing end, there 525 00:23:12,380 --> 00:23:15,200 are as many opportunities created 526 00:23:15,200 --> 00:23:18,060 as there are taken away. 527 00:23:18,060 --> 00:23:20,870 And so my guess is that in a year's time, 528 00:23:20,870 --> 00:23:23,670 the job market is going to look extraordinarily attractive, 529 00:23:23,670 --> 00:23:26,000 particularly for those individuals that 530 00:23:26,000 --> 00:23:31,110 are trained in the science and art of financial analysis. 531 00:23:31,110 --> 00:23:33,740 So you're all going to be very well equipped for that, 532 00:23:33,740 --> 00:23:35,540 even though you may not feel that way 533 00:23:35,540 --> 00:23:38,100 right now because of what's going on in the marketplace. 534 00:23:38,100 --> 00:23:40,910 So I wouldn't panic certainly. 535 00:23:40,910 --> 00:23:43,160 And by the way, you can see the opportunities 536 00:23:43,160 --> 00:23:44,600 that are already being created. 537 00:23:44,600 --> 00:23:48,740 Warren Buffett just spent $5 billion 538 00:23:48,740 --> 00:23:50,734 purchasing a stake in Goldman Sachs. 539 00:23:50,734 --> 00:23:53,150 And we're going to talk about that in a couple of lectures 540 00:23:53,150 --> 00:23:54,740 when we do common stock because I 541 00:23:54,740 --> 00:24:01,040 want to use it as an example of getting a good deal in markets. 542 00:24:01,040 --> 00:24:04,460 I mean, first of all, Warren Buffett given the success he's 543 00:24:04,460 --> 00:24:08,030 enjoyed as an investor, you know that when he plunks down 544 00:24:08,030 --> 00:24:10,580 $5 billion in cash, he's probably 545 00:24:10,580 --> 00:24:14,060 doing it for a good reason, not out of charity. 546 00:24:14,060 --> 00:24:17,330 And by the way, Goldman raised another $5 billion 547 00:24:17,330 --> 00:24:19,820 from additional rights issues. 548 00:24:19,820 --> 00:24:23,210 That's $10 billion of capital that they 549 00:24:23,210 --> 00:24:26,390 raised relatively quickly. 550 00:24:26,390 --> 00:24:29,150 Also Nomura is in the negotiations 551 00:24:29,150 --> 00:24:32,150 to purchase certain assets of Lehman Brothers. 552 00:24:32,150 --> 00:24:34,640 Lehman has a terrific franchise and has 553 00:24:34,640 --> 00:24:38,390 some very significant operations in Asia, as well as in the US. 554 00:24:38,390 --> 00:24:40,747 And it's a very smart move on Nomura's part 555 00:24:40,747 --> 00:24:41,830 to take advantage of that. 556 00:24:41,830 --> 00:24:43,190 So these are the kind of opportunities 557 00:24:43,190 --> 00:24:43,939 I'm talking about. 558 00:24:43,939 --> 00:24:46,220 And when Nomura buys Lehman, they're 559 00:24:46,220 --> 00:24:47,930 going to have to hire people in order 560 00:24:47,930 --> 00:24:50,060 to run the operations because you 561 00:24:50,060 --> 00:24:52,880 can bet that the whole dislocation ended up 562 00:24:52,880 --> 00:24:57,230 shaking loose a number of very talented professionals 563 00:24:57,230 --> 00:24:59,090 from those organizations. 564 00:24:59,090 --> 00:25:00,560 So they got to hire. 565 00:25:00,560 --> 00:25:03,230 It's going to mean the next two or three months, 566 00:25:03,230 --> 00:25:05,360 there may be some difficulties in getting 567 00:25:05,360 --> 00:25:07,610 the attention of these organizations 568 00:25:07,610 --> 00:25:10,580 because they're in the midst of trying to figure out exactly 569 00:25:10,580 --> 00:25:14,050 what kind of organization they are going to have 570 00:25:14,050 --> 00:25:15,530 when all the dust settles. 571 00:25:15,530 --> 00:25:17,270 But there are plenty of opportunities 572 00:25:17,270 --> 00:25:20,360 that are being created today, including, by the way, 573 00:25:20,360 --> 00:25:22,130 the opportunity for the US government 574 00:25:22,130 --> 00:25:24,724 to take advantage of all of these distressed assets. 575 00:25:24,724 --> 00:25:27,140 So one of the things that you should be careful about when 576 00:25:27,140 --> 00:25:29,510 you read that there's a $700 billion 577 00:25:29,510 --> 00:25:32,690 bailout, that is somewhat misleading in the sense 578 00:25:32,690 --> 00:25:35,210 that, first of all, we don't really know at this point 579 00:25:35,210 --> 00:25:38,660 exactly what the $700 billion will be for, 580 00:25:38,660 --> 00:25:40,730 how it will be used, or how it's dispersed, 581 00:25:40,730 --> 00:25:42,920 or is it really $700 billion. 582 00:25:42,920 --> 00:25:44,960 A lot of it depends upon how the money is spent 583 00:25:44,960 --> 00:25:47,040 and also what happens to housing markets. 584 00:25:47,040 --> 00:25:48,950 There is a scenario that I can imagine 585 00:25:48,950 --> 00:25:54,150 where the actual amount expended is either zero or negative. 586 00:25:54,150 --> 00:25:56,600 In other words, the government actually makes money 587 00:25:56,600 --> 00:25:59,420 from the current state of the markets because they 588 00:25:59,420 --> 00:26:03,410 can buy assets very cheaply, hold onto them forever 589 00:26:03,410 --> 00:26:07,470 until they pay off, and then gain the kind of profit 590 00:26:07,470 --> 00:26:11,340 that the original financial engineers were expecting 591 00:26:11,340 --> 00:26:14,490 but could not take advantage of because of this liquidity 592 00:26:14,490 --> 00:26:15,120 crunch. 593 00:26:15,120 --> 00:26:17,460 So we'll talk about that over the next few lectures 594 00:26:17,460 --> 00:26:19,650 because we're going to develop some techniques to be 595 00:26:19,650 --> 00:26:24,300 able to illustrate how these kind of arbitrage strategies 596 00:26:24,300 --> 00:26:24,960 work. 597 00:26:24,960 --> 00:26:26,006 Yeah. 598 00:26:26,006 --> 00:26:28,810 AUDIENCE: Thinking about Nomura, is it more certain 599 00:26:28,810 --> 00:26:31,190 that it's going to happen or are there many plans 600 00:26:31,190 --> 00:26:33,050 that are trying to buy the [INAUDIBLE]. 601 00:26:33,050 --> 00:26:35,370 ANDREW LO: Well, certainly there are a number of banks. 602 00:26:35,370 --> 00:26:37,080 I wouldn't say many, simply because there 603 00:26:37,080 --> 00:26:39,660 aren't that many banks that are well capitalized enough 604 00:26:39,660 --> 00:26:43,410 to be able to take on a large unit of a business 605 00:26:43,410 --> 00:26:44,730 as big as Lehman Brothers. 606 00:26:44,730 --> 00:26:48,090 So Nomura is one of a handful of banks that are engaged, 607 00:26:48,090 --> 00:26:51,775 but they seem to be the front runner at this point. 608 00:26:51,775 --> 00:26:53,275 AUDIENCE: Generally, what I've heard 609 00:26:53,275 --> 00:26:56,897 kind of from the Asian analyst in Lehman 610 00:26:56,897 --> 00:26:59,230 that I had spoken to is that it's quite likely that that 611 00:26:59,230 --> 00:27:01,302 might be not be true as well because we 612 00:27:01,302 --> 00:27:03,402 find a lot of [INAUDIBLE]. 613 00:27:03,402 --> 00:27:04,750 ANDREW LO: Oh, absolutely. 614 00:27:04,750 --> 00:27:06,940 There are a number of issues that will come up 615 00:27:06,940 --> 00:27:07,930 in any kind of a deal. 616 00:27:07,930 --> 00:27:09,430 And so you don't know whether or not 617 00:27:09,430 --> 00:27:12,096 something is going to go through until it actually goes through. 618 00:27:12,096 --> 00:27:14,800 The same thing could be said for what happened 619 00:27:14,800 --> 00:27:19,270 with Merrill Lynch, with AIG. 620 00:27:19,270 --> 00:27:21,910 All of these deals are sort of put together 621 00:27:21,910 --> 00:27:23,270 at the last minute. 622 00:27:23,270 --> 00:27:25,870 And either they get consummated or there's 623 00:27:25,870 --> 00:27:28,040 some hitch at the end that makes it difficult. 624 00:27:28,040 --> 00:27:30,100 So yeah, I mean, with a grain of salt, 625 00:27:30,100 --> 00:27:32,260 you should take all of these news reports. 626 00:27:32,260 --> 00:27:34,400 And literally until the deal is signed, 627 00:27:34,400 --> 00:27:36,400 you will not know whether or not something's on. 628 00:27:36,400 --> 00:27:40,480 But the point I'm illustrating is that these assets are not 629 00:27:40,480 --> 00:27:41,500 completely worthless. 630 00:27:41,500 --> 00:27:44,560 What's happened is a very significant liquidity crunch 631 00:27:44,560 --> 00:27:45,820 and panic. 632 00:27:45,820 --> 00:27:47,980 When that happens, the pricing of all these assets 633 00:27:47,980 --> 00:27:49,340 becomes questionable. 634 00:27:49,340 --> 00:27:49,960 OK. 635 00:27:49,960 --> 00:27:51,350 We're going to actually see an example of that. 636 00:27:51,350 --> 00:27:54,040 So if you wouldn't mind, let me put that off for a few minutes. 637 00:27:54,040 --> 00:27:56,123 And then if you have further questions about this, 638 00:27:56,123 --> 00:27:57,610 we can come back to it. 639 00:27:57,610 --> 00:28:01,840 Let me start-- so this is lecture six. 640 00:28:01,840 --> 00:28:03,850 And what I want to do is to start 641 00:28:03,850 --> 00:28:07,360 where we ended last time, which was a discussion of coupon 642 00:28:07,360 --> 00:28:10,300 bonds and how you price coupon bonds simply 643 00:28:10,300 --> 00:28:15,520 as a package or a portfolio of pure discount bonds. 644 00:28:15,520 --> 00:28:19,480 Underlying this approach to pricing coupon bonds 645 00:28:19,480 --> 00:28:22,420 is a very important principle. 646 00:28:22,420 --> 00:28:24,460 That's a principle that was given 647 00:28:24,460 --> 00:28:26,590 to you in the very first day of class 648 00:28:26,590 --> 00:28:28,900 where we talked about the six fundamental principles 649 00:28:28,900 --> 00:28:30,820 of financial markets. 650 00:28:30,820 --> 00:28:33,290 And it's the principle of the law of one price. 651 00:28:33,290 --> 00:28:35,890 So what I want to do today is to focus on that 652 00:28:35,890 --> 00:28:37,690 and talk about the law of one price 653 00:28:37,690 --> 00:28:42,430 and what it means for things like arbitrage, leverage, 654 00:28:42,430 --> 00:28:46,030 short selling, and relative pricing. 655 00:28:46,030 --> 00:28:48,582 Those are the key concepts we're going to cover today. 656 00:28:48,582 --> 00:28:50,290 So let me talk about the law of one price 657 00:28:50,290 --> 00:28:52,000 and remind you all what it is. 658 00:28:52,000 --> 00:28:53,270 It's a very simple idea. 659 00:28:53,270 --> 00:28:56,290 It's so simple that you might think it's obvious, 660 00:28:56,290 --> 00:29:01,060 but it's got some very, very dramatic implications. 661 00:29:01,060 --> 00:29:09,430 The law of one price says that two identical cash flows must 662 00:29:09,430 --> 00:29:13,800 have the same market price. 663 00:29:13,800 --> 00:29:14,300 OK. 664 00:29:14,300 --> 00:29:15,091 Let me repeat that. 665 00:29:15,091 --> 00:29:21,090 Two identical cash flows must have the same price. 666 00:29:21,090 --> 00:29:24,930 Now remember that when we think of an asset. 667 00:29:24,930 --> 00:29:27,540 We think of an asset as just the sequence of cash flows. 668 00:29:27,540 --> 00:29:29,480 That's what an asset is. 669 00:29:29,480 --> 00:29:33,810 So all I'm saying is that when you have two identical assets, 670 00:29:33,810 --> 00:29:36,460 they have to have the same price. 671 00:29:36,460 --> 00:29:39,250 That's not a very controversial statement. 672 00:29:39,250 --> 00:29:43,720 And this principle is one of the most important ideas 673 00:29:43,720 --> 00:29:45,250 in all of modern finance because it 674 00:29:45,250 --> 00:29:48,890 leads to the pricing of all sorts of securities, 675 00:29:48,890 --> 00:29:51,520 including all the derivatives that have ever 676 00:29:51,520 --> 00:29:53,320 been priced on Wall Street. 677 00:29:53,320 --> 00:29:56,340 They use this idea of the law of one price, OK. 678 00:29:56,340 --> 00:29:56,840 Yeah. 679 00:29:56,840 --> 00:29:58,798 AUDIENCE: But wouldn't you have to qualify that 680 00:29:58,798 --> 00:30:00,500 by saying it's at equilibrium? 681 00:30:00,500 --> 00:30:02,620 ANDREW LO: No, no. 682 00:30:02,620 --> 00:30:05,110 I don't have to qualify that at all. 683 00:30:05,110 --> 00:30:06,880 First, because this is a free country 684 00:30:06,880 --> 00:30:09,700 and I don't have to do anything I don't want to do. 685 00:30:09,700 --> 00:30:12,940 But more importantly, it's because I 686 00:30:12,940 --> 00:30:16,780 don't want to restrict it to an equilibrium. 687 00:30:16,780 --> 00:30:21,190 By equilibrium, you mean when supply equals demand, right? 688 00:30:21,190 --> 00:30:23,140 I don't care about supply and demand. 689 00:30:23,140 --> 00:30:26,380 Supply may very well not equal demand. 690 00:30:26,380 --> 00:30:28,460 That's OK with me. 691 00:30:28,460 --> 00:30:32,690 This principle of the law of one price, that two identical cash 692 00:30:32,690 --> 00:30:34,820 flows have to have the same market 693 00:30:34,820 --> 00:30:39,020 price, the only assumption that I need in order for that law 694 00:30:39,020 --> 00:30:44,720 to be true is that people prefer more money to less money. 695 00:30:44,720 --> 00:30:46,570 And it's not even people. 696 00:30:46,570 --> 00:30:49,730 I just need one person in the economy that prefers 697 00:30:49,730 --> 00:30:51,440 more money to less money. 698 00:30:51,440 --> 00:30:56,460 And I'm happy to volunteer for that position, OK? 699 00:30:56,460 --> 00:30:57,340 Why is that? 700 00:30:57,340 --> 00:31:03,810 It's because if that law is violated, if you can show me 701 00:31:03,810 --> 00:31:08,270 two identical cash flows that sell for different market 702 00:31:08,270 --> 00:31:13,460 prices, first of all, tell nobody but me about it. 703 00:31:13,460 --> 00:31:20,270 What I'm going to do is I'm going to buy the cheaper asset, 704 00:31:20,270 --> 00:31:24,530 I'm going to sell the more expensive asset. 705 00:31:24,530 --> 00:31:28,370 So as of today, I make money, right, 706 00:31:28,370 --> 00:31:31,550 because I bought the cheap, I sold the more expensive. 707 00:31:31,550 --> 00:31:35,060 That difference is positive for me. 708 00:31:35,060 --> 00:31:38,010 And then I argue that from that point on, 709 00:31:38,010 --> 00:31:41,960 I have no further risk and, in fact, no further obligations. 710 00:31:41,960 --> 00:31:45,710 I can just forget about the deal and take my money and spend it. 711 00:31:45,710 --> 00:31:46,400 Why? 712 00:31:46,400 --> 00:31:50,460 Because I've bought and sold identical cash flows. 713 00:31:50,460 --> 00:31:52,610 So from that point on in the future, 714 00:31:52,610 --> 00:31:56,450 all the cash flows cancel out. 715 00:31:56,450 --> 00:31:58,140 So I'm done. 716 00:31:58,140 --> 00:32:05,174 That's called an arbitrage, or more technically, a free lunch. 717 00:32:05,174 --> 00:32:07,090 I've been able to create money out of nothing. 718 00:32:07,090 --> 00:32:09,420 It doesn't assume supply equals demand. 719 00:32:09,420 --> 00:32:13,020 It doesn't assume any kind of mathematical formula 720 00:32:13,020 --> 00:32:14,940 for any kind of instrument. 721 00:32:14,940 --> 00:32:18,480 All it assumes is that more people 722 00:32:18,480 --> 00:32:21,330 prefer more money to less. 723 00:32:21,330 --> 00:32:23,580 AUDIENCE: So that means so that day when you auctioned 724 00:32:23,580 --> 00:32:25,860 the iPhone, then the only difference 725 00:32:25,860 --> 00:32:28,600 between an open package and the concealed packaged 726 00:32:28,600 --> 00:32:31,960 was that in one case you basically did not 727 00:32:31,960 --> 00:32:33,072 give enough information. 728 00:32:33,072 --> 00:32:33,780 ANDREW LO: Right. 729 00:32:33,780 --> 00:32:36,879 AUDIENCE: And it wasn't reaching a fair value and so-- 730 00:32:36,879 --> 00:32:38,920 ANDREW LO: Well, wait, wait, wait, wait a minute. 731 00:32:38,920 --> 00:32:42,059 Well, when you say fair value, that's a loaded term. 732 00:32:42,059 --> 00:32:43,350 What do you mean by fair value? 733 00:32:43,350 --> 00:32:46,380 It was a fair value, given all the information 734 00:32:46,380 --> 00:32:47,310 that the market had. 735 00:32:47,310 --> 00:32:49,726 AUDIENCE: But it's not because [INAUDIBLE] of that object. 736 00:32:49,726 --> 00:32:51,750 When the person buys objects that's packaged, 737 00:32:51,750 --> 00:32:54,076 once they open it, they'll know that the cash 738 00:32:54,076 --> 00:32:58,542 flow of that object is the same as if it were not packaged. 739 00:32:58,542 --> 00:33:00,355 And they're going to read the [INAUDIBLE], 740 00:33:00,355 --> 00:33:01,230 as we just mentioned. 741 00:33:01,230 --> 00:33:02,220 ANDREW LO: That's right, but don't you 742 00:33:02,220 --> 00:33:04,530 think there's a difference between the package wrapped 743 00:33:04,530 --> 00:33:06,047 and the package unwrapped? 744 00:33:06,047 --> 00:33:07,380 AUDIENCE: Yeah, one of them is-- 745 00:33:07,380 --> 00:33:08,915 I mean, it's just like a factory which 746 00:33:08,915 --> 00:33:11,090 will produce the same stuff but is valued at the market 747 00:33:11,090 --> 00:33:12,530 at a lower price than what it would be-- 748 00:33:12,530 --> 00:33:14,370 ANDREW LO: Right, but if one factory didn't tell you 749 00:33:14,370 --> 00:33:16,440 how it produced it and another factory did. 750 00:33:16,440 --> 00:33:18,740 You think that they would sell for the same price? 751 00:33:18,740 --> 00:33:21,031 AUDIENCE: The factories wouldn't, but their future cash 752 00:33:21,031 --> 00:33:23,100 flow into revenue could be the same. 753 00:33:23,100 --> 00:33:25,990 ANDREW LO: Only if it turns out that, as a matter of fact, 754 00:33:25,990 --> 00:33:27,300 it is identical. 755 00:33:27,300 --> 00:33:29,760 But you don't know that ahead of time. 756 00:33:29,760 --> 00:33:33,640 You can only price something with the information you have, 757 00:33:33,640 --> 00:33:34,380 OK. 758 00:33:34,380 --> 00:33:37,020 So when I say two cash flows are identical, 759 00:33:37,020 --> 00:33:40,620 I'm saying that we acknowledge that the cash 760 00:33:40,620 --> 00:33:43,140 flows are, in fact, identical. 761 00:33:43,140 --> 00:33:45,690 And we know that they're identical. 762 00:33:45,690 --> 00:33:48,350 If I put two packages upfront in the room, one is an iPod 763 00:33:48,350 --> 00:33:51,780 and the other one is wrapped so it looks like an iPod. 764 00:33:51,780 --> 00:33:54,450 It's got the same shape, the same dimensions, 765 00:33:54,450 --> 00:33:56,590 but it's wrapped. 766 00:33:56,590 --> 00:33:58,600 Would you say that they're identical? 767 00:33:58,600 --> 00:34:00,610 You can't know that. 768 00:34:00,610 --> 00:34:04,180 If you knew that, then you would price it accordingly. 769 00:34:04,180 --> 00:34:06,280 By the way, that gives you a very important piece 770 00:34:06,280 --> 00:34:07,880 of information. 771 00:34:07,880 --> 00:34:09,580 Suppose that I did that experiment, I 772 00:34:09,580 --> 00:34:14,272 had the iPod that was clearly unwrapped and it was an iPod. 773 00:34:14,272 --> 00:34:15,730 And then I had another package that 774 00:34:15,730 --> 00:34:19,449 was the identical dimension but it was wrapped, OK. 775 00:34:19,449 --> 00:34:25,179 And I auctioned them off and it became clear initially 776 00:34:25,179 --> 00:34:31,050 that the two were priced at about the same. 777 00:34:31,050 --> 00:34:34,500 Well, if you saw that, you would then 778 00:34:34,500 --> 00:34:39,710 know that it was quite likely that what 779 00:34:39,710 --> 00:34:41,719 was in the wrapped package was the same as what 780 00:34:41,719 --> 00:34:43,514 was in the unwrapped package, right? 781 00:34:43,514 --> 00:34:45,139 But the only reason you would know that 782 00:34:45,139 --> 00:34:47,810 is because somebody in the audience 783 00:34:47,810 --> 00:34:50,310 apparently bid the same price. 784 00:34:50,310 --> 00:34:52,190 Now why would they do that? 785 00:34:52,190 --> 00:34:56,389 Either they're knuckleheads or they know something 786 00:34:56,389 --> 00:34:57,590 that you don't know. 787 00:34:57,590 --> 00:34:59,390 And now that you looked at the price, 788 00:34:59,390 --> 00:35:03,030 you actually learn something about what's in there. 789 00:35:03,030 --> 00:35:08,330 So what matters for pricing is what the entire market knows, 790 00:35:08,330 --> 00:35:11,690 not just what you know, but what the entire market knows. 791 00:35:11,690 --> 00:35:13,290 Now going back to this arbitrage, 792 00:35:13,290 --> 00:35:15,290 let's not worry about informational asymmetries. 793 00:35:15,290 --> 00:35:18,740 So let's assume that we all know exactly what there is to know, 794 00:35:18,740 --> 00:35:22,090 which is that these two securities have the same cash 795 00:35:22,090 --> 00:35:22,850 flow. 796 00:35:22,850 --> 00:35:24,800 If they have the same cash flow, they've 797 00:35:24,800 --> 00:35:26,180 got to have the same price. 798 00:35:26,180 --> 00:35:29,340 And that's exactly what we saw last time with this example. 799 00:35:29,340 --> 00:35:31,940 Same cash flows and therefore, they 800 00:35:31,940 --> 00:35:33,470 have to have the same price. 801 00:35:33,470 --> 00:35:36,320 If they don't have the same price, then instead 802 00:35:36,320 --> 00:35:41,090 of feeling upset and despondent that somehow finance theory is 803 00:35:41,090 --> 00:35:44,900 in question, the most exciting thing for a finance professor 804 00:35:44,900 --> 00:35:48,040 is to see that this theory breaks down, 805 00:35:48,040 --> 00:35:52,320 because then we actually can go transact in the marketplace 806 00:35:52,320 --> 00:35:53,670 and make money. 807 00:35:53,670 --> 00:35:55,440 So if the law of one price fails, 808 00:35:55,440 --> 00:35:59,430 instead of calling me up and complaining about it, 809 00:35:59,430 --> 00:36:01,170 you should call me up and tell me 810 00:36:01,170 --> 00:36:03,390 what it is so I can take advantage of it, all right? 811 00:36:03,390 --> 00:36:05,040 It's a great thing. 812 00:36:05,040 --> 00:36:07,050 And here's the example. 813 00:36:07,050 --> 00:36:10,710 This price of a coupon bond is got 814 00:36:10,710 --> 00:36:15,810 to be equal to the prices of the discount bonds multiplied 815 00:36:15,810 --> 00:36:19,800 by the number of bonds you need in order to yield 816 00:36:19,800 --> 00:36:22,660 an identical cash flow. 817 00:36:22,660 --> 00:36:23,770 OK. 818 00:36:23,770 --> 00:36:25,829 Now if you have an identical cash flow, 819 00:36:25,829 --> 00:36:28,120 the left-hand side has to equal to the right-hand side. 820 00:36:28,120 --> 00:36:31,810 If it doesn't, if the price of the left-hand side 821 00:36:31,810 --> 00:36:35,020 is greater than the prices of the right-hand side, 822 00:36:35,020 --> 00:36:38,350 then you should feel very happy because what you're going to do 823 00:36:38,350 --> 00:36:39,112 is to make money. 824 00:36:39,112 --> 00:36:40,820 Now how much money are you going to make? 825 00:36:40,820 --> 00:36:41,980 Well, let's see. 826 00:36:41,980 --> 00:36:43,900 What you're going to do is you're going 827 00:36:43,900 --> 00:36:45,640 to buy the right-hand side. 828 00:36:45,640 --> 00:36:47,880 You're going to buy those bonds and you're 829 00:36:47,880 --> 00:36:51,700 gonna sell the left-hand side bond, so what you make 830 00:36:51,700 --> 00:36:53,590 is that difference, right? 831 00:36:53,590 --> 00:36:55,447 Because you're buying, you're spending 832 00:36:55,447 --> 00:36:56,530 a certain amount of money. 833 00:36:56,530 --> 00:36:58,540 That's the right-hand amount of money. 834 00:36:58,540 --> 00:37:01,780 And the left-hand side is what you're going to get. 835 00:37:01,780 --> 00:37:04,840 And so you're actually going to be 836 00:37:04,840 --> 00:37:08,050 able to make that difference. 837 00:37:08,050 --> 00:37:10,080 But here's the key. 838 00:37:10,080 --> 00:37:14,280 When you make that difference, it's not a risky investment. 839 00:37:14,280 --> 00:37:17,400 There is no risk. 840 00:37:17,400 --> 00:37:20,550 By the way, how much money did you have to spend? 841 00:37:20,550 --> 00:37:23,400 How much of your own personal wealth 842 00:37:23,400 --> 00:37:27,285 did you have to commit to this trade? 843 00:37:27,285 --> 00:37:28,789 AUDIENCE: Just the risk. 844 00:37:28,789 --> 00:37:29,830 ANDREW LO: Just the risk? 845 00:37:29,830 --> 00:37:31,266 What risk? 846 00:37:31,266 --> 00:37:33,266 AUDIENCE: The difference between them the moment 847 00:37:33,266 --> 00:37:34,220 they can buy and sell. 848 00:37:34,220 --> 00:37:35,969 ANDREW LO: Did you have to spend that? 849 00:37:35,969 --> 00:37:37,260 AUDIENCE: You can guarantee it. 850 00:37:37,260 --> 00:37:38,840 ANDREW LO: That's money that you get, 851 00:37:38,840 --> 00:37:40,520 not that you have to spend. 852 00:37:40,520 --> 00:37:42,770 Is there any money that comes out of your pocket 853 00:37:42,770 --> 00:37:44,480 to do this trade? 854 00:37:44,480 --> 00:37:48,350 No, because what you are buying is actually 855 00:37:48,350 --> 00:37:50,510 financed by what you sold. 856 00:37:50,510 --> 00:37:53,480 And then on top of that, you have a little extra leftover, 857 00:37:53,480 --> 00:37:54,960 OK? 858 00:37:54,960 --> 00:37:57,800 So this is like one of these infomercials at two o'clock 859 00:37:57,800 --> 00:37:59,780 in the morning, real estate, how to make 860 00:37:59,780 --> 00:38:02,450 a million dollars in real estate with no money down, right? 861 00:38:02,450 --> 00:38:04,424 You've put no money down. 862 00:38:04,424 --> 00:38:06,590 You haven't spent any money because what you've done 863 00:38:06,590 --> 00:38:09,110 is you've sold the bond and you've 864 00:38:09,110 --> 00:38:11,030 gotten this amount of cash. 865 00:38:11,030 --> 00:38:14,330 With that cash, you can buy these bonds 866 00:38:14,330 --> 00:38:17,450 and how do you know you have money left over? 867 00:38:17,450 --> 00:38:19,970 By assumption, I'm assuming that this price 868 00:38:19,970 --> 00:38:21,890 is greater than that price. 869 00:38:21,890 --> 00:38:23,990 So now you have money left over. 870 00:38:23,990 --> 00:38:25,640 You've put no money down. 871 00:38:25,640 --> 00:38:27,380 You have cash in the pocket. 872 00:38:27,380 --> 00:38:28,400 You have no risk. 873 00:38:28,400 --> 00:38:31,880 You have no obligations because all the future cash flows 874 00:38:31,880 --> 00:38:36,530 that you owe are financed completely by the bonds 875 00:38:36,530 --> 00:38:37,760 that you bought. 876 00:38:37,760 --> 00:38:41,040 One for one, dollar for dollar, it matches. 877 00:38:41,040 --> 00:38:45,020 So literally, as of today, you walk away from this transaction 878 00:38:45,020 --> 00:38:46,940 a richer individual. 879 00:38:46,940 --> 00:38:47,575 Yeah. 880 00:38:47,575 --> 00:38:49,449 AUDIENCE: Professor, isn't, like, by the time 881 00:38:49,449 --> 00:38:51,850 that you recognize a an arbitrage opportunity, 882 00:38:51,850 --> 00:38:53,280 it corrects itself? 883 00:38:53,280 --> 00:38:55,990 ANDREW LO: Well, let me get back to that. 884 00:38:55,990 --> 00:38:57,730 That's an interesting point. 885 00:38:57,730 --> 00:38:59,960 The question is, can these things really exist, 886 00:38:59,960 --> 00:39:03,100 because once they do, it's almost too 887 00:39:03,100 --> 00:39:04,795 late because they're gone. 888 00:39:04,795 --> 00:39:07,765 AUDIENCE: And then follow-up, is it just my imagination 889 00:39:07,765 --> 00:39:11,240 or do arbitrage desks exist in financial firms today? 890 00:39:11,240 --> 00:39:13,260 ANDREW LO: Arbitrage desks absolutely 891 00:39:13,260 --> 00:39:15,600 exist in financial firms. 892 00:39:15,600 --> 00:39:20,520 And what they do is look for this stuff all day long. 893 00:39:20,520 --> 00:39:22,050 That's what they do. 894 00:39:22,050 --> 00:39:25,860 And so is it true that by the time you identify, it's gone? 895 00:39:25,860 --> 00:39:29,940 Well, it's true if you're a finance academic, as well 896 00:39:29,940 --> 00:39:33,420 as a retail investor. 897 00:39:33,420 --> 00:39:36,270 But you guys, you're going to go out in the job market 898 00:39:36,270 --> 00:39:40,020 and you get to be hired by some of these arbitrage desks. 899 00:39:40,020 --> 00:39:41,850 So you're going to be doing this. 900 00:39:41,850 --> 00:39:44,430 In fact, you're going to be doing something 901 00:39:44,430 --> 00:39:45,750 quite a bit more complicated. 902 00:39:45,750 --> 00:39:47,119 I'll get to that in one minute. 903 00:39:47,119 --> 00:39:48,660 Before I do that, I want to make sure 904 00:39:48,660 --> 00:39:50,618 that everybody is with me about this arbitrage. 905 00:39:50,618 --> 00:39:51,331 Yes. 906 00:39:51,331 --> 00:39:53,215 AUDIENCE: Is there any assumption 907 00:39:53,215 --> 00:39:55,570 that there is no transaction cost? 908 00:39:55,570 --> 00:39:56,860 ANDREW LO: Very good point. 909 00:39:56,860 --> 00:39:59,710 Yes, in this context, there's an assumption 910 00:39:59,710 --> 00:40:03,610 that you can buy and sell freely with no transactions cost. 911 00:40:03,610 --> 00:40:06,250 Obviously, in the real world, there are transactions cost. 912 00:40:06,250 --> 00:40:08,207 You've got to stick those in and figure out 913 00:40:08,207 --> 00:40:10,540 whether you can still make money with transactions cost. 914 00:40:10,540 --> 00:40:16,850 Now one form of transactions cost is not a numerical cost, 915 00:40:16,850 --> 00:40:18,980 but it's a friction. 916 00:40:18,980 --> 00:40:21,590 What do you have to be able to do in order 917 00:40:21,590 --> 00:40:25,370 to do this transaction? 918 00:40:25,370 --> 00:40:29,240 What financial operation do you need in order 919 00:40:29,240 --> 00:40:30,831 to be able to get this deal done? 920 00:40:30,831 --> 00:40:31,330 Yeah. 921 00:40:31,330 --> 00:40:32,656 AUDIENCE: Well, you have to be able to short sell. 922 00:40:32,656 --> 00:40:34,230 ANDREW LO: Short sell, right. 923 00:40:34,230 --> 00:40:36,400 Remember we talked about short selling last time. 924 00:40:36,400 --> 00:40:39,590 That's selling something you don't own. 925 00:40:39,590 --> 00:40:43,130 So you have to borrow the bond from somebody 926 00:40:43,130 --> 00:40:46,720 and then sell it and get those proceeds. 927 00:40:46,720 --> 00:40:52,410 What if it were the case that somebody imposed a constraint 928 00:40:52,410 --> 00:40:54,660 that you can't short sell? 929 00:40:54,660 --> 00:40:57,450 Who would ever do that? 930 00:40:57,450 --> 00:41:00,596 Well, we've seen what happens in the marketplace that 931 00:41:00,596 --> 00:41:02,220 can generate that kind of a constraint. 932 00:41:02,220 --> 00:41:03,540 What happens if you can't short sell? 933 00:41:03,540 --> 00:41:04,039 Yeah. 934 00:41:04,039 --> 00:41:05,840 AUDIENCE: You need to upfront the cost. 935 00:41:05,840 --> 00:41:06,325 ANDREW LO: What's that? 936 00:41:06,325 --> 00:41:08,520 AUDIENCE: You need to put up the cost of the original security. 937 00:41:08,520 --> 00:41:10,920 ANDREW LO: Well, in fact, yes, you need to put up the cost, 938 00:41:10,920 --> 00:41:13,045 but it really defeats the purpose because if you're 939 00:41:13,045 --> 00:41:16,155 going to buy the bond and then sell the bond, 940 00:41:16,155 --> 00:41:18,630 you've not really done anything, right? 941 00:41:18,630 --> 00:41:22,050 This arbitrage argument relies on the fact 942 00:41:22,050 --> 00:41:24,330 that you can sell something you don't 943 00:41:24,330 --> 00:41:28,560 own by borrowing and shorting it and getting the proceeds, 944 00:41:28,560 --> 00:41:31,410 and then giving it back to the person you borrowed whenever 945 00:41:31,410 --> 00:41:34,580 they want, OK? 946 00:41:34,580 --> 00:41:37,370 If I don't allow you to short sell, 947 00:41:37,370 --> 00:41:40,360 this argument doesn't work anymore. 948 00:41:40,360 --> 00:41:44,410 And what that means is that this pricing relationship, 949 00:41:44,410 --> 00:41:48,630 this left-hand side has to equal the right-hand side, 950 00:41:48,630 --> 00:41:51,920 that relationship goes out the window. 951 00:41:51,920 --> 00:41:54,770 For the next several weeks and possibly several months, 952 00:41:54,770 --> 00:41:57,410 finance theory is going to be on vacation 953 00:41:57,410 --> 00:42:00,260 because the government has suspended short sales 954 00:42:00,260 --> 00:42:02,430 for certain securities. 955 00:42:02,430 --> 00:42:05,360 And so the kind of force of markets 956 00:42:05,360 --> 00:42:09,890 that drive prices towards not an equilibrium, but a pricing 957 00:42:09,890 --> 00:42:12,890 relationship that does not depend on equilibrium, 958 00:42:12,890 --> 00:42:15,719 but depends on the law of one price, 959 00:42:15,719 --> 00:42:17,760 that goes out the window if you can't short sell. 960 00:42:17,760 --> 00:42:19,600 Yeah, Megan. 961 00:42:19,600 --> 00:42:21,099 AUDIENCE: I guess I'm just wondering 962 00:42:21,099 --> 00:42:25,352 why the Treasury, just looking for insight on this, why 963 00:42:25,352 --> 00:42:27,435 the Treasury wouldn't just make the short interest 964 00:42:27,435 --> 00:42:32,075 on those short sales so high that it was almost prohibitive, 965 00:42:32,075 --> 00:42:35,540 but people who really wanted to short sell would, 966 00:42:35,540 --> 00:42:38,015 these instruments to hedge portfolios, 967 00:42:38,015 --> 00:42:40,010 could do that if they wanted to pay that. 968 00:42:40,010 --> 00:42:42,320 ANDREW LO: You know, that's a fantastic alternative. 969 00:42:42,320 --> 00:42:43,520 I think that would have been far better. 970 00:42:43,520 --> 00:42:44,840 You're absolutely right. 971 00:42:44,840 --> 00:42:46,970 Increase the cost of short selling 972 00:42:46,970 --> 00:42:48,470 by raising borrowing costs. 973 00:42:48,470 --> 00:42:51,450 By the way, when you short sell, as we said last time, 974 00:42:51,450 --> 00:42:52,460 it's not free. 975 00:42:52,460 --> 00:42:54,770 People aren't going to lend you the security for free. 976 00:42:54,770 --> 00:42:56,540 They're going to charge you for it. 977 00:42:56,540 --> 00:43:02,420 So what if instead of forbidding it altogether, 978 00:43:02,420 --> 00:43:06,050 why not just triple the cost or quadruple the cost? 979 00:43:06,050 --> 00:43:10,570 Therefore, only people who really, really need to do it 980 00:43:10,570 --> 00:43:11,749 will do it. 981 00:43:11,749 --> 00:43:13,790 The problem with that is more of a political one. 982 00:43:13,790 --> 00:43:17,570 The political problem is that we want these evildoers, 983 00:43:17,570 --> 00:43:20,270 these short sellers that are driving 984 00:43:20,270 --> 00:43:22,430 the prices of financial securities 985 00:43:22,430 --> 00:43:25,610 to stop their bad activities. 986 00:43:25,610 --> 00:43:28,700 And so what we're going to do is to mandate by law 987 00:43:28,700 --> 00:43:30,850 that they can't do that. 988 00:43:30,850 --> 00:43:34,040 Now, that may be a reasonable thing 989 00:43:34,040 --> 00:43:36,620 from a political perspective, but it's not a reasonable thing 990 00:43:36,620 --> 00:43:38,960 from an economic perspective, because what it does 991 00:43:38,960 --> 00:43:42,050 is it disrupts relationships like this, pricing 992 00:43:42,050 --> 00:43:43,650 relationships like this. 993 00:43:43,650 --> 00:43:44,150 Yeah. 994 00:43:44,150 --> 00:43:47,036 AUDIENCE: Can you actually change the borrowing costs 995 00:43:47,036 --> 00:43:50,561 for a few types of security [INAUDIBLE] 996 00:43:50,561 --> 00:43:54,980 by selling the short [INAUDIBLE] and shorting [INAUDIBLE] 997 00:43:54,980 --> 00:43:57,435 the interest rate [INAUDIBLE]. 998 00:43:57,435 --> 00:43:59,940 ANDREW LO: Well, if you're the government 999 00:43:59,940 --> 00:44:01,620 and you're in a time of crisis, it 1000 00:44:01,620 --> 00:44:04,930 seems like you can do anything you want. 1001 00:44:04,930 --> 00:44:07,920 So I mean practically, yes, you can say, 1002 00:44:07,920 --> 00:44:11,160 for all financial stocks that are on this list, 1003 00:44:11,160 --> 00:44:15,240 we will now charge an extra high rate of interest 1004 00:44:15,240 --> 00:44:16,530 for borrowing those stocks. 1005 00:44:16,530 --> 00:44:21,030 And, in fact, there exists a mechanism even before this rule 1006 00:44:21,030 --> 00:44:24,960 was put in place that for certain stocks that are quote 1007 00:44:24,960 --> 00:44:27,930 "hard-to-borrow"-- that's a technical term that Wall Street 1008 00:44:27,930 --> 00:44:29,790 firms, brokerage firms use. 1009 00:44:29,790 --> 00:44:31,800 Securities that are hard-to-borrow 1010 00:44:31,800 --> 00:44:34,170 means that they're very actively traded 1011 00:44:34,170 --> 00:44:36,660 and it's very hard to find a counterparty that's 1012 00:44:36,660 --> 00:44:39,270 willing to let you borrow it from them. 1013 00:44:39,270 --> 00:44:41,550 The hard-to-borrow stocks typically 1014 00:44:41,550 --> 00:44:43,200 are lent out at a premium. 1015 00:44:43,200 --> 00:44:45,270 So they are charged higher prices 1016 00:44:45,270 --> 00:44:47,640 for those that are very, very popular. 1017 00:44:47,640 --> 00:44:50,910 And by simply eliminating short sells, 1018 00:44:50,910 --> 00:44:53,070 you basically make those costs infinite. 1019 00:44:53,070 --> 00:44:54,510 That's exactly what's going on. 1020 00:44:54,510 --> 00:44:57,510 So would it have been better to make them finite, but bigger? 1021 00:44:57,510 --> 00:44:59,920 That would have been better than what they did, 1022 00:44:59,920 --> 00:45:03,270 which is making it infinite, but from the purely financial 1023 00:45:03,270 --> 00:45:05,610 markets perspective, it would be best 1024 00:45:05,610 --> 00:45:08,040 if there were no restrictions and no transactions cost 1025 00:45:08,040 --> 00:45:08,700 at all. 1026 00:45:08,700 --> 00:45:11,530 Obviously, transactions costs are inevitable. 1027 00:45:11,530 --> 00:45:14,400 So when you price these relationships, 1028 00:45:14,400 --> 00:45:20,250 the equality is going to be up to transactions cost. 1029 00:45:20,250 --> 00:45:22,266 There might be a little bit of a wedge 1030 00:45:22,266 --> 00:45:24,390 between the left-hand side and the right-hand side, 1031 00:45:24,390 --> 00:45:28,440 but the difference will have to be small enough 1032 00:45:28,440 --> 00:45:31,590 that apart from transactions costs, 1033 00:45:31,590 --> 00:45:34,230 they are not significantly different. 1034 00:45:34,230 --> 00:45:34,730 Yeah. 1035 00:45:34,730 --> 00:45:36,614 AUDIENCE: Could it be that they also 1036 00:45:36,614 --> 00:45:39,060 stopped the shorting because of some illegal transactions 1037 00:45:39,060 --> 00:45:41,660 or inside information? 1038 00:45:41,660 --> 00:45:43,740 ANDREW LO: Well, if it were illegal transactions, 1039 00:45:43,740 --> 00:45:45,330 the way they should have done it was to prosecute 1040 00:45:45,330 --> 00:45:47,790 the illegal parties, as opposed to stopping short sales 1041 00:45:47,790 --> 00:45:49,057 for everybody, right? 1042 00:45:49,057 --> 00:45:50,640 That would be a far more effective way 1043 00:45:50,640 --> 00:45:52,098 of dealing with illegal activities. 1044 00:45:52,098 --> 00:45:54,270 That's not what they were concerned about primarily. 1045 00:45:54,270 --> 00:45:58,080 The SEC has an enforcement division whose sole job 1046 00:45:58,080 --> 00:46:00,960 it is to check on all the kind of transactions that 1047 00:46:00,960 --> 00:46:02,730 may have occurred to see whether or not 1048 00:46:02,730 --> 00:46:04,851 there's any kind of illegal activity going on. 1049 00:46:04,851 --> 00:46:07,350 It wasn't the illegal activity that prompted the short sales 1050 00:46:07,350 --> 00:46:07,850 restriction. 1051 00:46:07,850 --> 00:46:11,280 It was really the concern that financial firms 1052 00:46:11,280 --> 00:46:13,770 were being pounded by short sellers that 1053 00:46:13,770 --> 00:46:15,780 were betting on them failing. 1054 00:46:15,780 --> 00:46:19,440 And the more pressure that they impose on the stock price 1055 00:46:19,440 --> 00:46:21,720 going down, down, down, the more likely 1056 00:46:21,720 --> 00:46:24,090 it is that people would lose confidence and then 1057 00:46:24,090 --> 00:46:26,460 all of a sudden stop doing business with it. 1058 00:46:26,460 --> 00:46:29,190 In many ways, that's what happened with Bear Stearns. 1059 00:46:29,190 --> 00:46:31,250 At least from the historical record, 1060 00:46:31,250 --> 00:46:33,000 it seems like what happened was that there 1061 00:46:33,000 --> 00:46:36,330 was a rumor that Bear Stearns was not going to be solvent, 1062 00:46:36,330 --> 00:46:39,120 even though they didn't have any particular pressure 1063 00:46:39,120 --> 00:46:42,720 to pay certain debts at that point in time. 1064 00:46:42,720 --> 00:46:45,930 And somehow that rumor grew into general fear 1065 00:46:45,930 --> 00:46:48,707 and the short sellers got in and started shorting the stock. 1066 00:46:48,707 --> 00:46:50,790 The stock price went down, people looked and said, 1067 00:46:50,790 --> 00:46:52,248 oh my god, the stock is going down, 1068 00:46:52,248 --> 00:46:54,546 I'd better take my business elsewhere. 1069 00:46:54,546 --> 00:46:55,920 And everybody started doing that, 1070 00:46:55,920 --> 00:46:57,150 and once everybody started doing that, 1071 00:46:57,150 --> 00:46:59,070 the firm began having great difficulties 1072 00:46:59,070 --> 00:47:00,520 in maintaining a business. 1073 00:47:00,520 --> 00:47:01,191 Yeah. 1074 00:47:01,191 --> 00:47:04,200 AUDIENCE: Even the days that short selling is not allowed, 1075 00:47:04,200 --> 00:47:06,560 then the investors who own the more expensive-- 1076 00:47:06,560 --> 00:47:07,560 ANDREW LO: That's right. 1077 00:47:07,560 --> 00:47:09,794 AUDIENCE: --asset are going to sell them because they 1078 00:47:09,794 --> 00:47:11,544 don't think if they don't sell this today, 1079 00:47:11,544 --> 00:47:12,540 I'm buying the right-hand-- 1080 00:47:12,540 --> 00:47:14,123 ANDREW LO: That's right, that's right. 1081 00:47:14,123 --> 00:47:18,661 AUDIENCE: So again, you do the [INAUDIBLE]. 1082 00:47:18,661 --> 00:47:20,160 ANDREW LO: That's a very good point. 1083 00:47:20,160 --> 00:47:21,030 Let me repeat it. 1084 00:47:21,030 --> 00:47:24,900 The point is that even if you're not allowed to short sell, 1085 00:47:24,900 --> 00:47:27,930 then the folks who own the left-hand side, who 1086 00:47:27,930 --> 00:47:30,910 own the coupon bond, they can say, hey, 1087 00:47:30,910 --> 00:47:36,120 my coupon bond is worth 110, but I can get the exact same payoff 1088 00:47:36,120 --> 00:47:38,340 by buying a bunch of pure discount bonds. 1089 00:47:38,340 --> 00:47:41,430 And it's only cost me 100 to buy them. 1090 00:47:41,430 --> 00:47:43,500 I'm going to sell my coupon bought at 110 1091 00:47:43,500 --> 00:47:46,530 and I'm going to buy $100 worth of these this discount bonds 1092 00:47:46,530 --> 00:47:48,750 and I just made $10. 1093 00:47:48,750 --> 00:47:52,260 Now that can happen as long as two things occur. 1094 00:47:52,260 --> 00:47:57,600 One, the person who owns the bond knows about this. 1095 00:47:57,600 --> 00:48:00,900 And two, they actually want to take the trouble 1096 00:48:00,900 --> 00:48:04,731 to do the trade or they're able to do the trade. 1097 00:48:04,731 --> 00:48:06,480 The problem is that most of the folks that 1098 00:48:06,480 --> 00:48:08,700 bought the bond on the left-hand side 1099 00:48:08,700 --> 00:48:12,420 are pension funds that are not in the business of doing 1100 00:48:12,420 --> 00:48:14,940 this kind of arbitrage transactions. 1101 00:48:14,940 --> 00:48:16,260 So they're trying to do that. 1102 00:48:16,260 --> 00:48:20,220 All they want to do is they've got a bunch of pension plan 1103 00:48:20,220 --> 00:48:20,820 participants. 1104 00:48:20,820 --> 00:48:22,380 They need to pay out their benefits. 1105 00:48:22,380 --> 00:48:23,550 They've got contributions. 1106 00:48:23,550 --> 00:48:25,250 They just want to match assets to liabilities. 1107 00:48:25,250 --> 00:48:27,750 They're not in the business of doing this kind of high speed 1108 00:48:27,750 --> 00:48:29,520 transaction. 1109 00:48:29,520 --> 00:48:32,460 So what that means is that you're still right, 1110 00:48:32,460 --> 00:48:36,280 that if they realize this relationship is there, 1111 00:48:36,280 --> 00:48:40,000 and they are in a position to do the trades, 1112 00:48:40,000 --> 00:48:41,890 they will sometimes. 1113 00:48:41,890 --> 00:48:46,140 And then that will force prices closer, 1114 00:48:46,140 --> 00:48:49,620 but it's not going to be the same kind of numerical identity 1115 00:48:49,620 --> 00:48:53,520 that has to hold when you've got greedy people like myself 1116 00:48:53,520 --> 00:48:55,620 trying to do the trades and being 1117 00:48:55,620 --> 00:48:59,046 able to do the trades at a moment's notice. 1118 00:48:59,046 --> 00:49:00,990 AUDIENCE: I'm especially more interested 1119 00:49:00,990 --> 00:49:02,934 about if these players are big enough 1120 00:49:02,934 --> 00:49:06,102 in the financial markets, then it will correct 1121 00:49:06,102 --> 00:49:07,310 and it could get out of that. 1122 00:49:07,310 --> 00:49:08,450 ANDREW LO: Exactly, right. 1123 00:49:08,450 --> 00:49:10,520 There are all sorts of additional complexities 1124 00:49:10,520 --> 00:49:13,320 of being able to do the trade that as a pension plan, 1125 00:49:13,320 --> 00:49:15,590 you're not even allowed to do, never mind whether you 1126 00:49:15,590 --> 00:49:16,839 want to do them or not. 1127 00:49:16,839 --> 00:49:18,380 So these are the kind of restrictions 1128 00:49:18,380 --> 00:49:21,530 that would present this gap. 1129 00:49:21,530 --> 00:49:23,970 But let's for now assume that there's no gap. 1130 00:49:23,970 --> 00:49:25,970 We're going to assume that there's no frictions. 1131 00:49:25,970 --> 00:49:28,340 We're going to assume that there's no short sales 1132 00:49:28,340 --> 00:49:29,630 prohibitions. 1133 00:49:29,630 --> 00:49:31,700 And when that happens, this pricing relationship 1134 00:49:31,700 --> 00:49:32,607 has to hold. 1135 00:49:32,607 --> 00:49:33,440 Now I promised you-- 1136 00:49:33,440 --> 00:49:35,315 I want to show you something more complicated 1137 00:49:35,315 --> 00:49:37,700 that all of you may do when you get out 1138 00:49:37,700 --> 00:49:41,180 of here, and that's this. 1139 00:49:41,180 --> 00:49:44,780 Instead of looking at just one bond, what 1140 00:49:44,780 --> 00:49:48,750 if we looked at a whole bunch of coupon bonds? 1141 00:49:48,750 --> 00:49:53,200 Now, let's take a look using this pricing 1142 00:49:53,200 --> 00:49:57,720 that's based on the law of one price and basic greed. 1143 00:49:57,720 --> 00:50:01,650 We've got n bonds here, one through n, 1144 00:50:01,650 --> 00:50:06,660 and each has its own coupon, whatever that is. 1145 00:50:06,660 --> 00:50:09,810 I'm just going to use notation to write down 1146 00:50:09,810 --> 00:50:13,440 that each bond has its own particular coupon, right? 1147 00:50:13,440 --> 00:50:15,600 So you've got a 3% 10 year bond. 1148 00:50:15,600 --> 00:50:18,250 You've got a 4% 30 year bond. 1149 00:50:18,250 --> 00:50:21,660 You may have 5 and 1/2% five year bond. 1150 00:50:21,660 --> 00:50:25,650 So some of these coupons may be zero 1151 00:50:25,650 --> 00:50:28,260 because capital T I'm going to assume 1152 00:50:28,260 --> 00:50:31,260 is the most extreme 30 year period, right? 1153 00:50:31,260 --> 00:50:33,426 So a five year bond would have coupons 1154 00:50:33,426 --> 00:50:34,800 for the first five years and then 1155 00:50:34,800 --> 00:50:37,170 for all of the coupon payments after that, I'm 1156 00:50:37,170 --> 00:50:40,500 going to have zero, zero, zero, zero, zero, right? 1157 00:50:40,500 --> 00:50:47,990 So this should hearken back to your high school algebra days, 1158 00:50:47,990 --> 00:50:52,070 where you have multiple equations 1159 00:50:52,070 --> 00:50:55,340 with multiple unknowns. 1160 00:50:55,340 --> 00:50:57,889 Now what's unknown here in these equations? 1161 00:50:57,889 --> 00:50:58,805 What are the unknowns? 1162 00:51:02,880 --> 00:51:06,370 Well, you observe the prices, right, from the marketplace, 1163 00:51:06,370 --> 00:51:09,199 so the left-hand side is not unknown. 1164 00:51:09,199 --> 00:51:10,490 What about the right-hand side? 1165 00:51:10,490 --> 00:51:11,782 What are the unknowns? 1166 00:51:11,782 --> 00:51:13,490 What do you observe, what are the knowns? 1167 00:51:13,490 --> 00:51:14,114 How about that? 1168 00:51:14,114 --> 00:51:15,850 Let's start with that. 1169 00:51:15,850 --> 00:51:16,480 Yeah. 1170 00:51:16,480 --> 00:51:16,960 AUDIENCE: The coupons. 1171 00:51:16,960 --> 00:51:18,209 ANDREW LO: The coupons, right. 1172 00:51:18,209 --> 00:51:23,530 If I tell you that I've got a 30 year 4 and 1/2% bond, 1173 00:51:23,530 --> 00:51:26,623 you know what the coupon is going to be, right? 1174 00:51:26,623 --> 00:51:28,590 AUDIENCE: Because we don't know the yield. 1175 00:51:28,590 --> 00:51:29,326 ANDREW LO: What's that? 1176 00:51:29,326 --> 00:51:30,159 AUDIENCE: The yield. 1177 00:51:30,159 --> 00:51:33,960 ANDREW LO: The yield is what we don't know. 1178 00:51:33,960 --> 00:51:34,460 All right. 1179 00:51:34,460 --> 00:51:38,500 That we either get from the marketplace or we 1180 00:51:38,500 --> 00:51:41,800 can try to solve it from these prices. 1181 00:51:41,800 --> 00:51:45,910 But how many different yields do we need in order 1182 00:51:45,910 --> 00:51:47,130 to price each bond? 1183 00:51:49,810 --> 00:51:51,100 These are T year bonds. 1184 00:51:51,100 --> 00:51:51,941 How many yields? 1185 00:51:51,941 --> 00:51:52,440 AUDIENCE: T. 1186 00:51:52,440 --> 00:51:57,070 ANDREW LO: Yeah, we need T yields, one for each year. 1187 00:51:57,070 --> 00:52:01,290 We have T yields in these equations 1188 00:52:01,290 --> 00:52:04,230 and they're the same across the different bonds, right? 1189 00:52:04,230 --> 00:52:08,040 Because we're using the same pure discount 1190 00:52:08,040 --> 00:52:13,340 bonds to replicate each of these coupon bonds. 1191 00:52:13,340 --> 00:52:14,690 I've got T unknowns. 1192 00:52:14,690 --> 00:52:16,960 How many equations do I have? 1193 00:52:16,960 --> 00:52:17,750 AUDIENCE: n. 1194 00:52:17,750 --> 00:52:19,790 ANDREW LO: n bonds, right? 1195 00:52:19,790 --> 00:52:26,630 Now, on any given day, you might have 200 to 300 bonds 1196 00:52:26,630 --> 00:52:27,350 that are trading. 1197 00:52:30,060 --> 00:52:34,680 But you've only got 30 unknowns. 1198 00:52:34,680 --> 00:52:40,290 So let's think back to your high school algebra or college 1199 00:52:40,290 --> 00:52:42,390 linear algebra days. 1200 00:52:42,390 --> 00:52:49,300 If you've got 200 equations and 30 unknowns, 1201 00:52:49,300 --> 00:52:50,730 how many solutions do you have? 1202 00:52:54,490 --> 00:52:56,830 Well, let's get simpler. 1203 00:52:56,830 --> 00:53:00,484 Suppose you had two equations and two unknowns. 1204 00:53:00,484 --> 00:53:01,650 AUDIENCE: Just one solution. 1205 00:53:01,650 --> 00:53:03,025 ANDREW LO: You have one solution, 1206 00:53:03,025 --> 00:53:05,190 assuming certain kind of conditions 1207 00:53:05,190 --> 00:53:07,950 that hold like invertability, which we're going to talk about 1208 00:53:07,950 --> 00:53:08,820 in a minute. 1209 00:53:08,820 --> 00:53:11,600 Two equations, two unknowns. 1210 00:53:11,600 --> 00:53:13,610 You have one solution. 1211 00:53:13,610 --> 00:53:17,890 How about one equation and two unknowns. 1212 00:53:17,890 --> 00:53:21,640 How many solutions? 1213 00:53:21,640 --> 00:53:22,910 Infinite. 1214 00:53:22,910 --> 00:53:25,540 OK, that's right, because you've got that extra degree 1215 00:53:25,540 --> 00:53:26,380 of freedom, right? 1216 00:53:26,380 --> 00:53:28,130 There's lots of different solutions. 1217 00:53:28,130 --> 00:53:33,570 What about three equations and two unknowns. 1218 00:53:33,570 --> 00:53:37,390 Now how many solutions do you have? 1219 00:53:37,390 --> 00:53:37,939 Yeah. 1220 00:53:37,939 --> 00:53:39,980 AUDIENCE: Because it's linear, you only have one. 1221 00:53:39,980 --> 00:53:41,600 ANDREW LO: It's linear. 1222 00:53:41,600 --> 00:53:43,030 Are you guaranteed to have one? 1223 00:53:43,030 --> 00:53:44,560 AUDIENCE: You might have zero. 1224 00:53:44,560 --> 00:53:46,580 ANDREW LO: You might have zero. 1225 00:53:46,580 --> 00:53:52,470 What are the conditions under which you would have one? 1226 00:53:52,470 --> 00:53:54,318 AUDIENCE: If the solution of two equations 1227 00:53:54,318 --> 00:53:55,710 applied for the third one. 1228 00:53:55,710 --> 00:53:56,690 ANDREW LO: Right. 1229 00:53:56,690 --> 00:53:58,900 There is a possibility you have one solution 1230 00:53:58,900 --> 00:54:01,050 if the solution of the two equations 1231 00:54:01,050 --> 00:54:04,060 actually applies to the third. 1232 00:54:04,060 --> 00:54:06,107 Do you remember under what condition-- 1233 00:54:06,107 --> 00:54:06,940 AUDIENCE: Exhausted. 1234 00:54:06,940 --> 00:54:07,939 ANDREW LO: --that, what? 1235 00:54:07,939 --> 00:54:09,076 AUDIENCE: Exhausted. 1236 00:54:09,076 --> 00:54:09,951 ANDREW LO: Exhausted? 1237 00:54:09,951 --> 00:54:12,890 That's not quite the term that mathematicians use. 1238 00:54:12,890 --> 00:54:16,910 There's something called linear dependence. 1239 00:54:16,910 --> 00:54:19,040 That's a very complicated word that 1240 00:54:19,040 --> 00:54:20,960 describes the fact that if you have these two 1241 00:54:20,960 --> 00:54:24,350 equations and two unknowns, and you have one solution, 1242 00:54:24,350 --> 00:54:27,650 you can just take an average of those two, a combination 1243 00:54:27,650 --> 00:54:29,630 of those two, and you'll get the third one. 1244 00:54:29,630 --> 00:54:35,320 You can actually replicate the third equation from those two. 1245 00:54:35,320 --> 00:54:37,940 What happens if you don't? 1246 00:54:37,940 --> 00:54:41,410 What happens if you cannot take combinations of the first two 1247 00:54:41,410 --> 00:54:44,050 equations to get the third? 1248 00:54:44,050 --> 00:54:45,101 What does that mean? 1249 00:54:45,101 --> 00:54:46,905 AUDIENCE: One of the numbers is wrong. 1250 00:54:46,905 --> 00:54:48,589 ANDREW LO: One of the numbers is wrong. 1251 00:54:48,589 --> 00:54:49,630 What do you mean by that? 1252 00:54:52,420 --> 00:54:55,210 AUDIENCE: It just couldn't be-- it can't be a solution. 1253 00:54:55,210 --> 00:54:57,130 ANDREW LO: It can't be a solution. 1254 00:54:57,130 --> 00:54:59,350 OK, now this is getting really interesting 1255 00:54:59,350 --> 00:55:01,330 because on the one hand, you're probably 1256 00:55:01,330 --> 00:55:04,300 getting confused about what any of this has to do with money. 1257 00:55:04,300 --> 00:55:05,716 In a minute, I'm going to tell you 1258 00:55:05,716 --> 00:55:08,980 it has everything to do with money, as you might expect. 1259 00:55:08,980 --> 00:55:10,914 If we've got two equations and two unknowns, 1260 00:55:10,914 --> 00:55:12,580 and we have one solution, that basically 1261 00:55:12,580 --> 00:55:16,780 says that there are two yields, a one year yield and a two year 1262 00:55:16,780 --> 00:55:21,540 yield that is able to price both bonds. 1263 00:55:21,540 --> 00:55:24,120 And that better be the case because we're 1264 00:55:24,120 --> 00:55:27,690 going to use these two yields to replicate the bonds. 1265 00:55:27,690 --> 00:55:31,780 And so this kind of a relationship has to hold. 1266 00:55:31,780 --> 00:55:37,930 Now if we add a third bond, if we add a third bond, 1267 00:55:37,930 --> 00:55:41,500 and those same two yields that worked for the first two bonds, 1268 00:55:41,500 --> 00:55:48,020 they don't work for the third bond, something's wrong, right? 1269 00:55:48,020 --> 00:55:52,200 It means that this third bond, its price 1270 00:55:52,200 --> 00:55:57,295 does not satisfy the relationship between those two 1271 00:55:57,295 --> 00:55:57,795 yields. 1272 00:56:00,650 --> 00:56:04,700 That's evidence of a mispricing. 1273 00:56:04,700 --> 00:56:06,680 Something is wrong. 1274 00:56:06,680 --> 00:56:09,170 But in this case, what's wrong is 1275 00:56:09,170 --> 00:56:11,930 that there's something mispriced between those two 1276 00:56:11,930 --> 00:56:16,140 bonds and the third. 1277 00:56:16,140 --> 00:56:18,080 So when you run into a situation like that-- 1278 00:56:18,080 --> 00:56:20,538 and we're going to give you an example in the problem set-- 1279 00:56:20,538 --> 00:56:23,090 when you come across that, what that means is 1280 00:56:23,090 --> 00:56:28,280 you should be extremely excited, as opposed to depressed 1281 00:56:28,280 --> 00:56:31,190 in math class, you know, gee, there's no solution. 1282 00:56:31,190 --> 00:56:33,800 In finance, what no solution means 1283 00:56:33,800 --> 00:56:35,450 is that there is a transaction. 1284 00:56:35,450 --> 00:56:39,290 There exists a linear combination of the first two 1285 00:56:39,290 --> 00:56:46,700 bonds and the third that A, costs you no money down; B, 1286 00:56:46,700 --> 00:56:49,700 will generate cash flow today; C, 1287 00:56:49,700 --> 00:56:54,280 will require no future payments of any sort, so it's riskless. 1288 00:56:54,280 --> 00:56:55,630 It is a free lunch. 1289 00:56:55,630 --> 00:56:57,219 It is an arbitrage. 1290 00:56:57,219 --> 00:56:59,260 Now that's with three equations and two unknowns. 1291 00:56:59,260 --> 00:57:00,610 Anybody can do that, right? 1292 00:57:00,610 --> 00:57:02,330 That's easy. 1293 00:57:02,330 --> 00:57:05,560 What if it were 200 equations and 30 unknowns? 1294 00:57:05,560 --> 00:57:07,129 Now, not so easy. 1295 00:57:07,129 --> 00:57:09,670 Now you actually have to know something about linear algebra. 1296 00:57:09,670 --> 00:57:13,210 Now the whole notion of what an invertible matrix is, 1297 00:57:13,210 --> 00:57:16,420 what the eigenvalues are, all the kind of infrastructure 1298 00:57:16,420 --> 00:57:19,210 that you can build for understanding this 1299 00:57:19,210 --> 00:57:22,330 becomes relevant as a quant trading 1300 00:57:22,330 --> 00:57:25,280 on a proprietary trading desk. 1301 00:57:25,280 --> 00:57:29,360 In the 1970s, a number of MIT graduates 1302 00:57:29,360 --> 00:57:32,044 were hired by Salomon Brothers. 1303 00:57:32,044 --> 00:57:34,210 They knew very little about fixed income securities. 1304 00:57:34,210 --> 00:57:38,050 They knew the basics, which is what was taught here, 1305 00:57:38,050 --> 00:57:41,830 but they didn't know much about market realities in practice. 1306 00:57:41,830 --> 00:57:45,310 And so when they went to solve their three equations and two 1307 00:57:45,310 --> 00:57:51,040 unknowns, they observed inconsistencies. 1308 00:57:51,040 --> 00:57:53,590 And they didn't do three equations and two unknowns, 1309 00:57:53,590 --> 00:57:56,800 they did 200 equations and 30 unknowns. 1310 00:57:56,800 --> 00:58:00,400 And in the 1970s, that was not easy to do because we didn't 1311 00:58:00,400 --> 00:58:02,740 have PCs, we didn't have Excel. 1312 00:58:02,740 --> 00:58:05,830 We didn't have a lot of the tools that we have today. 1313 00:58:05,830 --> 00:58:09,790 And what they did was they took these simultaneous linear 1314 00:58:09,790 --> 00:58:11,154 equations. 1315 00:58:11,154 --> 00:58:12,320 This is high school algebra. 1316 00:58:12,320 --> 00:58:15,700 Even back then it was high school algebra, OK? 1317 00:58:15,700 --> 00:58:19,840 And they just cranked through and looked for mispricing, 1318 00:58:19,840 --> 00:58:21,640 looked for no solutions. 1319 00:58:21,640 --> 00:58:25,460 And they found a lot of cases with no solutions. 1320 00:58:25,460 --> 00:58:29,780 In one of the years during the 1970s or 80s, 1321 00:58:29,780 --> 00:58:37,220 one of these MIT grads was paid an annual bonus of $22 million 1322 00:58:37,220 --> 00:58:40,890 for doing this, for solving simultaneous linear equations. 1323 00:58:40,890 --> 00:58:42,200 So this is an extraor-- 1324 00:58:42,200 --> 00:58:45,290 and if that was what he got paid, 1325 00:58:45,290 --> 00:58:48,170 you imagine what he generated for Salomon Brothers. 1326 00:58:48,170 --> 00:58:51,140 It was a lot more than $22 million. 1327 00:58:51,140 --> 00:58:56,450 This activity is known as fixed income arbitrage. 1328 00:58:56,450 --> 00:58:58,000 There are many other versions of it, 1329 00:58:58,000 --> 00:58:59,850 but this is the plain vanilla version. 1330 00:58:59,850 --> 00:59:02,030 And by the way, the plain vanilla version, 1331 00:59:02,030 --> 00:59:06,590 it still works in the sense that occasionally, 1332 00:59:06,590 --> 00:59:09,970 if you're quick enough and you have the right tools, 1333 00:59:09,970 --> 00:59:13,669 you can identify mispricings and take advantage of them quickly. 1334 00:59:13,669 --> 00:59:15,710 It doesn't last long, so you're absolutely right. 1335 00:59:15,710 --> 00:59:17,620 It doesn't last long. 1336 00:59:17,620 --> 00:59:19,370 But the person who gets paid is the person 1337 00:59:19,370 --> 00:59:22,310 who can do this the fastest and is 1338 00:59:22,310 --> 00:59:26,390 able to understand the interrelationships 1339 00:59:26,390 --> 00:59:27,732 among the securities. 1340 00:59:27,732 --> 00:59:29,690 And you can understand now why retail investors 1341 00:59:29,690 --> 00:59:33,080 have no chance of doing this kind of thing on their own. 1342 00:59:33,080 --> 00:59:36,650 This is something you definitely don't want to try at home, OK? 1343 00:59:36,650 --> 00:59:39,830 I know you guys have MATLAB and you can do matrix inversions, 1344 00:59:39,830 --> 00:59:43,100 but there are lots of other frictions, 1345 00:59:43,100 --> 00:59:45,620 transactions costs, and imperfections that you have 1346 00:59:45,620 --> 00:59:47,600 to build into this analysis. 1347 00:59:47,600 --> 00:59:50,900 But once you do, all sorts of interesting things 1348 00:59:50,900 --> 00:59:52,460 start popping out. 1349 00:59:52,460 --> 00:59:53,637 All right, question, yeah. 1350 00:59:53,637 --> 00:59:55,220 AUDIENCE: Can you give a couple reason 1351 00:59:55,220 --> 00:59:56,060 why this does still exist? 1352 00:59:56,060 --> 00:59:58,518 Like, why hasn't the arms race between everyone narrowed it 1353 00:59:58,518 --> 01:00:00,797 down to basic efficiency? 1354 01:00:00,797 --> 01:00:02,630 ANDREW LO: Well, it's actually much narrower 1355 01:00:02,630 --> 01:00:03,900 now than it used to be. 1356 01:00:03,900 --> 01:00:06,000 So in fact, the market has gotten much, 1357 01:00:06,000 --> 01:00:07,830 much more competitive. 1358 01:00:07,830 --> 01:00:09,870 But it's not down to zero precisely 1359 01:00:09,870 --> 01:00:12,780 because there are frictions and other aspects. 1360 01:00:12,780 --> 01:00:14,970 For example, some of these bonds, 1361 01:00:14,970 --> 01:00:18,180 they have weird features, like they're callable. 1362 01:00:18,180 --> 01:00:21,600 Or in some cases, they may have certain types 1363 01:00:21,600 --> 01:00:27,900 of other requirements and market institutional imperfections 1364 01:00:27,900 --> 01:00:30,000 that require you to build in those constraints 1365 01:00:30,000 --> 01:00:31,590 when you do the analysis. 1366 01:00:31,590 --> 01:00:34,470 And so it's really about who has the better model. 1367 01:00:34,470 --> 01:00:36,240 And frankly there's an arms race that's 1368 01:00:36,240 --> 01:00:38,400 been going on for the last three decades 1369 01:00:38,400 --> 01:00:40,830 as to who has the fastest computers. 1370 01:00:40,830 --> 01:00:42,870 The first supercomputer that was ever 1371 01:00:42,870 --> 01:00:45,000 installed on Wall Street, a Cray-2, 1372 01:00:45,000 --> 01:00:47,460 was installed at Salomon Brothers 1373 01:00:47,460 --> 01:00:51,520 doing simultaneous linear equations, among other things. 1374 01:00:51,520 --> 01:00:55,860 And so this is where technology has played a really big role 1375 01:00:55,860 --> 01:00:58,730 in the developments of market prices. 1376 01:00:58,730 --> 01:01:00,510 Another question? 1377 01:01:00,510 --> 01:01:08,380 OK, so this very, very simple idea, and again, it is simple, 1378 01:01:08,380 --> 01:01:11,110 has all sorts of important ramifications for the pricing 1379 01:01:11,110 --> 01:01:14,050 of bonds and other securities. 1380 01:01:14,050 --> 01:01:18,280 What that tells us is that market prices have 1381 01:01:18,280 --> 01:01:21,680 all sorts of information that are incorporated into it. 1382 01:01:21,680 --> 01:01:23,680 And one of the things that we want to understand 1383 01:01:23,680 --> 01:01:26,020 is how to interpret that information. 1384 01:01:26,020 --> 01:01:28,750 In particular, the first thing I want to do 1385 01:01:28,750 --> 01:01:31,164 is to understand the risks, all right, 1386 01:01:31,164 --> 01:01:33,580 because we talked about the fact that some of these market 1387 01:01:33,580 --> 01:01:36,580 prices may have missed the risks that were 1388 01:01:36,580 --> 01:01:38,930 implicit in some of the trades. 1389 01:01:38,930 --> 01:01:42,610 And so the question is why and how do we measure 1390 01:01:42,610 --> 01:01:45,740 the risk of a bond portfolio. 1391 01:01:45,740 --> 01:01:48,130 So what I want to do is to now look 1392 01:01:48,130 --> 01:01:51,550 at the market price of a bond in terms 1393 01:01:51,550 --> 01:01:56,770 of a function that has inputs and the price is the output. 1394 01:01:56,770 --> 01:01:58,540 And I want to ask the question, what kind 1395 01:01:58,540 --> 01:02:02,260 of fluctuation in the input will yield fluctuation 1396 01:02:02,260 --> 01:02:02,870 in the output? 1397 01:02:02,870 --> 01:02:04,870 You know, we now know how to price these things. 1398 01:02:04,870 --> 01:02:07,660 We now know how the relationships must work 1399 01:02:07,660 --> 01:02:10,500 from a present value approach. 1400 01:02:10,500 --> 01:02:13,030 And now what I want to do is to ask whether we 1401 01:02:13,030 --> 01:02:15,100 can measure the sensitivity. 1402 01:02:15,100 --> 01:02:19,030 So one way to do it is to just graph 1403 01:02:19,030 --> 01:02:22,127 the price of a bond as a function of its yield. 1404 01:02:22,127 --> 01:02:24,460 And we know that there's an inverse relationship, right? 1405 01:02:24,460 --> 01:02:27,740 Just like we saw with treasuries this week versus last week, 1406 01:02:27,740 --> 01:02:28,240 right? 1407 01:02:28,240 --> 01:02:30,730 Last week it was a big run on treasuries, lots of people 1408 01:02:30,730 --> 01:02:31,900 wanted to get into them. 1409 01:02:31,900 --> 01:02:34,150 Price goes up, yield goes down. 1410 01:02:34,150 --> 01:02:38,050 And this week, less pressure, so we have yield going up 1411 01:02:38,050 --> 01:02:40,180 and the prices coming down. 1412 01:02:40,180 --> 01:02:45,620 That provides us with one kind of measure of risk. 1413 01:02:45,620 --> 01:02:48,100 So the kind of measure I'm talking about 1414 01:02:48,100 --> 01:02:52,090 is the slope of this line. 1415 01:02:52,090 --> 01:02:55,300 The instantaneous slope that tells us 1416 01:02:55,300 --> 01:02:57,430 for a bit of a tweak in interest rates 1417 01:02:57,430 --> 01:03:00,550 or yield, what does that do to the market price? 1418 01:03:00,550 --> 01:03:03,130 Because obviously when you're an investor, 1419 01:03:03,130 --> 01:03:05,350 you're focusing on the price, right? 1420 01:03:05,350 --> 01:03:07,720 Yield is a convenient way of summarizing 1421 01:03:07,720 --> 01:03:10,232 the properties of a bond, but ultimately 1422 01:03:10,232 --> 01:03:12,190 what you care about in your portfolio is price. 1423 01:03:12,190 --> 01:03:15,160 And so the question is for a move in the interest rate, what 1424 01:03:15,160 --> 01:03:16,840 does that do to the price? 1425 01:03:16,840 --> 01:03:19,270 Well, it turns out that there is one way 1426 01:03:19,270 --> 01:03:23,710 to get at that that is somewhat more intuitive than just 1427 01:03:23,710 --> 01:03:25,450 looking at this kind of fluctuation. 1428 01:03:25,450 --> 01:03:30,220 It's called duration and it's named after a person Macaulay 1429 01:03:30,220 --> 01:03:33,340 who first proposed it as a way of measuring 1430 01:03:33,340 --> 01:03:36,130 how risky a bond is. 1431 01:03:36,130 --> 01:03:42,470 What Macaulay noted was that the longer the maturity of a bond, 1432 01:03:42,470 --> 01:03:48,890 the more sensitive is the bond price to the yield. 1433 01:03:48,890 --> 01:03:52,670 So for example, a 30 year bond, when you move the interest rate 1434 01:03:52,670 --> 01:03:56,810 by one basis point, will have a much, much larger price 1435 01:03:56,810 --> 01:04:00,650 fluctuation than a three month bond, right? 1436 01:04:00,650 --> 01:04:01,250 Why is that? 1437 01:04:01,250 --> 01:04:05,000 Anybody give me some intuition for why that should be? 1438 01:04:05,000 --> 01:04:06,530 Why that makes sense? 1439 01:04:06,530 --> 01:04:08,780 Why should a longer maturity bond 1440 01:04:08,780 --> 01:04:11,260 be more sensitive to changes in yield? 1441 01:04:11,260 --> 01:04:12,000 Yeah, Ken. 1442 01:04:12,000 --> 01:04:13,970 AUDIENCE: Because you're hanging on, 1443 01:04:13,970 --> 01:04:15,746 because the cash is tied up longer. 1444 01:04:15,746 --> 01:04:16,620 ANDREW LO: Yeah, and? 1445 01:04:16,620 --> 01:04:20,330 AUDIENCE: And because the risk-- 1446 01:04:20,330 --> 01:04:22,193 because the opportunity cost essentially 1447 01:04:22,193 --> 01:04:25,139 of having that money tied up for that long means 1448 01:04:25,139 --> 01:04:29,060 you can't spend it on all these other things over those 30 1449 01:04:29,060 --> 01:04:29,560 years. 1450 01:04:29,560 --> 01:04:30,560 ANDREW LO: That's right. 1451 01:04:30,560 --> 01:04:32,900 You're investing for a longer period of time 1452 01:04:32,900 --> 01:04:35,050 so, in fact, the opportunity costs, 1453 01:04:35,050 --> 01:04:37,570 as measured by the foregone interest, 1454 01:04:37,570 --> 01:04:39,220 is going to be much larger. 1455 01:04:39,220 --> 01:04:43,150 In other words, the discount rate that you use, 1456 01:04:43,150 --> 01:04:47,650 this one plus r, you've raised that to the 30th power, 1457 01:04:47,650 --> 01:04:51,100 not to the 1/4 power, and so something that's 1458 01:04:51,100 --> 01:04:54,590 raised to the 30th power in the denominator, 1459 01:04:54,590 --> 01:04:58,510 it has a much larger impact when you perturb that denominator 1460 01:04:58,510 --> 01:05:04,200 by a little bit, because you're actually increasing that power. 1461 01:05:04,200 --> 01:05:07,980 You're increasing that quantity by that 30th power. 1462 01:05:07,980 --> 01:05:09,940 Well, so if that's the case, if it's 1463 01:05:09,940 --> 01:05:13,780 the case that the longer the maturity, the more at risk 1464 01:05:13,780 --> 01:05:17,890 you are per basis point of interest rate fluctuation, 1465 01:05:17,890 --> 01:05:22,960 then why don't we just measure the average duration 1466 01:05:22,960 --> 01:05:24,190 of the bond? 1467 01:05:24,190 --> 01:05:26,980 By average duration, I mean how long does the bond 1468 01:05:26,980 --> 01:05:30,760 last when you weighed it by the coupon payments 1469 01:05:30,760 --> 01:05:32,210 that it pays you? 1470 01:05:32,210 --> 01:05:35,170 So for a pure discount bond, the duration is simple. 1471 01:05:35,170 --> 01:05:37,180 It's just the maturity date, right? 1472 01:05:37,180 --> 01:05:41,560 If you've got a 30 year strip that pays you $1 in 30 years, 1473 01:05:41,560 --> 01:05:44,170 the duration of that bond is just 30 years. 1474 01:05:44,170 --> 01:05:46,930 But what if you had a coupon bond that paid you 1475 01:05:46,930 --> 01:05:49,240 coupons all along the way? 1476 01:05:49,240 --> 01:05:52,240 Well, then, you should take a weighted average of the 30 1477 01:05:52,240 --> 01:05:54,610 years and give some weight to the early years 1478 01:05:54,610 --> 01:05:57,340 too, because the early years are years where 1479 01:05:57,340 --> 01:05:59,140 you're going to receive cash. 1480 01:05:59,140 --> 01:06:00,970 And therefore, interest rate fluctuations 1481 01:06:00,970 --> 01:06:04,850 are going to affect the value of those cash flows. 1482 01:06:04,850 --> 01:06:08,770 So the weighted average term to maturity 1483 01:06:08,770 --> 01:06:16,500 is simply equal to the sum of the date, 1, 2, 3, 4, 5, 6, 1484 01:06:16,500 --> 01:06:21,420 7, multiplied by a weight factor that sums to one. 1485 01:06:21,420 --> 01:06:26,280 And let's just use, as a weight factor, 1486 01:06:26,280 --> 01:06:32,850 the proportion of present value of cash flow on that date. 1487 01:06:35,560 --> 01:06:39,900 So if you take the weighted average 1488 01:06:39,900 --> 01:06:44,220 where you take the weights as the present value of the coupon 1489 01:06:44,220 --> 01:06:46,110 divided by the present value of the bond, 1490 01:06:46,110 --> 01:06:49,080 those weights certainly sum to one. 1491 01:06:49,080 --> 01:06:52,210 And then you're weighting that by the date, 1492 01:06:52,210 --> 01:06:57,030 the year that you get paid, that number will give you what's 1493 01:06:57,030 --> 01:07:01,920 called Macaulay duration. 1494 01:07:01,920 --> 01:07:07,260 So it turns out that the reason that Macaulay duration is 1495 01:07:07,260 --> 01:07:11,910 interesting is that when you take a look at bond prices 1496 01:07:11,910 --> 01:07:16,440 and you ask the question, for a certain percentage change, 1497 01:07:16,440 --> 01:07:18,990 a certain basis point change in the interest rate, what 1498 01:07:18,990 --> 01:07:22,620 does that do to the bond price as a percentage 1499 01:07:22,620 --> 01:07:24,180 of its current price? 1500 01:07:24,180 --> 01:07:26,670 So this is the sensitivity. 1501 01:07:26,670 --> 01:07:29,760 It turns out that you can show that that's actually 1502 01:07:29,760 --> 01:07:34,380 the negative of the Macaulay duration divided 1503 01:07:34,380 --> 01:07:38,170 by one plus the bond yield. 1504 01:07:38,170 --> 01:07:43,020 So this is a long way of stating that the duration gives you 1505 01:07:43,020 --> 01:07:45,360 a measure of how sensitive the bond 1506 01:07:45,360 --> 01:07:49,860 price is to changes in yield. 1507 01:07:49,860 --> 01:07:54,060 The longer the duration, the more sensitive 1508 01:07:54,060 --> 01:07:56,790 the bond is to changes in yield. 1509 01:07:56,790 --> 01:08:00,540 And duration now just means a weighted average 1510 01:08:00,540 --> 01:08:05,670 of all of the payout dates that a bond will have. 1511 01:08:05,670 --> 01:08:09,060 If a bond pays a lot of its cash up front 1512 01:08:09,060 --> 01:08:12,820 and very little in later periods, 1513 01:08:12,820 --> 01:08:15,865 is the duration high or low? 1514 01:08:15,865 --> 01:08:16,695 AUDIENCE: Low. 1515 01:08:16,695 --> 01:08:17,529 ANDREW LO: Low. 1516 01:08:17,529 --> 01:08:19,840 And so if a duration is low what that says 1517 01:08:19,840 --> 01:08:21,970 is that there's not a lot of sensitivity 1518 01:08:21,970 --> 01:08:25,240 to changes in yield on the bond price itself. 1519 01:08:25,240 --> 01:08:27,340 If on the other hand, all of your payment 1520 01:08:27,340 --> 01:08:30,370 is out in the future, way out in the future, that's 1521 01:08:30,370 --> 01:08:34,149 going to make it very interest rate sensitive. 1522 01:08:34,149 --> 01:08:37,930 And the negative number here indicates 1523 01:08:37,930 --> 01:08:42,340 that there's an inverse relationship between price 1524 01:08:42,340 --> 01:08:43,330 and yield. 1525 01:08:43,330 --> 01:08:48,279 So when bond investors look at a particular portfolio of bonds, 1526 01:08:48,279 --> 01:08:51,021 and this is key, they look at a portfolio of bonds 1527 01:08:51,021 --> 01:08:53,229 because that's what they're going to be investing in. 1528 01:08:53,229 --> 01:08:55,720 When you put your money in a money market fund 1529 01:08:55,720 --> 01:08:59,319 or in a bond fund, medium term, long term, 1530 01:08:59,319 --> 01:09:01,210 you're not putting it in one bond, 1531 01:09:01,210 --> 01:09:04,029 you're putting it in a whole set of bonds. 1532 01:09:04,029 --> 01:09:07,300 Your natural question is, how sensitive 1533 01:09:07,300 --> 01:09:11,020 is that portfolio to changes in interest rates? 1534 01:09:11,020 --> 01:09:15,490 And the answer is it's related to the duration. 1535 01:09:15,490 --> 01:09:17,740 And so if I told you that this portfolio has 1536 01:09:17,740 --> 01:09:21,200 a duration of five and 1/2 years, 1537 01:09:21,200 --> 01:09:23,590 that will give you some intuition for how sensitive 1538 01:09:23,590 --> 01:09:26,649 or how risky that portfolio is. 1539 01:09:26,649 --> 01:09:29,410 So duration is a measure that I've defined for a bond, 1540 01:09:29,410 --> 01:09:32,200 but you can define it for a portfolio of bonds, 1541 01:09:32,200 --> 01:09:36,649 simply by taking the cash flows at every period 1542 01:09:36,649 --> 01:09:39,729 and then computing a weighted average where the weights are 1543 01:09:39,729 --> 01:09:42,460 the present value of those cash flows as a function 1544 01:09:42,460 --> 01:09:45,710 of the entire portfolio. 1545 01:09:45,710 --> 01:09:50,870 OK, so here's an example where I've got a four year Treasury 1546 01:09:50,870 --> 01:09:56,810 note with a face value of $100, 7% coupon selling at a $103.50, 1547 01:09:56,810 --> 01:10:00,620 which yields 6%. 1548 01:10:00,620 --> 01:10:03,320 That's the yield, that's the why that 1549 01:10:03,320 --> 01:10:08,090 makes this 103.5 equal to the present value of all 1550 01:10:08,090 --> 01:10:11,926 of those coupon payments plus the return of principal. 1551 01:10:14,630 --> 01:10:18,620 And so here what I've done is to calculate for you 1552 01:10:18,620 --> 01:10:23,210 the cash flows of the bond, the present value of those cash 1553 01:10:23,210 --> 01:10:29,510 flows, and then the respective product of t 1554 01:10:29,510 --> 01:10:32,130 times the present value of cash flows. 1555 01:10:32,130 --> 01:10:36,200 So you can actually compute for yourself that duration number. 1556 01:10:36,200 --> 01:10:41,560 And you can get a sense of exactly what that is. 1557 01:10:41,560 --> 01:10:46,660 So the duration is about 7.13 years. 1558 01:10:46,660 --> 01:10:49,180 So duration is a measurement that 1559 01:10:49,180 --> 01:10:52,570 is in units of years or half year units. 1560 01:10:52,570 --> 01:10:55,840 Sorry, 7.13 half year units. 1561 01:10:55,840 --> 01:11:01,760 And the modified duration is going to be given by 6.92. 1562 01:11:01,760 --> 01:11:05,360 Price risk at a yield of 3% therefore 1563 01:11:05,360 --> 01:11:09,830 is going to be given by just this expression right here. 1564 01:11:09,830 --> 01:11:12,080 What that says is that if the yield moves up 1565 01:11:12,080 --> 01:11:15,920 by 1/10 of a percent or 10 basis points, 1566 01:11:15,920 --> 01:11:19,820 the bond price is going to decrease by 68 basis points. 1567 01:11:19,820 --> 01:11:23,390 That will give you a sense of how exposed you are. 1568 01:11:23,390 --> 01:11:25,580 If you have very long duration portfolios, 1569 01:11:25,580 --> 01:11:28,190 that means that you're going to be in for a wild ride 1570 01:11:28,190 --> 01:11:31,050 as interest rates swing around a lot. 1571 01:11:31,050 --> 01:11:33,740 And if you're willing to take on that risk, that's great, 1572 01:11:33,740 --> 01:11:37,670 but you're going to be at least compensated for that. 1573 01:11:41,270 --> 01:11:47,520 Macaulay duration, you can compute it in this way. 1574 01:11:47,520 --> 01:11:50,350 For intra-year coupons, that's a very straightforward 1575 01:11:50,350 --> 01:11:51,170 calculation. 1576 01:11:51,170 --> 01:11:53,260 So you want to make sure you know how to do that. 1577 01:11:53,260 --> 01:11:55,900 You simply just use the usual discounting 1578 01:11:55,900 --> 01:12:01,060 and dividing the yield by the appropriate payment periods. 1579 01:12:01,060 --> 01:12:05,740 And now the last concept that I want to cover today 1580 01:12:05,740 --> 01:12:09,100 is convexity. 1581 01:12:09,100 --> 01:12:14,380 Convexity is another measure of risk. 1582 01:12:14,380 --> 01:12:16,210 It's the second derivative. 1583 01:12:16,210 --> 01:12:24,870 What it measures is how the sensitivity itself changes. 1584 01:12:24,870 --> 01:12:28,380 And it turns out that convexity, as a measure, 1585 01:12:28,380 --> 01:12:33,750 gives you sort of a higher order approximation both to the price 1586 01:12:33,750 --> 01:12:36,330 of the bond, as well as how the bond 1587 01:12:36,330 --> 01:12:40,150 is going to move with respect to interest rates. 1588 01:12:40,150 --> 01:12:42,460 So let me just show you what the derivation is. 1589 01:12:42,460 --> 01:12:45,560 It's pretty straightforward, but if you have any questions, 1590 01:12:45,560 --> 01:12:48,440 I'm happy to discuss it. 1591 01:12:48,440 --> 01:12:51,910 You take the price of a bond and you take the second derivative 1592 01:12:51,910 --> 01:12:54,504 with respect to the yield. 1593 01:12:54,504 --> 01:12:55,920 What you're going to get out of it 1594 01:12:55,920 --> 01:13:00,010 is an expression that looks like this. 1595 01:13:00,010 --> 01:13:03,420 Now that expression in and of itself 1596 01:13:03,420 --> 01:13:06,300 has relatively little intuition. 1597 01:13:06,300 --> 01:13:11,340 But let me just write down the percentage change 1598 01:13:11,340 --> 01:13:15,660 in the first derivative as v sub m, 1599 01:13:15,660 --> 01:13:20,010 and then I'm going to show you an interesting relationship. 1600 01:13:20,010 --> 01:13:23,910 For those of you who remember your high school calculus 1601 01:13:23,910 --> 01:13:25,920 or college calculus class, you'll 1602 01:13:25,920 --> 01:13:28,750 remember there's something called a Taylor approximation, 1603 01:13:28,750 --> 01:13:29,250 right? 1604 01:13:29,250 --> 01:13:30,600 Taylor series. 1605 01:13:30,600 --> 01:13:34,020 This is a method of approximating nonlinear 1606 01:13:34,020 --> 01:13:38,070 relationships using polynomials, powers 1607 01:13:38,070 --> 01:13:40,470 of the variables in question. 1608 01:13:40,470 --> 01:13:44,094 If you took the bond price as a function of the yield, 1609 01:13:44,094 --> 01:13:46,260 it's a nonlinear function, of course, because you've 1610 01:13:46,260 --> 01:13:50,120 got that discounting going on. 1611 01:13:50,120 --> 01:13:52,030 Then you can ask the question, how 1612 01:13:52,030 --> 01:13:55,960 can I approximate the bond price as a function of the yield 1613 01:13:55,960 --> 01:14:02,680 if I'm willing to take a couple of terms of the approximation? 1614 01:14:02,680 --> 01:14:06,370 And when you do that, you get what 1615 01:14:06,370 --> 01:14:07,970 may look like an awful expression, 1616 01:14:07,970 --> 01:14:11,740 but actually it's quite beautiful in its own right. 1617 01:14:11,740 --> 01:14:15,790 What this says is that the price of the bond at a new interest 1618 01:14:15,790 --> 01:14:22,150 rate, at a new yield, if the yield changes, then 1619 01:14:22,150 --> 01:14:26,530 price of the bond at the new interest rate 1620 01:14:26,530 --> 01:14:28,720 is going to be equal to the price of the bond 1621 01:14:28,720 --> 01:14:30,790 at the old interest rate, multiplied 1622 01:14:30,790 --> 01:14:34,240 by a factor of something or other. 1623 01:14:34,240 --> 01:14:36,850 And that factor is going to be given 1624 01:14:36,850 --> 01:14:43,600 by one minus a term that's a linear function of the yield, 1625 01:14:43,600 --> 01:14:48,730 plus another term that is a quadratic function 1626 01:14:48,730 --> 01:14:51,045 of the change in the yield. 1627 01:14:51,045 --> 01:14:52,420 So this is what I mean when I say 1628 01:14:52,420 --> 01:14:56,140 this is a second order approximation to the pricing 1629 01:14:56,140 --> 01:14:58,060 relationship. 1630 01:14:58,060 --> 01:15:02,710 And this basically gives us a way 1631 01:15:02,710 --> 01:15:06,010 to figure out when yields move, what does that 1632 01:15:06,010 --> 01:15:08,400 do to my portfolio. 1633 01:15:08,400 --> 01:15:09,900 Now you might be thinking, gee, this 1634 01:15:09,900 --> 01:15:12,840 is an awful long way to go to try to figure that out. 1635 01:15:12,840 --> 01:15:15,450 Can't we just use an Excel spreadsheet 1636 01:15:15,450 --> 01:15:18,660 and then move the interest rate and then recalculate and see 1637 01:15:18,660 --> 01:15:20,340 what that does? 1638 01:15:20,340 --> 01:15:24,290 Today, you can, but in the 1970s, you couldn't. 1639 01:15:24,290 --> 01:15:25,860 You didn't have that ability. 1640 01:15:25,860 --> 01:15:29,400 So much of this framework was developed in the 1970s 1641 01:15:29,400 --> 01:15:34,410 because people wanted to have easy ways of not only pricing 1642 01:15:34,410 --> 01:15:38,730 bonds, but figuring out what the risk of their positions 1643 01:15:38,730 --> 01:15:40,650 were as bond traders. 1644 01:15:40,650 --> 01:15:42,636 And to do that quickly is very difficult. 1645 01:15:42,636 --> 01:15:44,010 You remember the story I told you 1646 01:15:44,010 --> 01:15:47,340 about when I got a mortgage 20 years ago 1647 01:15:47,340 --> 01:15:50,879 and the bank loan officer just could not figure out 1648 01:15:50,879 --> 01:15:52,170 what my mortgage payments were. 1649 01:15:52,170 --> 01:15:54,932 She had to go look for a book and try to thumb through what 1650 01:15:54,932 --> 01:15:55,890 those calculations are. 1651 01:15:55,890 --> 01:15:58,470 Well, imagine if you're a bond trader trading literally 1652 01:15:58,470 --> 01:16:00,210 every minute of the day, and there 1653 01:16:00,210 --> 01:16:04,020 was bond trading going on in the 1970s, believe it or not. 1654 01:16:04,020 --> 01:16:06,330 You have to figure out these pricing relationships. 1655 01:16:06,330 --> 01:16:07,900 And it was not so easy. 1656 01:16:07,900 --> 01:16:11,250 So a number of mathematicians came up 1657 01:16:11,250 --> 01:16:13,570 with these kind of relationships for bond prices. 1658 01:16:13,570 --> 01:16:15,060 In fact, it's funny. 1659 01:16:15,060 --> 01:16:16,830 Bond pricing is actually quite a bit more 1660 01:16:16,830 --> 01:16:20,040 of a mathematical art than equity pricing 1661 01:16:20,040 --> 01:16:21,480 simply because with a bond, there 1662 01:16:21,480 --> 01:16:23,140 aren't that many moving parts. 1663 01:16:23,140 --> 01:16:26,460 And so they aren't subject to mathematical analysis 1664 01:16:26,460 --> 01:16:29,280 like this, whereas with stock prices, 1665 01:16:29,280 --> 01:16:32,130 since there are so many factors impinging on it, 1666 01:16:32,130 --> 01:16:34,560 the actual tools that we use are quite a bit 1667 01:16:34,560 --> 01:16:38,730 less complex, at least from a historical perspective. 1668 01:16:38,730 --> 01:16:41,670 So the purpose of this is really just 1669 01:16:41,670 --> 01:16:45,840 to approximate the risk of a bond portfolio. 1670 01:16:45,840 --> 01:16:47,790 You want to know when you change yields what 1671 01:16:47,790 --> 01:16:49,290 that does to the portfolio. 1672 01:16:49,290 --> 01:16:52,050 And you also want to know if the yield changes 1673 01:16:52,050 --> 01:16:55,660 in volatility, what does that do to the portfolio. 1674 01:16:55,660 --> 01:16:58,080 So this first term here, this term 1675 01:16:58,080 --> 01:17:01,470 tells you about shifts in the interest rate. 1676 01:17:01,470 --> 01:17:05,400 What this term does is tell you about fluctuations 1677 01:17:05,400 --> 01:17:08,730 or volatility of interest rates. 1678 01:17:08,730 --> 01:17:10,650 And it turns out that volatility has 1679 01:17:10,650 --> 01:17:15,330 an impact on bond portfolios, as does changes 1680 01:17:15,330 --> 01:17:18,570 in the level of interest rates. 1681 01:17:18,570 --> 01:17:20,160 Just looking at this, can anybody 1682 01:17:20,160 --> 01:17:25,500 tell me off the top of their head what direction this goes? 1683 01:17:25,500 --> 01:17:29,540 In other words, if you are holding a bond and interest 1684 01:17:29,540 --> 01:17:35,230 rates rise, we know that bond prices will fall. 1685 01:17:35,230 --> 01:17:37,450 But what if the volatility of interest rates 1686 01:17:37,450 --> 01:17:40,930 rise, as they have over the last few weeks? 1687 01:17:40,930 --> 01:17:43,330 Yields have bounced around a lot more 1688 01:17:43,330 --> 01:17:44,920 lately than they have in the past. 1689 01:17:44,920 --> 01:17:46,758 What does that do to a bond? 1690 01:17:49,150 --> 01:17:51,150 Does it make it more valuable and less valuable? 1691 01:17:51,150 --> 01:17:53,440 Let's put it that way. 1692 01:17:53,440 --> 01:17:54,360 How do you know? 1693 01:17:54,360 --> 01:17:56,010 Less, more? 1694 01:17:56,010 --> 01:17:57,960 We have some volatility here. 1695 01:18:01,300 --> 01:18:03,880 Take a look at that expression. 1696 01:18:03,880 --> 01:18:08,980 v sub m is going to be the second derivative, 1697 01:18:08,980 --> 01:18:11,530 and then you've got a term there that's going 1698 01:18:11,530 --> 01:18:17,200 to be the change in the yield squared. 1699 01:18:17,200 --> 01:18:20,350 If the change in the yield squared goes up, 1700 01:18:20,350 --> 01:18:24,240 other things equal, and other things are never equal, 1701 01:18:24,240 --> 01:18:28,500 but economists like to say other things equal, 1702 01:18:28,500 --> 01:18:33,120 it actually makes bonds more valuable. 1703 01:18:33,120 --> 01:18:38,050 In this respect, owning a bond actually is sort of 1704 01:18:38,050 --> 01:18:39,619 like owning an option. 1705 01:18:39,619 --> 01:18:41,160 Now you don't know about options yet. 1706 01:18:41,160 --> 01:18:43,580 We're going to come to in a few lectures. 1707 01:18:43,580 --> 01:18:47,650 But it turns out that having an option when volatility goes up 1708 01:18:47,650 --> 01:18:49,690 can be very valuable. 1709 01:18:49,690 --> 01:18:53,020 And similarly for bonds, bonds have 1710 01:18:53,020 --> 01:18:55,120 option-like characteristics. 1711 01:18:55,120 --> 01:18:58,090 And we see that here with this approximation. 1712 01:18:58,090 --> 01:19:02,530 That second term will actually yield some actual value 1713 01:19:02,530 --> 01:19:04,420 when volatility goes up. 1714 01:19:04,420 --> 01:19:06,280 Now I do a numerical example here 1715 01:19:06,280 --> 01:19:08,860 that I'd like you to look through on your own 1716 01:19:08,860 --> 01:19:13,720 where I compute for you both the first and second terms 1717 01:19:13,720 --> 01:19:15,280 of that approximation. 1718 01:19:15,280 --> 01:19:19,180 And you can actually see how good the approximation is. 1719 01:19:19,180 --> 01:19:21,730 So I'd like you to take a look at that, make sure 1720 01:19:21,730 --> 01:19:23,920 you understand it, and next time, 1721 01:19:23,920 --> 01:19:26,830 be happy to answer questions about this. 1722 01:19:26,830 --> 01:19:29,110 What we're going to cover on Monday 1723 01:19:29,110 --> 01:19:33,550 is risky debt, which of course is directly related to what's 1724 01:19:33,550 --> 01:19:35,410 going on in markets today. 1725 01:19:35,410 --> 01:19:40,210 And so I'd like you to read up on that in the textbook. 1726 01:19:40,210 --> 01:19:42,130 And when we come back on Monday, we're 1727 01:19:42,130 --> 01:19:45,130 going to talk about debt ratings and possibly 1728 01:19:45,130 --> 01:19:49,980 what went wrong with all of these subprime securities.