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 --> 00:00:17,830 at ocw.mit.edu. 8 00:00:26,622 --> 00:00:28,830 ANDREW LO: Now, also, before I begin today's lecture, 9 00:00:28,830 --> 00:00:31,246 I want to comment a bit about what's going on in the news, 10 00:00:31,246 --> 00:00:36,990 because last time, on Monday, we said-- or I said-- 11 00:00:36,990 --> 00:00:39,045 that the Fed was going to cut rates. 12 00:00:39,045 --> 00:00:40,350 [LAUGHTER] 13 00:00:40,350 --> 00:00:44,880 And in fact, if you looked at the data on Monday 14 00:00:44,880 --> 00:00:47,580 and you looked at things like the Fed fund's future 15 00:00:47,580 --> 00:00:51,060 and other financial contracts, the market 16 00:00:51,060 --> 00:00:53,400 had priced in the fact that the Fed 17 00:00:53,400 --> 00:00:56,130 was going to cut at least 25 basis points, 18 00:00:56,130 --> 00:00:58,070 and actually a reasonable probability that it 19 00:00:58,070 --> 00:00:59,730 was going to cut 50. 20 00:00:59,730 --> 00:01:01,590 And of course, they did neither. 21 00:01:01,590 --> 00:01:03,960 They actually held rates steady. 22 00:01:03,960 --> 00:01:07,140 But they did do something. 23 00:01:07,140 --> 00:01:08,130 What did they do? 24 00:01:08,130 --> 00:01:09,150 Anybody know? 25 00:01:09,150 --> 00:01:09,828 Yeah. 26 00:01:09,828 --> 00:01:13,320 STUDENT: Extended [INAUDIBLE] 27 00:01:13,320 --> 00:01:15,340 ANDREW LO: How large a loan? 28 00:01:15,340 --> 00:01:20,520 $85 billion, which, even among friends, is a lot of money. 29 00:01:20,520 --> 00:01:22,230 [LAUGHTER] 30 00:01:22,230 --> 00:01:27,840 Now, this is yet again an extraordinary and unprecedented 31 00:01:27,840 --> 00:01:28,890 measure. 32 00:01:28,890 --> 00:01:32,820 We know that the Fed did backstop Bear Stearns. 33 00:01:32,820 --> 00:01:36,360 But the Fed didn't spend any direct money on Bear Stearns. 34 00:01:36,360 --> 00:01:39,210 They basically got JP Morgan to buy Bear Stearns 35 00:01:39,210 --> 00:01:41,700 and negotiated the deal. 36 00:01:41,700 --> 00:01:46,050 In this instance, the Fed is lending money to AIG, 37 00:01:46,050 --> 00:01:48,090 lending $85 billion. 38 00:01:48,090 --> 00:01:50,490 And AIG isn't even a bank. 39 00:01:50,490 --> 00:01:53,210 So what do you think is going on? 40 00:01:53,210 --> 00:01:54,716 Does that make sense? 41 00:01:54,716 --> 00:01:57,090 What does that tell you about what's going on in markets? 42 00:01:57,090 --> 00:02:00,480 The fact that everybody thought the Fed was gonna cut rates, 43 00:02:00,480 --> 00:02:01,620 and they didn't-- 44 00:02:01,620 --> 00:02:04,200 that shows a certain kind of restraint. 45 00:02:04,200 --> 00:02:05,910 In fact, I think it was in this class 46 00:02:05,910 --> 00:02:10,090 that somebody mentioned, well, rates are already down at 2%. 47 00:02:10,090 --> 00:02:11,490 How much more can they cut? 48 00:02:11,490 --> 00:02:13,622 I mean, if they cut 50 basis points, 49 00:02:13,622 --> 00:02:15,330 that leaves them very little flexibility. 50 00:02:15,330 --> 00:02:18,990 And also, if you think that the reason we are in this crisis 51 00:02:18,990 --> 00:02:22,620 is because borrowing has been so low for so long, that people 52 00:02:22,620 --> 00:02:24,990 have been going out making all these bad loans when they 53 00:02:24,990 --> 00:02:27,007 shouldn't be doing that to begin with, 54 00:02:27,007 --> 00:02:29,340 cutting rates is not going to really help that situation 55 00:02:29,340 --> 00:02:31,770 but can only encourage it. 56 00:02:31,770 --> 00:02:33,330 Nevertheless, there was a crisis. 57 00:02:33,330 --> 00:02:36,060 Certainly over the weekend, we had some very bad news. 58 00:02:36,060 --> 00:02:41,240 Lehman Brothers went under, and the Fed did what? 59 00:02:41,240 --> 00:02:42,230 Nothing. 60 00:02:42,230 --> 00:02:44,780 So if the Fed did nothing for Lehman, 61 00:02:44,780 --> 00:02:49,567 yet they extended an $85 billion loan for AIG, 62 00:02:49,567 --> 00:02:50,900 something's got to be different. 63 00:02:50,900 --> 00:02:51,200 Right? 64 00:02:51,200 --> 00:02:53,090 I mean, I guess you could see whether or not 65 00:02:53,090 --> 00:02:56,480 Ben Bernanke has a brother-in-law working at AIG, 66 00:02:56,480 --> 00:02:58,560 but I don't think that's it. 67 00:02:58,560 --> 00:02:59,253 Yeah. 68 00:02:59,253 --> 00:03:02,031 STUDENT: [? But today it was ?] reported that Barclays is 69 00:03:02,031 --> 00:03:04,320 actually going to go ahead and buy [? them. ?] So what 70 00:03:04,320 --> 00:03:04,820 changed-- 71 00:03:04,820 --> 00:03:06,980 ANDREW LO: Well, the announcement 72 00:03:06,980 --> 00:03:10,280 is that Barclays is buying some of the US operations of Lehman 73 00:03:10,280 --> 00:03:11,060 Brothers. 74 00:03:11,060 --> 00:03:14,510 They are cherry-picking the operations that they want. 75 00:03:14,510 --> 00:03:17,660 What Lehman tried to do over the weekend was broker a deal 76 00:03:17,660 --> 00:03:19,490 where Barclays would buy all of them, 77 00:03:19,490 --> 00:03:21,200 assume all their obligations, and allow 78 00:03:21,200 --> 00:03:24,450 them to keep on going as a going business concern. 79 00:03:24,450 --> 00:03:26,450 Barclays couldn't do that, because they couldn't 80 00:03:26,450 --> 00:03:28,670 get shareholder approval quickly enough, 81 00:03:28,670 --> 00:03:31,520 and also ostensibly because the Fed would not 82 00:03:31,520 --> 00:03:34,700 backstop any losses that Lehman had hidden in its books. 83 00:03:34,700 --> 00:03:36,890 And in a matter of 48 hours, it's, 84 00:03:36,890 --> 00:03:39,770 kind of, hard to figure out all the buried bodies 85 00:03:39,770 --> 00:03:42,770 in an organization as complex and as large as Lehman. 86 00:03:42,770 --> 00:03:47,120 But Barclays is going ahead and purchasing those units 87 00:03:47,120 --> 00:03:48,849 that they like, and there are many units 88 00:03:48,849 --> 00:03:51,140 at Lehman Brothers that are extraordinarily profitable, 89 00:03:51,140 --> 00:03:53,667 very good businesses with excellent people. 90 00:03:53,667 --> 00:03:55,250 So Barclays is going ahead with those. 91 00:03:55,250 --> 00:03:57,800 And by the way, there are all sorts of other sharks 92 00:03:57,800 --> 00:04:00,320 that are swimming around Lehman, cherry-picking various 93 00:04:00,320 --> 00:04:01,310 different groups. 94 00:04:01,310 --> 00:04:04,160 This is part of the problem with these this kind 95 00:04:04,160 --> 00:04:05,150 of financial distress. 96 00:04:05,150 --> 00:04:07,985 We're going to actually get to this at about lecture 18. 97 00:04:07,985 --> 00:04:09,860 We're going to talk about financial distress, 98 00:04:09,860 --> 00:04:11,943 and I'm going to bring you back to Lehman Brothers 99 00:04:11,943 --> 00:04:14,300 and ask you to think about the problems 100 00:04:14,300 --> 00:04:15,470 that this company faces. 101 00:04:15,470 --> 00:04:16,700 Because think about it. 102 00:04:16,700 --> 00:04:19,902 Now that it's been announced that Lehman is liquidating-- 103 00:04:19,902 --> 00:04:21,110 well, let me put it this way. 104 00:04:21,110 --> 00:04:22,550 Suppose you were working at Lehman Brothers, 105 00:04:22,550 --> 00:04:24,080 suppose that you've been there 15 years, 106 00:04:24,080 --> 00:04:25,455 and suppose that you were running 107 00:04:25,455 --> 00:04:28,389 one of the most successful proprietary trading groups 108 00:04:28,389 --> 00:04:29,180 at Lehman Brothers. 109 00:04:29,180 --> 00:04:32,630 And now, this news comes up, and it's a surprise to you. 110 00:04:32,630 --> 00:04:34,070 What is your first reaction? 111 00:04:34,070 --> 00:04:35,490 What are you going to do? 112 00:04:35,490 --> 00:04:35,990 Yeah? 113 00:04:35,990 --> 00:04:36,830 STUDENT: [INAUDIBLE] 114 00:04:36,830 --> 00:04:37,340 ANDREW LO: Right. 115 00:04:37,340 --> 00:04:38,480 That's certainly one thing. 116 00:04:38,480 --> 00:04:40,771 You're going to take a look at what your positions are. 117 00:04:40,771 --> 00:04:42,560 And then, after you establish that you're 118 00:04:42,560 --> 00:04:44,512 OK in terms of your trading positions, 119 00:04:44,512 --> 00:04:46,220 what's the next thing you're going to do? 120 00:04:46,220 --> 00:04:47,950 What are you gonna start thinking about? 121 00:04:47,950 --> 00:04:48,100 Yeah? 122 00:04:48,100 --> 00:04:49,430 STUDENT: Start bringing your resume? 123 00:04:49,430 --> 00:04:49,940 ANDREW LO: Exactly. 124 00:04:49,940 --> 00:04:51,560 You're going to start looking around. 125 00:04:51,560 --> 00:04:54,350 So you're going to talk to lots of other people about, maybe, 126 00:04:54,350 --> 00:04:56,379 moving your entire group of 15 people 127 00:04:56,379 --> 00:04:57,920 that you've hand-picked and developed 128 00:04:57,920 --> 00:04:58,954 over the last 15 years. 129 00:04:58,954 --> 00:05:00,620 And you're gonna start talking all sorts 130 00:05:00,620 --> 00:05:03,500 of other counter-parties to move your entire group. 131 00:05:03,500 --> 00:05:07,100 And now, Barclays decides to buy Lehman, the operations 132 00:05:07,100 --> 00:05:09,390 that you're a part of. 133 00:05:09,390 --> 00:05:11,640 But there's no slavery in the United States, 134 00:05:11,640 --> 00:05:13,800 at least not since the 1800s, which 135 00:05:13,800 --> 00:05:16,350 means that if you want to walk, you can. 136 00:05:16,350 --> 00:05:17,670 So if Lehman buys-- 137 00:05:17,670 --> 00:05:21,690 if Barclays buys Lehman and buys the group that you're in, 138 00:05:21,690 --> 00:05:24,210 and you're one of the most profitable parts of that, 139 00:05:24,210 --> 00:05:25,830 you don't have to stay. 140 00:05:25,830 --> 00:05:28,550 So in addition to paying for Lehman, 141 00:05:28,550 --> 00:05:30,300 Barclays is also gonna have to talk to you 142 00:05:30,300 --> 00:05:32,175 and get you to stay, which means that they're 143 00:05:32,175 --> 00:05:34,140 going to have to pay you an extra bonus and all 144 00:05:34,140 --> 00:05:35,790 of your people bonuses to stay. 145 00:05:35,790 --> 00:05:38,430 So now, the price of having to keep Lehman 146 00:05:38,430 --> 00:05:41,520 together has just gone up dramatically, 147 00:05:41,520 --> 00:05:44,580 because you've got to keep all of the talent, 148 00:05:44,580 --> 00:05:46,050 and it's very hard to do that. 149 00:05:46,050 --> 00:05:48,510 So the fact that Lehman is in trouble 150 00:05:48,510 --> 00:05:51,120 has caused all sorts of problems and will 151 00:05:51,120 --> 00:05:54,510 create additional amounts of frictions and payments 152 00:05:54,510 --> 00:05:56,400 that otherwise wouldn't have had to be. 153 00:05:56,400 --> 00:05:58,650 So I want you to keep that in the back of your minds-- 154 00:05:58,650 --> 00:05:59,983 the costs of financial distress. 155 00:05:59,983 --> 00:06:03,910 We're going to come back to that in, about, 10 lectures. 156 00:06:03,910 --> 00:06:06,210 OK so-- yeah, question? 157 00:06:06,210 --> 00:06:09,210 STUDENT: I heard a [? quote ?] with regards to the Fed action, 158 00:06:09,210 --> 00:06:11,560 that the Fed decided that the problem is not 159 00:06:11,560 --> 00:06:13,870 the cost of money but the supply of money. 160 00:06:13,870 --> 00:06:17,460 So they're going to infuse capital into the market. 161 00:06:17,460 --> 00:06:20,866 Is that just referring to the AIG 85 billion, 162 00:06:20,866 --> 00:06:23,520 or is there some other way that they're infusing capital? 163 00:06:23,520 --> 00:06:23,760 ANDREW LO: No. 164 00:06:23,760 --> 00:06:25,051 Well, that's certainly one way. 165 00:06:25,051 --> 00:06:28,350 But the other way is that they are allowing the other banks 166 00:06:28,350 --> 00:06:30,730 to borrow from them at a lower rate. 167 00:06:30,730 --> 00:06:33,060 So the discount window that typically banks 168 00:06:33,060 --> 00:06:34,890 go to borrow from the Fed-- 169 00:06:34,890 --> 00:06:37,260 they're making more money available in that way. 170 00:06:37,260 --> 00:06:39,870 And other central banks are doing the same thing-- 171 00:06:39,870 --> 00:06:41,880 injecting money into the system in order 172 00:06:41,880 --> 00:06:43,322 to calm the fears of individuals. 173 00:06:43,322 --> 00:06:45,780 STUDENT: Does that lower the effect of [? interest rate? ?] 174 00:06:45,780 --> 00:06:47,250 ANDREW LO: Well, we're going to see that in a minute. 175 00:06:47,250 --> 00:06:48,600 We're going to actually-- one of the things 176 00:06:48,600 --> 00:06:50,850 I want to talk about today is, exactly what do we 177 00:06:50,850 --> 00:06:52,500 see from market prices? 178 00:06:52,500 --> 00:06:55,560 Now, on Monday, I claimed that market prices was telling us, 179 00:06:55,560 --> 00:06:56,940 there's going to be a Fed cut. 180 00:06:56,940 --> 00:06:59,280 Clearly, it was wrong. 181 00:06:59,280 --> 00:07:02,280 Now, that's a very good lesson, because what 182 00:07:02,280 --> 00:07:05,267 this is telling us is that market prices have information, 183 00:07:05,267 --> 00:07:07,600 but as I told you last time, they're not a crystal ball. 184 00:07:07,600 --> 00:07:10,210 They're not perfect, and so they can be wrong. 185 00:07:10,210 --> 00:07:14,130 Apparently-- and this is now very speculative. 186 00:07:14,130 --> 00:07:16,800 Apparently, the Fed decided, as you pointed out, 187 00:07:16,800 --> 00:07:21,810 that it's not the availability of-- or rather the cost 188 00:07:21,810 --> 00:07:22,330 of funds. 189 00:07:22,330 --> 00:07:24,390 That's not what's important, but rather the availability. 190 00:07:24,390 --> 00:07:26,520 In other words, they're worried about a credit 191 00:07:26,520 --> 00:07:29,340 crisis, a crisis of liquidity. 192 00:07:29,340 --> 00:07:33,600 And AIG is a very important player in that respect-- 193 00:07:33,600 --> 00:07:35,910 apparently, much more so than Lehman. 194 00:07:35,910 --> 00:07:38,400 Because Fed didn't do anything to try to keep Lehman 195 00:07:38,400 --> 00:07:40,940 from going under, but an $85 billion 196 00:07:40,940 --> 00:07:45,330 loan was what they decided was appropriate for AIG. 197 00:07:45,330 --> 00:07:47,070 The reason for that-- 198 00:07:47,070 --> 00:07:48,510 the ostensible reason. 199 00:07:48,510 --> 00:07:50,310 Who knows what the real reasons may be? 200 00:07:50,310 --> 00:07:54,660 But the reasons that we think this happened 201 00:07:54,660 --> 00:07:59,250 is that AIG provides enormous amounts of insurance 202 00:07:59,250 --> 00:08:03,090 to a variety of other players in the credit markets. 203 00:08:03,090 --> 00:08:05,790 And if they go under, if they decide 204 00:08:05,790 --> 00:08:08,820 that they can't make good on those insurance claims, 205 00:08:08,820 --> 00:08:11,970 what happens is that those investors that 206 00:08:11,970 --> 00:08:15,450 are holding the paper that is backed 207 00:08:15,450 --> 00:08:20,580 by subprime assets and that are insured by AIG-- 208 00:08:20,580 --> 00:08:23,100 once the insurance disappears, they 209 00:08:23,100 --> 00:08:27,090 are obligated, a number of them, to sell those pieces of paper. 210 00:08:27,090 --> 00:08:28,920 If you're a pension fund, you are 211 00:08:28,920 --> 00:08:32,190 obligated to hold only investment grade assets. 212 00:08:32,190 --> 00:08:34,873 If it turns out that for any reason 213 00:08:34,873 --> 00:08:36,914 those assets become lower than investment grade-- 214 00:08:36,914 --> 00:08:39,122 and we're going to talk about this at 4 o'clock today 215 00:08:39,122 --> 00:08:39,960 at that proseminar. 216 00:08:39,960 --> 00:08:43,140 If it falls below investment grade, by law, 217 00:08:43,140 --> 00:08:47,669 you are obligated to get rid of those assets. 218 00:08:47,669 --> 00:08:49,710 Now, what do you think would happen to the market 219 00:08:49,710 --> 00:08:53,201 if everybody all at once decided to get rid of those assets? 220 00:08:53,201 --> 00:08:55,812 STUDENT: [INAUDIBLE] 221 00:08:55,812 --> 00:08:56,520 ANDREW LO: Right. 222 00:08:56,520 --> 00:08:58,890 And then, there'd be a mass panic. 223 00:08:58,890 --> 00:08:59,390 Right. 224 00:08:59,390 --> 00:09:00,745 STUDENT: I just have-- there's something 225 00:09:00,745 --> 00:09:02,348 simple that I don't understand. 226 00:09:02,348 --> 00:09:06,300 How can the interest rate go below the inflation rate? 227 00:09:06,300 --> 00:09:08,130 ANDREW LO: Well, it's not supposed to 228 00:09:08,130 --> 00:09:10,210 for any extended period of time. 229 00:09:10,210 --> 00:09:12,420 But for any short period of time, it certainly can. 230 00:09:12,420 --> 00:09:14,592 And what it says is that the real rate is negative 231 00:09:14,592 --> 00:09:16,050 or that the economy is contracting. 232 00:09:16,050 --> 00:09:18,496 STUDENT: So like right now, $1 a year from now 233 00:09:18,496 --> 00:09:20,490 is more valuable than it [? would be ?] today. 234 00:09:20,490 --> 00:09:21,420 Right? 235 00:09:21,420 --> 00:09:24,400 ANDREW LO: Well, if you take inflation into account, 236 00:09:24,400 --> 00:09:27,534 yes, in real terms, not in nominal terms. 237 00:09:27,534 --> 00:09:29,700 You can never have a negative nominal interest rate. 238 00:09:29,700 --> 00:09:30,450 Right? 239 00:09:30,450 --> 00:09:33,342 Unless, you know, somebody is burning dollar bills. 240 00:09:33,342 --> 00:09:34,800 But let me let me hold off on that, 241 00:09:34,800 --> 00:09:36,800 because I want to actually-- that brings us back 242 00:09:36,800 --> 00:09:38,454 to the end of last lecture. 243 00:09:38,454 --> 00:09:39,870 What I want to do today is, I want 244 00:09:39,870 --> 00:09:44,220 to talk about information specifically contained 245 00:09:44,220 --> 00:09:45,020 in interest rates. 246 00:09:45,020 --> 00:09:46,644 And we're going to actually take a look 247 00:09:46,644 --> 00:09:48,579 at what the short-term interest rate is. 248 00:09:48,579 --> 00:09:50,120 I think you'll be, kind of, surprised 249 00:09:50,120 --> 00:09:54,110 to see what the three-month T-bill rate is, as of today. 250 00:09:54,110 --> 00:09:57,300 Anybody know what it is? 251 00:09:57,300 --> 00:09:58,770 You've seen it? 252 00:09:58,770 --> 00:10:00,240 2%? 253 00:10:00,240 --> 00:10:01,210 No. 254 00:10:01,210 --> 00:10:01,710 No. 255 00:10:01,710 --> 00:10:03,180 It's lower. 256 00:10:03,180 --> 00:10:04,729 STUDENT: [INAUDIBLE] 257 00:10:04,729 --> 00:10:05,520 ANDREW LO: Let me-- 258 00:10:05,520 --> 00:10:06,644 we'll see in just a minute. 259 00:10:12,880 --> 00:10:15,430 Let me start today's lecture by going back 260 00:10:15,430 --> 00:10:19,010 to where we left off last time. 261 00:10:19,010 --> 00:10:22,000 Last time, we talked about the pricing of pure discount bonds, 262 00:10:22,000 --> 00:10:25,460 bonds that pay only principal at the end 263 00:10:25,460 --> 00:10:27,630 and no intermediate coupon payments. 264 00:10:27,630 --> 00:10:29,830 And we saw that the price today is simply 265 00:10:29,830 --> 00:10:32,950 equal to the face value or principal 266 00:10:32,950 --> 00:10:36,580 at the end of the maturity date, and then discounted back 267 00:10:36,580 --> 00:10:38,800 using the interest rate. 268 00:10:38,800 --> 00:10:40,930 And I pointed out at the end of last lecture 269 00:10:40,930 --> 00:10:44,020 that the interest rate can differ, 270 00:10:44,020 --> 00:10:45,370 depending on the horizon. 271 00:10:45,370 --> 00:10:47,500 So a one-year interest rate is not 272 00:10:47,500 --> 00:10:49,180 the same as a five-year interest rate, 273 00:10:49,180 --> 00:10:53,530 because the market has different expectations about how 274 00:10:53,530 --> 00:10:56,230 the economy will do and what the appropriate borrowing 275 00:10:56,230 --> 00:11:00,250 rate or the time rate of preference might be. 276 00:11:00,250 --> 00:11:03,430 So in fact, for every horizon-- 277 00:11:03,430 --> 00:11:06,100 one year, two years, three years, five years-- 278 00:11:06,100 --> 00:11:08,170 we have a different interest rate. 279 00:11:08,170 --> 00:11:10,750 It doesn't have to be different, but in general, it 280 00:11:10,750 --> 00:11:12,580 does tend to be different. 281 00:11:12,580 --> 00:11:16,690 How do we find out what these interest rates are? 282 00:11:16,690 --> 00:11:17,320 Yeah. 283 00:11:17,320 --> 00:11:18,220 STUDENT: The market. 284 00:11:18,220 --> 00:11:19,011 ANDREW LO: Exactly. 285 00:11:19,011 --> 00:11:19,630 The market. 286 00:11:19,630 --> 00:11:23,030 The way to do it is not to think about interest rates at all, 287 00:11:23,030 --> 00:11:25,570 but rather to auction off pieces of paper that 288 00:11:25,570 --> 00:11:30,310 pay $1,000 in a year, $1,000 in two years, 289 00:11:30,310 --> 00:11:32,500 $1,000 in three years, and so on. 290 00:11:32,500 --> 00:11:34,600 And we auction off each of these pieces of paper 291 00:11:34,600 --> 00:11:38,710 and see what the prices we fetch are, for those pieces of paper. 292 00:11:38,710 --> 00:11:40,720 Once we have the price and once we 293 00:11:40,720 --> 00:11:43,240 know the face value of $1,000, we 294 00:11:43,240 --> 00:11:45,550 can back out the interest rate. 295 00:11:45,550 --> 00:11:49,300 We can solve for the interest rate, r. 296 00:11:49,300 --> 00:11:51,050 So that's how we get the rates. 297 00:11:51,050 --> 00:11:53,672 And what I want to do today is to explicate 298 00:11:53,672 --> 00:11:54,880 what those rates really mean. 299 00:11:54,880 --> 00:11:57,250 I want to show you how to read the entrails 300 00:11:57,250 --> 00:12:01,150 and see that these rates contain enormous amounts of information 301 00:12:01,150 --> 00:12:02,290 about the future. 302 00:12:02,290 --> 00:12:04,460 Not all of that information is good. 303 00:12:04,460 --> 00:12:07,180 So sometimes, it's misleading and incorrect, 304 00:12:07,180 --> 00:12:11,330 but it's always useful in one form or another. 305 00:12:11,330 --> 00:12:14,080 Now, to do that, I want to develop 306 00:12:14,080 --> 00:12:15,940 a little bit of new notation and get 307 00:12:15,940 --> 00:12:19,720 you to think, yet again, differently about the evolution 308 00:12:19,720 --> 00:12:23,280 of interest rates over time. 309 00:12:23,280 --> 00:12:26,070 I'm going to define what's called a spot 310 00:12:26,070 --> 00:12:32,070 rate as the rate of interest between today 311 00:12:32,070 --> 00:12:34,470 and some other point in time. 312 00:12:34,470 --> 00:12:38,220 And I'm going to talk about future spot rates 313 00:12:38,220 --> 00:12:41,610 as the interest rates between some future date, 314 00:12:41,610 --> 00:12:45,510 and then another date even beyond that. 315 00:12:45,510 --> 00:12:51,450 So to be explicit, I wanted to find new notation called 316 00:12:51,450 --> 00:12:58,320 capital R. Uppercase R is meant to convey a one-year spot 317 00:12:58,320 --> 00:13:02,940 rate of interest at a particular point in time, t. 318 00:13:02,940 --> 00:13:03,810 OK? 319 00:13:03,810 --> 00:13:08,250 So capital R1 denotes the spot rate 320 00:13:08,250 --> 00:13:11,610 of interest between today and next year. 321 00:13:11,610 --> 00:13:16,080 Capital R3 denotes the spot rate of interest 322 00:13:16,080 --> 00:13:20,220 between years 2 and 3. 323 00:13:20,220 --> 00:13:24,360 And capital Rt denotes the one year spot rate 324 00:13:24,360 --> 00:13:27,690 between dates t minus 1 and t. 325 00:13:27,690 --> 00:13:28,380 OK? 326 00:13:28,380 --> 00:13:32,520 So these capital R's are always one-year rates, 327 00:13:32,520 --> 00:13:37,380 unlike the little r's, which can denote multi-year rates, 328 00:13:37,380 --> 00:13:40,020 depending on the application. 329 00:13:40,020 --> 00:13:44,640 Now, there's a reason I wanted to find these big R's. 330 00:13:44,640 --> 00:13:50,640 It turns out that if I have a pure discount bond that 331 00:13:50,640 --> 00:13:56,910 pays off at year t, then I can use the one-year spot rates 332 00:13:56,910 --> 00:13:59,660 to compute today's price. 333 00:13:59,660 --> 00:14:00,420 Right? 334 00:14:00,420 --> 00:14:03,610 The one-year spot rate, when you accumulate 335 00:14:03,610 --> 00:14:06,480 that, when you multiply them together, 336 00:14:06,480 --> 00:14:09,840 will give you the accumulated interest 337 00:14:09,840 --> 00:14:12,910 over this entire t-year period. 338 00:14:12,910 --> 00:14:16,980 So if I want to discount face value, F, 339 00:14:16,980 --> 00:14:19,770 and bring it back to year zero, I 340 00:14:19,770 --> 00:14:23,100 can just assume that there exists one rate. 341 00:14:23,100 --> 00:14:25,690 Or I can say, you know what? 342 00:14:25,690 --> 00:14:29,760 If there are multiple rates that differ year by year, 343 00:14:29,760 --> 00:14:33,210 I can use those individual rates. 344 00:14:33,210 --> 00:14:35,580 So I get that first equation. 345 00:14:35,580 --> 00:14:37,080 Now, we don't observe them. 346 00:14:37,080 --> 00:14:42,320 So this is a pure fiction, in terms of what I'm writing down. 347 00:14:42,320 --> 00:14:44,000 It's a theory. 348 00:14:44,000 --> 00:14:47,240 So I'm not telling you that we know what those big R's are. 349 00:14:47,240 --> 00:14:51,710 But I know that they exist, and whatever they are, 350 00:14:51,710 --> 00:14:56,320 this is what the price of the bond ought to be today. 351 00:14:56,320 --> 00:14:58,750 Any questions about that? 352 00:14:58,750 --> 00:14:59,920 OK. 353 00:14:59,920 --> 00:15:04,330 Now, what I do observe is the price and F. Those things, 354 00:15:04,330 --> 00:15:09,460 I get from the marketplace and the contract for these bonds. 355 00:15:09,460 --> 00:15:15,880 Therefore, it turns out that as a very simple identity, 356 00:15:15,880 --> 00:15:20,000 this expression, this little r-- 357 00:15:20,000 --> 00:15:23,630 which-- I'm adding some more complicated notation 358 00:15:23,630 --> 00:15:27,410 to indicate when I begin and when I end in terms 359 00:15:27,410 --> 00:15:28,910 of my horizon-- 360 00:15:28,910 --> 00:15:33,320 I can simply define this little r as being equal 361 00:15:33,320 --> 00:15:36,770 to the geometric average of these big R's. 362 00:15:36,770 --> 00:15:39,061 It's really just terminology at this point. 363 00:15:39,061 --> 00:15:39,560 Right? 364 00:15:39,560 --> 00:15:42,500 I'm simply saying that in reality, we 365 00:15:42,500 --> 00:15:47,910 have one-year interest rates that may change over time. 366 00:15:47,910 --> 00:15:50,190 And I know that the price of the bond today 367 00:15:50,190 --> 00:15:53,700 is equal to the future course of one-year interest rates 368 00:15:53,700 --> 00:15:56,652 as discounts over that period. 369 00:15:56,652 --> 00:15:58,110 When I use those as discount rates, 370 00:15:58,110 --> 00:16:01,500 I bring back the value F, and I get today's price. 371 00:16:01,500 --> 00:16:05,460 I can just as well write that chain of one-year interest 372 00:16:05,460 --> 00:16:08,820 rates as a single number, raised to the t-th power. 373 00:16:08,820 --> 00:16:11,010 I can always do that. 374 00:16:11,010 --> 00:16:15,330 You can think of this little r as an average, 375 00:16:15,330 --> 00:16:18,540 a geometric average, of the big R's. 376 00:16:18,540 --> 00:16:19,590 Right? 377 00:16:19,590 --> 00:16:22,860 So the strict definition is going to be-- 378 00:16:22,860 --> 00:16:27,810 little r is going to be the t-th root of the product, 379 00:16:27,810 --> 00:16:29,530 and then minus 1. 380 00:16:29,530 --> 00:16:31,530 That's what the little r is. 381 00:16:31,530 --> 00:16:32,520 All right? 382 00:16:32,520 --> 00:16:34,835 You take that product, and you raise that to the 1 383 00:16:34,835 --> 00:16:38,790 over t-th power or take the t-th root, 384 00:16:38,790 --> 00:16:41,574 and then subtract 1 from that-- that's what my little r is. 385 00:16:41,574 --> 00:16:43,240 Now, why am I going through all of this? 386 00:16:43,240 --> 00:16:45,630 It's because I want to show you that 387 00:16:45,630 --> 00:16:49,830 from a theoretical perspective, the little r, which 388 00:16:49,830 --> 00:16:53,380 we can observe, contains information 389 00:16:53,380 --> 00:16:55,270 about the future course of interest rates. 390 00:16:57,800 --> 00:17:02,120 Within the little r are all the big R's-- 391 00:17:02,120 --> 00:17:06,079 at least today's expectations of what those big R's are 392 00:17:06,079 --> 00:17:08,440 going to be. 393 00:17:08,440 --> 00:17:15,480 So it turns out that if we look into the little r's, we 394 00:17:15,480 --> 00:17:18,030 can actually develop insight about what's 395 00:17:18,030 --> 00:17:21,760 going to be happening next year, five years from now, 396 00:17:21,760 --> 00:17:23,387 30 years from now. 397 00:17:23,387 --> 00:17:25,470 Now, let me give you an example, just to make sure 398 00:17:25,470 --> 00:17:28,290 that we understand the mechanism by which these little r's 399 00:17:28,290 --> 00:17:31,710 and big R's are determined. 400 00:17:31,710 --> 00:17:36,630 Here's a set of prices of strips. 401 00:17:36,630 --> 00:17:40,590 These are treasury securities, issued by the US government. 402 00:17:40,590 --> 00:17:46,830 And then, a third party buys them, takes the coupons, 403 00:17:46,830 --> 00:17:49,560 creates separate securities, and sells 404 00:17:49,560 --> 00:17:52,080 those separate securities, each one of which 405 00:17:52,080 --> 00:17:53,820 is one of these coupons. 406 00:17:53,820 --> 00:17:56,670 So from our perspective, they look like pure discount bonds. 407 00:17:56,670 --> 00:17:59,340 There's no intermediate coupon payments 408 00:17:59,340 --> 00:18:01,620 for each one of these strips, and the maturity 409 00:18:01,620 --> 00:18:04,170 is three months, six months, one year, two years, 410 00:18:04,170 --> 00:18:05,580 up to 30 years. 411 00:18:05,580 --> 00:18:06,910 OK? 412 00:18:06,910 --> 00:18:08,210 And those are the prices. 413 00:18:08,210 --> 00:18:12,340 So a three-month strip is currently priced-- 414 00:18:12,340 --> 00:18:18,130 as of August the 1st, 2001, it was priced at a little bit less 415 00:18:18,130 --> 00:18:21,250 than the dollar. 416 00:18:21,250 --> 00:18:26,350 So how do we figure out what the little r is, associated 417 00:18:26,350 --> 00:18:27,750 with those various prices? 418 00:18:27,750 --> 00:18:29,110 Well, let's take an example. 419 00:18:29,110 --> 00:18:35,050 The five-year strip is priced at, about, $0.80 to the dollar. 420 00:18:35,050 --> 00:18:35,920 OK? 421 00:18:35,920 --> 00:18:39,280 So the price is 0.797, and that's 422 00:18:39,280 --> 00:18:43,180 equal to $1 paid five years later. 423 00:18:43,180 --> 00:18:46,930 So therefore, it's $1 discounted back five years. 424 00:18:46,930 --> 00:18:50,590 So I'm gonna use my little r, and the zero comma five 425 00:18:50,590 --> 00:18:54,610 indicates that it's today's spot rate for borrowing 426 00:18:54,610 --> 00:18:57,400 over a five-year horizon. 427 00:18:57,400 --> 00:19:00,040 And it turns out that when I solve for that, 428 00:19:00,040 --> 00:19:02,980 I get a number that's 4.64%. 429 00:19:02,980 --> 00:19:07,480 That's the rate of return, the cost of capital, 430 00:19:07,480 --> 00:19:12,640 the yield of that five period horizon. 431 00:19:16,480 --> 00:19:18,770 Any questions about this? 432 00:19:18,770 --> 00:19:19,800 Yeah. 433 00:19:19,800 --> 00:19:22,350 STUDENT: How do we do it, maybe, if it was one that 434 00:19:22,350 --> 00:19:24,039 was less than a year's horizon? 435 00:19:24,039 --> 00:19:26,080 ANDREW LO: So if it's less than a year's horizon, 436 00:19:26,080 --> 00:19:28,254 then you basically have to go the other way, 437 00:19:28,254 --> 00:19:29,170 in terms of the power. 438 00:19:29,170 --> 00:19:29,875 Right? 439 00:19:29,875 --> 00:19:31,180 STUDENT: [? 1 over 1/2. ?] 440 00:19:31,180 --> 00:19:32,170 ANDREW LO: Yeah. 441 00:19:32,170 --> 00:19:33,340 Exactly. 442 00:19:33,340 --> 00:19:33,900 That's right. 443 00:19:33,900 --> 00:19:35,200 Yeah, that's it. 444 00:19:35,200 --> 00:19:40,050 It's just a shorter time horizon than a year. 445 00:19:40,050 --> 00:19:43,900 Now, suppose that we observe a bunch of these 446 00:19:43,900 --> 00:19:45,400 as we do with the strips. 447 00:19:45,400 --> 00:19:47,830 So in other words, you've got a five-year rate, 448 00:19:47,830 --> 00:19:50,080 you've got a 10-year rate, you've got a two-year rate, 449 00:19:50,080 --> 00:19:51,500 and so on. 450 00:19:51,500 --> 00:19:53,270 What does that tell us about the future? 451 00:19:53,270 --> 00:19:56,360 Well, let's write down the big R's. 452 00:19:56,360 --> 00:19:59,480 Even though we don't see them, we know that somehow, 453 00:19:59,480 --> 00:20:01,430 implicitly, they're there. 454 00:20:01,430 --> 00:20:04,790 So what are the relationships between the little 455 00:20:04,790 --> 00:20:07,070 r's and the big R's? 456 00:20:07,070 --> 00:20:10,070 Well, you'll see something really neat emerge out of this. 457 00:20:10,070 --> 00:20:13,790 We'll start with a one-year strip. 458 00:20:13,790 --> 00:20:17,220 With a one-year strip, the little r and the big R 459 00:20:17,220 --> 00:20:20,700 are the same, because it's only one year. 460 00:20:20,700 --> 00:20:23,450 So there's a one-year big R, a one-year little r, 461 00:20:23,450 --> 00:20:26,420 and when you work out the math, they're 462 00:20:26,420 --> 00:20:29,060 actually equal to each other. 463 00:20:29,060 --> 00:20:32,150 But now, when you go with two years, three years, and t 464 00:20:32,150 --> 00:20:37,110 years, it gets a little bit more complicated. 465 00:20:37,110 --> 00:20:39,390 Take a look at what happens if you 466 00:20:39,390 --> 00:20:44,780 take the price of the one-year, and you divide that 467 00:20:44,780 --> 00:20:47,570 into the price of the two-year. 468 00:20:50,510 --> 00:20:54,050 These two securities-- the one-year and the two-year-- 469 00:20:54,050 --> 00:20:56,360 they have the same F, the same face value. 470 00:20:56,360 --> 00:20:58,147 They pay $1,000 at maturity. 471 00:20:58,147 --> 00:21:00,230 But one of them goes for one year, and one of them 472 00:21:00,230 --> 00:21:01,021 goes for two years. 473 00:21:01,021 --> 00:21:04,910 What happens when you take P 0,1, 474 00:21:04,910 --> 00:21:07,700 and you divide that by P 0,2? 475 00:21:07,700 --> 00:21:11,140 By the way, both of those prices exist today. 476 00:21:11,140 --> 00:21:11,980 Right? 477 00:21:11,980 --> 00:21:15,040 For example, if you take a look at the strips, 478 00:21:15,040 --> 00:21:18,880 the price of P 0,1 is 0.967. 479 00:21:18,880 --> 00:21:23,330 The price of P 0,2 is 0.927. 480 00:21:23,330 --> 00:21:28,730 If I take the price of 1 divided by the price of 2, 481 00:21:28,730 --> 00:21:29,550 what do I get? 482 00:21:29,550 --> 00:21:30,050 Yeah. 483 00:21:30,050 --> 00:21:31,299 STUDENT: [INAUDIBLE] 484 00:21:31,299 --> 00:21:32,090 ANDREW LO: Exactly. 485 00:21:32,090 --> 00:21:34,930 I get 1 plus R2. 486 00:21:34,930 --> 00:21:39,880 And so if I subtract 1 from that, I get R2. 487 00:21:39,880 --> 00:21:41,340 So let's just go back. 488 00:21:41,340 --> 00:21:43,980 I don't have a calculator with me, but I'm sure all of you do. 489 00:21:43,980 --> 00:21:46,010 Somebody do that division for me, will you? 490 00:21:46,010 --> 00:21:50,070 Can you take 0.967 and divide that by 0.927? 491 00:21:50,070 --> 00:21:52,990 What do you get? 492 00:21:52,990 --> 00:21:58,090 0.967 divided by 0.927. 493 00:21:58,090 --> 00:21:58,765 What's that? 494 00:21:58,765 --> 00:21:59,920 STUDENT: 1.04. 495 00:21:59,920 --> 00:22:02,630 ANDREW LO: 1.04-- and then, subtract 1 from that. 496 00:22:02,630 --> 00:22:03,990 4%. 497 00:22:03,990 --> 00:22:07,660 Actually, can you give me a few more digits of accuracy? 498 00:22:07,660 --> 00:22:08,520 STUDENT: [INAUDIBLE] 499 00:22:08,520 --> 00:22:09,478 ANDREW LO: What's that? 500 00:22:09,478 --> 00:22:10,810 STUDENT: 4.314. 501 00:22:10,810 --> 00:22:14,070 ANDREW LO: 4.314. 502 00:22:14,070 --> 00:22:20,370 So it turns out that in year 0, where 503 00:22:20,370 --> 00:22:23,610 we have all of these prices, we actually 504 00:22:23,610 --> 00:22:28,050 have a forecast for what big R2 is. 505 00:22:28,050 --> 00:22:31,200 Big R2 in this case is the borrowing cost 506 00:22:31,200 --> 00:22:33,060 between year 1 and year 2. 507 00:22:35,670 --> 00:22:38,070 But we're sitting at year 0. 508 00:22:38,070 --> 00:22:41,460 So implicit in the price of a two-year bond and a one-year 509 00:22:41,460 --> 00:22:42,090 bond-- 510 00:22:42,090 --> 00:22:47,250 implicit in that is a forecast of what the price is going 511 00:22:47,250 --> 00:22:49,110 to be, what the yield is going to be, 512 00:22:49,110 --> 00:22:50,610 or what the borrowing costs is going 513 00:22:50,610 --> 00:22:53,220 to be between years 1 and 2. 514 00:22:53,220 --> 00:22:56,900 In this case, 4.3% or so. 515 00:22:56,900 --> 00:23:02,330 And that's a really important observation. 516 00:23:02,330 --> 00:23:09,380 If you plot these little r's on a graph as a function of time, 517 00:23:09,380 --> 00:23:15,680 you actually get a sense of where the future big R's are 518 00:23:15,680 --> 00:23:17,490 going to lie. 519 00:23:17,490 --> 00:23:21,960 This plot, a plot of the r's as a function of time, 520 00:23:21,960 --> 00:23:25,320 is known as the term structure of interest rates or the yield 521 00:23:25,320 --> 00:23:30,540 curve, and it gives you a sense of where future interest 522 00:23:30,540 --> 00:23:32,160 rates are going to go. 523 00:23:32,160 --> 00:23:36,450 If the curve is upward-sloping, it says that as you go out 524 00:23:36,450 --> 00:23:41,310 into longer maturities, your average yield, 525 00:23:41,310 --> 00:23:44,990 the geometric average of all the big R's-- 526 00:23:44,990 --> 00:23:47,790 it's getting bigger as time grows, 527 00:23:47,790 --> 00:23:49,920 as the time horizon grows. 528 00:23:49,920 --> 00:23:53,400 If it's downward-sloping, it suggests 529 00:23:53,400 --> 00:23:58,830 that future interest rates, future big R's, are declining. 530 00:23:58,830 --> 00:24:01,440 I want to show you what the yield curve looks like today. 531 00:24:01,440 --> 00:24:05,730 Now, it turns out that we don't have a yield curve of strips 532 00:24:05,730 --> 00:24:08,850 as readily available as a yield curve that includes 533 00:24:08,850 --> 00:24:09,660 coupon payments. 534 00:24:09,660 --> 00:24:12,384 So I'm going to come back to the distinction 535 00:24:12,384 --> 00:24:13,300 a little bit later on. 536 00:24:13,300 --> 00:24:15,270 We haven't talked about coupon bonds yet, 537 00:24:15,270 --> 00:24:17,580 but I just want to show you what the yield curve is. 538 00:24:17,580 --> 00:24:20,280 So I'm on the Bloomberg website. 539 00:24:20,280 --> 00:24:22,470 This is publicly available, so I don't have 540 00:24:22,470 --> 00:24:24,110 a particular license for it. 541 00:24:24,110 --> 00:24:25,690 It's the public version. 542 00:24:25,690 --> 00:24:27,990 And if you click on market data, and then click 543 00:24:27,990 --> 00:24:31,240 on rates and bonds, you're going to get this page right here. 544 00:24:31,240 --> 00:24:34,380 So these are the different US treasury securities, 545 00:24:34,380 --> 00:24:35,790 the different horizons. 546 00:24:35,790 --> 00:24:36,870 These are the coupons. 547 00:24:36,870 --> 00:24:39,525 For less than a year, there are no coupon payments, 548 00:24:39,525 --> 00:24:41,610 so these are pure discount bonds. 549 00:24:41,610 --> 00:24:47,950 And there's the graph. 550 00:24:47,950 --> 00:24:49,870 That's it. 551 00:24:49,870 --> 00:24:54,910 That graph-- the green line is showing you the future course 552 00:24:54,910 --> 00:24:57,070 of interest rates. 553 00:24:57,070 --> 00:24:58,990 It's extremely low today. 554 00:24:58,990 --> 00:25:01,210 The scale is on the left-hand access. 555 00:25:01,210 --> 00:25:05,050 And by the way, these are in percent. 556 00:25:05,050 --> 00:25:12,610 So where we are today, for a three-month rate, 557 00:25:12,610 --> 00:25:14,740 is close to zero. 558 00:25:14,740 --> 00:25:17,560 It's actually three basis points, 559 00:25:17,560 --> 00:25:22,201 three basis points for a three-month T-bill. 560 00:25:22,201 --> 00:25:23,200 What does that tell you? 561 00:25:26,450 --> 00:25:32,686 What's the relationship between price and the little r? 562 00:25:32,686 --> 00:25:33,614 Yeah? 563 00:25:33,614 --> 00:25:37,362 STUDENT: [INAUDIBLE] 564 00:25:37,362 --> 00:25:39,040 ANDREW LO: Well, that's right. 565 00:25:39,040 --> 00:25:43,120 But how does that yield get so low? 566 00:25:43,120 --> 00:25:43,824 Yes? 567 00:25:43,824 --> 00:25:45,995 STUDENT: Because the price is extremely high. 568 00:25:45,995 --> 00:25:47,620 ANDREW LO: The price is extremely high. 569 00:25:47,620 --> 00:25:48,161 That's right. 570 00:25:48,161 --> 00:25:51,490 Price is equal to the three-month pay-out divided 571 00:25:51,490 --> 00:25:52,880 by 1 plus little r. 572 00:25:52,880 --> 00:25:56,830 If little r ends up being really, really tiny, 573 00:25:56,830 --> 00:26:00,670 it's only because the price is really high. 574 00:26:00,670 --> 00:26:01,840 Why would the price be high? 575 00:26:04,600 --> 00:26:06,870 STUDENT: Because US treasuries are the safe thing 576 00:26:06,870 --> 00:26:08,270 to own right now. 577 00:26:08,270 --> 00:26:10,920 ANDREW LO: At least, that's what many people think, exactly. 578 00:26:10,920 --> 00:26:14,460 There is a really strong flight to liquidity going on 579 00:26:14,460 --> 00:26:16,310 in markets, as of today. 580 00:26:16,310 --> 00:26:18,060 And how do you know that it's as of today? 581 00:26:18,060 --> 00:26:19,500 Well, take a look at the difference 582 00:26:19,500 --> 00:26:21,291 between the green line and the orange line. 583 00:26:21,291 --> 00:26:23,800 The orange line was what it was yesterday. 584 00:26:23,800 --> 00:26:25,100 You see, there's a difference. 585 00:26:25,100 --> 00:26:27,490 There's a noticeable difference on the short end that 586 00:26:27,490 --> 00:26:30,400 means a lot of people are out there buying treasury bills 587 00:26:30,400 --> 00:26:33,700 now, probably as we speak. 588 00:26:33,700 --> 00:26:37,300 Maybe you ought to go and buy some treasury bills. 589 00:26:37,300 --> 00:26:38,830 People are scared. 590 00:26:38,830 --> 00:26:40,930 And they're scared because of all the things 591 00:26:40,930 --> 00:26:43,990 that are going on in the news, and this is exactly what 592 00:26:43,990 --> 00:26:46,970 the Fed is trying to stave off. 593 00:26:46,970 --> 00:26:48,790 So you're absolutely right. 594 00:26:48,790 --> 00:26:51,250 The Fed is not worried about the cost of borrowing. 595 00:26:51,250 --> 00:26:52,930 They're worried about whether or not 596 00:26:52,930 --> 00:26:55,690 there's money out there to be able to calm 597 00:26:55,690 --> 00:26:59,410 the fears of market participants. 598 00:26:59,410 --> 00:27:00,126 Yeah? 599 00:27:00,126 --> 00:27:02,606 STUDENT: [INAUDIBLE] two days ago 600 00:27:02,606 --> 00:27:05,416 to today, [INAUDIBLE] probably the Fed didn't cut the interest 601 00:27:05,416 --> 00:27:07,070 rate once [INAUDIBLE]. 602 00:27:07,070 --> 00:27:10,500 They [INAUDIBLE]. 603 00:27:10,500 --> 00:27:11,500 ANDREW LO: That's right. 604 00:27:11,500 --> 00:27:14,470 They might have to, so that expectation actually 605 00:27:14,470 --> 00:27:15,970 is built into these prices. 606 00:27:15,970 --> 00:27:18,820 The market recognizes that, and they're worried. 607 00:27:18,820 --> 00:27:20,520 But think about that. 608 00:27:20,520 --> 00:27:23,020 If the Fed has said that they're going to be cutting rates-- 609 00:27:23,020 --> 00:27:26,310 possibly cutting rates in the future, and yet, 610 00:27:26,310 --> 00:27:30,270 the rate stays relatively high going forward, 611 00:27:30,270 --> 00:27:33,210 and rates go down today, what that's 612 00:27:33,210 --> 00:27:36,120 telling you is that the market is being driven by a panic 613 00:27:36,120 --> 00:27:37,360 reaction. 614 00:27:37,360 --> 00:27:39,480 Now, rates are going to go up. 615 00:27:39,480 --> 00:27:44,460 So the fact that you see the market determining a yield 616 00:27:44,460 --> 00:27:46,080 curve that's upward-sloping-- that's 617 00:27:46,080 --> 00:27:48,330 telling you that people expect that rates 618 00:27:48,330 --> 00:27:50,580 are going to go up, that rates have to go up, 619 00:27:50,580 --> 00:27:52,300 for one of two reasons. 620 00:27:52,300 --> 00:27:55,410 And in fact, you can take a look at the steepness of the yield 621 00:27:55,410 --> 00:27:58,800 curve as telling you what the market's expectations are 622 00:27:58,800 --> 00:28:00,690 for how quickly rates are going to go up 623 00:28:00,690 --> 00:28:02,770 and where they're going to go up. 624 00:28:02,770 --> 00:28:06,090 So you have to look at the x-axis a little bit 625 00:28:06,090 --> 00:28:07,150 differently. 626 00:28:07,150 --> 00:28:08,947 These are denominated in years, so this 627 00:28:08,947 --> 00:28:11,280 is three months, six months, one year, two, three, four, 628 00:28:11,280 --> 00:28:13,140 five, up to 10-- 629 00:28:13,140 --> 00:28:14,760 then, 15, 20, and 30. 630 00:28:14,760 --> 00:28:17,490 So these are long-term rates. 631 00:28:17,490 --> 00:28:21,930 And you can see that the yield curve really goes up sharply 632 00:28:21,930 --> 00:28:23,680 after the first three months. 633 00:28:23,680 --> 00:28:26,260 There's a big increase in the slope, 634 00:28:26,260 --> 00:28:29,370 and then it becomes a little bit more gradual. 635 00:28:29,370 --> 00:28:34,980 That's a sign of a short-term flight to quality or flight 636 00:28:34,980 --> 00:28:36,060 to liquidity. 637 00:28:36,060 --> 00:28:38,640 But the market expects, over time 638 00:28:38,640 --> 00:28:42,840 as things calm down, that interest rates will go up, 639 00:28:42,840 --> 00:28:45,030 for one of two reasons. 640 00:28:45,030 --> 00:28:47,910 Either there are inflationary pressures and that 641 00:28:47,910 --> 00:28:50,370 will drive rates up, or there are 642 00:28:50,370 --> 00:28:52,500 going to be some economic consequences of what's 643 00:28:52,500 --> 00:28:54,750 happening today, and that will ultimately 644 00:28:54,750 --> 00:28:56,740 cause rates to go up. 645 00:28:56,740 --> 00:28:59,215 Yeah. 646 00:28:59,215 --> 00:29:02,680 STUDENT: What's happening to the interest rates 647 00:29:02,680 --> 00:29:04,660 outside of this case? 648 00:29:04,660 --> 00:29:10,408 Because I'm from Argentina, and when we have crises, 649 00:29:10,408 --> 00:29:13,930 like [? internal ?] interest rates go up, 650 00:29:13,930 --> 00:29:16,780 because the probability of default increases. 651 00:29:16,780 --> 00:29:20,240 And now, I see here, it's the other way around, 652 00:29:20,240 --> 00:29:23,400 because they are not considering it will be-- 653 00:29:23,400 --> 00:29:24,400 ANDREW LO: That's right. 654 00:29:24,400 --> 00:29:26,570 It depends on the nature of the crisis. 655 00:29:26,570 --> 00:29:30,520 So in certain countries where there is a financial crisis, 656 00:29:30,520 --> 00:29:33,730 the typical reaction of monetary authorities 657 00:29:33,730 --> 00:29:36,280 is to flood the market with cash, 658 00:29:36,280 --> 00:29:39,070 because that's their reaction to a liquidity crunch. 659 00:29:39,070 --> 00:29:42,310 They want to reduce the prospect of having a kind of run 660 00:29:42,310 --> 00:29:46,900 on the banks, so they'll flood the market with their currency. 661 00:29:46,900 --> 00:29:49,630 When you do that, you encourage inflation, 662 00:29:49,630 --> 00:29:53,320 and that's why interest rates go up in those kinds of economies. 663 00:29:53,320 --> 00:29:57,220 The US, for better or for worse, has shown a certain degree 664 00:29:57,220 --> 00:30:01,330 of monetary restraint over the years in that while they do 665 00:30:01,330 --> 00:30:05,260 certainly cut interest rates-- and Alan Greenspan was very 666 00:30:05,260 --> 00:30:09,850 active in this respect over the last 10 or 15 years-- 667 00:30:09,850 --> 00:30:12,100 the fact is that there has been more 668 00:30:12,100 --> 00:30:16,840 measured control of monetary policy in the United States. 669 00:30:16,840 --> 00:30:19,810 What that means is that this is a symptom more 670 00:30:19,810 --> 00:30:21,820 of a short-term cash crunch. 671 00:30:21,820 --> 00:30:23,980 People are just putting money in treasury bills 672 00:30:23,980 --> 00:30:27,430 for the short term without any expectation 673 00:30:27,430 --> 00:30:30,880 that the Fed is going to dramatically increase the money 674 00:30:30,880 --> 00:30:31,690 supply. 675 00:30:31,690 --> 00:30:33,190 If they did that, you would then see 676 00:30:33,190 --> 00:30:35,500 interest rates rise, because inflation would 677 00:30:35,500 --> 00:30:38,210 be much more of a problem. 678 00:30:38,210 --> 00:30:39,020 OK. 679 00:30:39,020 --> 00:30:39,740 Yes? 680 00:30:39,740 --> 00:30:43,534 STUDENT: [INAUDIBLE] European Central Bank? 681 00:30:43,534 --> 00:30:44,200 ANDREW LO: Yeah. 682 00:30:44,200 --> 00:30:49,740 STUDENT: --normally raises the interest rates [INAUDIBLE].. 683 00:30:49,740 --> 00:30:50,740 ANDREW LO: That's right. 684 00:30:50,740 --> 00:30:52,870 They do raise it, and that's one of the reasons why 685 00:30:52,870 --> 00:30:55,140 the Fed did not cut it. 686 00:30:55,140 --> 00:30:58,000 It's because they are concerned with inflation. 687 00:30:58,000 --> 00:31:00,100 And so if they ended up cutting interest rates, 688 00:31:00,100 --> 00:31:03,790 while that might stave off certain credit crunches, 689 00:31:03,790 --> 00:31:05,958 that would actually encourage inflation. 690 00:31:05,958 --> 00:31:08,398 STUDENT: So inflation does encourage higher interest 691 00:31:08,398 --> 00:31:10,840 rates, but what is the [? advantage ?] of it? 692 00:31:10,840 --> 00:31:12,390 ANDREW LO: Inflation causes-- 693 00:31:12,390 --> 00:31:16,210 so I see the confusion, and let me make a distinction. 694 00:31:16,210 --> 00:31:18,640 There are two different interest rates that are going on. 695 00:31:18,640 --> 00:31:20,240 There is the market rate of interest, 696 00:31:20,240 --> 00:31:21,560 which is what this is. 697 00:31:21,560 --> 00:31:25,670 And then, there is the Fed's stated federal funds rate, 698 00:31:25,670 --> 00:31:28,480 which is what it charges its other member 699 00:31:28,480 --> 00:31:30,070 banks for borrowing. 700 00:31:30,070 --> 00:31:34,120 The Fed is able to control what it charges to other banks. 701 00:31:34,120 --> 00:31:36,430 The Fed cannot control these rates. 702 00:31:36,430 --> 00:31:40,810 So the interest rates that you're thinking about, that-- 703 00:31:40,810 --> 00:31:43,420 for example, when the ECB raises rates, 704 00:31:43,420 --> 00:31:49,090 they do so, so as to discourage lots of borrowing and lending, 705 00:31:49,090 --> 00:31:53,500 and reduce the amount of money that's in circulation. 706 00:31:53,500 --> 00:31:56,350 And that decreases business activity, 707 00:31:56,350 --> 00:31:58,860 which then reduces the pressure on inflation. 708 00:31:58,860 --> 00:31:59,680 OK? 709 00:31:59,680 --> 00:32:02,240 So that's what they do in response, 710 00:32:02,240 --> 00:32:04,570 but they don't control the interest rate determined 711 00:32:04,570 --> 00:32:06,380 by the market for treasury bills. 712 00:32:06,380 --> 00:32:08,830 And in these interest rates, these 30-year rates, 713 00:32:08,830 --> 00:32:11,230 as opposed to overnight borrowing rates and Fed funds 714 00:32:11,230 --> 00:32:13,780 rates, these rates give you a sense 715 00:32:13,780 --> 00:32:17,260 of what the market is expecting over time. 716 00:32:17,260 --> 00:32:19,070 [? Megan, ?] do you have a question? 717 00:32:19,070 --> 00:32:25,440 STUDENT: [INAUDIBLE] As it cuts the interest rates, 718 00:32:25,440 --> 00:32:31,810 [INAUDIBLE] had an impact [INAUDIBLE] the actual banks 719 00:32:31,810 --> 00:32:43,570 that [? spread ?] over time [INAUDIBLE] to stave off that 720 00:32:43,570 --> 00:32:44,600 credit crunch-- 721 00:32:44,600 --> 00:32:45,850 ANDREW LO: Well, that's right. 722 00:32:45,850 --> 00:32:48,140 I think that when you think about the instruments 723 00:32:48,140 --> 00:32:52,220 that the Fed has for managing monetary policy, credit, 724 00:32:52,220 --> 00:32:55,540 and liquidity, it's actually pretty minimal. 725 00:32:55,540 --> 00:32:58,130 I mean, they have one variable. 726 00:32:58,130 --> 00:32:58,630 You know? 727 00:32:58,630 --> 00:33:02,575 Imagine flying a mirror plane and you get one control. 728 00:33:02,575 --> 00:33:03,450 You pick the control. 729 00:33:03,450 --> 00:33:06,280 You want to be able to control the wheels, or the ailerons, 730 00:33:06,280 --> 00:33:07,891 or the--? 731 00:33:07,891 --> 00:33:09,910 It's very, very hard to try to manage 732 00:33:09,910 --> 00:33:12,280 the economy with one variable. 733 00:33:12,280 --> 00:33:14,380 Now, the Fed has other policy instruments 734 00:33:14,380 --> 00:33:17,920 that are a little bit more complex, like the discount 735 00:33:17,920 --> 00:33:19,630 window, like moral suasion. 736 00:33:19,630 --> 00:33:21,250 The New York Fed can go to these banks 737 00:33:21,250 --> 00:33:22,680 and say, what are you guys doing? 738 00:33:22,680 --> 00:33:24,510 Are you nuts? 739 00:33:24,510 --> 00:33:29,080 But what's going on now is that because the crisis has reached 740 00:33:29,080 --> 00:33:31,990 such an extraordinary level, they're not 741 00:33:31,990 --> 00:33:33,250 worrying about interest rates. 742 00:33:33,250 --> 00:33:34,791 They're actually trying to figure out 743 00:33:34,791 --> 00:33:37,390 how to stave off some kind of mass panic. 744 00:33:37,390 --> 00:33:39,910 And so getting directly involved with AIG, 745 00:33:39,910 --> 00:33:42,910 getting in discussions with Bear Stearns and JP Morgan-- 746 00:33:42,910 --> 00:33:44,600 they really have no choice. 747 00:33:44,600 --> 00:33:49,390 And it's a signal of, sort of, how desperate times are. 748 00:33:49,390 --> 00:33:50,480 One last question? 749 00:33:50,480 --> 00:33:54,086 STUDENT: [INAUDIBLE] My understanding is first 750 00:33:54,086 --> 00:33:55,877 that the Fed is not a federal organization. 751 00:33:55,877 --> 00:33:58,118 It's made up of a number of banks, 752 00:33:58,118 --> 00:34:00,309 so that it's not a government entity, 753 00:34:00,309 --> 00:34:02,600 but the government has appointed representatives to it. 754 00:34:02,600 --> 00:34:04,790 And at the same time, where does the Fed 755 00:34:04,790 --> 00:34:06,380 get all their money from? 756 00:34:06,380 --> 00:34:08,830 ANDREW LO: Well, this is more of a question 757 00:34:08,830 --> 00:34:11,850 that you probably should be asking your macro instructor. 758 00:34:11,850 --> 00:34:14,560 I'm happy to answer it, but the macro folks 759 00:34:14,560 --> 00:34:17,290 may disagree with what I'm about to tell you. 760 00:34:17,290 --> 00:34:19,120 The Fed is a government organization. 761 00:34:19,120 --> 00:34:21,310 It's separate from the government in the sense 762 00:34:21,310 --> 00:34:24,340 that it's not a political organization, 763 00:34:24,340 --> 00:34:27,010 but it does have the full backing of the government, 764 00:34:27,010 --> 00:34:29,770 and it has powers granted to it as part 765 00:34:29,770 --> 00:34:34,060 of the various legal proposals that 766 00:34:34,060 --> 00:34:37,750 were developed to create the Federal Reserve system. 767 00:34:37,750 --> 00:34:39,520 Where does the Fed get its money from? 768 00:34:39,520 --> 00:34:41,350 It gets its money from the treasury. 769 00:34:41,350 --> 00:34:43,870 So the Fed can actually engage in what 770 00:34:43,870 --> 00:34:46,030 are called open market operations 771 00:34:46,030 --> 00:34:49,870 and can actually contract or expand money supply, 772 00:34:49,870 --> 00:34:53,199 based upon what the treasury will allow it to do 773 00:34:53,199 --> 00:34:55,630 or will work with it to do. 774 00:34:55,630 --> 00:34:57,490 And the Fed controls the borrowing rate 775 00:34:57,490 --> 00:35:01,780 among all of the member banks, and actually, all 776 00:35:01,780 --> 00:35:03,532 of the major banks are members. 777 00:35:03,532 --> 00:35:05,740 So it's not like you can start up your bank tomorrow. 778 00:35:05,740 --> 00:35:08,480 In order to start a bank and deal with the public, 779 00:35:08,480 --> 00:35:10,870 you need a bank charter, and the bank charter 780 00:35:10,870 --> 00:35:12,370 is issued by the government. 781 00:35:12,370 --> 00:35:14,020 And once you're part of that network, 782 00:35:14,020 --> 00:35:16,792 you are part of the Federal Reserve system. 783 00:35:16,792 --> 00:35:19,155 STUDENT: Aren't they losing money from, say, 784 00:35:19,155 --> 00:35:20,530 the fallout of these [? banks? ?] 785 00:35:20,530 --> 00:35:22,810 Aren't they, in essence, losing also themselves? 786 00:35:22,810 --> 00:35:25,760 ANDREW LO: Well, they're not trying to make money. 787 00:35:25,760 --> 00:35:27,610 That's not their objective. 788 00:35:27,610 --> 00:35:30,400 And if they're losing money, ultimately, it's 789 00:35:30,400 --> 00:35:32,080 not them that is losing money. 790 00:35:32,080 --> 00:35:33,580 It is-- who? 791 00:35:33,580 --> 00:35:34,564 STUDENT: [INAUDIBLE] 792 00:35:34,564 --> 00:35:35,230 ANDREW LO: Yeah. 793 00:35:35,230 --> 00:35:36,130 We're losing money. 794 00:35:36,130 --> 00:35:37,411 It's government-sponsored. 795 00:35:37,411 --> 00:35:39,160 So that's one of the reasons why, I think, 796 00:35:39,160 --> 00:35:42,544 the Fed has been so concerned about bailing out 797 00:35:42,544 --> 00:35:43,210 Lehman Brothers. 798 00:35:43,210 --> 00:35:46,690 And even the bailout of Bear Stearns, which did not 799 00:35:46,690 --> 00:35:49,690 necessarily cost them anything-- 800 00:35:49,690 --> 00:35:52,390 the fact that they were willing to provide this backstop 801 00:35:52,390 --> 00:35:54,520 guarantee in order to make the deal happen-- 802 00:35:54,520 --> 00:35:57,430 that implicit insurance is a cost 803 00:35:57,430 --> 00:35:59,230 that we ultimately end up paying. 804 00:35:59,230 --> 00:36:00,924 They got a huge amount of heat for that, 805 00:36:00,924 --> 00:36:03,340 and that's one of the reasons why they decided to back off 806 00:36:03,340 --> 00:36:04,589 from the Lehman Brothers deal. 807 00:36:04,589 --> 00:36:08,320 It's because they would have gotten huge, huge backlash 808 00:36:08,320 --> 00:36:10,130 from that kind of an event. 809 00:36:10,130 --> 00:36:12,340 Now, AIG-- the fact that they went and did 810 00:36:12,340 --> 00:36:14,380 something there tells you something 811 00:36:14,380 --> 00:36:16,930 about how important AIG is, or what 812 00:36:16,930 --> 00:36:21,160 repercussions might have come about if they had let AIG fail. 813 00:36:21,160 --> 00:36:22,930 So that says more, not about the Fed, 814 00:36:22,930 --> 00:36:25,090 but more about the situation with AIG 815 00:36:25,090 --> 00:36:27,460 and the specific financial transactions 816 00:36:27,460 --> 00:36:29,610 that they were engaged in. 817 00:36:29,610 --> 00:36:30,110 OK. 818 00:36:30,110 --> 00:36:31,280 Let me continue on. 819 00:36:31,280 --> 00:36:34,130 And sorry, I want to hold off questions for a little bit 820 00:36:34,130 --> 00:36:38,720 longer, but I do want to cover some additional material. 821 00:36:38,720 --> 00:36:40,550 So this is the expression that we just 822 00:36:40,550 --> 00:36:43,430 described for getting a sense of future interest rates. 823 00:36:43,430 --> 00:36:47,030 And we saw, given today's yield curve, 824 00:36:47,030 --> 00:36:49,310 that there is some sense that interest rates are 825 00:36:49,310 --> 00:36:50,660 going to rise. 826 00:36:50,660 --> 00:36:53,300 But it turns out that the yield curve contains 827 00:36:53,300 --> 00:36:56,870 all sorts of information, not just about one-year rates, 828 00:36:56,870 --> 00:37:00,530 but in fact, about multi-year rates. 829 00:37:00,530 --> 00:37:02,270 This is a clear example. 830 00:37:02,270 --> 00:37:04,190 This is one example. 831 00:37:04,190 --> 00:37:07,580 And it turns out that there's another example that 832 00:37:07,580 --> 00:37:09,950 makes this a little bit clearer, which is 833 00:37:09,950 --> 00:37:13,130 future rates and forward rates. 834 00:37:13,130 --> 00:37:15,560 These are all very confusing terminology, 835 00:37:15,560 --> 00:37:17,960 unless you sit down and read through it carefully, 836 00:37:17,960 --> 00:37:20,780 so I would encourage you all to do that after this lecture. 837 00:37:20,780 --> 00:37:22,730 There's a lot of notation in this lecture, 838 00:37:22,730 --> 00:37:25,010 but not a lot of conceptual challenges. 839 00:37:25,010 --> 00:37:26,690 Because all the conceptual challenges, 840 00:37:26,690 --> 00:37:29,570 we derived when we talked about net present value rules. 841 00:37:29,570 --> 00:37:32,900 So most of this is just lots of notation and terminology. 842 00:37:32,900 --> 00:37:35,700 So let me describe the terminology here. 843 00:37:35,700 --> 00:37:39,470 At date zero, if we focus on the price of a bond, 844 00:37:39,470 --> 00:37:41,670 that matures at time t minus 1. 845 00:37:41,670 --> 00:37:44,570 And at date zero, if we focus on the price of a bond that 846 00:37:44,570 --> 00:37:48,860 matures at day t, and we take the ratio of those two, 847 00:37:48,860 --> 00:37:53,480 then it turns out, we're getting an implicit forecast 848 00:37:53,480 --> 00:37:58,650 of the future one-year spot rate between t minus 1 and t. 849 00:37:58,650 --> 00:37:59,150 Right? 850 00:37:59,150 --> 00:38:02,370 That's just what we did with r2. 851 00:38:02,370 --> 00:38:05,580 So this is true in general, and there's 852 00:38:05,580 --> 00:38:09,390 a name for this forecast. 853 00:38:09,390 --> 00:38:13,800 It's called, today's forward rate 854 00:38:13,800 --> 00:38:18,090 between dates t minus 1 and t. 855 00:38:18,090 --> 00:38:23,040 It is a forecast of the future spot rate 856 00:38:23,040 --> 00:38:25,320 between dates t minus 1 and t. 857 00:38:25,320 --> 00:38:25,890 OK? 858 00:38:25,890 --> 00:38:28,230 We don't know what that spot rate is going to be, 859 00:38:28,230 --> 00:38:29,036 in general. 860 00:38:29,036 --> 00:38:31,410 We don't know what future interest rates are going to be. 861 00:38:31,410 --> 00:38:32,550 It's uncertain. 862 00:38:32,550 --> 00:38:35,760 But today, implicit in today's prices 863 00:38:35,760 --> 00:38:39,330 is a forecast of that unknown future, 864 00:38:39,330 --> 00:38:42,780 and we're going to call that forecast the forward rate. 865 00:38:45,370 --> 00:38:48,490 That is really meant to convey that it is a rate that we 866 00:38:48,490 --> 00:38:53,560 observe today, and it is meant to capture the market's best 867 00:38:53,560 --> 00:38:58,750 guess about what the future spot rate will be. 868 00:38:58,750 --> 00:39:00,670 OK? 869 00:39:00,670 --> 00:39:04,270 So this is, I know, a little bit confusing. 870 00:39:04,270 --> 00:39:07,030 And just to give you a summary of all the notation 871 00:39:07,030 --> 00:39:08,950 and terminology we've defined today-- 872 00:39:08,950 --> 00:39:11,200 we have a spot rate. 873 00:39:11,200 --> 00:39:14,860 A spot rate is the rate that you have to pay 874 00:39:14,860 --> 00:39:20,220 or that you will earn on the spot, for a period of time. 875 00:39:20,220 --> 00:39:23,980 So you've got the two-year spot rate today. 876 00:39:23,980 --> 00:39:27,520 You've also got future spot rates, which you 877 00:39:27,520 --> 00:39:30,070 don't know and don't observe. 878 00:39:30,070 --> 00:39:34,810 You also have a forward rate, which you do observe today. 879 00:39:34,810 --> 00:39:38,530 And the forward rate is a rate that applies 880 00:39:38,530 --> 00:39:41,560 over some period in the future. 881 00:39:41,560 --> 00:39:46,820 And it's today's best guess of what that future rate will be. 882 00:39:46,820 --> 00:39:52,130 Now, we can see the implicit forecasts 883 00:39:52,130 --> 00:39:55,970 that are in the yield curve. 884 00:39:55,970 --> 00:39:58,730 The one-year spot rate today also 885 00:39:58,730 --> 00:40:02,470 happens to be equal to the one-year forward rate. 886 00:40:02,470 --> 00:40:06,350 However, if you take a look at the two-year spot rate 887 00:40:06,350 --> 00:40:09,380 and compare that with the one-year spot rate, 888 00:40:09,380 --> 00:40:15,190 you can compute the one-year forward rate 889 00:40:15,190 --> 00:40:18,920 for borrowing between years 1 and 2. 890 00:40:18,920 --> 00:40:23,770 And similarly, if you compare the four-year spot rate 891 00:40:23,770 --> 00:40:25,810 with the three-year spot rate, you 892 00:40:25,810 --> 00:40:28,240 will be able to figure out what the forward rate is 893 00:40:28,240 --> 00:40:33,340 for borrowing one year between 3 and 4. 894 00:40:33,340 --> 00:40:35,282 OK? 895 00:40:35,282 --> 00:40:36,990 Now, you might think this is complicated. 896 00:40:36,990 --> 00:40:37,410 Believe me. 897 00:40:37,410 --> 00:40:39,243 It gets even more complicated when you think 898 00:40:39,243 --> 00:40:41,310 about multi-year forward rates. 899 00:40:41,310 --> 00:40:43,860 So suppose I asked you, what is the two-year borrowing 900 00:40:43,860 --> 00:40:46,770 rate, three years from now? 901 00:40:46,770 --> 00:40:50,010 Then, what you would do is to take a five-year bond 902 00:40:50,010 --> 00:40:52,440 and compare that to a three-year bond, 903 00:40:52,440 --> 00:40:56,520 and that would give you the two-year forward rate today, 904 00:40:56,520 --> 00:40:58,300 starting in year 3. 905 00:40:58,300 --> 00:40:59,370 OK? 906 00:40:59,370 --> 00:41:00,700 Lots of different rates. 907 00:41:00,700 --> 00:41:03,030 This is, again, why I've told you, every time you 908 00:41:03,030 --> 00:41:04,890 have a problem like this, draw a timeline. 909 00:41:04,890 --> 00:41:08,130 Otherwise, you're going to get hopelessly confused. 910 00:41:08,130 --> 00:41:11,580 Now, in general, you can define forward 911 00:41:11,580 --> 00:41:15,220 interest rates between any two points in time, between time t1 912 00:41:15,220 --> 00:41:16,710 and t2. 913 00:41:16,710 --> 00:41:21,120 And so the typical forward transaction 914 00:41:21,120 --> 00:41:25,590 is one where today, we agree to do a deal that 915 00:41:25,590 --> 00:41:28,530 starts at some point t1 in the future 916 00:41:28,530 --> 00:41:31,950 and concludes at some point t2 in the future. 917 00:41:31,950 --> 00:41:34,620 And that's known as a forward transaction. 918 00:41:34,620 --> 00:41:37,260 It's a transaction that we agree upon today, 919 00:41:37,260 --> 00:41:40,260 to engage in sometime in the future. 920 00:41:42,990 --> 00:41:44,700 Now, I want to work through an example, 921 00:41:44,700 --> 00:41:46,770 because this is a bit confusing. 922 00:41:46,770 --> 00:41:49,930 So let me show you how this might work, 923 00:41:49,930 --> 00:41:53,860 and why the whole idea of forward rates and future spot 924 00:41:53,860 --> 00:41:56,650 rates is so important. 925 00:41:56,650 --> 00:42:00,130 A practical example is that you are the chief financial officer 926 00:42:00,130 --> 00:42:03,100 of a multinational company based in the US, 927 00:42:03,100 --> 00:42:07,390 and you're going to get $10 million a year 928 00:42:07,390 --> 00:42:10,935 from now, from operations overseas. 929 00:42:10,935 --> 00:42:13,060 And it's going to come back in the form of dollars, 930 00:42:13,060 --> 00:42:14,643 but it's not going to come back today. 931 00:42:14,643 --> 00:42:17,480 It's going to come back exactly one year from today. 932 00:42:17,480 --> 00:42:21,104 Now, you've got to pay dividends two years from today. 933 00:42:21,104 --> 00:42:23,020 So you're going to use that money that's going 934 00:42:23,020 --> 00:42:25,070 to come in a year from now. 935 00:42:25,070 --> 00:42:29,790 And then, at the end of year 2, you're going to pay it out. 936 00:42:29,790 --> 00:42:32,580 And so you don't want to take that money next year 937 00:42:32,580 --> 00:42:33,870 and fool around with it. 938 00:42:33,870 --> 00:42:36,000 You don't know what interest rates are going to be. 939 00:42:36,000 --> 00:42:37,860 But what you'd like to be able to do 940 00:42:37,860 --> 00:42:43,020 is, today, lock in a rate of return between years 1 and 2. 941 00:42:43,020 --> 00:42:46,710 Because you know that you're going to need to get that money 942 00:42:46,710 --> 00:42:50,140 invested in year 1, and you'd like 943 00:42:50,140 --> 00:42:52,750 to be able to pay it out in year 2. 944 00:42:52,750 --> 00:42:54,274 And you want to do that all today. 945 00:42:54,274 --> 00:42:55,190 So how do you do that? 946 00:42:55,190 --> 00:42:57,490 Well, you go to the financial markets, 947 00:42:57,490 --> 00:42:59,177 and you look at the yield curve. 948 00:42:59,177 --> 00:43:00,760 And you see what the one-year rate is, 949 00:43:00,760 --> 00:43:02,140 and what the two-year rate is. 950 00:43:02,140 --> 00:43:05,620 And what you get from looking at the newspaper is, 951 00:43:05,620 --> 00:43:13,320 the one-year rate is 5%, and the two-year rate is 7%. 952 00:43:13,320 --> 00:43:16,050 Question-- is 7% a spot rate, forward rate, 953 00:43:16,050 --> 00:43:18,787 or future spot rate? 954 00:43:18,787 --> 00:43:19,620 STUDENT: [INAUDIBLE] 955 00:43:19,620 --> 00:43:22,147 ANDREW LO: It's a spot rate of what? 956 00:43:22,147 --> 00:43:22,980 STUDENT: [INAUDIBLE] 957 00:43:22,980 --> 00:43:23,771 ANDREW LO: Exactly. 958 00:43:23,771 --> 00:43:26,310 It is today's spot rate between now and two years from now. 959 00:43:26,310 --> 00:43:27,480 It's a two-year spot rate. 960 00:43:27,480 --> 00:43:28,470 Right. 961 00:43:28,470 --> 00:43:31,440 What you care about, though, for the example 962 00:43:31,440 --> 00:43:34,152 I just gave you, is what? 963 00:43:34,152 --> 00:43:36,130 STUDENT: [INAUDIBLE] 964 00:43:36,130 --> 00:43:37,000 ANDREW LO: Exactly. 965 00:43:37,000 --> 00:43:39,370 You care about the one-year spot rate in one year, 966 00:43:39,370 --> 00:43:42,460 the future one-year spot rate, which-- 967 00:43:42,460 --> 00:43:44,110 you don't know what it's going to be. 968 00:43:44,110 --> 00:43:45,430 That's uncertain. 969 00:43:45,430 --> 00:43:48,850 But you do have the-- 970 00:43:48,850 --> 00:43:51,571 what rate do you have today? 971 00:43:51,571 --> 00:43:52,570 The forward rate, right. 972 00:43:52,570 --> 00:43:53,440 You have a forward rate. 973 00:43:53,440 --> 00:43:55,190 Because you've got the two-year spot rate, 974 00:43:55,190 --> 00:43:57,080 and you've got the one-year spot rate. 975 00:43:57,080 --> 00:44:03,620 So when you compare the two, implicitly in those two rates 976 00:44:03,620 --> 00:44:05,780 is the forecast of the future one-year spot rate 977 00:44:05,780 --> 00:44:10,250 or today's forward rate between years 1 and 2. 978 00:44:10,250 --> 00:44:11,130 All right. 979 00:44:11,130 --> 00:44:12,890 Now, let's get to brass tacks. 980 00:44:12,890 --> 00:44:16,860 How do you go about locking in the rates between years 1 981 00:44:16,860 --> 00:44:18,680 and 2? 982 00:44:18,680 --> 00:44:24,620 Well, here's a really cool transaction that you can do. 983 00:44:24,620 --> 00:44:32,980 Today, borrow $9.524 million for a year. 984 00:44:32,980 --> 00:44:36,430 How do you know you can do that? 985 00:44:36,430 --> 00:44:38,059 STUDENT: [INAUDIBLE] 986 00:44:38,059 --> 00:44:38,850 ANDREW LO: Exactly. 987 00:44:38,850 --> 00:44:40,810 You've got the one-year interest rate at 5%. 988 00:44:40,810 --> 00:44:42,240 So if that's really a market rate, 989 00:44:42,240 --> 00:44:44,656 that means that you should be able to borrow at that rate. 990 00:44:44,656 --> 00:44:45,360 OK? 991 00:44:45,360 --> 00:44:49,330 So when you're borrowing money, what are you doing? 992 00:44:49,330 --> 00:44:52,914 You're-- are you buying a bond? 993 00:44:52,914 --> 00:44:53,830 You're selling a bond. 994 00:44:53,830 --> 00:44:54,890 You're issuing a bond. 995 00:44:54,890 --> 00:44:55,681 Right. 996 00:44:55,681 --> 00:44:56,180 OK. 997 00:44:56,180 --> 00:44:59,499 So you borrowed $9.52 million dollars today. 998 00:44:59,499 --> 00:45:01,040 Now, in a minute, I'll explain to you 999 00:45:01,040 --> 00:45:04,100 why that number is so weird. 1000 00:45:04,100 --> 00:45:11,610 Then, after you get the money today, 1001 00:45:11,610 --> 00:45:16,600 I'm going to ask you to put it into the two-year bond. 1002 00:45:16,600 --> 00:45:24,030 So you got $9.52 million in cash, 1003 00:45:24,030 --> 00:45:26,442 and you put it into a two-year bond. 1004 00:45:26,442 --> 00:45:27,900 So let's take a look at what you've 1005 00:45:27,900 --> 00:45:29,834 done with that transaction. 1006 00:45:33,550 --> 00:45:37,880 The outcome looks like this. 1007 00:45:37,880 --> 00:45:41,864 In year zero, you've borrowed 9.52, 1008 00:45:41,864 --> 00:45:43,280 and then you've taken the proceeds 1009 00:45:43,280 --> 00:45:47,780 and you've bought a bond at 9.52. 1010 00:45:47,780 --> 00:45:54,060 So in fact, your net expenditures is nothing. 1011 00:45:54,060 --> 00:45:55,890 You borrowed money, you took that money, 1012 00:45:55,890 --> 00:45:57,140 and you bought something else. 1013 00:45:57,140 --> 00:45:58,136 You've loaned it out. 1014 00:45:58,136 --> 00:46:00,510 You borrowed money for one year, and you've loaned it out 1015 00:46:00,510 --> 00:46:01,470 for two years. 1016 00:46:01,470 --> 00:46:02,730 That's what you've done. 1017 00:46:02,730 --> 00:46:05,190 So today, you actually have zero, 1018 00:46:05,190 --> 00:46:08,910 in terms of your assets and liabilities. 1019 00:46:08,910 --> 00:46:10,620 Now, let's see what happens next year. 1020 00:46:10,620 --> 00:46:18,440 In one year's time, that 9.52 to magically turns into 10, 1021 00:46:18,440 --> 00:46:23,810 but it's a negative 10, meaning you borrowed 9.52. 1022 00:46:23,810 --> 00:46:26,750 You've got to pay back 9.52 with interest. 1023 00:46:26,750 --> 00:46:28,840 How much interest? 1024 00:46:28,840 --> 00:46:29,659 5%. 1025 00:46:29,659 --> 00:46:30,700 That's the one-year rate. 1026 00:46:30,700 --> 00:46:35,420 So now, you actually have to pay back $10 million. 1027 00:46:35,420 --> 00:46:37,770 Well, it just so happens, you have $10 million. 1028 00:46:37,770 --> 00:46:38,372 How? 1029 00:46:38,372 --> 00:46:40,580 From the money that's coming in from your subsidiary, 1030 00:46:40,580 --> 00:46:43,040 that repatriation amount of money. 1031 00:46:43,040 --> 00:46:45,650 So you take that $10 million, you pay it back, 1032 00:46:45,650 --> 00:46:48,450 and you're done with that part of your portfolio. 1033 00:46:48,450 --> 00:46:49,670 What do you have left? 1034 00:46:49,670 --> 00:46:54,700 What you have left is a bond that 1035 00:46:54,700 --> 00:46:59,780 will pay you money in the year after that, between years 1 1036 00:46:59,780 --> 00:47:01,070 and 2. 1037 00:47:01,070 --> 00:47:03,080 And there you go. 1038 00:47:03,080 --> 00:47:06,080 You get paid $10.9 million. 1039 00:47:06,080 --> 00:47:09,140 You've done all of this transaction today. 1040 00:47:09,140 --> 00:47:12,710 You've locked in the rates today. 1041 00:47:12,710 --> 00:47:13,900 OK? 1042 00:47:13,900 --> 00:47:14,400 Yeah? 1043 00:47:14,400 --> 00:47:17,780 STUDENT: You locked in the one-year spot rate [INAUDIBLE]?? 1044 00:47:17,780 --> 00:47:18,850 ANDREW LO: That's right. 1045 00:47:18,850 --> 00:47:22,460 Well, you're locking in the forward rate, 1046 00:47:22,460 --> 00:47:24,480 which is the forecast-- 1047 00:47:24,480 --> 00:47:24,980 right. 1048 00:47:24,980 --> 00:47:28,340 It's what the market expects the future one-year spot 1049 00:47:28,340 --> 00:47:29,210 rate will be. 1050 00:47:29,210 --> 00:47:31,550 Now, that's a good point that you bring up, 1051 00:47:31,550 --> 00:47:36,540 which is, let's say that in year 1, 1052 00:47:36,540 --> 00:47:39,270 it turns out that at that point in time, 1053 00:47:39,270 --> 00:47:44,900 the one-year spot rate is 7%. 1054 00:47:44,900 --> 00:47:46,340 Are you happy or are you sad? 1055 00:47:50,380 --> 00:47:52,225 Some people say said, some people say happy. 1056 00:47:56,250 --> 00:48:01,080 If the one-year spot rate one year from now is 7%, 1057 00:48:01,080 --> 00:48:02,827 and you've done this deal already-- 1058 00:48:02,827 --> 00:48:04,020 STUDENT: You're happy. 1059 00:48:04,020 --> 00:48:05,020 ANDREW LO: You're happy. 1060 00:48:05,020 --> 00:48:05,700 That's right. 1061 00:48:05,700 --> 00:48:09,930 Because, what are you getting on your portfolio? 1062 00:48:09,930 --> 00:48:10,950 9%. 1063 00:48:10,950 --> 00:48:12,480 Now, wait a minute. 1064 00:48:12,480 --> 00:48:13,860 How do you get 9%? 1065 00:48:13,860 --> 00:48:16,020 I thought that I told you the two-year rate was 7%. 1066 00:48:22,730 --> 00:48:25,595 I'm purposely confusing you, so I'm hoping it works. 1067 00:48:25,595 --> 00:48:27,470 And then, I'm going to try to un-confuse you, 1068 00:48:27,470 --> 00:48:30,590 and I hope that works, too. 1069 00:48:30,590 --> 00:48:32,960 5% is the one-year spot rate. 1070 00:48:32,960 --> 00:48:35,380 7% is the two-year spot rate. 1071 00:48:35,380 --> 00:48:36,452 Yeah. 1072 00:48:36,452 --> 00:48:38,992 STUDENT: [INAUDIBLE] 1073 00:48:38,992 --> 00:48:39,700 ANDREW LO: Right. 1074 00:48:39,700 --> 00:48:40,960 That's right. 1075 00:48:40,960 --> 00:48:47,230 The rate between years 1 and 2 is around 9%. 1076 00:48:47,230 --> 00:48:49,060 And the reason it's got to be that way 1077 00:48:49,060 --> 00:48:52,280 is, the 7% that I told you-- 1078 00:48:52,280 --> 00:48:53,239 that's a two-year rate. 1079 00:48:53,239 --> 00:48:53,738 Right? 1080 00:48:53,738 --> 00:48:55,190 That's the average of two years. 1081 00:48:55,190 --> 00:48:57,570 But you know what the rate is the first year. 1082 00:48:57,570 --> 00:48:59,550 The first year rate is 5%. 1083 00:48:59,550 --> 00:49:02,300 So if something averages to 7% over 2 years, 1084 00:49:02,300 --> 00:49:05,130 but the first year is 5, the second year 1085 00:49:05,130 --> 00:49:06,410 has got to be greater than 7. 1086 00:49:06,410 --> 00:49:09,950 Otherwise, the average can't be 7. 1087 00:49:09,950 --> 00:49:11,870 In fact, the second year rate-- 1088 00:49:11,870 --> 00:49:15,890 the one year rate between years 1 and 2 is around 9%. 1089 00:49:15,890 --> 00:49:22,360 And so that's why if when you arrive at the end of year 1, 1090 00:49:22,360 --> 00:49:24,250 ready to borrow for one more year, 1091 00:49:24,250 --> 00:49:26,590 and you've already locked in a 9% rate, 1092 00:49:26,590 --> 00:49:30,280 you are pretty happy that the rate at that time is 7. 1093 00:49:30,280 --> 00:49:35,620 However, if I told you that the rate at that time was 15, 1094 00:49:35,620 --> 00:49:37,740 you'll be kicking yourself, because you locked 1095 00:49:37,740 --> 00:49:40,425 in a 9% rate, and yet it's 15%. 1096 00:49:43,080 --> 00:49:46,440 So there's room for regret as well as celebration, 1097 00:49:46,440 --> 00:49:48,310 depending on what the market is going to do. 1098 00:49:48,310 --> 00:49:51,030 But the point is that in year zero, 1099 00:49:51,030 --> 00:49:52,590 I don't know what it's going to be. 1100 00:49:52,590 --> 00:49:54,390 And I'm not a hedge fund manager. 1101 00:49:54,390 --> 00:49:55,200 I'm not a trader. 1102 00:49:55,200 --> 00:49:55,784 I don't care-- 1103 00:49:55,784 --> 00:49:57,949 I don't want to make a bet on future interest rates. 1104 00:49:57,949 --> 00:49:59,790 I just want to get this problem solved. 1105 00:49:59,790 --> 00:50:02,340 And right now, today, I can actually 1106 00:50:02,340 --> 00:50:04,860 solve my problem of figuring out how 1107 00:50:04,860 --> 00:50:07,650 to invest my money between years 1 and 2 1108 00:50:07,650 --> 00:50:11,400 by doing this very simple transaction in open markets 1109 00:50:11,400 --> 00:50:13,300 with market-determined interest rates. 1110 00:50:13,300 --> 00:50:16,270 And I know, as long as the interest rates are not nuts, 1111 00:50:16,270 --> 00:50:18,300 then I'm getting a reasonable deal. 1112 00:50:18,300 --> 00:50:19,516 Yeah? 1113 00:50:19,516 --> 00:50:22,530 STUDENT: This is one of the main [? things that you can do. ?] 1114 00:50:22,530 --> 00:50:26,258 Could you please [INAUDIBLE] is it even similar in the same-- 1115 00:50:26,258 --> 00:50:29,302 at the end of year 1, I get my 10 million, 1116 00:50:29,302 --> 00:50:35,354 put it in [INAUDIBLE],, because it's pretty much [INAUDIBLE].. 1117 00:50:35,354 --> 00:50:36,020 ANDREW LO: Yeah. 1118 00:50:36,020 --> 00:50:37,395 But the problem is that you don't 1119 00:50:37,395 --> 00:50:39,820 know what that one-year T-bill rate will be, 1120 00:50:39,820 --> 00:50:42,950 whereas right now, you know that it's 9%. 1121 00:50:42,950 --> 00:50:45,320 Right now, you know it's 9%, and it 1122 00:50:45,320 --> 00:50:47,810 seems like a pretty good deal to go ahead and do it. 1123 00:50:47,810 --> 00:50:51,530 If, however, you think that interest rates are going 1124 00:50:51,530 --> 00:50:55,790 to go up much more than the market thinks, 1125 00:50:55,790 --> 00:50:57,590 then you may want to wait. 1126 00:50:57,590 --> 00:51:01,040 But now, you're becoming an interest rate speculator. 1127 00:51:01,040 --> 00:51:02,390 You're taking a risk. 1128 00:51:02,390 --> 00:51:05,570 And as a CFO, that's generally not your job and not 1129 00:51:05,570 --> 00:51:06,631 your level of competency. 1130 00:51:06,631 --> 00:51:07,130 Right? 1131 00:51:07,130 --> 00:51:10,148 You're not there trying to forecast interest rates. 1132 00:51:10,148 --> 00:51:11,146 Yeah? 1133 00:51:11,146 --> 00:51:14,570 STUDENT: [INAUDIBLE] 1134 00:51:14,570 --> 00:51:15,570 ANDREW LO: That's right. 1135 00:51:15,570 --> 00:51:19,220 The 9.524 is the present value of $10 million today, 1136 00:51:19,220 --> 00:51:20,900 at the rate of 5% interest. 1137 00:51:23,900 --> 00:51:25,520 So the way that I did this-- 1138 00:51:25,520 --> 00:51:28,010 and you know, this is a good illustration 1139 00:51:28,010 --> 00:51:30,140 of what I've been telling you about finance 1140 00:51:30,140 --> 00:51:31,730 not being a spectator sport. 1141 00:51:31,730 --> 00:51:33,470 I suspect that all of you understand 1142 00:51:33,470 --> 00:51:36,110 the lectures that I've given so far about present value, 1143 00:51:36,110 --> 00:51:38,420 about time value of money, and the fact that you've got 1144 00:51:38,420 --> 00:51:39,711 to use the right exchange rate. 1145 00:51:39,711 --> 00:51:42,500 It all is pretty straightforward. 1146 00:51:42,500 --> 00:51:45,890 But putting it into practice is not so easy, at least for me. 1147 00:51:45,890 --> 00:51:48,320 I don't find this example so transparent. 1148 00:51:48,320 --> 00:51:50,840 You have to actually spend some time thinking about it, 1149 00:51:50,840 --> 00:51:52,370 thinking about where the money is coming from, 1150 00:51:52,370 --> 00:51:54,080 where the money is going, how much money 1151 00:51:54,080 --> 00:51:56,440 you have at any point in time. 1152 00:51:56,440 --> 00:51:59,040 But when you work it out, it all makes sense. 1153 00:51:59,040 --> 00:52:01,220 And so I would encourage all of you 1154 00:52:01,220 --> 00:52:03,350 to spend some time working this out. 1155 00:52:03,350 --> 00:52:05,021 OK, question? 1156 00:52:05,021 --> 00:52:05,520 Yeah. 1157 00:52:05,520 --> 00:52:12,940 STUDENT: [INAUDIBLE] 1158 00:52:12,940 --> 00:52:14,380 ANDREW LO: Yes, there are ways you 1159 00:52:14,380 --> 00:52:16,720 can engage in a forward contract, of course. 1160 00:52:16,720 --> 00:52:18,460 So you don't have to do this. 1161 00:52:18,460 --> 00:52:21,520 But the fact is doing this is so simple. 1162 00:52:21,520 --> 00:52:22,720 Why not? 1163 00:52:22,720 --> 00:52:25,960 And if it's simple, most likely, it'll be cheap. 1164 00:52:25,960 --> 00:52:29,030 If it's complex, that's when you're going to pay for it. 1165 00:52:29,030 --> 00:52:29,530 Right? 1166 00:52:29,530 --> 00:52:32,590 So I'm happy to structure a derivative product for you. 1167 00:52:32,590 --> 00:52:34,030 Let's call it a structured product 1168 00:52:34,030 --> 00:52:35,571 that we trade over the counter, where 1169 00:52:35,571 --> 00:52:38,440 I offer you a forward contract, one-year borrowing, 1170 00:52:38,440 --> 00:52:40,660 with certain terms and privileges, and so on. 1171 00:52:40,660 --> 00:52:42,521 And by the time we're done, I'm going 1172 00:52:42,521 --> 00:52:44,770 to charge you a transaction fee of-- oh, I don't know, 1173 00:52:44,770 --> 00:52:46,720 maybe 5%. 1174 00:52:46,720 --> 00:52:49,990 Versus, you buy a two-year bond and a one-year bill, 1175 00:52:49,990 --> 00:52:51,020 and you're done. 1176 00:52:51,020 --> 00:52:51,520 Right? 1177 00:52:51,520 --> 00:52:53,260 So that's the difference. 1178 00:52:53,260 --> 00:52:56,450 It's really the ease with which you can implement the strategy. 1179 00:52:56,450 --> 00:52:58,270 All of you right now, today-- 1180 00:52:58,270 --> 00:52:59,410 all of you can do this. 1181 00:52:59,410 --> 00:53:00,610 You can do this. 1182 00:53:00,610 --> 00:53:02,500 You can actually trade in these markets. 1183 00:53:02,500 --> 00:53:05,110 Set up a brokerage account, trade these treasury 1184 00:53:05,110 --> 00:53:07,540 instruments, and do this yourself. 1185 00:53:07,540 --> 00:53:09,100 In fact, you can do this online. 1186 00:53:09,100 --> 00:53:11,660 So it's very, very simple. 1187 00:53:11,660 --> 00:53:12,935 And-- yeah? 1188 00:53:12,935 --> 00:53:15,790 STUDENT: [INAUDIBLE] $10 million? 1189 00:53:15,790 --> 00:53:17,035 ANDREW LO: Oh, yeah. 1190 00:53:17,035 --> 00:53:17,826 [STUDENTS LAUGHING] 1191 00:53:17,826 --> 00:53:19,350 Well, that's the hard part. 1192 00:53:19,350 --> 00:53:20,269 Yeah. 1193 00:53:20,269 --> 00:53:22,060 There's an old Steve Martin joke that says, 1194 00:53:22,060 --> 00:53:24,220 I'm going to show you how to make a million dollars 1195 00:53:24,220 --> 00:53:25,420 and pay no taxes. 1196 00:53:25,420 --> 00:53:27,910 First, get a million dollars. 1197 00:53:27,910 --> 00:53:30,610 So yes, that's the hard part. 1198 00:53:30,610 --> 00:53:32,140 OK. 1199 00:53:32,140 --> 00:53:36,850 So now, this transaction today locks you 1200 00:53:36,850 --> 00:53:40,720 into a 9% rate between years 1 and 2. 1201 00:53:40,720 --> 00:53:42,490 And so going back to the question 1202 00:53:42,490 --> 00:53:43,977 that [? Anan ?] raised, should you 1203 00:53:43,977 --> 00:53:45,310 do this or should you just wait? 1204 00:53:45,310 --> 00:53:47,380 Well, it depends. 1205 00:53:47,380 --> 00:53:50,560 Do you feel lucky? 1206 00:53:50,560 --> 00:53:53,210 Do you think you can do better than 9%? 1207 00:53:53,210 --> 00:53:54,627 I mean, today, 9% looks wonderful, 1208 00:53:54,627 --> 00:53:56,918 but that's not with the rate you're going to get today. 1209 00:53:56,918 --> 00:53:58,840 In fact, if we go back to the Bloomberg site, 1210 00:53:58,840 --> 00:54:00,940 you can see what kind of rate you would lock 1211 00:54:00,940 --> 00:54:03,280 in today between years 1 and 2. 1212 00:54:03,280 --> 00:54:06,390 And I promise you, it's nowhere near 9%. 1213 00:54:06,390 --> 00:54:09,010 And so again, you might actually say-- 1214 00:54:09,010 --> 00:54:11,620 in today's low interest rate environment, 1215 00:54:11,620 --> 00:54:14,290 you might say, look, I think that inflation 1216 00:54:14,290 --> 00:54:17,950 is going to heat up a great deal over the next year, 1217 00:54:17,950 --> 00:54:23,470 and therefore what's implicit in today's forecast of future spot 1218 00:54:23,470 --> 00:54:26,780 rates is lower than I think it ought to be. 1219 00:54:26,780 --> 00:54:29,470 So I'm going to hold off. 1220 00:54:29,470 --> 00:54:30,125 That's a bet. 1221 00:54:30,125 --> 00:54:31,750 And so you're going to take some risks. 1222 00:54:31,750 --> 00:54:32,431 That's all. 1223 00:54:32,431 --> 00:54:34,930 And for those people who are good at taking risks like that, 1224 00:54:34,930 --> 00:54:35,888 they end up doing well. 1225 00:54:35,888 --> 00:54:38,830 For those who don't, they end up losing out 1226 00:54:38,830 --> 00:54:41,789 on good opportunities. 1227 00:54:41,789 --> 00:54:44,330 There's another example that I'd like you to look at and work 1228 00:54:44,330 --> 00:54:45,260 through on your own. 1229 00:54:45,260 --> 00:54:47,000 It's very similar to the first one, 1230 00:54:47,000 --> 00:54:49,760 but it just gives you practice in thinking about timelines, 1231 00:54:49,760 --> 00:54:52,190 moving money back and forth, and trying 1232 00:54:52,190 --> 00:54:57,380 to understand how to structure the payoffs in order to satisfy 1233 00:54:57,380 --> 00:54:59,370 certain consumption patterns. 1234 00:54:59,370 --> 00:55:02,060 So if you look at this example and work it through, 1235 00:55:02,060 --> 00:55:05,150 that will give you more practice on how to deal 1236 00:55:05,150 --> 00:55:06,150 with these transactions. 1237 00:55:09,430 --> 00:55:13,930 Now, if there are no more questions about pure discount 1238 00:55:13,930 --> 00:55:17,740 bonds, I want to turn to the more general case of coupon 1239 00:55:17,740 --> 00:55:18,350 bonds. 1240 00:55:18,350 --> 00:55:21,730 These are bonds that pay off coupons. 1241 00:55:21,730 --> 00:55:24,700 And really, the theory behind coupon bonds 1242 00:55:24,700 --> 00:55:28,660 is virtually identical to that of discount bonds, in the sense 1243 00:55:28,660 --> 00:55:32,780 that you can always look at a coupon bond 1244 00:55:32,780 --> 00:55:35,480 as a package of discount bonds. 1245 00:55:35,480 --> 00:55:36,850 Right? 1246 00:55:36,850 --> 00:55:38,740 That's, sort of, the opposite of a strip. 1247 00:55:38,740 --> 00:55:41,980 A strip takes a coupon bond and breaks it up 1248 00:55:41,980 --> 00:55:45,310 into what look like little discount bonds. 1249 00:55:45,310 --> 00:55:48,250 Well, if you think about what a coupon bond is, 1250 00:55:48,250 --> 00:55:51,691 it's really just a collection of discount bonds 1251 00:55:51,691 --> 00:55:52,690 at different maturities. 1252 00:55:52,690 --> 00:55:55,210 That's the way to think about it. 1253 00:55:55,210 --> 00:55:56,740 Here's a simple example. 1254 00:55:56,740 --> 00:56:00,550 A three-year bond with a 5% coupon 1255 00:56:00,550 --> 00:56:02,050 is going to look like this. 1256 00:56:02,050 --> 00:56:05,721 It's going to pay 50, 50, and then 1,050. 1257 00:56:05,721 --> 00:56:07,720 Now, as I mentioned, there are some coupon bonds 1258 00:56:07,720 --> 00:56:09,730 that pay semiannually. 1259 00:56:09,730 --> 00:56:12,730 So when they say that there's a coupon of 3%, 1260 00:56:12,730 --> 00:56:14,980 it's 3% every six months. 1261 00:56:14,980 --> 00:56:16,540 So you have to take that into account 1262 00:56:16,540 --> 00:56:18,280 when you're computing the present values 1263 00:56:18,280 --> 00:56:20,480 of these objects. 1264 00:56:20,480 --> 00:56:21,310 How do we do it? 1265 00:56:21,310 --> 00:56:25,660 Exactly the same way as we do for pure discount bonds. 1266 00:56:25,660 --> 00:56:29,380 Take the coupons, each of them, and discount them back 1267 00:56:29,380 --> 00:56:35,040 to the present, using either the big R's or the little r's. 1268 00:56:35,040 --> 00:56:38,200 Either way, you ought to get the same answer, 1269 00:56:38,200 --> 00:56:42,150 because the little r's are simply the geometric averages 1270 00:56:42,150 --> 00:56:43,360 of the big R's. 1271 00:56:43,360 --> 00:56:44,650 OK? 1272 00:56:44,650 --> 00:56:48,390 However, instead of using the little r's 1273 00:56:48,390 --> 00:56:53,890 for the different payments, coupon bonds 1274 00:56:53,890 --> 00:57:01,680 are often quoted with a single number that is a yield. 1275 00:57:01,680 --> 00:57:05,360 So the theoretically correct way to write the price 1276 00:57:05,360 --> 00:57:06,910 is given up there. 1277 00:57:06,910 --> 00:57:09,500 P0 is equal to C, all the coupons, 1278 00:57:09,500 --> 00:57:12,350 divided by the appropriate big R's. 1279 00:57:12,350 --> 00:57:15,320 Or we could replace every one of those big R's 1280 00:57:15,320 --> 00:57:17,480 with the appropriate little r. 1281 00:57:17,480 --> 00:57:21,590 By appropriate little r, I mean, little r 0,1, little r 0,2, 1282 00:57:21,590 --> 00:57:23,750 too little r 0,3-- 1283 00:57:23,750 --> 00:57:25,470 each of those. 1284 00:57:25,470 --> 00:57:29,900 But we can also calculate an average 1285 00:57:29,900 --> 00:57:34,130 of all of those little r's and just use one variable. 1286 00:57:34,130 --> 00:57:36,590 And to simplify notation, I'm going to give it a completely 1287 00:57:36,590 --> 00:57:43,670 different symbol, Y, and say, , what is that single number, Y, 1288 00:57:43,670 --> 00:57:47,960 that will give me the price of the bond? 1289 00:57:47,960 --> 00:57:52,970 And that Y is known as the particular bond's yield. 1290 00:57:52,970 --> 00:57:56,870 It is the single interest rate which, 1291 00:57:56,870 --> 00:58:00,110 if interest rates were constant throughout time, 1292 00:58:00,110 --> 00:58:04,760 would make the present value of all the coupons and principal 1293 00:58:04,760 --> 00:58:07,610 equal to the current price. 1294 00:58:07,610 --> 00:58:10,560 So if you think about a mortgage, 1295 00:58:10,560 --> 00:58:13,860 and you ask the question, if the mortgage rate 1296 00:58:13,860 --> 00:58:20,430 is 5%, what is the value of the loan, 1297 00:58:20,430 --> 00:58:24,590 that's exactly this expression right here. 1298 00:58:24,590 --> 00:58:29,886 Now, obviously, when you get a fixed rate mortgage of 5.89%, 1299 00:58:29,886 --> 00:58:31,760 you know that the interest rate is not really 1300 00:58:31,760 --> 00:58:33,710 going to be 5.98% forever. 1301 00:58:33,710 --> 00:58:35,840 The interest rate changes every year. 1302 00:58:35,840 --> 00:58:41,750 But that 5.98% is an average of the 30-year period where 1303 00:58:41,750 --> 00:58:44,360 you're going to be borrowing that mortgage money. 1304 00:58:44,360 --> 00:58:48,590 So you can think of this coupon bond in exactly the same way. 1305 00:58:48,590 --> 00:58:52,010 We quote this number Y as a yield. 1306 00:58:52,010 --> 00:58:54,890 Sometimes, we talk about yield instead of prices. 1307 00:58:54,890 --> 00:58:56,690 But the way that we figure out the yield 1308 00:58:56,690 --> 00:58:59,330 is, we take this 30-year bond that 1309 00:58:59,330 --> 00:59:02,840 pays 5% a year, we auction it off, 1310 00:59:02,840 --> 00:59:04,940 and we figure out what the price is. 1311 00:59:04,940 --> 00:59:07,470 Given the price, we can find the yield. 1312 00:59:10,300 --> 00:59:13,850 Finding the yield is not so easy in this case, 1313 00:59:13,850 --> 00:59:18,300 because in this case, unlike just taking a simple geometric 1314 00:59:18,300 --> 00:59:21,750 average, which is what we did to calculate the little r's from 1315 00:59:21,750 --> 00:59:22,530 the big R's-- 1316 00:59:22,530 --> 00:59:26,830 in this case, in order to find the Y, 1317 00:59:26,830 --> 00:59:30,760 we actually have to solve an equation that 1318 00:59:30,760 --> 00:59:32,080 can be highly non-linear. 1319 00:59:32,080 --> 00:59:34,480 In fact, it's a polynomial. 1320 00:59:34,480 --> 00:59:38,230 It's a t-th order polynomial. 1321 00:59:38,230 --> 00:59:41,350 And for those of you high school math team jocks, 1322 00:59:41,350 --> 00:59:45,850 you'll remember that when you've got a t-th order 1323 00:59:45,850 --> 00:59:49,930 polynomial, first of all, you have a lot of solutions. 1324 00:59:49,930 --> 00:59:52,280 How many solutions do you typically have? 1325 00:59:52,280 --> 00:59:53,500 t. 1326 00:59:53,500 --> 00:59:57,250 And of those solutions, how many of them 1327 00:59:57,250 --> 01:00:00,067 are guaranteed to be real numbers? 1328 01:00:03,511 --> 01:00:04,010 Right. 1329 01:00:04,010 --> 01:00:06,740 There's no guarantee that any of them are real. 1330 01:00:06,740 --> 01:00:08,690 Now, you might ask, what do you mean by real? 1331 01:00:08,690 --> 01:00:10,790 Well, if you're asking me, you don't need to know. 1332 01:00:10,790 --> 01:00:13,400 [LAUGHTER] Don't-- don't. 1333 01:00:13,400 --> 01:00:16,370 It means numbers that we encounter in reality. 1334 01:00:16,370 --> 01:00:18,409 Let's put it that way. 1335 01:00:18,409 --> 01:00:20,450 It turns out that there are numbers that actually 1336 01:00:20,450 --> 01:00:22,310 don't exist in reality. 1337 01:00:22,310 --> 01:00:24,170 They're called complex numbers. 1338 01:00:24,170 --> 01:00:28,130 And they are quite complex, so I won't talk about them. 1339 01:00:28,130 --> 01:00:30,004 But these kinds of equations-- 1340 01:00:30,004 --> 01:00:31,670 it turns out that they're not guaranteed 1341 01:00:31,670 --> 01:00:33,950 to even have real solutions. 1342 01:00:33,950 --> 01:00:37,240 Now, it turns out that for bonds, 1343 01:00:37,240 --> 01:00:39,640 where the coupon payments are all positive 1344 01:00:39,640 --> 01:00:41,800 and the principle is all positive, 1345 01:00:41,800 --> 01:00:43,500 it turns out in that very restrictive-- 1346 01:00:43,500 --> 01:00:44,710 and the price is positive. 1347 01:00:44,710 --> 01:00:49,300 It turns out in those cases, you actually do get a real number-- 1348 01:00:49,300 --> 01:00:51,340 at least, one real number. 1349 01:00:51,340 --> 01:00:52,900 The problem is that in some cases, 1350 01:00:52,900 --> 01:00:54,520 you get multiple real numbers. 1351 01:00:54,520 --> 01:00:57,280 And then, it's very, very hard to figure out which yield 1352 01:00:57,280 --> 01:00:58,621 is the correct one to use. 1353 01:00:58,621 --> 01:01:00,370 The only reason I'm telling you about this 1354 01:01:00,370 --> 01:01:03,940 is because it turns out as a matter of convention, 1355 01:01:03,940 --> 01:01:09,100 very often, people will quote these little Y yields when 1356 01:01:09,100 --> 01:01:10,774 they talk about coupon bonds. 1357 01:01:10,774 --> 01:01:12,190 But the way to think about that is 1358 01:01:12,190 --> 01:01:13,660 to think about the price, which is 1359 01:01:13,660 --> 01:01:16,780 the present value of the coupon payments as a present discount 1360 01:01:16,780 --> 01:01:21,400 value of the interest that really applies between today 1361 01:01:21,400 --> 01:01:22,810 and date t. 1362 01:01:22,810 --> 01:01:25,360 In fact, in order to do this present value calculation, 1363 01:01:25,360 --> 01:01:27,070 you need not just one interest rate. 1364 01:01:27,070 --> 01:01:30,710 How many interest rates do you need? 1365 01:01:30,710 --> 01:01:32,180 t, right? 1366 01:01:32,180 --> 01:01:35,030 You're at year zero, and you've got payments 1367 01:01:35,030 --> 01:01:37,520 for every single year between 1 and t. 1368 01:01:37,520 --> 01:01:40,838 So you need interest rates that apply between 0 and 1, 0 1369 01:01:40,838 --> 01:01:43,260 and 2, 0 and 3, and so on. 1370 01:01:43,260 --> 01:01:46,440 You need t interest rates or exchange rates. 1371 01:01:46,440 --> 01:01:46,940 Right? 1372 01:01:46,940 --> 01:01:49,700 Or exchanges between different dates. 1373 01:01:49,700 --> 01:01:52,850 But now, the yield is important because it 1374 01:01:52,850 --> 01:01:57,170 allows us to quote the pseudo rate of return 1375 01:01:57,170 --> 01:02:01,070 of this bond in a single number. 1376 01:02:01,070 --> 01:02:06,860 And very often, people will plot the Y's as a function 1377 01:02:06,860 --> 01:02:09,810 of the horizon of these bonds. 1378 01:02:09,810 --> 01:02:12,200 So when I showed you that yield curve-- 1379 01:02:12,200 --> 01:02:13,370 let me get that back. 1380 01:02:16,870 --> 01:02:17,720 Whoops. 1381 01:02:17,720 --> 01:02:18,470 I just had it. 1382 01:02:23,440 --> 01:02:26,460 Let's take a look at this again. 1383 01:02:26,460 --> 01:02:32,190 These treasury bonds from years 2 to years 30-- 1384 01:02:32,190 --> 01:02:36,210 those have coupon payments, and those are the coupon rates. 1385 01:02:36,210 --> 01:02:41,040 And they have prices, and they have yields. 1386 01:02:41,040 --> 01:02:47,210 So what's plotted here is not the little r. 1387 01:02:47,210 --> 01:02:50,870 It's the Y for the coupon bonds. 1388 01:02:50,870 --> 01:02:53,990 And so the reason that they're not the same 1389 01:02:53,990 --> 01:02:57,620 is because the yields, the little Y's, depend 1390 01:02:57,620 --> 01:02:59,680 on the coupon payments. 1391 01:02:59,680 --> 01:03:02,150 And really strictly speaking, we don't 1392 01:03:02,150 --> 01:03:05,000 care about coupon payments when we look at time to maturity. 1393 01:03:05,000 --> 01:03:06,749 We just want to know, what is the interest 1394 01:03:06,749 --> 01:03:11,130 rate between 0 and 1, 0 and 2, 0 and 3, 0 and 5, and so on. 1395 01:03:11,130 --> 01:03:13,670 But this is a reasonable proxy as long 1396 01:03:13,670 --> 01:03:16,130 as the coupons don't look too crazy 1397 01:03:16,130 --> 01:03:18,240 and are not too different from each other. 1398 01:03:18,240 --> 01:03:20,369 And you can see that the coupons are all, sort of, 1399 01:03:20,369 --> 01:03:21,410 in the same neighborhood. 1400 01:03:21,410 --> 01:03:25,340 Some of them are 2.3% versus 4.5%, 1401 01:03:25,340 --> 01:03:26,600 but they're not so different. 1402 01:03:26,600 --> 01:03:32,630 So this gives us an indication of what the strip's yield 1403 01:03:32,630 --> 01:03:33,750 curve would look like. 1404 01:03:44,860 --> 01:03:47,950 Here's an example of the historical yield 1405 01:03:47,950 --> 01:03:50,650 curve for US Treasury securities, 1406 01:03:50,650 --> 01:03:53,560 and let me just show you a plot. 1407 01:03:53,560 --> 01:03:55,720 They move around a lot. 1408 01:03:55,720 --> 01:03:58,330 So these yield curves tell us something 1409 01:03:58,330 --> 01:04:01,270 about the average interest rate across 1410 01:04:01,270 --> 01:04:03,020 various different maturities. 1411 01:04:03,020 --> 01:04:05,440 So if you look at the yellow line, 1412 01:04:05,440 --> 01:04:10,490 that's a one-year yield over time. 1413 01:04:10,490 --> 01:04:12,580 So this is not the yield curve anymore. 1414 01:04:12,580 --> 01:04:15,250 This is a plot of the time series 1415 01:04:15,250 --> 01:04:18,960 of one-year yields over time. 1416 01:04:18,960 --> 01:04:24,360 And you can see that starting when the sample began in 1982, 1417 01:04:24,360 --> 01:04:31,450 the one-year yield for US Treasury bills is 12%. 1418 01:04:31,450 --> 01:04:34,450 12% back in 1982-- 1419 01:04:34,450 --> 01:04:39,730 and there is a point at which one of the longer maturity 1420 01:04:39,730 --> 01:04:44,410 instruments reaches a peak of 16% or 17%. 1421 01:04:44,410 --> 01:04:48,040 Remember, I told you, I was looking to get a house 1422 01:04:48,040 --> 01:04:50,560 and get a mortgage at 18%. 1423 01:04:50,560 --> 01:04:54,320 That was a 30-year fixed rate back in the 1980s. 1424 01:04:54,320 --> 01:04:58,450 So borrowing rates are very, very low 1425 01:04:58,450 --> 01:05:01,360 by these historical standards. 1426 01:05:01,360 --> 01:05:04,390 If borrowing rates are very low, what 1427 01:05:04,390 --> 01:05:08,830 does that tell you about credit and about the amount of cash 1428 01:05:08,830 --> 01:05:12,940 sloshing around in the economy? 1429 01:05:12,940 --> 01:05:13,625 Yeah? 1430 01:05:13,625 --> 01:05:14,960 STUDENT: [INAUDIBLE] 1431 01:05:14,960 --> 01:05:16,960 ANDREW LO: Exactly-- lots and lots 1432 01:05:16,960 --> 01:05:18,950 and lots of money available. 1433 01:05:18,950 --> 01:05:20,560 So for those of you who are thinking 1434 01:05:20,560 --> 01:05:22,582 about entrepreneurial ventures-- if you're 1435 01:05:22,582 --> 01:05:24,040 thinking about raising capital, you 1436 01:05:24,040 --> 01:05:27,040 might be depressed by what's going on in markets today. 1437 01:05:27,040 --> 01:05:30,560 But look at the interest rate and ask yourself, 1438 01:05:30,560 --> 01:05:35,010 gee, would I rather start a company today or back in 1982? 1439 01:05:35,010 --> 01:05:36,970 There's a heck of a lot more money sloshing 1440 01:05:36,970 --> 01:05:39,800 around the system today. 1441 01:05:39,800 --> 01:05:42,670 In fact, a few years ago, I talked to a couple 1442 01:05:42,670 --> 01:05:44,507 of MIT undergraduates. 1443 01:05:44,507 --> 01:05:46,340 One of them came up and asked me whether I'd 1444 01:05:46,340 --> 01:05:49,180 be willing to advise them on some internet company they 1445 01:05:49,180 --> 01:05:50,680 wanted to start. 1446 01:05:50,680 --> 01:05:53,414 And you know, I said, well, you know, where are you 1447 01:05:53,414 --> 01:05:54,580 going to get your financing? 1448 01:05:54,580 --> 01:05:55,770 And they said, oh, don't worry about that. 1449 01:05:55,770 --> 01:05:57,460 We've already got it all set. 1450 01:05:57,460 --> 01:06:00,310 You know, we've got 10 of us, and each of us 1451 01:06:00,310 --> 01:06:04,660 is able to borrow $1,000 each on credit cards, 1452 01:06:04,660 --> 01:06:10,810 and we each have 10 credit cards, so that's $100,000. 1453 01:06:10,810 --> 01:06:12,990 And I'm saying, $100,000 on credit cards? 1454 01:06:12,990 --> 01:06:15,620 I mean, you guys are going to be paying 18% a year 1455 01:06:15,620 --> 01:06:16,750 or something on that. 1456 01:06:16,750 --> 01:06:18,208 And they said, yeah, you know what? 1457 01:06:18,208 --> 01:06:20,860 That's the cheapest venture financing you'll ever find. 1458 01:06:20,860 --> 01:06:24,100 And they're right, because those are non-recourse loans. 1459 01:06:24,100 --> 01:06:25,810 They don't take a piece of your company. 1460 01:06:25,810 --> 01:06:29,096 And 18% for a venture is actually pretty attractive. 1461 01:06:29,096 --> 01:06:30,970 Well, look at what the borrowing rate is now. 1462 01:06:30,970 --> 01:06:33,257 Now, you can't borrow at this rate for ventures, 1463 01:06:33,257 --> 01:06:35,590 but it indicates that there's a lot of credit out there, 1464 01:06:35,590 --> 01:06:38,900 and there's still a lot of credit out there. 1465 01:06:38,900 --> 01:06:40,810 In fact, the treasury and the Fed 1466 01:06:40,810 --> 01:06:42,880 would argue there's too much credit out there. 1467 01:06:42,880 --> 01:06:45,171 And that's why we're in the problems that we are today. 1468 01:06:45,171 --> 01:06:46,300 Because too many people-- 1469 01:06:46,300 --> 01:06:49,320 people that should not have been leveraging and borrowing 1470 01:06:49,320 --> 01:06:50,680 have done so. 1471 01:06:50,680 --> 01:06:54,490 And now, we're feeling the pains of a contraction. 1472 01:06:54,490 --> 01:06:56,890 So this is the history of yield curves. 1473 01:06:56,890 --> 01:07:01,090 And at a given point in time, we can take a look at yield curves 1474 01:07:01,090 --> 01:07:03,580 and see how that curve changes day to day. 1475 01:07:03,580 --> 01:07:06,770 I showed you today's yield curve, which is upward sloping. 1476 01:07:06,770 --> 01:07:10,180 But you know, there was a period back in 2000 1477 01:07:10,180 --> 01:07:13,390 where this yield curve was actually upward-sloping, 1478 01:07:13,390 --> 01:07:17,250 and then downward-sloping. 1479 01:07:17,250 --> 01:07:20,840 Why would the yield curve be downward-sloping? 1480 01:07:20,840 --> 01:07:22,490 What that tells you is that there's 1481 01:07:22,490 --> 01:07:26,480 an expectation of the market participants 1482 01:07:26,480 --> 01:07:31,010 that interest rates in the long run have got to come down, 1483 01:07:31,010 --> 01:07:33,740 and that there's going to be some kind of Fed policy 1484 01:07:33,740 --> 01:07:37,430 shift possible within three years, five years, 10 years, 1485 01:07:37,430 --> 01:07:40,650 that would make that more likely than not. 1486 01:07:40,650 --> 01:07:44,240 So by looking at these yield curves over different dates, 1487 01:07:44,240 --> 01:07:47,450 you can get a sense of how the market's expectations are 1488 01:07:47,450 --> 01:07:52,260 of the future, which I think is a tremendous ability 1489 01:07:52,260 --> 01:07:54,260 to actually look into the future-- at least look 1490 01:07:54,260 --> 01:08:00,954 into the future as predicted by all the market participants. 1491 01:08:00,954 --> 01:08:03,120 This is just that yield curve that I told you about. 1492 01:08:03,120 --> 01:08:04,800 This is not in your notes, but I was 1493 01:08:04,800 --> 01:08:06,716 able to copy that from Bloomberg this morning. 1494 01:08:06,716 --> 01:08:08,940 You have that in the public website. 1495 01:08:08,940 --> 01:08:15,090 And now, the next topic I want to take on-- very briefly, 1496 01:08:15,090 --> 01:08:19,170 because there's a lot to be said about models of the yield 1497 01:08:19,170 --> 01:08:21,960 curve, and I won't take up class time to do that. 1498 01:08:21,960 --> 01:08:26,069 This is something that is a topic that's 1499 01:08:26,069 --> 01:08:29,729 more significantly focused on in investments 1500 01:08:29,729 --> 01:08:32,160 and in fixed-income securities. 1501 01:08:32,160 --> 01:08:35,460 But one of the things that we'd like to be able to do 1502 01:08:35,460 --> 01:08:39,300 is to try to model that term structure interest rates. 1503 01:08:39,300 --> 01:08:41,189 Is there any logic that we can come up 1504 01:08:41,189 --> 01:08:43,800 with that explains why the yield curve is 1505 01:08:43,800 --> 01:08:47,939 upward-sloping or backward-bending or inverted? 1506 01:08:47,939 --> 01:08:51,060 And it turns out that there are a number of theories 1507 01:08:51,060 --> 01:08:53,340 that have come to be proposed. 1508 01:08:53,340 --> 01:08:55,590 I'm not going to cover any of these in any depth, 1509 01:08:55,590 --> 01:08:57,881 but I want to at least mention the names so that you'll 1510 01:08:57,881 --> 01:09:00,569 know that there are theories out there that will tell you 1511 01:09:00,569 --> 01:09:04,170 whether or not the yield curve should be so steeply sloped 1512 01:09:04,170 --> 01:09:05,310 or not. 1513 01:09:05,310 --> 01:09:07,735 There's something called the Expectations Hypothesis. 1514 01:09:07,735 --> 01:09:09,359 There is something called the Liquidity 1515 01:09:09,359 --> 01:09:10,620 Preference Hypothesis. 1516 01:09:10,620 --> 01:09:13,859 There is a Preferred Habitat Model, Market Segmentation 1517 01:09:13,859 --> 01:09:14,620 Model. 1518 01:09:14,620 --> 01:09:17,609 And then, there are a whole slew of extraordinarily 1519 01:09:17,609 --> 01:09:21,359 sophisticated and complex mathematical models, 1520 01:09:21,359 --> 01:09:22,229 one of which-- 1521 01:09:22,229 --> 01:09:23,812 and probably the best known of which-- 1522 01:09:23,812 --> 01:09:27,660 was developed by our very own John Cox and Steve Ross. 1523 01:09:27,660 --> 01:09:30,630 The Cox-Ingersoll-Ross model of the term structure 1524 01:09:30,630 --> 01:09:34,170 of interest rates is probably the single best known yield 1525 01:09:34,170 --> 01:09:35,260 curve model. 1526 01:09:35,260 --> 01:09:36,930 It's a very complicated model, but it 1527 01:09:36,930 --> 01:09:39,246 has some pretty significant implications 1528 01:09:39,246 --> 01:09:40,620 for whether the yield curve ought 1529 01:09:40,620 --> 01:09:42,540 to be upward-sloping or downward-sloping, 1530 01:09:42,540 --> 01:09:45,390 or how it changes over time. 1531 01:09:45,390 --> 01:09:49,200 I'll give you one example of what these theories are, 1532 01:09:49,200 --> 01:09:51,090 and I won't spend much time on it, 1533 01:09:51,090 --> 01:09:53,880 but I want to at least leave you with some intuition 1534 01:09:53,880 --> 01:09:56,190 for how you would go about modeling it. 1535 01:09:56,190 --> 01:10:04,630 So one model says that today's forward rates are in fact 1536 01:10:04,630 --> 01:10:10,470 the best guess of what future spot rates are likely to be, 1537 01:10:10,470 --> 01:10:14,100 and that's known as the Expectations Hypothesis. 1538 01:10:14,100 --> 01:10:17,340 This hypothesis states that today's forward rate, which 1539 01:10:17,340 --> 01:10:24,560 is what we do observe, is equal to the mathematical expectation 1540 01:10:24,560 --> 01:10:30,210 today, of the future one-year spot rate. 1541 01:10:30,210 --> 01:10:31,710 Now, you might say, well, that's not 1542 01:10:31,710 --> 01:10:32,876 that's not much of a theory. 1543 01:10:32,876 --> 01:10:34,420 I mean, what else could it be? 1544 01:10:34,420 --> 01:10:37,200 Well, it turns out that there is another theory called 1545 01:10:37,200 --> 01:10:40,320 the Preferred Liquidity Preference Theory that 1546 01:10:40,320 --> 01:10:46,420 says that the longer the term of borrowing, 1547 01:10:46,420 --> 01:10:50,200 the more you're going to have to pay a premium for people 1548 01:10:50,200 --> 01:10:56,660 to lend to you, because people would prefer liquidity. 1549 01:10:56,660 --> 01:11:00,710 So the longer you demand the borrowing 1550 01:11:00,710 --> 01:11:04,880 for a greater period of time, the more you have to pay-- 1551 01:11:04,880 --> 01:11:08,130 much more so than just linearly. 1552 01:11:08,130 --> 01:11:11,210 So in particular, the Expectations Hypothesis 1553 01:11:11,210 --> 01:11:14,020 suggests that the yield curve is flat. 1554 01:11:14,020 --> 01:11:14,930 Right? 1555 01:11:14,930 --> 01:11:18,810 There's no impact on borrowing for two years, three years, 1556 01:11:18,810 --> 01:11:20,360 five years, 10 years. 1557 01:11:20,360 --> 01:11:23,120 The future rate is just equal to-- 1558 01:11:23,120 --> 01:11:28,110 today's forward rate is the expectation of the future. 1559 01:11:28,110 --> 01:11:28,610 OK? 1560 01:11:28,610 --> 01:11:30,410 It's a fair bet. 1561 01:11:30,410 --> 01:11:32,480 Liquidity Preference says that the yield curve 1562 01:11:32,480 --> 01:11:36,030 should be upward-sloping, because it's 1563 01:11:36,030 --> 01:11:39,690 going to be more costly for you to borrow 1564 01:11:39,690 --> 01:11:42,900 over a three-year period than a one-year period, simply 1565 01:11:42,900 --> 01:11:46,920 because it's going to entail somebody 1566 01:11:46,920 --> 01:11:49,637 giving up their money for a longer period of time. 1567 01:11:49,637 --> 01:11:50,970 They're going to be less liquid. 1568 01:11:50,970 --> 01:11:54,150 You're going to have to bribe them to be willing to give up 1569 01:11:54,150 --> 01:11:56,810 that liquidity. 1570 01:11:56,810 --> 01:11:59,960 That's the Liquidity Preference Theory. 1571 01:11:59,960 --> 01:12:01,610 The Preferred Habitat Theory says, 1572 01:12:01,610 --> 01:12:06,470 you know, there are preferred maturities that people have. 1573 01:12:06,470 --> 01:12:08,120 And for those maturities, you're going 1574 01:12:08,120 --> 01:12:11,930 to have different rates than for those that people don't prefer. 1575 01:12:11,930 --> 01:12:14,060 So if you want a 30-year maturity-- 1576 01:12:14,060 --> 01:12:16,504 and that's not preferred because it's too far off-- 1577 01:12:16,504 --> 01:12:18,170 then you're gonna have to pay a premium. 1578 01:12:18,170 --> 01:12:20,870 On the Other Hand, 10 years is a period 1579 01:12:20,870 --> 01:12:23,840 that a number of pension funds prefer, 1580 01:12:23,840 --> 01:12:27,480 so you may not have to pay as much for those preferred 1581 01:12:27,480 --> 01:12:29,200 habitats. 1582 01:12:29,200 --> 01:12:34,320 And to give you a sense of where academics is today, 1583 01:12:34,320 --> 01:12:36,420 none of these models work. 1584 01:12:36,420 --> 01:12:39,600 None of them can fully explain movements 1585 01:12:39,600 --> 01:12:42,640 in the yield curve, which, by the way, 1586 01:12:42,640 --> 01:12:44,670 is a wonderful opportunity for all of you. 1587 01:12:44,670 --> 01:12:48,090 Because if you have a model that does work, 1588 01:12:48,090 --> 01:12:50,490 then you can do extraordinarily well. 1589 01:12:50,490 --> 01:12:54,030 You can turn very, very small forecast power 1590 01:12:54,030 --> 01:12:56,680 into enormous amounts of wealth very, 1591 01:12:56,680 --> 01:12:58,710 very quickly on Wall Street. 1592 01:12:58,710 --> 01:13:00,384 Yes? 1593 01:13:00,384 --> 01:13:09,667 STUDENT: [INAUDIBLE] 1594 01:13:09,667 --> 01:13:10,500 ANDREW LO: Does he-- 1595 01:13:10,500 --> 01:13:12,099 STUDENT: [INAUDIBLE] 1596 01:13:12,099 --> 01:13:13,390 ANDREW LO: You can't patent it. 1597 01:13:13,390 --> 01:13:13,889 Right. 1598 01:13:13,889 --> 01:13:17,290 So does he get anything out of that besides notoriety? 1599 01:13:17,290 --> 01:13:19,130 Well, that's a good question. 1600 01:13:19,130 --> 01:13:22,030 The question has to do with, I guess, the difference 1601 01:13:22,030 --> 01:13:26,020 between academic endeavors and business endeavors. 1602 01:13:26,020 --> 01:13:27,880 As an academic, what you're trying to do 1603 01:13:27,880 --> 01:13:30,430 is to make a name for yourself and to put out 1604 01:13:30,430 --> 01:13:33,460 research ideas that will have an impact 1605 01:13:33,460 --> 01:13:36,980 with your colleagues and the particular area that you're in. 1606 01:13:36,980 --> 01:13:39,490 So if you're asking, did Professor Cox 1607 01:13:39,490 --> 01:13:40,540 get rich off of this? 1608 01:13:40,540 --> 01:13:43,180 The answer is, no, probably not. 1609 01:13:43,180 --> 01:13:44,680 Neither did Black-Scholes, actually, 1610 01:13:44,680 --> 01:13:46,930 when they published their Black-Scholes option pricing 1611 01:13:46,930 --> 01:13:47,440 formula. 1612 01:13:47,440 --> 01:13:49,648 That was the same year that the Chicago Board Options 1613 01:13:49,648 --> 01:13:51,820 Exchange started trading, and everybody just 1614 01:13:51,820 --> 01:13:54,750 used the option pricing formula almost from the very start. 1615 01:13:54,750 --> 01:13:56,170 Did they make money off of that? 1616 01:13:56,170 --> 01:13:57,622 No, they didn't. 1617 01:13:57,622 --> 01:13:58,330 And you're right. 1618 01:13:58,330 --> 01:13:59,620 You can't patent it. 1619 01:13:59,620 --> 01:14:03,880 So very often, in financial firms, 1620 01:14:03,880 --> 01:14:05,140 when they have good ideas-- 1621 01:14:05,140 --> 01:14:06,700 so for example, I do believe there 1622 01:14:06,700 --> 01:14:09,610 are term structure models out there that work reasonably 1623 01:14:09,610 --> 01:14:10,410 well. 1624 01:14:10,410 --> 01:14:11,620 They're not published. 1625 01:14:11,620 --> 01:14:15,640 They're kept as the Coca-Colas of financial markets. 1626 01:14:15,640 --> 01:14:16,990 They're trade secrets. 1627 01:14:16,990 --> 01:14:19,540 And so if you go there to work and ultimately 1628 01:14:19,540 --> 01:14:22,840 work with the right people, you will learn such trade secrets, 1629 01:14:22,840 --> 01:14:25,600 which, by the way, is one of the reasons why when Barclays 1630 01:14:25,600 --> 01:14:28,060 acquires Lehman and wants to keep all of these 1631 01:14:28,060 --> 01:14:30,040 really, really terrific people together, 1632 01:14:30,040 --> 01:14:32,270 they're going to have to offer premia to do that. 1633 01:14:32,270 --> 01:14:35,230 And so that's part of the cost of financial distress 1634 01:14:35,230 --> 01:14:37,210 when you disturb the status quo. 1635 01:14:40,380 --> 01:14:44,860 That's a few models of the term structure of interest rates. 1636 01:14:44,860 --> 01:14:49,140 And I want to talk about one last topic on coupon bonds 1637 01:14:49,140 --> 01:14:52,980 before concluding this lecture. 1638 01:14:52,980 --> 01:14:55,350 Next lecture on Monday, we're going to take up 1639 01:14:55,350 --> 01:14:57,390 measures of interest rate risk. 1640 01:14:57,390 --> 01:14:59,850 We're going to look explicitly at what happens when 1641 01:14:59,850 --> 01:15:01,320 interest rates bounce around. 1642 01:15:01,320 --> 01:15:04,080 Before we get to that, though, I want to talk about another way 1643 01:15:04,080 --> 01:15:06,720 to value coupon bonds, and it's exactly the idea 1644 01:15:06,720 --> 01:15:11,070 that I said before, of using pure discount bonds to do so. 1645 01:15:11,070 --> 01:15:14,790 If I have a pure discount bond, I 1646 01:15:14,790 --> 01:15:18,450 can use that to price coupon bonds by building up 1647 01:15:18,450 --> 01:15:20,490 a package of discount bonds. 1648 01:15:20,490 --> 01:15:22,920 The example of the strips is given here. 1649 01:15:22,920 --> 01:15:25,740 You've got a three-year 5% bond, and it turns out 1650 01:15:25,740 --> 01:15:28,560 that you can show that that three-year 5% bond is going 1651 01:15:28,560 --> 01:15:33,060 to be identical to 50 one-year strips, 50 two-year strips, 1652 01:15:33,060 --> 01:15:37,050 and 1050 three-year strips, each strip 1653 01:15:37,050 --> 01:15:42,600 paying $1 in years 1, 2, and 3. 1654 01:15:42,600 --> 01:15:43,950 Any question about that claim? 1655 01:15:43,950 --> 01:15:46,950 Anybody want to argue with me that that's not true? 1656 01:15:46,950 --> 01:15:48,840 It's pretty obvious, right? 1657 01:15:48,840 --> 01:15:53,100 Well, this actually has a very dramatic implication, 1658 01:15:53,100 --> 01:15:56,530 and let me tell you what that implication is. 1659 01:15:56,530 --> 01:16:03,040 The implication is that the price of a three-year 5% bond 1660 01:16:03,040 --> 01:16:08,660 better be equal to the cost of 50 one-year strips, 50 1661 01:16:08,660 --> 01:16:12,100 two-year strips, and 1050 three-year strips. 1662 01:16:12,100 --> 01:16:14,740 The price of this three-year bond 1663 01:16:14,740 --> 01:16:18,220 better be equal to what it costs to put that portfolio of strips 1664 01:16:18,220 --> 01:16:20,260 together today. 1665 01:16:20,260 --> 01:16:23,000 Why? 1666 01:16:23,000 --> 01:16:24,200 Why should it be equal? 1667 01:16:24,200 --> 01:16:24,923 Yes. 1668 01:16:24,923 --> 01:16:25,770 STUDENT: [INAUDIBLE] 1669 01:16:25,770 --> 01:16:26,540 ANDREW LO: What is arbitrage? 1670 01:16:26,540 --> 01:16:27,801 We haven't defined that. 1671 01:16:27,801 --> 01:16:32,030 STUDENT: [INAUDIBLE] basically, if the prices are different, 1672 01:16:32,030 --> 01:16:34,150 [INAUDIBLE] buy the one or sell the other, 1673 01:16:34,150 --> 01:16:35,979 so they come together [INAUDIBLE].. 1674 01:16:35,979 --> 01:16:36,770 ANDREW LO: Exactly. 1675 01:16:36,770 --> 01:16:41,510 There is a way to make money if the price 1676 01:16:41,510 --> 01:16:45,380 of that three-year bond is anything other than the cost 1677 01:16:45,380 --> 01:16:47,540 of that package of strips. 1678 01:16:47,540 --> 01:16:49,050 So let's do an example. 1679 01:16:49,050 --> 01:16:51,560 Suppose that the price of a three-year bond 1680 01:16:51,560 --> 01:16:54,800 is greater than the cost of the strips. 1681 01:16:54,800 --> 01:16:56,900 Tell me what to do. 1682 01:16:56,900 --> 01:16:57,510 Yeah? 1683 01:16:57,510 --> 01:16:59,970 STUDENT: Buy those strips, package them into a bond, 1684 01:16:59,970 --> 01:17:01,484 and then sell it. 1685 01:17:01,484 --> 01:17:02,902 Sell the bond to the market. 1686 01:17:02,902 --> 01:17:04,610 Just keep doing that over and over again. 1687 01:17:04,610 --> 01:17:05,200 ANDREW LO: OK. 1688 01:17:05,200 --> 01:17:07,450 So let's talk about this slowly. 1689 01:17:07,450 --> 01:17:09,200 I first buy those strips. 1690 01:17:09,200 --> 01:17:11,360 I buy the portfolio strips. 1691 01:17:11,360 --> 01:17:13,810 And then, I take this bond that's 1692 01:17:13,810 --> 01:17:18,130 trading in the open marketplace, and I sell it. 1693 01:17:18,130 --> 01:17:20,860 How do I sell something I don't own? 1694 01:17:20,860 --> 01:17:22,732 Short-sell it, yes. 1695 01:17:22,732 --> 01:17:25,190 Short-selling, which you can read about and Brealey, Myers, 1696 01:17:25,190 --> 01:17:29,390 and Allen, is when, if you don't own the security, 1697 01:17:29,390 --> 01:17:32,910 you can borrow it from a broker, and then sell it, 1698 01:17:32,910 --> 01:17:35,091 and you'll collect the money from selling it. 1699 01:17:35,091 --> 01:17:36,590 Now, the broker, obviously, is going 1700 01:17:36,590 --> 01:17:39,830 to want you to keep that money in that brokerage firm 1701 01:17:39,830 --> 01:17:41,720 so that you don't run away with it. 1702 01:17:41,720 --> 01:17:44,477 Because you've borrowed the security at some point, 1703 01:17:44,477 --> 01:17:45,560 you've got to pay it back. 1704 01:17:45,560 --> 01:17:47,018 You've got to return that security. 1705 01:17:47,018 --> 01:17:47,870 Right? 1706 01:17:47,870 --> 01:17:51,770 So the transaction is, you buy these strips, 1707 01:17:51,770 --> 01:17:55,970 you short-sell the bond, and what have you done? 1708 01:17:55,970 --> 01:17:59,370 Have you made money or lost money on day one? 1709 01:17:59,370 --> 01:18:00,120 You've made money. 1710 01:18:00,120 --> 01:18:00,619 Why? 1711 01:18:00,619 --> 01:18:03,225 Because buying costs less than the amount of money 1712 01:18:03,225 --> 01:18:04,100 you get from selling. 1713 01:18:04,100 --> 01:18:05,850 And how do you know that? 1714 01:18:05,850 --> 01:18:09,050 Because I just assumed that it's more expensive for you 1715 01:18:09,050 --> 01:18:12,320 to get the three-year bond than the package of strips. 1716 01:18:12,320 --> 01:18:15,410 So you've made money today, but you 1717 01:18:15,410 --> 01:18:19,670 have no further obligations, because what you end up 1718 01:18:19,670 --> 01:18:21,850 getting from the strips-- you've bought the strips, 1719 01:18:21,850 --> 01:18:24,860 so you're going to get their coupons or their face value. 1720 01:18:24,860 --> 01:18:28,850 You're going to use those to pay the coupons of the bonds 1721 01:18:28,850 --> 01:18:31,450 that you sold. 1722 01:18:31,450 --> 01:18:33,580 And therefore, you have no further obligations, 1723 01:18:33,580 --> 01:18:36,190 but you have a pile of money in front of you. 1724 01:18:36,190 --> 01:18:37,570 That's pretty cool. 1725 01:18:37,570 --> 01:18:41,560 And if you do that a lot, that pile of money grows. 1726 01:18:41,560 --> 01:18:45,089 So obviously, we know it's not easy to do that. 1727 01:18:45,089 --> 01:18:46,630 And if it's not easy to do that, that 1728 01:18:46,630 --> 01:18:50,200 means that our assumption that the bond was greater 1729 01:18:50,200 --> 01:18:52,990 than the cost of the strips can't be true. 1730 01:18:52,990 --> 01:18:55,180 If you reverse the logic, you get the same kind 1731 01:18:55,180 --> 01:18:56,830 of argument in reverse. 1732 01:18:56,830 --> 01:18:58,570 Therefore, the only thing that could be 1733 01:18:58,570 --> 01:19:00,850 is that the prices are equal to each other. 1734 01:19:00,850 --> 01:19:02,650 Next time, what we're going to do 1735 01:19:02,650 --> 01:19:05,119 is show that a little bit of linear algebra 1736 01:19:05,119 --> 01:19:06,910 is going to allow you to make tons of money 1737 01:19:06,910 --> 01:19:08,770 by comparing all sorts of bonds and looking 1738 01:19:08,770 --> 01:19:10,280 at these kinds of relationships. 1739 01:19:10,280 --> 01:19:10,780 OK. 1740 01:19:10,780 --> 01:19:14,460 I'll see you at 4:00, if you're interested.