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 00:00:21,690 --> 00:00:25,620 ANDREW LO: So what I want to do in this lecture is to provide 9 00:00:25,620 --> 00:00:30,570 a quick overview of the equity business, 10 00:00:30,570 --> 00:00:35,250 and then talk about a couple of simple but rather powerful 11 00:00:35,250 --> 00:00:38,700 models to price equities-- we're using the exact same tools that 12 00:00:38,700 --> 00:00:40,110 we've developed-- 13 00:00:40,110 --> 00:00:42,960 and then talk a bit about growth opportunities and growth 14 00:00:42,960 --> 00:00:44,440 stocks. 15 00:00:44,440 --> 00:00:46,770 OK, so industry overview. 16 00:00:46,770 --> 00:00:47,770 What is equity? 17 00:00:47,770 --> 00:00:51,540 As I said, it's an ownership in a corporation. 18 00:00:51,540 --> 00:00:54,780 And typically, when you own a piece of a corporation, 19 00:00:54,780 --> 00:00:57,310 you're owning that sequence of cash flows. 20 00:00:57,310 --> 00:01:00,810 There are two components of possible cash flows 21 00:01:00,810 --> 00:01:03,360 for a piece of equity security. 22 00:01:03,360 --> 00:01:05,760 One is dividends. 23 00:01:05,760 --> 00:01:07,950 But, of course, we know that there are companies 24 00:01:07,950 --> 00:01:09,020 that don't pay dividends. 25 00:01:09,020 --> 00:01:13,440 Typically, companies that are early stage growth companies, 26 00:01:13,440 --> 00:01:15,570 they want to conserve their cash, because they've 27 00:01:15,570 --> 00:01:18,360 got lots and lots of investment ideas 28 00:01:18,360 --> 00:01:19,690 that they want to implement. 29 00:01:19,690 --> 00:01:22,530 And so any cash that's generated internally, 30 00:01:22,530 --> 00:01:26,190 they're going to be plowing back into current operations. 31 00:01:26,190 --> 00:01:30,440 So growth companies typically don't pay dividends. 32 00:01:30,440 --> 00:01:32,540 But you still get value from the security, 33 00:01:32,540 --> 00:01:35,990 because as the firm grows, as the corporation becomes 34 00:01:35,990 --> 00:01:38,570 more valuable, that piece of paper that you hold 35 00:01:38,570 --> 00:01:39,740 becomes more valuable. 36 00:01:39,740 --> 00:01:42,020 So in other words, you get capital gains 37 00:01:42,020 --> 00:01:45,050 or price appreciation of that piece of paper. 38 00:01:45,050 --> 00:01:48,530 And if you want to get value out of that price appreciation, 39 00:01:48,530 --> 00:01:51,660 you could always sell it, right? 40 00:01:51,660 --> 00:01:55,980 So those are the two ways of getting value. 41 00:01:55,980 --> 00:01:58,170 It's dividends-- and by the way, there 42 00:01:58,170 --> 00:01:59,760 are two different forms of dividends. 43 00:01:59,760 --> 00:02:03,120 Cash dividends or stock dividends, 44 00:02:03,120 --> 00:02:07,200 both of which provide additional value. 45 00:02:07,200 --> 00:02:09,389 But also the fact is that you could sell it, 46 00:02:09,389 --> 00:02:12,330 and so you can get money from capital gains. 47 00:02:12,330 --> 00:02:16,110 Now there are a couple of key characteristics of common stock 48 00:02:16,110 --> 00:02:18,690 that are distinct from bonds. 49 00:02:18,690 --> 00:02:20,550 The cash flows we will be able to analyze 50 00:02:20,550 --> 00:02:23,970 using the same tools, but those tools will ultimately 51 00:02:23,970 --> 00:02:27,480 give us different answers, because the legal structure 52 00:02:27,480 --> 00:02:32,660 for equities is different than for bonds. 53 00:02:32,660 --> 00:02:36,380 And I have to say, that whoever invented equities-- 54 00:02:36,380 --> 00:02:39,800 this is many, many centuries ago-- 55 00:02:39,800 --> 00:02:43,910 really was a brilliant financial innovator, 56 00:02:43,910 --> 00:02:48,860 because equities have just an enormously powerful ability 57 00:02:48,860 --> 00:02:52,910 to provide proper motivation and incentives for innovation, 58 00:02:52,910 --> 00:02:54,260 all sorts of innovation. 59 00:02:54,260 --> 00:02:55,910 And let me explain what that means. 60 00:02:55,910 --> 00:02:58,340 First of all, one aspect of equities 61 00:02:58,340 --> 00:02:59,810 that I think you all probably know 62 00:02:59,810 --> 00:03:04,550 is that they are the residual claimant to a corporation's 63 00:03:04,550 --> 00:03:08,180 assets after the bondholders. 64 00:03:08,180 --> 00:03:12,380 In other words, bondholders have first dibs 65 00:03:12,380 --> 00:03:16,580 on the assets of the company, but their claim on those assets 66 00:03:16,580 --> 00:03:21,680 is only equal to the face value or promised payments 67 00:03:21,680 --> 00:03:23,890 of that debt, right? 68 00:03:23,890 --> 00:03:26,800 They don't have access to any more than what 69 00:03:26,800 --> 00:03:29,800 the face value of that bond is, as well as 70 00:03:29,800 --> 00:03:32,650 the coupons along the way. 71 00:03:32,650 --> 00:03:36,730 And to say that equity holders are the residual claimant 72 00:03:36,730 --> 00:03:39,790 means that they get everything else. 73 00:03:39,790 --> 00:03:41,500 Now you might say, gee, that's not really 74 00:03:41,500 --> 00:03:44,260 all that interesting, because you're second in line. 75 00:03:44,260 --> 00:03:48,700 Well, it's very interesting if being second in line 76 00:03:48,700 --> 00:03:52,810 means that you get access to all of the upside of a company's 77 00:03:52,810 --> 00:03:54,880 growth and success. 78 00:03:54,880 --> 00:03:57,970 I'm sure that you've all heard of stories of entrepreneurs 79 00:03:57,970 --> 00:04:02,680 that have made many hundreds of times what they put 80 00:04:02,680 --> 00:04:06,850 into a company, whereas the bondholders may have gotten 81 00:04:06,850 --> 00:04:11,710 a handsome return of 10, 15, 20%, 82 00:04:11,710 --> 00:04:15,100 but that's the upper bound as to what they can get. 83 00:04:15,100 --> 00:04:21,940 As a bondholder, your upside is capped, it's limited, OK? 84 00:04:21,940 --> 00:04:26,060 Whereas, as the residual claimant, as the equity holder, 85 00:04:26,060 --> 00:04:29,930 you have no limit on your upside, right? 86 00:04:29,930 --> 00:04:34,170 Because once the bondholders get paid, you get everything else. 87 00:04:34,170 --> 00:04:38,210 Now the other aspect of equity that's really important 88 00:04:38,210 --> 00:04:41,060 is something called limited liability-- 89 00:04:41,060 --> 00:04:47,390 the fact that, as an equity holder, the most you can lose 90 00:04:47,390 --> 00:04:49,530 is everything. 91 00:04:49,530 --> 00:04:53,000 Now that might not seem like a good deal, but trust me, 92 00:04:53,000 --> 00:04:55,490 it's an amazing deal. 93 00:04:55,490 --> 00:05:01,170 By everything, we mean everything that you put in, 94 00:05:01,170 --> 00:05:03,840 so it's not literally everything. 95 00:05:03,840 --> 00:05:07,290 For example, you don't lose your life. 96 00:05:07,290 --> 00:05:08,880 You don't lose your freedom. 97 00:05:08,880 --> 00:05:10,650 You don't lose your pinkie. 98 00:05:10,650 --> 00:05:14,940 You don't lose any other body parts, or loved ones. 99 00:05:14,940 --> 00:05:20,650 All you are at risk of losing is what you put in to the venture. 100 00:05:20,650 --> 00:05:24,060 So that's what limited liability means. 101 00:05:24,060 --> 00:05:25,920 And the reason that it's an innovation 102 00:05:25,920 --> 00:05:29,220 is, prior to the modern-day corporation 103 00:05:29,220 --> 00:05:31,650 and limited liability, it used to be 104 00:05:31,650 --> 00:05:36,360 the case that entrepreneurs faced unlimited liability, 105 00:05:36,360 --> 00:05:39,360 or you could be put in prison if you were 106 00:05:39,360 --> 00:05:42,480 to default on your obligations. 107 00:05:42,480 --> 00:05:46,740 The fact that there is a downside limit to what you 108 00:05:46,740 --> 00:05:51,810 could possibly lose is a tremendous boon to innovation, 109 00:05:51,810 --> 00:05:56,490 because now it means that each and every one of you 110 00:05:56,490 --> 00:06:01,230 can go out and start your own company 111 00:06:01,230 --> 00:06:05,820 and risk whatever money you want to put into the company, 112 00:06:05,820 --> 00:06:07,610 but no more. 113 00:06:07,610 --> 00:06:10,570 And if it doesn't work out, well, you 114 00:06:10,570 --> 00:06:14,150 can walk away and do it again. 115 00:06:14,150 --> 00:06:17,390 And I suspect many of you know of 116 00:06:17,390 --> 00:06:21,890 so-called serial entrepreneurs that just go from one company 117 00:06:21,890 --> 00:06:23,389 to another to another. 118 00:06:23,389 --> 00:06:25,430 Many years ago, when I was at the Wharton School, 119 00:06:25,430 --> 00:06:30,080 I heard a talk by the person who started up Domino's Pizza. 120 00:06:30,080 --> 00:06:32,810 I unfortunately don't remember his name, 121 00:06:32,810 --> 00:06:35,570 but he was giving a talk in one of these CEO series 122 00:06:35,570 --> 00:06:42,410 and he's a billionaire, because of the incredible growth 123 00:06:42,410 --> 00:06:45,590 of Domino's Pizza in the country. 124 00:06:45,590 --> 00:06:48,170 And somebody asked this fellow, how 125 00:06:48,170 --> 00:06:51,260 did you know that having a national pizza chain 126 00:06:51,260 --> 00:06:54,070 was going to succeed as well as it did? 127 00:06:54,070 --> 00:06:55,640 And he's very honest. 128 00:06:55,640 --> 00:06:59,500 He said, you know, I didn't know. 129 00:06:59,500 --> 00:07:03,130 You know, this was my ninth company. 130 00:07:03,130 --> 00:07:05,524 The first eight went bankrupt. 131 00:07:05,524 --> 00:07:06,940 And if this one had gone bankrupt, 132 00:07:06,940 --> 00:07:09,360 I probably would've started a tenth. 133 00:07:09,360 --> 00:07:12,220 And I think that's just a wonderful expression 134 00:07:12,220 --> 00:07:14,560 of the power of modern capitalism 135 00:07:14,560 --> 00:07:18,550 and limited liability, because here's an individual that just 136 00:07:18,550 --> 00:07:20,662 really wanted to do something on his own 137 00:07:20,662 --> 00:07:22,120 and wanted to make a success of it, 138 00:07:22,120 --> 00:07:24,549 and was willing to work his heart out time 139 00:07:24,549 --> 00:07:26,590 after time after time until he hit upon something 140 00:07:26,590 --> 00:07:28,210 that was really valuable. 141 00:07:28,210 --> 00:07:31,330 And that's the power of limited liability. 142 00:07:31,330 --> 00:07:37,510 Think what innovation would be if we decided 143 00:07:37,510 --> 00:07:41,420 that if your first company fails, from that point on, 144 00:07:41,420 --> 00:07:44,140 you would never be allowed to start a company ever again. 145 00:07:44,140 --> 00:07:45,890 Think how many people would take the risk 146 00:07:45,890 --> 00:07:48,670 or take the plunge to do something like starting up 147 00:07:48,670 --> 00:07:50,330 your own company. 148 00:07:50,330 --> 00:07:52,870 So the fact that we have a security that 149 00:07:52,870 --> 00:07:55,000 limits your downside, and that limits 150 00:07:55,000 --> 00:07:57,280 the downside of other investors that 151 00:07:57,280 --> 00:08:00,160 want to join you in your venture, really 152 00:08:00,160 --> 00:08:04,960 allows for capital formation to occur at a rate 153 00:08:04,960 --> 00:08:09,470 and at a scale that would be impossible without it. 154 00:08:09,470 --> 00:08:12,650 Now there's also voting rights and the ability 155 00:08:12,650 --> 00:08:14,540 to access public markets. 156 00:08:14,540 --> 00:08:17,060 What that means is that you can actually 157 00:08:17,060 --> 00:08:20,240 get other people, large numbers of people, 158 00:08:20,240 --> 00:08:23,270 to co-invest with you. 159 00:08:23,270 --> 00:08:25,490 So that's particularly important when 160 00:08:25,490 --> 00:08:29,370 you're thinking about taking on very, very ambitious projects. 161 00:08:29,370 --> 00:08:33,890 For example, if you want to start up a biotech company. 162 00:08:33,890 --> 00:08:36,580 Biotech companies require more than a few hundred thousand 163 00:08:36,580 --> 00:08:38,929 dollars to get started. 164 00:08:38,929 --> 00:08:41,059 I think a few hundred thousand dollars would maybe 165 00:08:41,059 --> 00:08:44,570 buy you a quarter of a centrifuge these days. 166 00:08:44,570 --> 00:08:47,970 Doesn't really help for starting up a biotech company. 167 00:08:47,970 --> 00:08:49,580 And so if we didn't have the ability 168 00:08:49,580 --> 00:08:51,950 to access public markets, if we didn't have the ability 169 00:08:51,950 --> 00:08:55,790 to bring the power of the public to bear 170 00:08:55,790 --> 00:08:58,490 on a particular investment opportunity, 171 00:08:58,490 --> 00:09:00,510 it wouldn't get done. 172 00:09:00,510 --> 00:09:05,460 So that combination of limited liability and ability 173 00:09:05,460 --> 00:09:08,400 to access public markets, and then voting rights 174 00:09:08,400 --> 00:09:12,990 that give investors some say in how the company is run, 175 00:09:12,990 --> 00:09:15,060 is really the secret to unlocking 176 00:09:15,060 --> 00:09:21,210 the power of the masses for development of innovation 177 00:09:21,210 --> 00:09:23,112 and capital formation. 178 00:09:23,112 --> 00:09:25,320 Now there's another point that I wanted to make here, 179 00:09:25,320 --> 00:09:26,520 which is short sales. 180 00:09:26,520 --> 00:09:29,160 I think that by now you should have 181 00:09:29,160 --> 00:09:31,950 an appreciation for the importance of short sales. 182 00:09:31,950 --> 00:09:37,470 Short sales allow information to get into the market price that 183 00:09:37,470 --> 00:09:40,500 may not be positive news, but is nevertheless 184 00:09:40,500 --> 00:09:42,850 important for people to have. 185 00:09:42,850 --> 00:09:45,690 And so the ability to short sell a security 186 00:09:45,690 --> 00:09:48,840 is a method for allowing investors 187 00:09:48,840 --> 00:09:51,330 to get information into the market price 188 00:09:51,330 --> 00:09:54,780 as quickly and as easily as possible. 189 00:09:54,780 --> 00:09:57,150 Those of you who participated in the trading game 190 00:09:57,150 --> 00:10:00,420 that we did a couple of weeks ago on that Friday-- 191 00:10:00,420 --> 00:10:03,150 you know, when we go over the results towards the end 192 00:10:03,150 --> 00:10:05,820 of this course, when we talk about efficient markets, 193 00:10:05,820 --> 00:10:08,250 I'm going to show you that the prices that 194 00:10:08,250 --> 00:10:11,700 occurred in that marketplace was not very efficient. 195 00:10:11,700 --> 00:10:13,700 Part of the reason that it wasn't very efficient 196 00:10:13,700 --> 00:10:15,980 is because we didn't allow you to short sell. 197 00:10:15,980 --> 00:10:20,210 And so those of you who had the information that at one point 198 00:10:20,210 --> 00:10:24,220 the stock was worthless, the most you could have done 199 00:10:24,220 --> 00:10:27,910 was to divest yourself of shares that you already owned. 200 00:10:27,910 --> 00:10:30,580 But once you did that, that was the end, 201 00:10:30,580 --> 00:10:31,990 and you're out of the market. 202 00:10:31,990 --> 00:10:33,910 You couldn't do anything more. 203 00:10:33,910 --> 00:10:37,210 If, on the other hand, we allowed you to short sell, 204 00:10:37,210 --> 00:10:39,700 you would have driven that price down to 0, where 205 00:10:39,700 --> 00:10:42,480 it belonged at that point. 206 00:10:42,480 --> 00:10:46,560 And so the ability to short sell is a very, very important 207 00:10:46,560 --> 00:10:49,140 aspect of capital market efficiency 208 00:10:49,140 --> 00:10:53,970 and for making prices as informative as you can. 209 00:10:53,970 --> 00:10:57,540 Now there are two markets for equities-- primary market 210 00:10:57,540 --> 00:10:58,830 and secondary market. 211 00:10:58,830 --> 00:11:03,360 Primary market means the market where securities are 212 00:11:03,360 --> 00:11:05,650 issued for the very first time. 213 00:11:05,650 --> 00:11:07,890 Primary, that's what primary means. 214 00:11:07,890 --> 00:11:12,870 Secondary you could think of as the market for used securities. 215 00:11:12,870 --> 00:11:14,850 We have a market for used cars. 216 00:11:14,850 --> 00:11:16,770 You have a market for used homes. 217 00:11:16,770 --> 00:11:18,640 And there's a market for used securities. 218 00:11:18,640 --> 00:11:21,139 I know you don't really think of the New York Stock Exchange 219 00:11:21,139 --> 00:11:23,370 as such, but, in fact, it is. 220 00:11:23,370 --> 00:11:26,490 It just turns out that used securities are just 221 00:11:26,490 --> 00:11:31,780 as good as new securities, and in many ways, better. 222 00:11:31,780 --> 00:11:36,340 And so the steps for getting a primary security issued 223 00:11:36,340 --> 00:11:39,070 is very different than the steps for dealing 224 00:11:39,070 --> 00:11:40,972 with secondary markets. 225 00:11:40,972 --> 00:11:42,430 For the most part, what we're going 226 00:11:42,430 --> 00:11:43,870 to be talking about in this course 227 00:11:43,870 --> 00:11:48,790 is secondary market transactions and dynamics. 228 00:11:48,790 --> 00:11:51,340 However, there is obviously a lot more 229 00:11:51,340 --> 00:11:52,990 to be said about primary markets. 230 00:11:52,990 --> 00:11:57,130 I'm going to leave that to other courses in the Finance group, 231 00:11:57,130 --> 00:12:03,490 including M&A and capital budgeting and venture capital. 232 00:12:03,490 --> 00:12:06,910 Those are courses that deal with the dynamics 233 00:12:06,910 --> 00:12:08,450 of the primary market. 234 00:12:08,450 --> 00:12:11,440 These are the markets that you would care about 235 00:12:11,440 --> 00:12:14,560 if you're doing an IPO, launching a new company, 236 00:12:14,560 --> 00:12:17,796 and issuing securities for the very first time. 237 00:12:17,796 --> 00:12:19,420 So I won't spend too much time on that. 238 00:12:19,420 --> 00:12:21,253 If you're interested, you're welcome to read 239 00:12:21,253 --> 00:12:24,107 the relevant chapters in the textbook. 240 00:12:24,107 --> 00:12:25,690 But what we're going to do is to focus 241 00:12:25,690 --> 00:12:28,320 on the behavior of secondary markets, 242 00:12:28,320 --> 00:12:30,250 in particular, in the price formation 243 00:12:30,250 --> 00:12:35,080 mechanism for secondary market securities. 244 00:12:35,080 --> 00:12:38,110 Here's a little bit of a summary about how 245 00:12:38,110 --> 00:12:39,850 these markets have developed. 246 00:12:39,850 --> 00:12:42,850 You can see that for primary markets, 247 00:12:42,850 --> 00:12:45,520 the IPO market goes through cycles. 248 00:12:45,520 --> 00:12:48,970 There are periods where the market's very, very active, 249 00:12:48,970 --> 00:12:52,060 and there are periods where the market is pretty quiet 250 00:12:52,060 --> 00:12:55,360 and not a lot is going on. 251 00:12:55,360 --> 00:12:58,990 That has to do a lot with the business cycle 252 00:12:58,990 --> 00:13:02,217 and with the credit cycle-- how much money there is out there. 253 00:13:02,217 --> 00:13:04,300 And it's obviously very important for those of you 254 00:13:04,300 --> 00:13:05,883 who are thinking about doing startups, 255 00:13:05,883 --> 00:13:08,410 because when you do a startup and you get funding 256 00:13:08,410 --> 00:13:10,870 from a venture capitalist, the way the venture 257 00:13:10,870 --> 00:13:13,810 capitalist ultimately gets paid is not 258 00:13:13,810 --> 00:13:17,320 by the satisfaction of being part of your wonderful company, 259 00:13:17,320 --> 00:13:20,410 but rather by having your company go public 260 00:13:20,410 --> 00:13:24,010 and having securities be issued so that the venture 261 00:13:24,010 --> 00:13:28,400 capitalist can cash out at those public market prices. 262 00:13:28,400 --> 00:13:33,850 So the venture capital and technology industries 263 00:13:33,850 --> 00:13:37,930 are very much caught up in the business cycle and credit cycle 264 00:13:37,930 --> 00:13:39,760 as well, and so this gives you a little bit 265 00:13:39,760 --> 00:13:43,490 of a picture of how that's changed over time. 266 00:13:43,490 --> 00:13:46,180 On the other hand, the secondary market 267 00:13:46,180 --> 00:13:47,950 has a somewhat different set of dynamics. 268 00:13:47,950 --> 00:13:51,460 It's related, but not nearly as highly correlated 269 00:13:51,460 --> 00:13:53,710 as you might expect. 270 00:13:53,710 --> 00:13:57,190 This is an example of the dynamics 271 00:13:57,190 --> 00:14:02,500 of public secondary markets, the NYSE and NASDAQ 272 00:14:02,500 --> 00:14:05,380 over the last few years. 273 00:14:05,380 --> 00:14:08,860 What this displays is the trading volume, 274 00:14:08,860 --> 00:14:12,820 both measured in terms of shares as well as 275 00:14:12,820 --> 00:14:17,510 in composite fraction on the NYSE volume. 276 00:14:17,510 --> 00:14:20,320 And you can see that over time that the share 277 00:14:20,320 --> 00:14:23,260 volume, the amount of shares traded, 278 00:14:23,260 --> 00:14:27,516 has just gone up year on year, and this year 279 00:14:27,516 --> 00:14:28,390 will be no different. 280 00:14:28,390 --> 00:14:31,720 2008 will be a tremendously significant year 281 00:14:31,720 --> 00:14:34,780 for the amount of shares traded on the exchange. 282 00:14:34,780 --> 00:14:39,220 Lots more participation in public markets, and the volume, 283 00:14:39,220 --> 00:14:41,710 while there may be little bits of a dip that are functions 284 00:14:41,710 --> 00:14:45,100 of business cycles, not nearly as sensitive 285 00:14:45,100 --> 00:14:46,565 as the primary market is. 286 00:14:46,565 --> 00:14:47,065 Yeah. 287 00:14:47,065 --> 00:14:49,927 AUDIENCE: Is the internet also, you know, more volume? 288 00:14:49,927 --> 00:14:51,010 ANDREW LO: Oh, absolutely. 289 00:14:51,010 --> 00:14:53,500 Well, there are a number of technological innovations 290 00:14:53,500 --> 00:14:57,400 that have made this market increase so quickly. 291 00:14:57,400 --> 00:14:58,570 So the internet is one. 292 00:14:58,570 --> 00:15:00,350 Now all of us can trade on the internet. 293 00:15:00,350 --> 00:15:04,195 In fact, when I was teaching Finance back in, let's see, 294 00:15:04,195 --> 00:15:07,900 was it 2000 or 2001? 295 00:15:07,900 --> 00:15:10,990 I remember during the middle of the day 296 00:15:10,990 --> 00:15:15,670 one of the undergraduates in the class 297 00:15:15,670 --> 00:15:19,900 looked at some kind of cell phone device and then ran out. 298 00:15:19,900 --> 00:15:23,512 And he came back in shortly before the end of class, 299 00:15:23,512 --> 00:15:24,970 and at the end of class I asked him 300 00:15:24,970 --> 00:15:26,595 if everything was all right, because he 301 00:15:26,595 --> 00:15:27,720 seemed really distressed. 302 00:15:27,720 --> 00:15:29,094 And then he said that he just had 303 00:15:29,094 --> 00:15:32,260 to respond to a margin call on his equity position 304 00:15:32,260 --> 00:15:34,240 that he'd put on the day before. 305 00:15:34,240 --> 00:15:35,810 This is an undergraduate. 306 00:15:35,810 --> 00:15:40,180 He's trading on his little cell phone. 307 00:15:40,180 --> 00:15:41,740 That's a technological innovation 308 00:15:41,740 --> 00:15:46,300 that has actually increased the volume in these exchanges. 309 00:15:46,300 --> 00:15:48,280 But there are other technological innovations 310 00:15:48,280 --> 00:15:49,100 as well. 311 00:15:49,100 --> 00:15:53,260 For example, something called ECNs, electronic communications 312 00:15:53,260 --> 00:15:54,340 networks. 313 00:15:54,340 --> 00:15:57,940 These are-- essentially, they started out as bulletin boards, 314 00:15:57,940 --> 00:16:00,430 where large buyers and sellers of equities 315 00:16:00,430 --> 00:16:03,160 could come together anonymously and transact 316 00:16:03,160 --> 00:16:07,240 with each other at relatively inexpensive prices. 317 00:16:07,240 --> 00:16:10,510 They can cut out the middleman and reduce the bid offer spread 318 00:16:10,510 --> 00:16:14,690 by hitting a transaction price that was right in the middle. 319 00:16:14,690 --> 00:16:19,540 ECNs have grown tremendously since the early, the mid 90s, 320 00:16:19,540 --> 00:16:21,790 when they started, and now account 321 00:16:21,790 --> 00:16:23,790 for a pretty significant fraction of the volume. 322 00:16:23,790 --> 00:16:27,280 Electronic order routing, electronic trading, 323 00:16:27,280 --> 00:16:31,660 all of these technologies have caused this kind of increase 324 00:16:31,660 --> 00:16:34,880 in the equity market trading over the last several years. 325 00:16:34,880 --> 00:16:37,910 So today, as an individual investor, 326 00:16:37,910 --> 00:16:39,760 you can trade much more quickly. 327 00:16:39,760 --> 00:16:41,910 You can trade much more cheaply. 328 00:16:41,910 --> 00:16:44,990 And you can trade much more easily than ever before. 329 00:16:44,990 --> 00:16:47,440 So consumers have benefited a great deal. 330 00:16:47,440 --> 00:16:52,750 Along the way, a number of hedge funds and other investors 331 00:16:52,750 --> 00:16:55,630 have ended up going out of business because they have not 332 00:16:55,630 --> 00:16:58,090 been able to compete effectively with these kind 333 00:16:58,090 --> 00:16:59,365 of technological innovations. 334 00:16:59,365 --> 00:17:02,590 And this is what I mentioned last time, that technology 335 00:17:02,590 --> 00:17:06,400 plays a very important role in financial markets now, 336 00:17:06,400 --> 00:17:08,770 much more so than ever before. 337 00:17:08,770 --> 00:17:11,650 It used to be that it mattered who you knew, 338 00:17:11,650 --> 00:17:13,220 rather than what you knew. 339 00:17:13,220 --> 00:17:15,790 That it was the old boys network that mattered, 340 00:17:15,790 --> 00:17:17,609 instead of the computer network. 341 00:17:17,609 --> 00:17:19,359 And that the graduates of Harvard and Yale 342 00:17:19,359 --> 00:17:23,752 had an advantage over the graduates of MIT and Caltech. 343 00:17:23,752 --> 00:17:25,210 That's been flipped on its head now 344 00:17:25,210 --> 00:17:26,376 over the last several years. 345 00:17:26,376 --> 00:17:31,270 It's what I call the revenge of the nerds, which bodes well 346 00:17:31,270 --> 00:17:32,306 for all of you. 347 00:17:32,306 --> 00:17:33,060 [LAUGHTER] 348 00:17:33,060 --> 00:17:41,930 OK, so let me now turn to the very first valuation 349 00:17:41,930 --> 00:17:46,010 model that was ever developed for equities. 350 00:17:46,010 --> 00:17:47,390 It couldn't be simpler. 351 00:17:47,390 --> 00:17:49,190 It's a model that I think all of you 352 00:17:49,190 --> 00:17:52,070 are going to immediately understand, 353 00:17:52,070 --> 00:17:53,750 and yet the implications are going 354 00:17:53,750 --> 00:17:57,380 to be really far-reaching and profound. 355 00:17:57,380 --> 00:18:00,530 This is called the Dividend Discount Model, 356 00:18:00,530 --> 00:18:03,320 and it starts with the recognition 357 00:18:03,320 --> 00:18:06,320 that, when you invest in a company, what you're getting 358 00:18:06,320 --> 00:18:09,230 for that piece of paper, this common equity, 359 00:18:09,230 --> 00:18:14,120 you're getting the rights to the flow of cash forever. 360 00:18:14,120 --> 00:18:16,050 And what kind of cash are we talking about? 361 00:18:16,050 --> 00:18:18,250 Well, we're talking about dividends. 362 00:18:18,250 --> 00:18:21,890 So it's true that not all stocks pay dividends, 363 00:18:21,890 --> 00:18:26,000 but eventually you would figure the stock will pay dividend 364 00:18:26,000 --> 00:18:27,500 at some point, right? 365 00:18:27,500 --> 00:18:31,010 For years, Microsoft never paid a dividend. 366 00:18:31,010 --> 00:18:34,670 But about, was it five years ago or six years ago? 367 00:18:34,670 --> 00:18:37,670 They announced that they're starting to pay dividends. 368 00:18:37,670 --> 00:18:38,480 Why? 369 00:18:38,480 --> 00:18:41,180 Because they had accumulated so much cash 370 00:18:41,180 --> 00:18:45,500 that they didn't have enough things to invest that cash in, 371 00:18:45,500 --> 00:18:49,370 so they figured, let's give some of it back to the investors. 372 00:18:49,370 --> 00:18:52,880 In their early days, they kept every penny of their earnings 373 00:18:52,880 --> 00:18:55,700 to reinvest, because they had so many different opportunities 374 00:18:55,700 --> 00:18:56,780 to take advantage of. 375 00:18:56,780 --> 00:18:59,660 But because they became so mature 376 00:18:59,660 --> 00:19:02,035 and they had already a number of investment projects 377 00:19:02,035 --> 00:19:03,410 that were quite valuable, and yet 378 00:19:03,410 --> 00:19:05,332 were still generating so much cash, 379 00:19:05,332 --> 00:19:07,290 they decided to return some of it to investors. 380 00:19:07,290 --> 00:19:09,890 So at some point, you're going to get dividends. 381 00:19:09,890 --> 00:19:13,200 And if a company never, ever pays dividends, 382 00:19:13,200 --> 00:19:14,900 well, then, it should be worth 0, right? 383 00:19:14,900 --> 00:19:17,210 If it pays you no cash forever, then that 384 00:19:17,210 --> 00:19:18,680 seems like a very bad asset. 385 00:19:18,680 --> 00:19:19,190 Yeah. 386 00:19:19,190 --> 00:19:22,064 AUDIENCE: What stops the board of directors [INAUDIBLE] 387 00:19:22,064 --> 00:19:26,189 really depends on [INAUDIBLE] issuing dividends [INAUDIBLE].. 388 00:19:26,189 --> 00:19:28,480 ANDREW LO: Well, first of all, if they issued dividends 389 00:19:28,480 --> 00:19:30,160 to pay themselves, that's fine, as long 390 00:19:30,160 --> 00:19:33,080 as they pay all the other shareholders at the same time. 391 00:19:33,080 --> 00:19:37,630 So the answer is, in principle, nothing stops them, 392 00:19:37,630 --> 00:19:40,930 but what makes them decide against that 393 00:19:40,930 --> 00:19:43,600 is if they have uses for the cash other 394 00:19:43,600 --> 00:19:45,310 than paying themselves. 395 00:19:45,310 --> 00:19:48,460 If, as a company, you have no idea what to do with the money 396 00:19:48,460 --> 00:19:50,530 you are generating, well, first of all, 397 00:19:50,530 --> 00:19:52,180 that suggests that maybe you're not 398 00:19:52,180 --> 00:19:54,220 doing your job, because as a company, 399 00:19:54,220 --> 00:19:56,770 you're supposed to be coming up with valuable ways of earning 400 00:19:56,770 --> 00:19:58,190 money for your investors. 401 00:19:58,190 --> 00:20:01,550 However, it may be that your company is very mature, stable, 402 00:20:01,550 --> 00:20:03,469 there's no growth, there's nothing going on, 403 00:20:03,469 --> 00:20:05,260 and all the cash that you're generating you 404 00:20:05,260 --> 00:20:06,490 don't know what to do with. 405 00:20:06,490 --> 00:20:08,830 In that case, you may very well return all of that money 406 00:20:08,830 --> 00:20:09,371 to investors. 407 00:20:09,371 --> 00:20:11,650 That's nothing wrong with that. 408 00:20:11,650 --> 00:20:13,950 The idea behind having a vote though, 409 00:20:13,950 --> 00:20:16,560 is that you want to make sure that the board of directors, 410 00:20:16,560 --> 00:20:19,770 who typically do own or are responsible to shareholders 411 00:20:19,770 --> 00:20:23,470 that own large blocks of shares, will be deciding in the best 412 00:20:23,470 --> 00:20:24,720 interests of the shareholders. 413 00:20:24,720 --> 00:20:27,090 And it could be that the best interest of the shareholders 414 00:20:27,090 --> 00:20:28,500 is to give them back their money, 415 00:20:28,500 --> 00:20:31,500 because we, the mature company that we are, 416 00:20:31,500 --> 00:20:33,722 don't have any other uses for the money. 417 00:20:33,722 --> 00:20:34,571 Yeah. 418 00:20:34,571 --> 00:20:36,570 AUDIENCE: [INAUDIBLE] that, if the company never 419 00:20:36,570 --> 00:20:39,622 pays dividends, [INAUDIBLE]. 420 00:20:39,622 --> 00:20:42,574 What about the [INAUDIBLE]? 421 00:20:42,574 --> 00:20:44,341 Is there no value [INAUDIBLE]? 422 00:20:44,341 --> 00:20:45,840 ANDREW LO: Well, but think about it. 423 00:20:45,840 --> 00:20:48,700 If a company keeps on appreciating in value, 424 00:20:48,700 --> 00:20:52,180 but never pays out a dividend, what's happening to the cash? 425 00:20:52,180 --> 00:20:55,750 You know, when I say never, I mean never. 426 00:20:55,750 --> 00:20:58,180 So I don't just mean like in 10 years or in 20 years. 427 00:20:58,180 --> 00:20:59,440 I mean never. 428 00:20:59,440 --> 00:21:01,510 So can you think of a company that 429 00:21:01,510 --> 00:21:03,970 appreciates in value all the time, 430 00:21:03,970 --> 00:21:05,890 but never, ever, ever pays a dividend? 431 00:21:05,890 --> 00:21:08,690 There's no cash, so you'll never get any cash. 432 00:21:08,690 --> 00:21:09,190 That's-- 433 00:21:09,190 --> 00:21:10,814 AUDIENCE: Well, then, wouldn't you make a profit 434 00:21:10,814 --> 00:21:11,772 by selling [INAUDIBLE]? 435 00:21:11,772 --> 00:21:14,990 ANDREW LO: Oh, yes, you could make a profit by selling, 436 00:21:14,990 --> 00:21:18,070 but if you sell a security to somebody 437 00:21:18,070 --> 00:21:22,370 else and they know for a fact that it never, ever, 438 00:21:22,370 --> 00:21:26,240 ever, ever pays any money, well, then, 439 00:21:26,240 --> 00:21:28,902 that's called a Ponzi scheme, right? 440 00:21:28,902 --> 00:21:30,860 In other words, you're selling a piece of paper 441 00:21:30,860 --> 00:21:32,870 that's worthless to somebody and hoping 442 00:21:32,870 --> 00:21:36,350 that they are a bigger fool than you are for having bought it. 443 00:21:36,350 --> 00:21:39,620 So when I say it never pays any cash, I really mean it. 444 00:21:39,620 --> 00:21:43,010 If it never-- if you know for sure that it never, ever 445 00:21:43,010 --> 00:21:49,220 pays any cash, then it can't be worth anything, right? 446 00:21:49,220 --> 00:21:51,874 If you don't believe that, then I have a piece of paper 447 00:21:51,874 --> 00:21:53,540 that I would like you to take a look at, 448 00:21:53,540 --> 00:21:56,320 and I would like to sell you, OK? 449 00:21:56,320 --> 00:21:56,820 Yeah. 450 00:21:56,820 --> 00:21:59,214 AUDIENCE: Could it be like coupons and, like, the company 451 00:21:59,214 --> 00:21:59,714 dissolves? 452 00:21:59,714 --> 00:22:00,560 ANDREW LO: What's that? 453 00:22:00,560 --> 00:22:01,400 AUDIENCE: Even if it never pays dividends, 454 00:22:01,400 --> 00:22:02,620 you could still get something back 455 00:22:02,620 --> 00:22:04,270 if the company dissolves [INAUDIBLE].. 456 00:22:04,270 --> 00:22:05,600 ANDREW LO: Well, then it does pay something. 457 00:22:05,600 --> 00:22:07,010 That's a liquidating dividend. 458 00:22:07,010 --> 00:22:09,230 Then that violates my condition that it never, ever, 459 00:22:09,230 --> 00:22:11,720 ever pays anything, right? 460 00:22:11,720 --> 00:22:12,680 And that's the point. 461 00:22:12,680 --> 00:22:16,880 If the company is growing and it has value, 462 00:22:16,880 --> 00:22:19,670 then you know for a fact that either A, 463 00:22:19,670 --> 00:22:22,550 it will pay you a dividend at some point, or B, 464 00:22:22,550 --> 00:22:24,200 if it doesn't and it gets liquidated, 465 00:22:24,200 --> 00:22:25,700 then when it gets liquidated, you'll 466 00:22:25,700 --> 00:22:27,440 get a pro rata share of whatever's 467 00:22:27,440 --> 00:22:30,050 in the company, in which case, that's a payment. 468 00:22:30,050 --> 00:22:34,160 So to say that a company never, ever pays a dividend, 469 00:22:34,160 --> 00:22:38,750 I literally mean it will never, ever pay anything, OK? 470 00:22:38,750 --> 00:22:41,020 And in that case, it can't be worth anything 471 00:22:41,020 --> 00:22:42,480 if you know that. 472 00:22:42,480 --> 00:22:45,920 But if you can find somebody who will buy it anyway, 473 00:22:45,920 --> 00:22:48,190 then that's an example of an arbitrage. 474 00:22:48,190 --> 00:22:49,280 That's a free lunch. 475 00:22:49,280 --> 00:22:54,860 And so you can do that a lot if you can find people like that. 476 00:22:54,860 --> 00:22:58,760 OK, so we're going to apply the very basic principles 477 00:22:58,760 --> 00:23:04,190 of present value analysis to a security that pays dividends. 478 00:23:04,190 --> 00:23:08,300 So let's let the price of a stock, Pt, 479 00:23:08,300 --> 00:23:11,570 today, be given by that. 480 00:23:11,570 --> 00:23:15,350 Let Dt be the cash dividend that gets paid at time t. 481 00:23:15,350 --> 00:23:18,860 And by the way, Dt could be 0 for many, many years 482 00:23:18,860 --> 00:23:22,020 and at some point become positive, all right? 483 00:23:22,020 --> 00:23:23,900 Dt can never be negative, right? 484 00:23:23,900 --> 00:23:26,510 We're not talking about taking money from investors. 485 00:23:26,510 --> 00:23:30,710 It pays either a positive amount or 0. 486 00:23:30,710 --> 00:23:35,390 And I'm going to let E sub t be the expectation 487 00:23:35,390 --> 00:23:36,770 operator at time t. 488 00:23:36,770 --> 00:23:39,530 So now I'm going to explicitly recognize 489 00:23:39,530 --> 00:23:43,400 that these dividends are not known in advance. 490 00:23:43,400 --> 00:23:47,750 Unlike bonds, where you know the coupons in advance, 491 00:23:47,750 --> 00:23:49,700 I don't know the dividends in advance. 492 00:23:49,700 --> 00:23:50,950 So I'm going to have to guess. 493 00:23:50,950 --> 00:23:53,390 I'm going to have to make a forecast as to what they are. 494 00:23:53,390 --> 00:24:00,170 And let me let r sub t be the so-called risk-adjusted return 495 00:24:00,170 --> 00:24:04,130 that is commensurate with the risks of the dividends that 496 00:24:04,130 --> 00:24:05,060 are there. 497 00:24:05,060 --> 00:24:07,700 I'm going to wave my hands at this point 498 00:24:07,700 --> 00:24:10,940 as to how we get the dividend discount 499 00:24:10,940 --> 00:24:14,210 return, the appropriate risk-adjusted return, 500 00:24:14,210 --> 00:24:18,770 but I'll come back to that in a few lectures, when we go over 501 00:24:18,770 --> 00:24:22,250 methods for determining the appropriate risk adjustment, 502 00:24:22,250 --> 00:24:22,790 OK? 503 00:24:22,790 --> 00:24:25,250 But for now, let's assume that we have it, 504 00:24:25,250 --> 00:24:28,110 and we get it from the marketplace, right? 505 00:24:28,110 --> 00:24:31,010 Just like we got the yield from the marketplace, 506 00:24:31,010 --> 00:24:34,070 it's a sum total of everybody's fears, 507 00:24:34,070 --> 00:24:37,230 expectations, hopes, and so on. 508 00:24:37,230 --> 00:24:41,780 So with these components defined, 509 00:24:41,780 --> 00:24:46,430 I'm now going to simply write the price of my instrument 510 00:24:46,430 --> 00:24:50,834 as this value function of the future cash flows, right? 511 00:24:50,834 --> 00:24:52,250 That's the most general expression 512 00:24:52,250 --> 00:24:55,160 we started with on day one. 513 00:24:55,160 --> 00:25:00,350 And given what we now know about present value and valuing cash 514 00:25:00,350 --> 00:25:04,970 flows that come in the future, it's not a big leap of faith 515 00:25:04,970 --> 00:25:09,350 to put some structure on this valuation operator, OK? 516 00:25:09,350 --> 00:25:14,230 The value of this sequence of future cash flows 517 00:25:14,230 --> 00:25:19,950 is simply equal to the expectation today, time t, 518 00:25:19,950 --> 00:25:25,320 of future dividends out into the infinite future, 519 00:25:25,320 --> 00:25:31,260 discounted back by the appropriate risk-adjusted rate 520 00:25:31,260 --> 00:25:32,650 of return. 521 00:25:32,650 --> 00:25:36,450 Now you'll notice that the rate of return, this r, I 522 00:25:36,450 --> 00:25:41,400 put a subscript, t, plus 1, and t plus 2, and so on. 523 00:25:41,400 --> 00:25:44,640 I'm explicitly recognizing the fact 524 00:25:44,640 --> 00:25:47,460 that the appropriate risk-adjustment changes 525 00:25:47,460 --> 00:25:51,330 over time as market conditions change 526 00:25:51,330 --> 00:25:57,640 and as the business changes, OK? 527 00:25:57,640 --> 00:26:01,600 So it could be that the risk-adjusted return 528 00:26:01,600 --> 00:26:05,610 for a one-year cash flow is this, 529 00:26:05,610 --> 00:26:09,000 but the risk-adjusted return for a two-year cash flow 530 00:26:09,000 --> 00:26:10,320 is different. 531 00:26:10,320 --> 00:26:14,190 Just like we have a yield curve for riskless bonds, 532 00:26:14,190 --> 00:26:20,460 we may have a yield curve for risky cash flows, OK? 533 00:26:20,460 --> 00:26:22,380 And if I really wanted to be a masochist when 534 00:26:22,380 --> 00:26:24,840 it comes to notation, what I could do 535 00:26:24,840 --> 00:26:27,480 is to have a double subscript that 536 00:26:27,480 --> 00:26:32,160 says that this is the appropriate risk-adjusted 537 00:26:32,160 --> 00:26:35,790 return between years t and t plus 1, 538 00:26:35,790 --> 00:26:39,390 and then this is between years t and t plus 2, 539 00:26:39,390 --> 00:26:44,520 and so on, because these discount rates may be 540 00:26:44,520 --> 00:26:46,830 completely different tomorrow. 541 00:26:46,830 --> 00:26:49,530 In other words, tomorrow's discount rate 542 00:26:49,530 --> 00:26:54,390 for a one-year cash flow may be different than today's discount 543 00:26:54,390 --> 00:26:58,080 rate for a one-year cash flow, right? 544 00:26:58,080 --> 00:27:03,810 So I can have a whole string of discount rates for today, 545 00:27:03,810 --> 00:27:07,440 and a completely different string of discount rates 546 00:27:07,440 --> 00:27:11,040 for tomorrow and for every day in the future. 547 00:27:11,040 --> 00:27:14,530 These things change all the time. 548 00:27:14,530 --> 00:27:17,890 I think you'll see now why I told you earlier equities is 549 00:27:17,890 --> 00:27:21,220 a lot more complicated than fixed income instruments. 550 00:27:21,220 --> 00:27:25,250 It's because there are two sources of uncertainty. 551 00:27:25,250 --> 00:27:31,690 One is the discount rate, and the other is the cash flows. 552 00:27:31,690 --> 00:27:34,390 And moreover, the discount rate that we're talking about, 553 00:27:34,390 --> 00:27:38,850 it's not the risk-free discount rate, 554 00:27:38,850 --> 00:27:41,430 but it's the risk-adjusted discount rate. 555 00:27:41,430 --> 00:27:44,180 And if risks change over time, as certainly they 556 00:27:44,180 --> 00:27:47,300 have over the past even few days, 557 00:27:47,300 --> 00:27:49,620 then the discount rate should change. 558 00:27:49,620 --> 00:27:51,860 So in addition to the term structure 559 00:27:51,860 --> 00:27:54,680 effect of different yields, we also 560 00:27:54,680 --> 00:27:58,520 have the risk effect of looking out into the future, given 561 00:27:58,520 --> 00:28:01,830 current market conditions. 562 00:28:01,830 --> 00:28:04,100 So while this expression is tidy, 563 00:28:04,100 --> 00:28:07,050 and it looks nice and clean, in order 564 00:28:07,050 --> 00:28:09,150 to turn this into an actual number 565 00:28:09,150 --> 00:28:10,884 that you can look at and decide, gee, 566 00:28:10,884 --> 00:28:12,300 do I want to invest in this stock? 567 00:28:12,300 --> 00:28:14,640 Is it undervalued or overvalued? 568 00:28:14,640 --> 00:28:16,890 It's going to take a lot of work. 569 00:28:16,890 --> 00:28:19,950 So before we get to that work, I want 570 00:28:19,950 --> 00:28:23,730 to spend some time thinking about simpler things, 571 00:28:23,730 --> 00:28:27,360 and try to come up with relatively simple implications 572 00:28:27,360 --> 00:28:29,750 of this relatively robust model. 573 00:28:29,750 --> 00:28:30,527 Question? 574 00:28:30,527 --> 00:28:31,461 AUDIENCE: Yes, sir. 575 00:28:31,461 --> 00:28:34,263 Does rt take into account the riskiness 576 00:28:34,263 --> 00:28:38,120 of the company itself, or is it of the marketplace? 577 00:28:38,120 --> 00:28:40,391 ANDREW LO: The answer is yes. 578 00:28:40,391 --> 00:28:41,810 It's both. 579 00:28:41,810 --> 00:28:44,000 It's the riskiness of the company, 580 00:28:44,000 --> 00:28:46,940 as well as the riskiness of the aggregate set 581 00:28:46,940 --> 00:28:48,040 of market conditions. 582 00:28:48,040 --> 00:28:49,640 It's both. 583 00:28:49,640 --> 00:28:51,620 And so we have to figure out how that factors 584 00:28:51,620 --> 00:28:53,364 into this equation. 585 00:28:53,364 --> 00:28:55,530 That's going to take us a few lectures to get there. 586 00:28:55,530 --> 00:28:57,310 But the answer is both. 587 00:28:57,310 --> 00:28:57,960 Yeah. 588 00:28:57,960 --> 00:28:59,460 AUDIENCE: Would you say it's related 589 00:28:59,460 --> 00:29:02,800 to the riskiness of the expectation of the dividend 590 00:29:02,800 --> 00:29:06,362 being whatever it is at time t? 591 00:29:06,362 --> 00:29:07,070 ANDREW LO: Well-- 592 00:29:07,070 --> 00:29:10,920 AUDIENCE: If I were to know that the first dividend is absolute 593 00:29:10,920 --> 00:29:14,750 certain, but after that, not so much, 594 00:29:14,750 --> 00:29:17,470 then could I replace rt with a risk-free rate, 595 00:29:17,470 --> 00:29:22,640 but rt plus 2 with something else, and so forth? 596 00:29:22,640 --> 00:29:25,670 ANDREW LO: Yes, assuming that that dividend really 597 00:29:25,670 --> 00:29:26,630 was risk-free. 598 00:29:26,630 --> 00:29:28,220 Yes, that's right. 599 00:29:28,220 --> 00:29:30,680 So the idea behind the discount rate-- 600 00:29:30,680 --> 00:29:34,460 and, by the way, I'm going to ask you to explain this to me. 601 00:29:34,460 --> 00:29:36,050 So I'm going to make a statement, 602 00:29:36,050 --> 00:29:38,540 and then I'm going to ask you to justify it, OK? 603 00:29:38,540 --> 00:29:40,010 The statement is this-- 604 00:29:40,010 --> 00:29:44,240 the discount rate that's used in the denominator of each 605 00:29:44,240 --> 00:29:47,670 of these fractions, that discount rate 606 00:29:47,670 --> 00:29:51,420 has to be risk-adjusted in a way to reflect 607 00:29:51,420 --> 00:29:55,710 the risks of the numerator, as well as general market 608 00:29:55,710 --> 00:29:56,530 conditions. 609 00:29:56,530 --> 00:29:58,860 It has to be commensurate with the risks 610 00:29:58,860 --> 00:30:00,720 of that particular numerator. 611 00:30:00,720 --> 00:30:06,270 So if this numerator is much less risky than this numerator, 612 00:30:06,270 --> 00:30:08,370 I would argue that you would have 613 00:30:08,370 --> 00:30:10,590 to use a different discount rate, one 614 00:30:10,590 --> 00:30:13,530 that's higher for the more risky numerator 615 00:30:13,530 --> 00:30:15,240 than for the less risky. 616 00:30:15,240 --> 00:30:18,780 Now justify that for me. 617 00:30:18,780 --> 00:30:23,087 Why is that a reasonable thing to want to do? 618 00:30:23,087 --> 00:30:23,587 Yeah. 619 00:30:23,587 --> 00:30:26,128 AUDIENCE: Because you're getting more return on [INAUDIBLE].. 620 00:30:28,310 --> 00:30:29,310 ANDREW LO: That's right. 621 00:30:29,310 --> 00:30:31,620 AUDIENCE: Your discount rate would be [INAUDIBLE].. 622 00:30:31,620 --> 00:30:32,619 ANDREW LO: That's right. 623 00:30:32,619 --> 00:30:34,110 You get more return on your capital 624 00:30:34,110 --> 00:30:36,240 for something of greater risk on average, 625 00:30:36,240 --> 00:30:38,694 because you've got to be rewarded for bearing that risk. 626 00:30:38,694 --> 00:30:40,110 And if you're not rewarded, you're 627 00:30:40,110 --> 00:30:43,120 not going to take on that risk. 628 00:30:43,120 --> 00:30:44,020 How do you know that? 629 00:30:44,020 --> 00:30:46,061 How do you know that you're going to get rewarded 630 00:30:46,061 --> 00:30:47,370 for taking on that risk? 631 00:30:47,370 --> 00:30:50,554 Where did you get that from, besides me? 632 00:30:50,554 --> 00:30:52,970 AUDIENCE: That's just the law of the jungle, I don't know. 633 00:30:52,970 --> 00:30:54,170 [LAUGHTER] 634 00:30:54,170 --> 00:30:55,680 ANDREW LO: You're right. 635 00:30:55,680 --> 00:30:56,940 It's a law of the jungle. 636 00:30:56,940 --> 00:30:58,765 But in this case, what is the jungle? 637 00:30:58,765 --> 00:30:59,640 AUDIENCE: [INAUDIBLE] 638 00:30:59,640 --> 00:31:00,889 ANDREW LO: Exactly, thank you. 639 00:31:00,889 --> 00:31:01,800 The market. 640 00:31:01,800 --> 00:31:02,790 Excellent. 641 00:31:02,790 --> 00:31:03,360 The market. 642 00:31:03,360 --> 00:31:06,420 The market is the jungle from which you 643 00:31:06,420 --> 00:31:08,680 compete for scarce resources. 644 00:31:08,680 --> 00:31:11,970 And in order to get your pet project funded, 645 00:31:11,970 --> 00:31:14,550 you've got to provide the right incentives for people 646 00:31:14,550 --> 00:31:17,200 to buy into your project. 647 00:31:17,200 --> 00:31:19,410 So that's the logic of the justification. 648 00:31:19,410 --> 00:31:22,290 Now let me go one step farther and say, 649 00:31:22,290 --> 00:31:26,560 suppose that you want to replicate these cash flows. 650 00:31:26,560 --> 00:31:31,180 Suppose that you want to create a portfolio that gives you 651 00:31:31,180 --> 00:31:33,080 these kind of cash flows. 652 00:31:33,080 --> 00:31:36,370 Well, then, you've got to go to the marketplace 653 00:31:36,370 --> 00:31:39,340 and figure out what the appropriate opportunity cost is 654 00:31:39,340 --> 00:31:42,045 for each of those cash flows and then discount them, 655 00:31:42,045 --> 00:31:43,420 because that's what the market is 656 00:31:43,420 --> 00:31:45,560 charging for those cash flows. 657 00:31:45,560 --> 00:31:48,940 So that's why you have to get the appropriate discount 658 00:31:48,940 --> 00:31:53,440 rate matched to the appropriate cash flow, all right? 659 00:31:53,440 --> 00:31:57,490 It comes straight out of what we learned about bond pricing, 660 00:31:57,490 --> 00:32:00,670 but now we're adding an extra dimension-- risk. 661 00:32:00,670 --> 00:32:03,430 And I'm not going to be able to talk about it in any more 662 00:32:03,430 --> 00:32:06,490 detail than this until we put more quantitative structure 663 00:32:06,490 --> 00:32:08,110 on what we even mean by risk. 664 00:32:08,110 --> 00:32:10,570 I mean, you all take for granted, when I say risk, 665 00:32:10,570 --> 00:32:13,370 you say, yes, you understand what risk is. 666 00:32:13,370 --> 00:32:17,350 But in order for us to justify a particular expression for how 667 00:32:17,350 --> 00:32:19,660 to make that kind of adjustment, we 668 00:32:19,660 --> 00:32:22,370 have to be very specific about how to measure risk. 669 00:32:22,370 --> 00:32:24,740 So in about three or four lectures, 670 00:32:24,740 --> 00:32:27,830 I'm going to actually propose a method for measuring risk. 671 00:32:27,830 --> 00:32:29,720 And once we have that method in hand, 672 00:32:29,720 --> 00:32:32,680 we can then make that risk adjustment extremely 673 00:32:32,680 --> 00:32:33,280 explicitly. 674 00:32:33,280 --> 00:32:35,620 I'm going to give you a formula that you can actually 675 00:32:35,620 --> 00:32:38,860 compute in an Excel spreadsheet that will tell you exactly 676 00:32:38,860 --> 00:32:43,540 whether the number should be 6.5% or 7.3% or 8.9%. 677 00:32:43,540 --> 00:32:46,163 You're going to actually see how to do that yourself. 678 00:32:46,163 --> 00:32:47,462 Yeah. 679 00:32:47,462 --> 00:32:48,980 AUDIENCE: The score wasn't implying 680 00:32:48,980 --> 00:32:52,296 that those time structured to when dividends paid out. 681 00:32:52,296 --> 00:32:55,382 Like, the time between t plus 1 and t plus 2 682 00:32:55,382 --> 00:32:57,590 doesn't have to be the same as t plus 2 and t plus 3. 683 00:32:57,590 --> 00:32:59,090 ANDREW LO: Correct, correct. 684 00:32:59,090 --> 00:33:01,350 It doesn't have to be the same. 685 00:33:01,350 --> 00:33:04,670 And if it's not the same, then the difference in horizon 686 00:33:04,670 --> 00:33:08,840 should be reflected by the implicit size of that discount 687 00:33:08,840 --> 00:33:09,500 rate. 688 00:33:09,500 --> 00:33:11,097 Yeah. 689 00:33:11,097 --> 00:33:14,031 AUDIENCE: [INAUDIBLE] the company's bond yield 690 00:33:14,031 --> 00:33:17,460 [INAUDIBLE]? 691 00:33:17,460 --> 00:33:19,850 ANDREW LO: Well, you tell me. 692 00:33:19,850 --> 00:33:23,290 Can we use the company's bond yield 693 00:33:23,290 --> 00:33:26,040 to use as a discount rate for the equity? 694 00:33:26,040 --> 00:33:27,130 Well, that depends. 695 00:33:27,130 --> 00:33:29,700 It depends on whether or not the equity and the bond 696 00:33:29,700 --> 00:33:32,730 are of comparable risk, right? 697 00:33:32,730 --> 00:33:35,400 Remember, it's not the company that 698 00:33:35,400 --> 00:33:37,230 determines the discount rate. 699 00:33:37,230 --> 00:33:38,520 It's not the company-- 700 00:33:38,520 --> 00:33:41,640 or rather, it's not determined by fiat, 701 00:33:41,640 --> 00:33:45,270 or by announcement of a company's particular policies. 702 00:33:45,270 --> 00:33:49,260 What determines the yield is the riskiness 703 00:33:49,260 --> 00:33:52,340 of that yield and the marketplace. 704 00:33:52,340 --> 00:33:56,120 The market determines that particular price, 705 00:33:56,120 --> 00:34:00,290 not the individual, or not the sources of those funds. 706 00:34:00,290 --> 00:34:03,820 AUDIENCE: Whenever [INAUDIBLE] of the company's bonds 707 00:34:03,820 --> 00:34:06,254 do not reflect on the company's equity? 708 00:34:06,254 --> 00:34:07,670 ANDREW LO: Oh, of course, they do, 709 00:34:07,670 --> 00:34:09,380 but they reflect in a very specific way, 710 00:34:09,380 --> 00:34:10,340 and we're going to talk about that when 711 00:34:10,340 --> 00:34:11,840 we get into capital structure. 712 00:34:11,840 --> 00:34:13,790 Companies that have very high leverage 713 00:34:13,790 --> 00:34:15,889 are going to have more risky equity than companies 714 00:34:15,889 --> 00:34:17,600 with very low leverage. 715 00:34:17,600 --> 00:34:20,719 So the leverage does have an impact on the equity. 716 00:34:20,719 --> 00:34:22,699 We're going to come to that in a little while. 717 00:34:22,699 --> 00:34:24,157 There is a relationship, all right? 718 00:34:24,157 --> 00:34:27,440 But for now, let's look at these securities in isolation 719 00:34:27,440 --> 00:34:28,790 and not worry about it. 720 00:34:28,790 --> 00:34:30,739 And I'm going to keep coming back to the idea 721 00:34:30,739 --> 00:34:34,219 that it's not the company that gets to determine the discount 722 00:34:34,219 --> 00:34:36,770 rate, but rather it's the company's riskiness-- 723 00:34:36,770 --> 00:34:40,949 or rather the riskiness of the cash flows and the market's 724 00:34:40,949 --> 00:34:43,860 assessment of the cost of that riskiness-- 725 00:34:43,860 --> 00:34:45,570 that determines the interest rate. 726 00:34:45,570 --> 00:34:48,900 A few years ago, there was a faculty member 727 00:34:48,900 --> 00:34:52,550 at Carnegie Mellon who won a Nobel Prize, 728 00:34:52,550 --> 00:34:57,600 and it ended up that he was one of the highest paid 729 00:34:57,600 --> 00:35:00,300 professors at the time. 730 00:35:00,300 --> 00:35:05,080 And so he was being interviewed by the school newspaper, 731 00:35:05,080 --> 00:35:07,047 and they said, Professor So and So, 732 00:35:07,047 --> 00:35:09,130 do you think it's appropriate that even though you 733 00:35:09,130 --> 00:35:11,850 won a Nobel Prize, that you should get 734 00:35:11,850 --> 00:35:15,330 paid twice as much as some of the other faculty who 735 00:35:15,330 --> 00:35:19,420 are Nobel Prize-winning physicists and fields medalists 736 00:35:19,420 --> 00:35:21,840 in the Mathematics department, and so on? 737 00:35:21,840 --> 00:35:25,740 I mean, do you think it's fair that your salary is twice 738 00:35:25,740 --> 00:35:30,180 as high as other people in the school? 739 00:35:30,180 --> 00:35:36,030 And the faculty member, who is an economist, said, listen son. 740 00:35:36,030 --> 00:35:38,490 The university does not determine my equilibrium 741 00:35:38,490 --> 00:35:39,510 salary. 742 00:35:39,510 --> 00:35:42,600 They only determine what city I work in. 743 00:35:42,600 --> 00:35:45,330 In other words, the salary of an individual 744 00:35:45,330 --> 00:35:48,290 is not determined by that particular institution. 745 00:35:48,290 --> 00:35:50,250 It's determined by the marketplace. 746 00:35:50,250 --> 00:35:53,082 The marketplace bids on that faculty member, 747 00:35:53,082 --> 00:35:54,540 and the highest bidder, presumably, 748 00:35:54,540 --> 00:35:56,850 will be able to get that faculty member. 749 00:35:56,850 --> 00:35:59,040 The same thing with these cash flows. 750 00:35:59,040 --> 00:36:01,246 It's not the company's debt, or the company's 751 00:36:01,246 --> 00:36:02,620 weighted average cost of capital, 752 00:36:02,620 --> 00:36:03,450 which we don't know what it is yet, 753 00:36:03,450 --> 00:36:05,380 but I'll define a little later on. 754 00:36:05,380 --> 00:36:07,200 It's not the company that gets to choose 755 00:36:07,200 --> 00:36:08,580 what the discount rate is. 756 00:36:08,580 --> 00:36:12,900 The question is, given the riskiness of that cash flow, 757 00:36:12,900 --> 00:36:17,040 what does the market tell me is the fair rate of return 758 00:36:17,040 --> 00:36:18,090 for that cash flow? 759 00:36:18,090 --> 00:36:21,600 That's the number I want to plug into that denominator. 760 00:36:21,600 --> 00:36:22,650 Yeah, question. 761 00:36:22,650 --> 00:36:25,450 AUDIENCE: The market may determine the discount rate, 762 00:36:25,450 --> 00:36:28,697 but the company determines the growth rate on the dividend, 763 00:36:28,697 --> 00:36:29,196 right? 764 00:36:29,196 --> 00:36:31,380 They get to decide what the dividend is. 765 00:36:31,380 --> 00:36:33,150 ANDREW LO: Well, they get to decide 766 00:36:33,150 --> 00:36:35,160 what the dividend is subject to their ability 767 00:36:35,160 --> 00:36:36,467 to pay that dividend. 768 00:36:36,467 --> 00:36:38,550 But if it turns out that they make a bad decision, 769 00:36:38,550 --> 00:36:39,630 and they pay out all the dividends, 770 00:36:39,630 --> 00:36:41,421 and they have no more money, and they can't 771 00:36:41,421 --> 00:36:43,260 grow the company anymore, then who 772 00:36:43,260 --> 00:36:45,660 determines what's worth what? 773 00:36:45,660 --> 00:36:48,320 Ultimately, the market. 774 00:36:48,320 --> 00:36:52,730 The market is the final arbiter in all of these calculations. 775 00:36:52,730 --> 00:36:54,950 At least that's the theory of finance. 776 00:36:54,950 --> 00:36:58,670 That's the basic, plain vanilla, frictionless model, OK? 777 00:36:58,670 --> 00:37:02,120 It's the market that determines these interest rates. 778 00:37:02,120 --> 00:37:04,340 Later on, after we go through the basics 779 00:37:04,340 --> 00:37:06,380 and you understand the frictionless model, 780 00:37:06,380 --> 00:37:08,030 I'm going to introduce frictions, 781 00:37:08,030 --> 00:37:11,810 and then you'll see what impact corporate policies have 782 00:37:11,810 --> 00:37:13,010 on these implications. 783 00:37:13,010 --> 00:37:15,110 In some cases, corporate directors 784 00:37:15,110 --> 00:37:19,580 can actually do a lot of harm by making suboptimal decisions 785 00:37:19,580 --> 00:37:21,510 that go against the market. 786 00:37:21,510 --> 00:37:24,320 In other cases, you could argue that corporate decision-makers 787 00:37:24,320 --> 00:37:26,120 know more than the market and are 788 00:37:26,120 --> 00:37:29,330 able to make bets that the market is not capable of doing. 789 00:37:29,330 --> 00:37:31,340 That's certainly possible, because who knows 790 00:37:31,340 --> 00:37:33,110 the company better than you do? 791 00:37:33,110 --> 00:37:37,130 Although a market expert would say 792 00:37:37,130 --> 00:37:39,650 it's not knowing the company that will determine 793 00:37:39,650 --> 00:37:41,300 the value of the company. 794 00:37:41,300 --> 00:37:43,400 It's knowing how that company compares 795 00:37:43,400 --> 00:37:46,019 to all the other companies that are out there that determines 796 00:37:46,019 --> 00:37:47,060 the value of the company. 797 00:37:47,060 --> 00:37:48,980 And you, as the corporate insider, 798 00:37:48,980 --> 00:37:50,720 may know your business very well, 799 00:37:50,720 --> 00:37:52,370 but you don't know how you stack up 800 00:37:52,370 --> 00:37:55,250 against the 25 other businesses in your industry, 801 00:37:55,250 --> 00:37:59,110 and we, the market, know better than you, the individual. 802 00:37:59,110 --> 00:38:01,720 That's the argument that would be made against that. 803 00:38:01,720 --> 00:38:03,700 AUDIENCE: In the case of refinanced stocks, 804 00:38:03,700 --> 00:38:04,887 can I use the same formula? 805 00:38:04,887 --> 00:38:06,470 ANDREW LO: We're going to get to that. 806 00:38:06,470 --> 00:38:07,730 We're going to talk about preferred stocks. 807 00:38:07,730 --> 00:38:09,080 That's a separate issue. 808 00:38:09,080 --> 00:38:12,000 Preferred stocks have a different priority of claim, 809 00:38:12,000 --> 00:38:15,290 and that's going to require some slightly different 810 00:38:15,290 --> 00:38:16,995 modifications to this formula. 811 00:38:16,995 --> 00:38:17,529 Yeah. 812 00:38:17,529 --> 00:38:19,820 AUDIENCE: So I had a question about the expected value. 813 00:38:19,820 --> 00:38:24,090 So yesterday in the example, you discounted the 1,000 to 900 814 00:38:24,090 --> 00:38:25,455 [INAUDIBLE] Et. 815 00:38:25,455 --> 00:38:28,991 So what else do you need to discount in the r 816 00:38:28,991 --> 00:38:30,860 to account for the risk? 817 00:38:30,860 --> 00:38:32,480 ANDREW LO: Well, I mean, you have 818 00:38:32,480 --> 00:38:36,170 to take into account the fact that there are other competing 819 00:38:36,170 --> 00:38:38,060 opportunities for this particular project 820 00:38:38,060 --> 00:38:39,450 in the marketplace. 821 00:38:39,450 --> 00:38:41,630 And so it's not just the risk of this project, 822 00:38:41,630 --> 00:38:44,030 but rather how the risk of this project 823 00:38:44,030 --> 00:38:48,260 stacks up against the risks of all other possible projects 824 00:38:48,260 --> 00:38:51,040 that you would be competing for in the open market. 825 00:38:51,040 --> 00:38:52,290 Let me put it to you this way. 826 00:38:52,290 --> 00:38:54,300 Let's do a simple thought experiment. 827 00:38:54,300 --> 00:38:59,090 Suppose that instead of these as being dividend 828 00:38:59,090 --> 00:39:03,740 streams for a given company, let's do the following thought 829 00:39:03,740 --> 00:39:04,890 experiment. 830 00:39:04,890 --> 00:39:06,860 Let's imagine doing a strip, OK? 831 00:39:06,860 --> 00:39:08,660 You all know what strips are now, right? 832 00:39:08,660 --> 00:39:11,090 So let's think about stripping out dividends, OK? 833 00:39:11,090 --> 00:39:13,070 It's a very weird thought experiment, granted, 834 00:39:13,070 --> 00:39:14,520 but just bear with me. 835 00:39:14,520 --> 00:39:17,760 Let's suppose that instead of one company, 836 00:39:17,760 --> 00:39:21,290 I generate an infinity of companies. 837 00:39:21,290 --> 00:39:25,820 Each company lives only for one dividend payment, 838 00:39:25,820 --> 00:39:27,530 after which it gets liquidated. 839 00:39:27,530 --> 00:39:32,370 So each of these cash flows, Dt plus 1, Dt plus 2, 840 00:39:32,370 --> 00:39:35,760 each one of these things is a separate and independent 841 00:39:35,760 --> 00:39:38,220 company that gets liquidated right 842 00:39:38,220 --> 00:39:42,070 after it pays the dividend, OK? 843 00:39:42,070 --> 00:39:45,910 Now how would you value a portfolio 844 00:39:45,910 --> 00:39:49,240 of all of these companies? 845 00:39:49,240 --> 00:39:51,400 Well, you would do this, right? 846 00:39:51,400 --> 00:39:54,550 For each company, you would figure out 847 00:39:54,550 --> 00:39:56,956 what the appropriate discount rate is, 848 00:39:56,956 --> 00:39:58,330 and the appropriate discount rate 849 00:39:58,330 --> 00:40:01,210 reflects not just the time value of money, 850 00:40:01,210 --> 00:40:06,470 but the appropriate riskiness of that cash flow. 851 00:40:06,470 --> 00:40:08,875 For example, if I took that company-- let's 852 00:40:08,875 --> 00:40:11,000 actually do a thought experiment of how we do that. 853 00:40:11,000 --> 00:40:13,400 Let's go through the motions, OK. 854 00:40:13,400 --> 00:40:16,160 I've got a piece of paper that is something 855 00:40:16,160 --> 00:40:22,490 that funds nanotechnology in a very specific application. 856 00:40:22,490 --> 00:40:25,910 And this company is going to require 857 00:40:25,910 --> 00:40:28,190 a certain amount of investment, and then it'll 858 00:40:28,190 --> 00:40:34,250 pay off all of its earnings in 2013, December, 859 00:40:34,250 --> 00:40:36,680 and then it'll liquidate and be done with, OK? 860 00:40:36,680 --> 00:40:39,700 That's the company. 861 00:40:39,700 --> 00:40:43,830 How do I figure out the price of the company today? 862 00:40:48,270 --> 00:40:48,770 Anybody? 863 00:40:48,770 --> 00:40:50,670 How do I figure out the price? 864 00:40:50,670 --> 00:40:53,630 I have this piece of paper that says in 2013, 865 00:40:53,630 --> 00:40:56,569 the company will liquidate, and I 866 00:40:56,569 --> 00:40:57,860 want to know what the price is. 867 00:40:57,860 --> 00:41:01,490 What's the first thing you would do with that proposal 868 00:41:01,490 --> 00:41:02,914 if you got it in the mail? 869 00:41:02,914 --> 00:41:04,080 What would you want to know? 870 00:41:04,080 --> 00:41:04,600 Yeah. 871 00:41:04,600 --> 00:41:06,599 AUDIENCE: I would want to know, like, if there's 872 00:41:06,599 --> 00:41:08,058 a security I can buy in the market, 873 00:41:08,058 --> 00:41:09,515 is the company going to pay for it? 874 00:41:09,515 --> 00:41:11,390 Because it's the same risk return profile. 875 00:41:11,390 --> 00:41:13,190 And I look at the marketplace for that. 876 00:41:13,190 --> 00:41:14,210 ANDREW LO: Why would you do that? 877 00:41:14,210 --> 00:41:15,668 AUDIENCE: Because there's no reason 878 00:41:15,668 --> 00:41:19,400 I would go through the hassle, or friction, as you call it, 879 00:41:19,400 --> 00:41:21,110 of pricing a new company if I could just 880 00:41:21,110 --> 00:41:22,340 go online and buy it. 881 00:41:22,340 --> 00:41:23,990 ANDREW LO: Right, that's one logic, 882 00:41:23,990 --> 00:41:29,282 but another logic is that you have money looking for a home. 883 00:41:29,282 --> 00:41:30,740 You can put it in this new venture, 884 00:41:30,740 --> 00:41:32,900 or you can put it in this existing company. 885 00:41:32,900 --> 00:41:34,696 And if they're comparable, then at least 886 00:41:34,696 --> 00:41:36,320 you have some sense of what it's worth. 887 00:41:36,320 --> 00:41:37,940 Exactly. 888 00:41:37,940 --> 00:41:39,740 In order to figure out whether or not 889 00:41:39,740 --> 00:41:41,960 you can get a comparable security, 890 00:41:41,960 --> 00:41:45,150 you need to know what the cash flow is for that nanotechnology 891 00:41:45,150 --> 00:41:46,210 startup, right? 892 00:41:46,210 --> 00:41:50,000 So you might think first about estimating the expected cash 893 00:41:50,000 --> 00:41:54,610 flow in the liquidating dividend in 2013. 894 00:41:54,610 --> 00:41:59,650 OK, so you calculate the numerator, all right? 895 00:41:59,650 --> 00:42:01,600 And you find a company out there that has 896 00:42:01,600 --> 00:42:03,730 that same kind of cash flow. 897 00:42:03,730 --> 00:42:06,070 You have to find one that has the same profile, 898 00:42:06,070 --> 00:42:10,900 so it does it in 2013, at which point it gets liquidated. 899 00:42:10,900 --> 00:42:12,190 But let's even forget about-- 900 00:42:12,190 --> 00:42:14,080 suppose we didn't have such a company. 901 00:42:14,080 --> 00:42:16,280 Suppose we didn't have an existing security. 902 00:42:16,280 --> 00:42:19,270 So this is literally a fresh start. 903 00:42:19,270 --> 00:42:21,490 You've got a piece of paper that gives you 904 00:42:21,490 --> 00:42:25,330 the claim to a company that liquidates in 2013 with one 905 00:42:25,330 --> 00:42:26,680 cash flow only. 906 00:42:26,680 --> 00:42:28,870 And now you've estimated that cash flow to be 907 00:42:28,870 --> 00:42:34,750 approximately $27 million, OK? 908 00:42:34,750 --> 00:42:36,570 So now you've got the numerator. 909 00:42:36,570 --> 00:42:39,987 A piece of paper that pays $27 million. 910 00:42:39,987 --> 00:42:41,320 How do you figure out its price? 911 00:42:44,040 --> 00:42:44,990 What would you do? 912 00:42:44,990 --> 00:42:46,520 Yeah. 913 00:42:46,520 --> 00:42:50,335 AUDIENCE: Calculate the risk that it's going to [INAUDIBLE],, 914 00:42:50,335 --> 00:42:52,930 also you have the time [INAUDIBLE].. 915 00:42:52,930 --> 00:42:54,430 ANDREW LO: OK, and you've done that, 916 00:42:54,430 --> 00:42:55,360 and that's the $27 million. 917 00:42:55,360 --> 00:42:57,151 AUDIENCE: That's included in the valuation. 918 00:42:57,151 --> 00:42:58,720 ANDREW LO: Right, the $27 million 919 00:42:58,720 --> 00:43:02,290 includes the probability that it actually is 0, 920 00:43:02,290 --> 00:43:05,710 so the expected value is 27 million. 921 00:43:05,710 --> 00:43:07,693 How would you go about-- yeah. 922 00:43:07,693 --> 00:43:09,818 AUDIENCE: Wouldn't it actually be two [INAUDIBLE],, 923 00:43:09,818 --> 00:43:12,188 so when the 27 million liquidates, 924 00:43:12,188 --> 00:43:14,895 you get the value of the assets? 925 00:43:14,895 --> 00:43:17,647 ANDREW LO: The liquidation value is the 27 million on average. 926 00:43:17,647 --> 00:43:19,480 AUDIENCE: [INAUDIBLE] two payments for that. 927 00:43:19,480 --> 00:43:21,396 ANDREW LO: No, no, no, it's just one payment-- 928 00:43:21,396 --> 00:43:23,110 27 million on expectation. 929 00:43:23,110 --> 00:43:24,670 Oh, it may be two possibilities. 930 00:43:24,670 --> 00:43:28,900 Maybe you either get 54 million with 50% probability, 931 00:43:28,900 --> 00:43:31,360 or nothing with 50% probability, so the expectation 932 00:43:31,360 --> 00:43:34,001 is 27 million. 933 00:43:34,001 --> 00:43:34,750 What would you do? 934 00:43:34,750 --> 00:43:34,960 Yeah. 935 00:43:34,960 --> 00:43:36,418 AUDIENCE: I think if you're already 936 00:43:36,418 --> 00:43:41,800 weighted in the probability [INAUDIBLE] 0 [INAUDIBLE] 937 00:43:41,800 --> 00:43:43,720 ANDREW LO: Suppose you don't know what to use. 938 00:43:43,720 --> 00:43:45,819 Suppose you want to figure out what the price is. 939 00:43:45,819 --> 00:43:47,110 AUDIENCE: [INAUDIBLE] discount. 940 00:43:47,110 --> 00:43:48,910 ANDREW LO: Yeah, I know what you mean. 941 00:43:48,910 --> 00:43:50,990 But suppose that you didn't have that. 942 00:43:50,990 --> 00:43:51,957 What would you do? 943 00:43:51,957 --> 00:43:56,860 AUDIENCE: [INAUDIBLE] at the yield curve just 944 00:43:56,860 --> 00:44:01,080 to get an idea of what in 2010, at least 945 00:44:01,080 --> 00:44:03,582 either a risk-free security or a security 946 00:44:03,582 --> 00:44:06,700 with that same credit risk. 947 00:44:06,700 --> 00:44:09,160 You know, what discount rate that would go in there, 948 00:44:09,160 --> 00:44:10,500 discounting by that [INAUDIBLE]. 949 00:44:10,500 --> 00:44:12,420 ANDREW LO: You could do that, but now we're 950 00:44:12,420 --> 00:44:13,836 getting more and more complicated. 951 00:44:13,836 --> 00:44:16,750 Isn't there an easier way to figure out what the price is? 952 00:44:16,750 --> 00:44:17,500 Exactly. 953 00:44:17,500 --> 00:44:19,270 You know, let's let the market decide. 954 00:44:19,270 --> 00:44:20,730 Auction it off. 955 00:44:20,730 --> 00:44:24,460 Now when you auction it off, you take the highest bidder, right? 956 00:44:24,460 --> 00:44:25,606 And you get a number. 957 00:44:25,606 --> 00:44:26,980 I don't know what that number is, 958 00:44:26,980 --> 00:44:29,970 but let's just say the number is, I don't know, 15 million. 959 00:44:32,485 --> 00:44:34,610 You've got somebody who's willing to pay 15 million 960 00:44:34,610 --> 00:44:39,740 today for a cash flow that gives them expected 27 million 961 00:44:39,740 --> 00:44:42,180 in 2013. 962 00:44:42,180 --> 00:44:49,160 With those two numbers, that gives you r, doesn't it? 963 00:44:49,160 --> 00:44:51,170 That's how r is established. 964 00:44:51,170 --> 00:44:53,030 It's established the exact same way 965 00:44:53,030 --> 00:44:56,540 that we establish r for riskless bonds. 966 00:44:56,540 --> 00:44:58,160 The way that US treasuries ended up 967 00:44:58,160 --> 00:45:01,280 being three basis points on September 18th was, 968 00:45:01,280 --> 00:45:03,680 basically, tons of people wanted to buy these securities, 969 00:45:03,680 --> 00:45:06,920 bidding down the yield and bidding up the price. 970 00:45:06,920 --> 00:45:10,160 So if we had this piece of paper that paid only one 971 00:45:10,160 --> 00:45:13,580 dividend in 2013 and we auctioned it off, 972 00:45:13,580 --> 00:45:14,870 we would get a yield. 973 00:45:14,870 --> 00:45:17,694 The yield would be a risk-adjusted yield. 974 00:45:17,694 --> 00:45:19,610 I don't know how the risk adjustment got made. 975 00:45:19,610 --> 00:45:22,831 So you could be quite right that you take the risk-free yield, 976 00:45:22,831 --> 00:45:24,580 and you add on top of that a credit spread 977 00:45:24,580 --> 00:45:26,060 and who knows what. 978 00:45:26,060 --> 00:45:29,430 The point is, the market did it for us, OK? 979 00:45:29,430 --> 00:45:32,010 So what I'm getting after with this formula 980 00:45:32,010 --> 00:45:37,590 is I want to use those discount rates that are determined 981 00:45:37,590 --> 00:45:39,240 by the marketplace. 982 00:45:39,240 --> 00:45:41,880 Because if ever I have to sell my company, 983 00:45:41,880 --> 00:45:43,380 if ever I have to take this company 984 00:45:43,380 --> 00:45:45,452 and break it apart and get rid of it, 985 00:45:45,452 --> 00:45:47,160 and the market is going to pay me for it, 986 00:45:47,160 --> 00:45:49,140 the way that the market is going to evaluate 987 00:45:49,140 --> 00:45:51,830 the different pieces is just the way that I described. 988 00:45:51,830 --> 00:45:55,260 It'll look at each cash flow, look at how risky it is, 989 00:45:55,260 --> 00:45:57,370 look at the opportunity cost of other investments 990 00:45:57,370 --> 00:46:00,360 that they can get the same risk return profile for, 991 00:46:00,360 --> 00:46:03,780 and they'll pay that amount, which will implicitly 992 00:46:03,780 --> 00:46:06,720 give me the appropriate yield. 993 00:46:06,720 --> 00:46:07,442 Yeah. 994 00:46:07,442 --> 00:46:09,150 AUDIENCE: So let's say that me purchasing 995 00:46:09,150 --> 00:46:11,810 a stock with this calculation, do 996 00:46:11,810 --> 00:46:14,832 I have to assume that this calculation is wrong? 997 00:46:14,832 --> 00:46:16,790 Because why would I pay out money for something 998 00:46:16,790 --> 00:46:21,340 that's going to be exactly the same, kind of discounted, cash 999 00:46:21,340 --> 00:46:22,964 flow back to right now? 1000 00:46:22,964 --> 00:46:24,380 ANDREW LO: So that's a good point. 1001 00:46:24,380 --> 00:46:25,550 Let me repeat the question. 1002 00:46:25,550 --> 00:46:27,844 The question's why-- in order for you to buy the stock, 1003 00:46:27,844 --> 00:46:29,260 would you have to assume that this 1004 00:46:29,260 --> 00:46:33,260 is wrong, or rather, that the market price is not 1005 00:46:33,260 --> 00:46:35,130 equal to this? 1006 00:46:35,130 --> 00:46:37,721 Well, the answer is no, you don't have to. 1007 00:46:37,721 --> 00:46:40,220 Although if you did, that would provide a motivation for you 1008 00:46:40,220 --> 00:46:42,200 to want to do that. 1009 00:46:42,200 --> 00:46:45,680 But it could be that you simply want the risk and reward 1010 00:46:45,680 --> 00:46:48,230 of this particular cash flow. 1011 00:46:48,230 --> 00:46:49,940 What's wrong with that? 1012 00:46:49,940 --> 00:46:52,640 Suppose that the security is fairly priced. 1013 00:46:52,640 --> 00:46:54,680 So this equation at the very bottom 1014 00:46:54,680 --> 00:46:56,900 says that the price of the security 1015 00:46:56,900 --> 00:47:00,350 is equal to the present value of all the future expected 1016 00:47:00,350 --> 00:47:06,320 cash flows discounted at the fair rate of return. 1017 00:47:06,320 --> 00:47:08,180 That's a perfectly reasonable thing 1018 00:47:08,180 --> 00:47:09,800 for somebody to want to invest in, 1019 00:47:09,800 --> 00:47:14,210 if they like that kind of risk/reward combination. 1020 00:47:14,210 --> 00:47:17,360 So some people want to put their money in Google, 1021 00:47:17,360 --> 00:47:20,510 and some people want to put their money in IBM, 1022 00:47:20,510 --> 00:47:23,654 and some people want to put their money in US Steel. 1023 00:47:23,654 --> 00:47:25,070 Those are different companies that 1024 00:47:25,070 --> 00:47:27,200 have different rates of return based 1025 00:47:27,200 --> 00:47:30,230 upon their different risks and cash flows, 1026 00:47:30,230 --> 00:47:33,970 and even if those things are fairly priced, 1027 00:47:33,970 --> 00:47:36,550 it's not like you're going to make no money. 1028 00:47:36,550 --> 00:47:40,180 You're going to make money based upon the fair market rate 1029 00:47:40,180 --> 00:47:42,460 of return for that security. 1030 00:47:42,460 --> 00:47:45,220 Now if you think you've got a better mousetrap, 1031 00:47:45,220 --> 00:47:47,950 and you can identify mispriced securities, 1032 00:47:47,950 --> 00:47:52,340 that gives you a whole another reason for investing. 1033 00:47:52,340 --> 00:47:54,980 But even without any mistakes being 1034 00:47:54,980 --> 00:47:58,892 made, even with if market prices are perfectly fair, 1035 00:47:58,892 --> 00:48:00,350 people want to invest, because they 1036 00:48:00,350 --> 00:48:03,320 want the return that those kind of investments 1037 00:48:03,320 --> 00:48:06,170 give them, right? 1038 00:48:06,170 --> 00:48:10,460 OK, so let's consider some simple cases. 1039 00:48:10,460 --> 00:48:13,010 In order for us to really make use of this formula, which 1040 00:48:13,010 --> 00:48:17,720 at this level of generality really is useless, 1041 00:48:17,720 --> 00:48:20,010 let's try to simplify and see what we get. 1042 00:48:20,010 --> 00:48:21,890 And we're going to simplify in the ways 1043 00:48:21,890 --> 00:48:23,180 that we've done before. 1044 00:48:23,180 --> 00:48:29,100 Let's assume that dividends are fixed throughout time, 1045 00:48:29,100 --> 00:48:33,050 and given by a number D, OK? 1046 00:48:33,050 --> 00:48:37,140 And let's assume that the risks don't change over time 1047 00:48:37,140 --> 00:48:42,130 and are given by a discount rate r. 1048 00:48:42,130 --> 00:48:48,800 Well, if you fix D and you fix r, magically, what you get 1049 00:48:48,800 --> 00:48:51,440 is that the price of the security 1050 00:48:51,440 --> 00:48:56,820 is equal to our old friend, the perpetuity formula, D over r, 1051 00:48:56,820 --> 00:48:57,650 OK? 1052 00:48:57,650 --> 00:48:59,180 Not that surprising. 1053 00:48:59,180 --> 00:49:01,460 If you have a constant stream of dividends, 1054 00:49:01,460 --> 00:49:04,420 with a constant discount rate, then the price 1055 00:49:04,420 --> 00:49:06,200 is equal to D over r. 1056 00:49:06,200 --> 00:49:09,500 Now, again, this may seem totally trivial to you, 1057 00:49:09,500 --> 00:49:13,490 but it does provide a very interesting observation. 1058 00:49:13,490 --> 00:49:16,340 Number one, the price of common stock 1059 00:49:16,340 --> 00:49:19,910 is an increasing function of the expected cash 1060 00:49:19,910 --> 00:49:22,410 flows in the form of future dividends. 1061 00:49:22,410 --> 00:49:26,630 So if you expect there to be higher dividends going forward, 1062 00:49:26,630 --> 00:49:28,160 the price should go up, and if you 1063 00:49:28,160 --> 00:49:30,500 expect lower dividends going forward, 1064 00:49:30,500 --> 00:49:31,590 the price should go down. 1065 00:49:31,590 --> 00:49:33,122 So that's a nice insight. 1066 00:49:33,122 --> 00:49:35,330 Another insight, though, is that the price of a stock 1067 00:49:35,330 --> 00:49:39,390 is inversely proportional to its discount rate. 1068 00:49:39,390 --> 00:49:42,140 If interest rates go up in general, 1069 00:49:42,140 --> 00:49:44,420 if interest rates go up, what should 1070 00:49:44,420 --> 00:49:46,568 happen to the stock price? 1071 00:49:46,568 --> 00:49:47,456 AUDIENCE: [INAUDIBLE] 1072 00:49:47,456 --> 00:49:48,940 ANDREW LO: Exactly, it should go down. 1073 00:49:48,940 --> 00:49:50,606 There are two ways of thinking about it. 1074 00:49:50,606 --> 00:49:53,680 One is that future cash flows are 1075 00:49:53,680 --> 00:49:57,490 going to have to be discounted at a higher price. 1076 00:49:57,490 --> 00:50:00,190 Or two, the demand for stocks will not 1077 00:50:00,190 --> 00:50:04,060 be as great, because now the opportunity for earning higher 1078 00:50:04,060 --> 00:50:07,570 return exists in other securities like bonds, 1079 00:50:07,570 --> 00:50:09,790 and so that will reduce the demand for stocks 1080 00:50:09,790 --> 00:50:14,460 and the price will come down, right? 1081 00:50:14,460 --> 00:50:17,630 So that's a very nice model, but we 1082 00:50:17,630 --> 00:50:19,970 can make it a little bit nicer by allowing 1083 00:50:19,970 --> 00:50:21,350 the dividends to grow. 1084 00:50:21,350 --> 00:50:23,750 So now suppose you have a growth company, a company 1085 00:50:23,750 --> 00:50:27,230 where the dividends are expected to grow at a rate of g 1086 00:50:27,230 --> 00:50:28,830 every period. 1087 00:50:28,830 --> 00:50:32,870 Well, then, once again, we have our old friend, the perpetuity, 1088 00:50:32,870 --> 00:50:35,420 with growing coupons, right? 1089 00:50:35,420 --> 00:50:39,170 D over r minus g. 1090 00:50:39,170 --> 00:50:42,580 And now, as I think I alluded to early on when 1091 00:50:42,580 --> 00:50:47,030 we went through this formula, we have in this very, very simple 1092 00:50:47,030 --> 00:50:52,210 expression one explanation for the technology 1093 00:50:52,210 --> 00:50:59,040 bubble, both how it got so big, and secondly, how it burst. 1094 00:50:59,040 --> 00:51:04,750 If r is close to g, if the growth rate is very large, 1095 00:51:04,750 --> 00:51:07,040 you're going to get a very big price. 1096 00:51:07,040 --> 00:51:13,520 And if there are rapid changes in what people expect g to be, 1097 00:51:13,520 --> 00:51:15,890 or what people estimate g to be, you 1098 00:51:15,890 --> 00:51:19,880 can get very rapid shocks in the level of prices, 1099 00:51:19,880 --> 00:51:25,720 including price one-ups and then crashes, right? 1100 00:51:25,720 --> 00:51:26,320 Yeah. 1101 00:51:26,320 --> 00:51:29,900 AUDIENCE: What kind of confuses me is that, I mean, yeah, 1102 00:51:29,900 --> 00:51:32,130 so is r greater than g? 1103 00:51:32,130 --> 00:51:34,010 And r greater than g is necessary 1104 00:51:34,010 --> 00:51:36,190 in order to get that [INAUDIBLE] efficient. 1105 00:51:36,190 --> 00:51:39,630 But is there any more meaning to that, 1106 00:51:39,630 --> 00:51:41,221 or is this just a mathematical thing? 1107 00:51:41,221 --> 00:51:42,720 ANDREW LO: There is meaning to that. 1108 00:51:42,720 --> 00:51:44,580 The meaning is actually quite simple, 1109 00:51:44,580 --> 00:51:46,260 and we alluded to it when we first 1110 00:51:46,260 --> 00:51:47,880 went through this formula. 1111 00:51:47,880 --> 00:51:51,030 Suppose that r were not greater than g. 1112 00:51:51,030 --> 00:51:53,854 Suppose r were less than g. 1113 00:51:53,854 --> 00:51:57,280 What that's telling you is that the rate of growth 1114 00:51:57,280 --> 00:52:00,160 of this security, or this cash flow, or this dividend, 1115 00:52:00,160 --> 00:52:05,350 the rate of growth is much faster than the interest rate, 1116 00:52:05,350 --> 00:52:06,400 all right? 1117 00:52:06,400 --> 00:52:10,990 So you've got wealth that's growing over time faster 1118 00:52:10,990 --> 00:52:14,950 than the interest rate, which means that if it really is true 1119 00:52:14,950 --> 00:52:17,740 that it'll last out into perpetuity, then 1120 00:52:17,740 --> 00:52:20,590 in very short order you should become bigger 1121 00:52:20,590 --> 00:52:24,065 than the entire planet's GDP, right? 1122 00:52:24,065 --> 00:52:26,440 Because you're going to be bigger than the interest rate. 1123 00:52:26,440 --> 00:52:29,050 So the rate at which assets in the future 1124 00:52:29,050 --> 00:52:31,540 are being deflated to the present 1125 00:52:31,540 --> 00:52:33,610 is actually less than the rate of what 1126 00:52:33,610 --> 00:52:35,260 you're growing your wealth. 1127 00:52:35,260 --> 00:52:39,860 Pretty soon, you're going to become richer than God himself, 1128 00:52:39,860 --> 00:52:41,500 and we know that that can't happen. 1129 00:52:41,500 --> 00:52:42,708 AUDIENCE: But isn't it that-- 1130 00:52:42,708 --> 00:52:45,970 I mean, so right now, the inflation rate 1131 00:52:45,970 --> 00:52:48,220 is greater than the interest rate, for example, right? 1132 00:52:48,220 --> 00:52:49,564 ANDREW LO: That's right now. 1133 00:52:49,564 --> 00:52:51,730 That's right now, but this is out of the perpetuity. 1134 00:52:51,730 --> 00:52:53,334 Do you believe that that's sustainable 1135 00:52:53,334 --> 00:52:54,250 out of the perpetuity? 1136 00:52:54,250 --> 00:52:54,819 AUDIENCE: No. 1137 00:52:54,819 --> 00:52:56,860 ANDREW LO: Well, then, this formula doesn't work. 1138 00:52:56,860 --> 00:53:01,240 This formula is a formula that's predicated on infinity, 1139 00:53:01,240 --> 00:53:03,872 not 10 years, not 20 years. 1140 00:53:03,872 --> 00:53:05,830 As we mentioned, when we went over the formula, 1141 00:53:05,830 --> 00:53:11,180 China has been growing at a rate of 10% for the last 15 years. 1142 00:53:11,180 --> 00:53:13,720 Do you think 10% growth rate is sustainable? 1143 00:53:13,720 --> 00:53:16,504 If China continues to grow at 10%, 1144 00:53:16,504 --> 00:53:18,670 pretty soon we're all going to be speaking Mandarin. 1145 00:53:18,670 --> 00:53:22,750 I mean, it's just not possible for a country 1146 00:53:22,750 --> 00:53:26,020 to both be reasonably-sized and not totally dominant, 1147 00:53:26,020 --> 00:53:27,940 and to have a rate of growth so much 1148 00:53:27,940 --> 00:53:30,160 larger than what can be sustained 1149 00:53:30,160 --> 00:53:31,860 over a long period of time. 1150 00:53:31,860 --> 00:53:33,160 And so that's the key. 1151 00:53:33,160 --> 00:53:35,430 This is a formula that's about infinity. 1152 00:53:35,430 --> 00:53:38,160 It's not about five years or 10 years. 1153 00:53:38,160 --> 00:53:39,800 OK, another question. 1154 00:53:39,800 --> 00:53:41,100 No. 1155 00:53:41,100 --> 00:53:45,630 OK, so in this case, the Gordon growth model 1156 00:53:45,630 --> 00:53:48,630 allows us to get an expression that tells us 1157 00:53:48,630 --> 00:53:52,320 if there are very, very significant growth 1158 00:53:52,320 --> 00:53:54,810 opportunities that can actually push up 1159 00:53:54,810 --> 00:53:57,450 the price of a stock dramatically. 1160 00:53:57,450 --> 00:54:00,750 If somehow all of us decide that those growth opportunities no 1161 00:54:00,750 --> 00:54:04,620 longer exist because we have new information, then boom, 1162 00:54:04,620 --> 00:54:06,600 it disappears, OK? 1163 00:54:06,600 --> 00:54:08,850 A good example of this is cold fusion. 1164 00:54:08,850 --> 00:54:11,540 I don't know how many of you remember, 15 or 20 years ago, 1165 00:54:11,540 --> 00:54:14,820 there was a big controversy about the Pons and Fleischmann 1166 00:54:14,820 --> 00:54:17,760 experiment, where they did an experiment where it seemed 1167 00:54:17,760 --> 00:54:21,520 like they generated heat, but heat not from a chemical 1168 00:54:21,520 --> 00:54:24,250 reaction, but from a nuclear reaction 1169 00:54:24,250 --> 00:54:26,890 in a standard laboratory setting. 1170 00:54:26,890 --> 00:54:30,580 And typically, you need very, very unusual conditions 1171 00:54:30,580 --> 00:54:33,610 to generate thermonuclear reactions that 1172 00:54:33,610 --> 00:54:35,320 can create that kind of heat. 1173 00:54:35,320 --> 00:54:40,780 Now in the end, they were discredited and, apparently, 1174 00:54:40,780 --> 00:54:43,750 although there's still controversy out there, 1175 00:54:43,750 --> 00:54:46,180 it doesn't seem like it was a nuclear reaction. 1176 00:54:46,180 --> 00:54:50,880 But if it were, if it was possible to generate 1177 00:54:50,880 --> 00:54:55,830 a nuclear reaction at room temperature, what that could 1178 00:54:55,830 --> 00:55:00,550 have meant is that it would eliminate 1179 00:55:00,550 --> 00:55:02,770 all of the energy problems of the world, 1180 00:55:02,770 --> 00:55:06,580 because you'd be able to run your car on tap water. 1181 00:55:06,580 --> 00:55:09,550 And the amount of energy in an ounce of tap water 1182 00:55:09,550 --> 00:55:13,100 is enough to fuel your car for about a year. 1183 00:55:13,100 --> 00:55:14,320 So think about it. 1184 00:55:14,320 --> 00:55:19,176 If that technology really worked to have worked out, 1185 00:55:19,176 --> 00:55:21,050 what do you think the value of that would be? 1186 00:55:21,050 --> 00:55:23,150 What's the g in that case? 1187 00:55:23,150 --> 00:55:25,550 And you can understand why people 1188 00:55:25,550 --> 00:55:29,960 would have invested hundreds of billions of dollars 1189 00:55:29,960 --> 00:55:31,550 into that kind of an opportunity, 1190 00:55:31,550 --> 00:55:34,730 if it were, in fact, a real opportunity. 1191 00:55:34,730 --> 00:55:37,820 There was a short time where we didn't know, 1192 00:55:37,820 --> 00:55:41,740 and during that time, r minus g looked pretty small. 1193 00:55:41,740 --> 00:55:45,230 g looked big relative to r, all right. 1194 00:55:45,230 --> 00:55:49,190 And so that created very, very large swings 1195 00:55:49,190 --> 00:55:52,599 in prices of both traditional energy companies 1196 00:55:52,599 --> 00:55:53,390 like oil companies. 1197 00:55:53,390 --> 00:55:55,730 You can imagine what oil companies would be worth 1198 00:55:55,730 --> 00:55:58,820 if we figured out how to run cars on water, right? 1199 00:55:58,820 --> 00:56:03,470 That would maybe be justifiable in light of how much they've 1200 00:56:03,470 --> 00:56:05,220 made over the years. 1201 00:56:05,220 --> 00:56:08,570 But the point is that it creates enormous opportunity 1202 00:56:08,570 --> 00:56:12,080 and potential dislocation so that the expectations 1203 00:56:12,080 --> 00:56:14,240 of the market matter a great deal, and this is why. 1204 00:56:14,240 --> 00:56:17,520 This is how it actually gets incorporated. 1205 00:56:17,520 --> 00:56:19,820 Now I'm going to take that equation 1206 00:56:19,820 --> 00:56:23,030 and turn it around, turn it on its head, 1207 00:56:23,030 --> 00:56:25,490 and it'll give us another insight into how 1208 00:56:25,490 --> 00:56:32,720 to think about the discount rate and the value of corporations. 1209 00:56:32,720 --> 00:56:36,980 If the price of a stock today is given by D over r minus g, 1210 00:56:36,980 --> 00:56:42,620 then I can flip things around and say that r minus g 1211 00:56:42,620 --> 00:56:44,990 is equal to D over P, right? 1212 00:56:44,990 --> 00:56:52,910 The dividend price ratio is equal to r minus g, or r-- 1213 00:56:52,910 --> 00:56:56,690 the discount rate that I'm using for the cash flows-- 1214 00:56:56,690 --> 00:57:02,330 is given by the dividend yield plus the rate of growth 1215 00:57:02,330 --> 00:57:08,440 implicit in that company's investment opportunity set. 1216 00:57:08,440 --> 00:57:09,920 Now why is this interesting? 1217 00:57:09,920 --> 00:57:12,160 Well, in order for you to understand 1218 00:57:12,160 --> 00:57:14,080 the importance of this expression, 1219 00:57:14,080 --> 00:57:17,230 you have to realize that, for many years, 1220 00:57:17,230 --> 00:57:21,580 stock analysts would look at a company's discount rate 1221 00:57:21,580 --> 00:57:26,600 or cost of capital by simply using the dividend yield. 1222 00:57:26,600 --> 00:57:29,470 So in the exact same way that if you have a bond, 1223 00:57:29,470 --> 00:57:32,320 and you see what the coupons are, and you take the coupon 1224 00:57:32,320 --> 00:57:34,810 and divide it by the price, that gives you 1225 00:57:34,810 --> 00:57:39,160 a sense of what your rate of return is over a given period. 1226 00:57:39,160 --> 00:57:41,650 When you look at a stock, and you want to ask the question, 1227 00:57:41,650 --> 00:57:43,390 how much am I earning on that stock? 1228 00:57:43,390 --> 00:57:46,000 What is the rate of return on that stock for me, 1229 00:57:46,000 --> 00:57:47,130 the investor? 1230 00:57:47,130 --> 00:57:49,550 You take the dividends that you get paid every quarter, 1231 00:57:49,550 --> 00:57:50,650 and you take that dividend and you divide it 1232 00:57:50,650 --> 00:57:52,060 by the stock price, and that gives you 1233 00:57:52,060 --> 00:57:53,170 a sort of rate of return, right? 1234 00:57:53,170 --> 00:57:54,545 Because if you think about buying 1235 00:57:54,545 --> 00:57:58,210 the stock for a price, P, and then getting cash flows of D 1236 00:57:58,210 --> 00:58:01,540 every quarter, or every period, then your yield, 1237 00:58:01,540 --> 00:58:04,180 your rate of return, is D over P. 1238 00:58:04,180 --> 00:58:09,010 That's called the dividend price ratio, or dividend yield. 1239 00:58:09,010 --> 00:58:11,140 What this expression says is something 1240 00:58:11,140 --> 00:58:15,430 that every MIT graduate knows in his or her heart, which 1241 00:58:15,430 --> 00:58:19,180 is that technology adds value above 1242 00:58:19,180 --> 00:58:22,270 and beyond what you observe in current cash flows. 1243 00:58:22,270 --> 00:58:26,080 It's not just the dividend that gives a company value, 1244 00:58:26,080 --> 00:58:29,720 it's the ability for companies to grow over time. 1245 00:58:29,720 --> 00:58:32,320 It's not just the company's current plant and equipment 1246 00:58:32,320 --> 00:58:34,420 and operations that give it value, 1247 00:58:34,420 --> 00:58:38,530 it is all of the interesting, wonderful, innovative, creative 1248 00:58:38,530 --> 00:58:41,440 ideas that are locked up in that company that 1249 00:58:41,440 --> 00:58:43,480 may one day be implemented and allow 1250 00:58:43,480 --> 00:58:46,660 it to grow far beyond the founders' wildest dreams. 1251 00:58:46,660 --> 00:58:49,150 That also has to be factored into the rate of return 1252 00:58:49,150 --> 00:58:50,540 of the company. 1253 00:58:50,540 --> 00:58:54,220 And this simple little dividend yield model tells us this. 1254 00:58:54,220 --> 00:58:57,130 It says that the required rate of return, 1255 00:58:57,130 --> 00:59:00,320 the risk-adjusted discount rate, the cost of capital, the user 1256 00:59:00,320 --> 00:59:03,750 cost, whatever you want to call it, this r, 1257 00:59:03,750 --> 00:59:05,290 has two pieces to it. 1258 00:59:05,290 --> 00:59:10,140 One is the cash that you get on a regular basis, the dividends 1259 00:59:10,140 --> 00:59:13,600 that the current operations generate, 1260 00:59:13,600 --> 00:59:21,770 plus the growth opportunities of those dividends 1261 00:59:21,770 --> 00:59:25,680 out into the infinite future, OK? 1262 00:59:25,680 --> 00:59:29,180 Now remember, the way that we structured this dividend 1263 00:59:29,180 --> 00:59:33,140 payment, the way that we had our formula set up, 1264 00:59:33,140 --> 00:59:35,090 the dividends are the dividends that get 1265 00:59:35,090 --> 00:59:37,400 paid next period, right? 1266 00:59:37,400 --> 00:59:40,290 If you go back and look at the formula, 1267 00:59:40,290 --> 00:59:45,590 this is the price today, and it's 1268 00:59:45,590 --> 00:59:49,280 given by the dividends paid at time t plus 1. 1269 00:59:49,280 --> 00:59:52,160 So this price that I'm using in my notation 1270 00:59:52,160 --> 00:59:55,850 is the current ex-dividend price, 1271 00:59:55,850 --> 00:59:59,740 meaning this period's dividend has been paid already, 1272 00:59:59,740 --> 01:00:02,710 and now the value to this piece of paper 1273 01:00:02,710 --> 01:00:08,950 is the future dividend, starting next period, t plus 1. 1274 01:00:08,950 --> 01:00:15,290 So when I say D is fixed, it's fixed, 1275 01:00:15,290 --> 01:00:19,460 but it's getting paid next period, OK? 1276 01:00:19,460 --> 01:00:23,660 So in this expression, this D is actually 1277 01:00:23,660 --> 01:00:26,460 next period's dividend. 1278 01:00:26,460 --> 01:00:28,530 But remember that when I'm trying 1279 01:00:28,530 --> 01:00:32,700 to value the company today, I don't observe next period's 1280 01:00:32,700 --> 01:00:35,040 dividend, which is random, but I know how much was just 1281 01:00:35,040 --> 01:00:38,270 paid in the most recent period. 1282 01:00:38,270 --> 01:00:41,677 So if I want to use D, and there's growth, 1283 01:00:41,677 --> 01:00:44,260 I actually have to take the most recent dividend, the one that 1284 01:00:44,260 --> 01:00:47,890 just got paid, and multiply that by 1 plus g 1285 01:00:47,890 --> 01:00:51,400 to get the value of next period's dividend. 1286 01:00:51,400 --> 01:00:55,516 So that's why this expression I've corrected-- 1287 01:00:55,516 --> 01:00:56,890 not corrected, it's not that it's 1288 01:00:56,890 --> 01:01:00,880 wrong-- it's just I've changed the expression so that it 1289 01:01:00,880 --> 01:01:05,680 is D sub 0, which is the most recent dividend that was just 1290 01:01:05,680 --> 01:01:11,010 paid multiplied by 1 plus g divided by P. 1291 01:01:11,010 --> 01:01:11,950 So I just do that-- 1292 01:01:11,950 --> 01:01:13,950 if you want to use this formula, and by the way, 1293 01:01:13,950 --> 01:01:15,750 you can actually go out and use this now. 1294 01:01:15,750 --> 01:01:17,458 I would actually encourage you to use it. 1295 01:01:17,458 --> 01:01:19,590 Go out and take a look at your favorite stock, 1296 01:01:19,590 --> 01:01:21,360 and take a look at its dividend yield. 1297 01:01:21,360 --> 01:01:23,850 You can find it on yahoofinance.com as well as 1298 01:01:23,850 --> 01:01:25,320 other web sites. 1299 01:01:25,320 --> 01:01:29,880 And then you make a guess as to what the appropriate growth 1300 01:01:29,880 --> 01:01:33,210 rate is, and try to figure out whether it 1301 01:01:33,210 --> 01:01:35,760 fits this equation, OK? 1302 01:01:35,760 --> 01:01:38,040 You can observe dividends. 1303 01:01:38,040 --> 01:01:40,740 You can observe today's price. 1304 01:01:40,740 --> 01:01:43,080 And you have to make an assumption about what 1305 01:01:43,080 --> 01:01:44,430 you think the growth rate is. 1306 01:01:44,430 --> 01:01:46,740 And when you plug that in, that will give you 1307 01:01:46,740 --> 01:01:49,080 an estimate of what the cost of capital 1308 01:01:49,080 --> 01:01:51,430 is for that particular company. 1309 01:01:51,430 --> 01:01:51,930 Yeah. 1310 01:01:51,930 --> 01:01:55,470 AUDIENCE: So like this exercise without the [INAUDIBLE],, 1311 01:01:55,470 --> 01:01:59,560 with just the perpetuity formula, D over r, incurs-- 1312 01:01:59,560 --> 01:02:01,500 I mean, every stock that I look at 1313 01:02:01,500 --> 01:02:07,290 seems to be more than the dividends divided by-- 1314 01:02:07,290 --> 01:02:08,490 ANDREW LO: That's right. 1315 01:02:08,490 --> 01:02:09,720 Exactly. 1316 01:02:09,720 --> 01:02:12,006 That's because why? 1317 01:02:12,006 --> 01:02:14,850 Why is it, if you just use D over P, 1318 01:02:14,850 --> 01:02:17,490 every single stock looks like it's overvalued. 1319 01:02:17,490 --> 01:02:18,446 What are you missing? 1320 01:02:18,446 --> 01:02:18,832 AUDIENCE: g. 1321 01:02:18,832 --> 01:02:19,873 ANDREW LO: Yeah, exactly. 1322 01:02:19,873 --> 01:02:20,970 Right, you're missing g. 1323 01:02:20,970 --> 01:02:25,580 AUDIENCE: But then g turns out to be higher than r, right? 1324 01:02:25,580 --> 01:02:27,040 ANDREW LO: Well, no, no, no. 1325 01:02:27,040 --> 01:02:27,810 How did you get r? 1326 01:02:27,810 --> 01:02:28,250 AUDIENCE: OK, OK. 1327 01:02:28,250 --> 01:02:28,850 We don't know r 1328 01:02:28,850 --> 01:02:29,975 ANDREW LO: We don't know r. 1329 01:02:29,975 --> 01:02:32,060 That's what we're trying to figure out, right? 1330 01:02:32,060 --> 01:02:34,961 So you just said you're looking at D over P, 1331 01:02:34,961 --> 01:02:36,710 and you're trying to figure out implicitly 1332 01:02:36,710 --> 01:02:40,740 what that implies for the growth rate of stocks. 1333 01:02:40,740 --> 01:02:44,179 Take a look at this expression in light of future growth 1334 01:02:44,179 --> 01:02:46,470 opportunities and you'll see that dividend yield is not 1335 01:02:46,470 --> 01:02:47,400 the only story. 1336 01:02:47,400 --> 01:02:50,190 You've got to use other expressions. 1337 01:02:50,190 --> 01:02:50,861 Yeah. 1338 01:02:50,861 --> 01:02:53,266 AUDIENCE: So looking at that [INAUDIBLE] about it 1339 01:02:53,266 --> 01:02:57,120 on an annualized basis or between dividend payment? 1340 01:02:57,120 --> 01:02:59,790 ANDREW LO: Well it should be on an annualized-- well, 1341 01:02:59,790 --> 01:03:03,042 it should be on whatever cycle the dividends get paid. 1342 01:03:03,042 --> 01:03:04,500 So if dividends get paid quarterly, 1343 01:03:04,500 --> 01:03:06,210 then it's a quarterly growth rate. 1344 01:03:06,210 --> 01:03:08,940 If it's an annual payment, then it's an annual growth rate. 1345 01:03:08,940 --> 01:03:11,040 So the benefit of this expression 1346 01:03:11,040 --> 01:03:13,870 is that there is no timing that's been assumed. 1347 01:03:13,870 --> 01:03:17,040 It's just whatever the periods are. 1348 01:03:17,040 --> 01:03:21,976 So if it's quarterly dividends, use quarterly growth rate. 1349 01:03:21,976 --> 01:03:22,600 Yeah, question. 1350 01:03:22,600 --> 01:03:25,001 AUDIENCE: We can't just go out and use this model 1351 01:03:25,001 --> 01:03:26,925 on just about any company, right? 1352 01:03:26,925 --> 01:03:28,820 Doesn't the company have to, I guess, 1353 01:03:28,820 --> 01:03:31,110 pay dividends and use dividends as, perhaps, 1354 01:03:31,110 --> 01:03:34,455 a way to represent the [INAUDIBLE] of the company? 1355 01:03:34,455 --> 01:03:35,330 ANDREW LO: Well, yes. 1356 01:03:35,330 --> 01:03:37,820 So if it doesn't have dividends, then this formula 1357 01:03:37,820 --> 01:03:39,920 is not going to be all that interesting, right? 1358 01:03:39,920 --> 01:03:41,150 D's going to be 0. 1359 01:03:41,150 --> 01:03:43,400 But remember, this is not the current D. 1360 01:03:43,400 --> 01:03:47,660 This is the steady state D. And if companies 1361 01:03:47,660 --> 01:03:49,820 are in the early part of their growth phase, 1362 01:03:49,820 --> 01:03:52,153 it's going to be hard to estimate what that steady state 1363 01:03:52,153 --> 01:03:52,679 D is. 1364 01:03:52,679 --> 01:03:54,470 So there'll be other expressions that we're 1365 01:03:54,470 --> 01:03:56,420 going to derive in a few minutes, 1366 01:03:56,420 --> 01:03:59,420 where we use accounting identities to relate dividends 1367 01:03:59,420 --> 01:04:02,180 to earnings or to cash flows. 1368 01:04:02,180 --> 01:04:04,730 It used to be the case that instead of using dividends, 1369 01:04:04,730 --> 01:04:06,380 you would use earnings, because even 1370 01:04:06,380 --> 01:04:08,840 though companies that don't pay out dividends, 1371 01:04:08,840 --> 01:04:10,940 they still have earnings. 1372 01:04:10,940 --> 01:04:13,840 Well, that is until the internet came about, right? 1373 01:04:13,840 --> 01:04:17,260 Then you had companies that actually had no earnings. 1374 01:04:17,260 --> 01:04:20,320 So how do you valuate a company that has no dividends 1375 01:04:20,320 --> 01:04:22,750 and has no earnings, and has negative cash flows? 1376 01:04:22,750 --> 01:04:25,390 In fact, if you use those models, the more negative 1377 01:04:25,390 --> 01:04:27,610 the cash flow, the higher the value. 1378 01:04:27,610 --> 01:04:30,280 So something weird is going on. 1379 01:04:30,280 --> 01:04:32,260 It has to do with the fact that these 1380 01:04:32,260 --> 01:04:35,230 are meant to be steady state formulas, and not 1381 01:04:35,230 --> 01:04:37,900 formulas for individual time periods. 1382 01:04:37,900 --> 01:04:39,820 If there are individual time periods where 1383 01:04:39,820 --> 01:04:42,460 you have zero cash flows or negative cash flows because 1384 01:04:42,460 --> 01:04:45,400 of growth, you'll have to make adjustments in the formulas, 1385 01:04:45,400 --> 01:04:47,495 and I'll show you how to do that in a few minutes. 1386 01:04:47,495 --> 01:04:47,994 Yeah. 1387 01:04:47,994 --> 01:04:49,785 AUDIENCE: Do you have to change the formula 1388 01:04:49,785 --> 01:04:53,980 if, let's say, the board decides to change dividend [INAUDIBLE]?? 1389 01:04:53,980 --> 01:04:56,140 ANDREW LO: Well, again, this formula 1390 01:04:56,140 --> 01:04:58,390 is really meant to be steady state dividends, right. 1391 01:04:58,390 --> 01:05:01,420 So if they change the dividends, what you should not use 1392 01:05:01,420 --> 01:05:02,290 is this. 1393 01:05:02,290 --> 01:05:04,420 What you should go back and use, which 1394 01:05:04,420 --> 01:05:06,880 is going to be a bit more complicated, 1395 01:05:06,880 --> 01:05:10,720 is this, the bottom equation, right? 1396 01:05:10,720 --> 01:05:13,250 So this equation is always correct, 1397 01:05:13,250 --> 01:05:14,770 because this is completely general. 1398 01:05:14,770 --> 01:05:17,510 Dividends at time t plus k out into the future. 1399 01:05:17,510 --> 01:05:21,100 And so if you know the future path of dividends, 1400 01:05:21,100 --> 01:05:24,610 or if you have an expectation of what that future path is, 1401 01:05:24,610 --> 01:05:26,060 you can use this formula. 1402 01:05:26,060 --> 01:05:28,240 But look how difficult this is. 1403 01:05:28,240 --> 01:05:30,730 I mean, think about how an equity analyst 1404 01:05:30,730 --> 01:05:33,324 has to make his living. 1405 01:05:33,324 --> 01:05:34,990 They've got to figure out, not only what 1406 01:05:34,990 --> 01:05:37,850 the appropriate discount rate is, which is hard enough, 1407 01:05:37,850 --> 01:05:39,350 but they've going to figure out what 1408 01:05:39,350 --> 01:05:41,890 the appropriate path of dividends are, 1409 01:05:41,890 --> 01:05:45,550 not just what the dividends will be in steady state, 1410 01:05:45,550 --> 01:05:48,100 because they may not be able to do that. 1411 01:05:48,100 --> 01:05:50,260 They may want to figure out what the dividends are 1412 01:05:50,260 --> 01:05:53,080 going to be next year, the year after, the year after that. 1413 01:05:53,080 --> 01:05:55,200 So there's a lot of work to be done. 1414 01:05:55,200 --> 01:05:55,700 It's hard. 1415 01:05:55,700 --> 01:05:57,220 It's hard work. 1416 01:05:57,220 --> 01:06:00,220 But more importantly, it's not just hard work, 1417 01:06:00,220 --> 01:06:02,527 it's actually very inaccurate work. 1418 01:06:02,527 --> 01:06:04,360 In other words, it's really hard to estimate 1419 01:06:04,360 --> 01:06:06,860 this thing with any degree of accuracy, so what do you know? 1420 01:06:06,860 --> 01:06:09,390 You know you're going to be wrong most of the time. 1421 01:06:09,390 --> 01:06:15,080 Imagine a job where you go into the job knowing that if you do 1422 01:06:15,080 --> 01:06:17,510 really well, you're a genius. 1423 01:06:17,510 --> 01:06:19,010 You're at the top of your class. 1424 01:06:19,010 --> 01:06:22,850 You're the best that's ever done this thing. 1425 01:06:22,850 --> 01:06:27,510 And in that case, you're going to be right 52% of the time. 1426 01:06:27,510 --> 01:06:29,100 52% of the time. 1427 01:06:29,100 --> 01:06:31,680 That means you're wrong 48% of the time. 1428 01:06:31,680 --> 01:06:33,180 That's pretty discouraging. 1429 01:06:33,180 --> 01:06:35,790 But that's really the nature of this task. 1430 01:06:35,790 --> 01:06:37,020 It's really hard. 1431 01:06:37,020 --> 01:06:40,110 You know, it's like trying to do weather forecasting, 1432 01:06:40,110 --> 01:06:43,440 but weather forecasting over the next 30 years, 1433 01:06:43,440 --> 01:06:46,140 and then taking the sum total of all of those decisions, 1434 01:06:46,140 --> 01:06:48,300 putting it into a portfolio, and then investing 1435 01:06:48,300 --> 01:06:51,100 your life savings in that. 1436 01:06:51,100 --> 01:06:52,850 That's kind of tough, right? 1437 01:06:52,850 --> 01:06:54,670 But it's also exciting. 1438 01:06:54,670 --> 01:06:57,470 Yeah, question? 1439 01:06:57,470 --> 01:06:59,010 OK, oh yes. 1440 01:06:59,010 --> 01:07:05,494 AUDIENCE: [INAUDIBLE] If dividend 1441 01:07:05,494 --> 01:07:07,478 is going to change in the future, 1442 01:07:07,478 --> 01:07:11,942 wouldn't this formula be likened to the annuity equation? 1443 01:07:11,942 --> 01:07:15,117 So that point in time when it changes, for which-- 1444 01:07:15,117 --> 01:07:15,950 [INTERPOSING VOICES] 1445 01:07:15,950 --> 01:07:18,810 ANDREW LO: You would use the annuity discount formula 1446 01:07:18,810 --> 01:07:20,050 in pieces. 1447 01:07:20,050 --> 01:07:23,790 So for example, if the cash flows for the first 10 years 1448 01:07:23,790 --> 01:07:26,370 look like one thing, and then the next 20 years 1449 01:07:26,370 --> 01:07:27,764 look like another thing, and then 1450 01:07:27,764 --> 01:07:30,180 the next 30 years look like something else, what you could 1451 01:07:30,180 --> 01:07:35,169 do is apply the annuity discount formula to the first 10 years, 1452 01:07:35,169 --> 01:07:36,960 and then apply the annuity discount formula 1453 01:07:36,960 --> 01:07:39,480 with a different discount rate and a different cash flow 1454 01:07:39,480 --> 01:07:42,330 to the next 20, and then discount that back and then 1455 01:07:42,330 --> 01:07:44,290 discount that back 10 more years, 1456 01:07:44,290 --> 01:07:48,030 and then do that to the next 30, and then discount it back 1457 01:07:48,030 --> 01:07:49,020 to the very beginning. 1458 01:07:49,020 --> 01:07:50,550 So exactly. 1459 01:07:50,550 --> 01:07:54,510 That's the way to do it, which is effectively doing it 1460 01:07:54,510 --> 01:07:58,470 like this, but it's hard. 1461 01:07:58,470 --> 01:08:03,750 I mean, it's hard enough to estimate cash flows next year. 1462 01:08:03,750 --> 01:08:06,060 And I can tell you there are a lot of firms 1463 01:08:06,060 --> 01:08:09,695 that have forecasted this year's cash flows last year are 1464 01:08:09,695 --> 01:08:11,070 scratching their heads, wondering 1465 01:08:11,070 --> 01:08:13,050 how they can be so far off. 1466 01:08:13,050 --> 01:08:17,580 Now imagine doing it 30 years hence. 1467 01:08:17,580 --> 01:08:20,430 I mean, it's an impossible task. 1468 01:08:20,430 --> 01:08:23,374 But at the end of the day, it has to be done. 1469 01:08:23,374 --> 01:08:26,040 In other words, whether you want to make those forecasts or not, 1470 01:08:26,040 --> 01:08:28,327 people are going to trade your stock. 1471 01:08:28,327 --> 01:08:30,160 And so if you're not making those forecasts, 1472 01:08:30,160 --> 01:08:32,160 well, somebody else is going to, because they've 1473 01:08:32,160 --> 01:08:33,569 got to trade the stock. 1474 01:08:33,569 --> 01:08:35,520 So what we want to do is to figure out 1475 01:08:35,520 --> 01:08:39,510 a slightly better mousetrap of understanding what 1476 01:08:39,510 --> 01:08:41,729 those forecasts are telling us. 1477 01:08:41,729 --> 01:08:46,760 And if we can literally get 52% correct rates, 1478 01:08:46,760 --> 01:08:49,609 we're going to be rich beyond our wildest expectations. 1479 01:08:49,609 --> 01:08:51,481 That's really hard to do. 1480 01:08:51,481 --> 01:08:53,689 And it's just the nature of this particular endeavor. 1481 01:08:53,689 --> 01:08:57,620 It's very difficult to estimate cash flows, discount rates, 1482 01:08:57,620 --> 01:09:02,984 and risk conditions so far out into the future. 1483 01:09:02,984 --> 01:09:04,427 Question, yes. 1484 01:09:04,427 --> 01:09:06,806 AUDIENCE: You said we could use this formula to calculate 1485 01:09:06,806 --> 01:09:09,770 the firm's cost of capital. 1486 01:09:09,770 --> 01:09:11,859 I'm wondering why would we do that? 1487 01:09:11,859 --> 01:09:13,760 Why do I care about the firm's cost? 1488 01:09:13,760 --> 01:09:16,729 I think it's much more interesting to calculate 1489 01:09:16,729 --> 01:09:18,651 the growth rate [INAUDIBLE]. 1490 01:09:18,651 --> 01:09:21,109 ANDREW LO: Well, in order to calculate the cost of capital, 1491 01:09:21,109 --> 01:09:22,468 you need the growth rate. 1492 01:09:22,468 --> 01:09:27,630 AUDIENCE: OK but, I mean, I think 1493 01:09:27,630 --> 01:09:29,799 it's easier to get the cost of capital 1494 01:09:29,799 --> 01:09:32,250 and guess the growth rate. 1495 01:09:32,250 --> 01:09:35,387 I just don't understand why I would be interested in getting 1496 01:09:35,387 --> 01:09:36,696 to know this firm's cost-- 1497 01:09:36,696 --> 01:09:38,279 ANDREW LO: In the cost of capital, OK. 1498 01:09:38,279 --> 01:09:42,359 Well, you would have to wait about another seven lectures 1499 01:09:42,359 --> 01:09:45,132 for that, because there is a reason why you care 1500 01:09:45,132 --> 01:09:46,590 about the cost of capital, and that 1501 01:09:46,590 --> 01:09:50,850 is that if you're trying to decide how to spend your firm's 1502 01:09:50,850 --> 01:09:55,140 money, if you're a CFO and you're allocating cash 1503 01:09:55,140 --> 01:09:57,450 across different activities, you need 1504 01:09:57,450 --> 01:10:00,000 to know what your firm's cost of capital 1505 01:10:00,000 --> 01:10:02,940 is so that you get a sense of what the opportunity cost 1506 01:10:02,940 --> 01:10:04,980 versus taking that money and investing it 1507 01:10:04,980 --> 01:10:07,960 in other opportunities outside the firm. 1508 01:10:07,960 --> 01:10:10,290 So in order to make decisions, you need that number. 1509 01:10:10,290 --> 01:10:13,650 AUDIENCE: If I'm in [INAUDIBLE],, as an investor outside, 1510 01:10:13,650 --> 01:10:16,380 like, looking at the stock market, [INAUDIBLE]?? 1511 01:10:16,380 --> 01:10:17,922 ANDREW LO: Well, you do, in the sense 1512 01:10:17,922 --> 01:10:19,671 that you want to know whether you're going 1513 01:10:19,671 --> 01:10:20,770 to get your money's worth. 1514 01:10:20,770 --> 01:10:23,910 I mean, if you're investing in one company versus another, 1515 01:10:23,910 --> 01:10:25,530 in order to make that decision, you 1516 01:10:25,530 --> 01:10:28,130 need to know what the rate of return is, right? 1517 01:10:28,130 --> 01:10:30,270 So it's actually quite important. 1518 01:10:30,270 --> 01:10:32,540 It's very important for decision-making 1519 01:10:32,540 --> 01:10:34,322 what that number is. 1520 01:10:34,322 --> 01:10:35,530 AUDIENCE: Right after return. 1521 01:10:35,530 --> 01:10:37,350 It's not cost of capital. 1522 01:10:37,350 --> 01:10:39,432 If I look it that way. 1523 01:10:39,432 --> 01:10:41,390 ANDREW LO: So let's call it the rate of return. 1524 01:10:41,390 --> 01:10:42,520 That's right, yeah. 1525 01:10:42,520 --> 01:10:45,560 Well, and by the way, the reason that I always 1526 01:10:45,560 --> 01:10:48,140 use four or five names for the same quantity 1527 01:10:48,140 --> 01:10:50,777 is to sensitize you to the fact that people 1528 01:10:50,777 --> 01:10:52,860 look at these numbers from different perspectives. 1529 01:10:52,860 --> 01:10:55,800 So when I use the term cost of capital, 1530 01:10:55,800 --> 01:10:58,380 I'm thinking about it as a corporate manager who 1531 01:10:58,380 --> 01:11:01,050 has internal funds that are going to be deployed 1532 01:11:01,050 --> 01:11:02,490 in different activities. 1533 01:11:02,490 --> 01:11:09,060 And the cost of that capital as a CFO is given by r. 1534 01:11:09,060 --> 01:11:11,790 Now as an investor external to the company, 1535 01:11:11,790 --> 01:11:13,960 I'm thinking about how to invest my money. 1536 01:11:13,960 --> 01:11:16,920 I want to know what my rate of return is. 1537 01:11:16,920 --> 01:11:21,060 And as a regulator that wants to understand 1538 01:11:21,060 --> 01:11:23,670 what the appropriate capital charge is 1539 01:11:23,670 --> 01:11:26,460 for different kinds of activities that are going 1540 01:11:26,460 --> 01:11:28,980 to be appropriate for borrowing and lending, 1541 01:11:28,980 --> 01:11:32,730 I also need to know what the appropriate risk adjustments 1542 01:11:32,730 --> 01:11:34,930 are to that particular number. 1543 01:11:34,930 --> 01:11:36,650 Yeah. 1544 01:11:36,650 --> 01:11:40,350 AUDIENCE: I was wondering how frequently 1545 01:11:40,350 --> 01:11:43,760 the companies actually change their dividend policy. 1546 01:11:43,760 --> 01:11:45,530 Is it every year, every few years? 1547 01:11:45,530 --> 01:11:48,290 And also are there exceptions? 1548 01:11:48,290 --> 01:11:51,290 Like is there a reason sometimes where 1549 01:11:51,290 --> 01:11:54,190 a company who is, like, growing to issue dividends, 1550 01:11:54,190 --> 01:11:57,320 or for a company that's got a lot of cash to not do so? 1551 01:11:57,320 --> 01:11:59,400 ANDREW LO: So that's a great question. 1552 01:11:59,400 --> 01:12:02,030 The question is how companies set their dividend policy. 1553 01:12:02,030 --> 01:12:04,550 The short answer is that companies 1554 01:12:04,550 --> 01:12:09,980 don't like to pay dividends unless they know for a fact 1555 01:12:09,980 --> 01:12:14,760 that they can maintain the level for a good long period of time. 1556 01:12:14,760 --> 01:12:16,460 And the reason is simple. 1557 01:12:16,460 --> 01:12:20,840 When a company cuts dividends, that's considered bad news. 1558 01:12:20,840 --> 01:12:23,570 No matter how you slice it, when a company decides 1559 01:12:23,570 --> 01:12:27,560 to reduce its dividends, the typical response is uh oh, it's 1560 01:12:27,560 --> 01:12:31,250 cash-strapped, or it's in trouble, there's a problem. 1561 01:12:31,250 --> 01:12:34,280 So once you know that, then as a corporate financial-- 1562 01:12:34,280 --> 01:12:35,900 chief financial officer-- 1563 01:12:35,900 --> 01:12:37,520 you will not recommend to the board 1564 01:12:37,520 --> 01:12:41,330 to cut dividends unless there's a really significant issue 1565 01:12:41,330 --> 01:12:42,200 with the firm. 1566 01:12:42,200 --> 01:12:44,690 And therefore, as a result, you're 1567 01:12:44,690 --> 01:12:47,720 not going to either pay or raise dividends 1568 01:12:47,720 --> 01:12:50,030 unless you think you can support that level 1569 01:12:50,030 --> 01:12:52,550 for a good long time. 1570 01:12:52,550 --> 01:12:54,560 So because of that reason, you're right, 1571 01:12:54,560 --> 01:12:57,560 dividends don't get changed very often. 1572 01:12:57,560 --> 01:13:01,100 And actually, it's quite costly in some senses 1573 01:13:01,100 --> 01:13:03,044 to change that dividend policy, not just 1574 01:13:03,044 --> 01:13:05,210 from the corporate perspective, but from shareholder 1575 01:13:05,210 --> 01:13:05,780 perception. 1576 01:13:05,780 --> 01:13:07,113 AUDIENCE: What about exceptions? 1577 01:13:07,113 --> 01:13:10,080 Like why would a company currently 1578 01:13:10,080 --> 01:13:12,200 do something that is different from-- 1579 01:13:12,200 --> 01:13:14,280 ANDREW LO: There are exceptions because 1580 01:13:14,280 --> 01:13:16,770 of certain circumstances that are unique to the company. 1581 01:13:16,770 --> 01:13:19,800 For example, a company could be in a cash crunch, 1582 01:13:19,800 --> 01:13:22,560 like, right now, because of some kind of capital charge 1583 01:13:22,560 --> 01:13:27,660 due to a certain underperforming securities, in which case 1584 01:13:27,660 --> 01:13:32,190 they may declare a temporary suspension of dividends. 1585 01:13:32,190 --> 01:13:34,440 The other side of the equation is that a company 1586 01:13:34,440 --> 01:13:35,920 may have gotten a big windfall. 1587 01:13:35,920 --> 01:13:38,156 They just decided to sell a division, 1588 01:13:38,156 --> 01:13:39,780 and they've got a large amount of cash. 1589 01:13:39,780 --> 01:13:41,220 They don't know what to do with all the cash, 1590 01:13:41,220 --> 01:13:43,140 so what they'll do is that they'll pay out 1591 01:13:43,140 --> 01:13:45,240 an extraordinary dividend. 1592 01:13:45,240 --> 01:13:47,700 Extra ordinary dividend, which means 1593 01:13:47,700 --> 01:13:50,790 that it's a one-time thing, and then from that point on, 1594 01:13:50,790 --> 01:13:53,458 they'll go back to a regular dividend policy. 1595 01:13:53,458 --> 01:13:53,958 Yeah. 1596 01:13:53,958 --> 01:13:55,902 AUDIENCE: What does a [INAUDIBLE].. 1597 01:14:05,690 --> 01:14:09,172 How you want to invest in billions of dollars. 1598 01:14:09,172 --> 01:14:12,420 Do you borrow money to invest versus [INAUDIBLE] dividend 1599 01:14:12,420 --> 01:14:13,009 [INAUDIBLE]? 1600 01:14:13,009 --> 01:14:15,300 ANDREW LO: Well, it depends on how much money you have. 1601 01:14:15,300 --> 01:14:18,602 It depends upon what your shareholders want to have done. 1602 01:14:18,602 --> 01:14:20,060 I mean, that's certainly a decision 1603 01:14:20,060 --> 01:14:21,726 that a corporate financial manager would 1604 01:14:21,726 --> 01:14:24,050 have to make in concert with the shareholders, 1605 01:14:24,050 --> 01:14:25,850 as well as the CEO. 1606 01:14:25,850 --> 01:14:27,992 And that's a strategic decision. 1607 01:14:27,992 --> 01:14:29,450 But in order to make that decision, 1608 01:14:29,450 --> 01:14:31,574 you've got to have a few things at your fingertips. 1609 01:14:31,574 --> 01:14:34,052 You've got to have the opportunity cost of capital. 1610 01:14:34,052 --> 01:14:36,260 You've got to figure out what your borrowing cost is. 1611 01:14:36,260 --> 01:14:37,400 And in order to figure out your borrowing 1612 01:14:37,400 --> 01:14:39,780 cost, what do you need to know about your debt? 1613 01:14:39,780 --> 01:14:43,555 AUDIENCE: [INAUDIBLE] 1614 01:14:43,555 --> 01:14:44,430 ANDREW LO: How risky. 1615 01:14:44,430 --> 01:14:47,292 And how do we measure risk with corporate debt? 1616 01:14:47,292 --> 01:14:48,750 We just talked about it last class. 1617 01:14:48,750 --> 01:14:49,534 Hint, hint. 1618 01:14:49,534 --> 01:14:50,320 AUDIENCE: You got to rate it. 1619 01:14:50,320 --> 01:14:51,986 ANDREW LO: Yeah, you need a rate, right. 1620 01:14:51,986 --> 01:14:54,540 So you have to figure out whether or not 1621 01:14:54,540 --> 01:14:57,450 the cost of funds from internally-generated sources 1622 01:14:57,450 --> 01:14:59,670 is cheaper or more expensive than going 1623 01:14:59,670 --> 01:15:01,470 to the external capital markets. 1624 01:15:01,470 --> 01:15:05,400 Right now, I would say that it's extremely expensive 1625 01:15:05,400 --> 01:15:08,280 to go out into capital markets, if you could do it at all. 1626 01:15:08,280 --> 01:15:10,530 If you're going to raise money, you're 1627 01:15:10,530 --> 01:15:12,270 going to be paying up through the nose. 1628 01:15:12,270 --> 01:15:16,170 General Electric credit default swap today 1629 01:15:16,170 --> 01:15:19,440 was priced at 700 basis points. 1630 01:15:19,440 --> 01:15:23,420 This is AAA-rated security, at 700 basis points credit. 1631 01:15:23,420 --> 01:15:25,020 It's crazy! 1632 01:15:25,020 --> 01:15:27,077 But people don't want to lend right now. 1633 01:15:27,077 --> 01:15:29,160 So if you want to borrow in capital markets today, 1634 01:15:29,160 --> 01:15:31,010 good luck.