1 00:00:00,090 --> 00:00:02,430 The following content is provided under a Creative 2 00:00:02,430 --> 00:00:03,850 Commons license. 3 00:00:03,850 --> 00:00:06,060 Your support will help MIT OpenCourseWare 4 00:00:06,060 --> 00:00:10,150 continue to offer high-quality educational resources for free. 5 00:00:10,150 --> 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 --> 00:00:17,860 at ocw.mit.edu. 8 00:00:21,370 --> 00:00:22,160 ANDREW LO: OK. 9 00:00:22,160 --> 00:00:25,280 What I'd like to do today is to continue where we left off 10 00:00:25,280 --> 00:00:29,510 last time in talking about this risk-reward trade-off, which 11 00:00:29,510 --> 00:00:33,170 ultimately will allow us to be able to figure out 12 00:00:33,170 --> 00:00:37,310 how to calculate the proper discount rate for any project 13 00:00:37,310 --> 00:00:38,480 under the sun. 14 00:00:38,480 --> 00:00:43,220 Now, where we left off last time was this equation and the one 15 00:00:43,220 --> 00:00:44,240 after it. 16 00:00:44,240 --> 00:00:46,910 This equation we actually derived. 17 00:00:46,910 --> 00:00:48,950 I showed you how to get this equation 18 00:00:48,950 --> 00:00:54,140 from this particular bullet and the tangency line. 19 00:00:54,140 --> 00:00:56,690 And today I am going to give you names for them. 20 00:00:56,690 --> 00:01:00,680 The bullet, as we've said before, is the frontier. 21 00:01:00,680 --> 00:01:02,450 It's the set of frontier portfolios. 22 00:01:02,450 --> 00:01:04,910 And the upper arc of that bullet is 23 00:01:04,910 --> 00:01:06,740 called the efficient frontier. 24 00:01:06,740 --> 00:01:09,590 Now the tangency line has a special name too. 25 00:01:09,590 --> 00:01:15,140 That tangency line is known as the capital market line 26 00:01:15,140 --> 00:01:19,220 because it represents what all efficient capital markets 27 00:01:19,220 --> 00:01:22,160 should represent in terms of risk-reward trade-off. 28 00:01:22,160 --> 00:01:25,100 So if you are an efficient portfolio manager, 29 00:01:25,100 --> 00:01:27,190 you want to be on that line. 30 00:01:27,190 --> 00:01:28,650 OK? 31 00:01:28,650 --> 00:01:32,340 So the capital market line, the equation 32 00:01:32,340 --> 00:01:36,020 for that tangency line, is given by this. 33 00:01:36,020 --> 00:01:39,030 The expected rate of return is equal to the risk-free rate 34 00:01:39,030 --> 00:01:42,090 plus some kind of risk premium, where the risk premium 35 00:01:42,090 --> 00:01:46,800 is given by a multiple of the market's risk premium, 36 00:01:46,800 --> 00:01:50,310 or the market excess return. 37 00:01:50,310 --> 00:01:53,250 And the multiple is simply the ratio 38 00:01:53,250 --> 00:01:57,420 of the riskiness of your efficient portfolio 39 00:01:57,420 --> 00:01:59,880 relative to the market portfolio, 40 00:01:59,880 --> 00:02:02,940 or the tangency portfolio. 41 00:02:02,940 --> 00:02:04,650 If it's twice as risky, you're going 42 00:02:04,650 --> 00:02:06,040 to get twice the risk premium. 43 00:02:06,040 --> 00:02:07,680 If it's half as risky, you're going 44 00:02:07,680 --> 00:02:09,639 to get half the risk premium. 45 00:02:09,639 --> 00:02:11,460 And we said last time that, while this 46 00:02:11,460 --> 00:02:16,110 is helpful and interesting and even possibly useful, 47 00:02:16,110 --> 00:02:17,970 it's going to be of limited applicability 48 00:02:17,970 --> 00:02:22,020 because not everything is an efficient portfolio. 49 00:02:22,020 --> 00:02:24,480 What we mean by an efficient portfolio, 50 00:02:24,480 --> 00:02:28,410 the intuition for what an efficient portfolio is, 51 00:02:28,410 --> 00:02:33,470 is a portfolio where you cannot do better. 52 00:02:33,470 --> 00:02:37,580 By cannot do better, I mean you can't get less risk for that 53 00:02:37,580 --> 00:02:43,070 same level of return, or you can't get more expected return 54 00:02:43,070 --> 00:02:44,990 for that same level of risk. 55 00:02:44,990 --> 00:02:47,550 That's what we mean by an efficient portfolio. 56 00:02:47,550 --> 00:02:50,030 It's the best you can do. 57 00:02:50,030 --> 00:02:54,440 Now, most investments are, frankly, not efficient. 58 00:02:54,440 --> 00:02:58,040 If you pick an arbitrary stock, like IBM, that's 59 00:02:58,040 --> 00:02:59,510 not an efficient portfolio. 60 00:02:59,510 --> 00:03:01,100 It doesn't mean it's no good. 61 00:03:01,100 --> 00:03:02,970 It doesn't mean you don't want to hold it. 62 00:03:02,970 --> 00:03:04,820 But it means that you would never 63 00:03:04,820 --> 00:03:11,900 want to hold just IBM because if you mixed IBM with other stuff, 64 00:03:11,900 --> 00:03:13,820 you can always do better. 65 00:03:13,820 --> 00:03:16,070 By do better, again I'm going to reiterate, 66 00:03:16,070 --> 00:03:19,160 I mean you can have higher expected return 67 00:03:19,160 --> 00:03:23,630 for the same level of risk or lower risk for the same level 68 00:03:23,630 --> 00:03:24,540 of expected return. 69 00:03:24,540 --> 00:03:25,970 That's what I mean by do better. 70 00:03:25,970 --> 00:03:29,450 So you would never want to hold IBM just by itself 71 00:03:29,450 --> 00:03:30,890 because you can do better, right? 72 00:03:30,890 --> 00:03:35,780 You can do better in getting up to that Northwest quadrant 73 00:03:35,780 --> 00:03:39,150 from the IBM point. 74 00:03:39,150 --> 00:03:43,130 But even though IBM is not efficient, 75 00:03:43,130 --> 00:03:45,200 you might still want to hold it. 76 00:03:45,200 --> 00:03:46,910 And more importantly, you might still 77 00:03:46,910 --> 00:03:49,760 want to know what the appropriate discount 78 00:03:49,760 --> 00:03:56,090 rate is for companies that are like IBM. 79 00:03:56,090 --> 00:03:57,800 That's what we're going to do next. 80 00:03:57,800 --> 00:04:02,660 Where I left off last time was not the capital market line, 81 00:04:02,660 --> 00:04:07,130 but this equation, which I did not derive, but which I argued 82 00:04:07,130 --> 00:04:10,640 comes from the equilibrium argument 83 00:04:10,640 --> 00:04:14,990 that Bill Sharpe made 50 years ago. 84 00:04:14,990 --> 00:04:18,440 And this really relies on the fact 85 00:04:18,440 --> 00:04:21,079 that, if markets are in equilibrium, 86 00:04:21,079 --> 00:04:23,660 there is a relationship between risk 87 00:04:23,660 --> 00:04:27,980 and expected return for all securities, not just 88 00:04:27,980 --> 00:04:29,900 efficient portfolios. 89 00:04:29,900 --> 00:04:34,610 But any arbitrary security has to satisfy this equation 90 00:04:34,610 --> 00:04:38,090 if supply equals demand, if there's an equilibrium. 91 00:04:38,090 --> 00:04:40,580 If everybody holds the tangency portfolio, 92 00:04:40,580 --> 00:04:42,590 and the tangency portfolio therefore 93 00:04:42,590 --> 00:04:45,860 is the market portfolio, in that situation, 94 00:04:45,860 --> 00:04:47,660 this equation has to hold. 95 00:04:47,660 --> 00:04:51,120 So where we left off was to try to interpret this equation. 96 00:04:51,120 --> 00:04:53,510 This equation is almost identical to the capital market 97 00:04:53,510 --> 00:04:54,034 line. 98 00:04:54,034 --> 00:04:55,200 There's only one difference. 99 00:04:55,200 --> 00:04:58,910 The only difference is that the multiplier, the thing that 100 00:04:58,910 --> 00:05:01,520 multiplies the market risk premium, 101 00:05:01,520 --> 00:05:03,785 is not sigma p over sigma m. 102 00:05:03,785 --> 00:05:05,420 It is beta. 103 00:05:05,420 --> 00:05:09,620 And beta, we said, was the ratio of the covariance 104 00:05:09,620 --> 00:05:11,550 of an asset with the market divided 105 00:05:11,550 --> 00:05:12,800 by the variance of the market. 106 00:05:12,800 --> 00:05:17,920 It is a measure of that particular asset's riskiness. 107 00:05:17,920 --> 00:05:20,720 It's not variance anymore, or standard deviation, 108 00:05:20,720 --> 00:05:21,990 it's something else. 109 00:05:21,990 --> 00:05:24,140 And so I want to spend this class talking 110 00:05:24,140 --> 00:05:28,880 about what that something else is and why it makes sense. 111 00:05:28,880 --> 00:05:31,910 First of all, let's make sure we understand the equation. 112 00:05:31,910 --> 00:05:33,920 I want to do a few special cases, 113 00:05:33,920 --> 00:05:37,070 and then I'm going to take apart this notion of beta 114 00:05:37,070 --> 00:05:41,400 as being the right measure of risk in all circumstances. 115 00:05:41,400 --> 00:05:45,480 So the first thing I want to do is to look at some examples. 116 00:05:45,480 --> 00:05:48,262 Let's take an example where the beta is equal to 1. 117 00:05:48,262 --> 00:05:51,260 If the beta is equal to 1, what that's saying 118 00:05:51,260 --> 00:05:57,320 is that the covariance between the asset and the market 119 00:05:57,320 --> 00:05:59,570 divided by the variance of the market, 120 00:05:59,570 --> 00:06:01,970 that number is equal to 1. 121 00:06:01,970 --> 00:06:04,460 If that's the case, then it turns out 122 00:06:04,460 --> 00:06:08,660 that the expected rate of return of this asset with a beta of 1 123 00:06:08,660 --> 00:06:11,457 is going to be just equal to the market risk premium. 124 00:06:11,457 --> 00:06:13,790 Or the expected return is equal to the market's expected 125 00:06:13,790 --> 00:06:15,410 rate of return. 126 00:06:15,410 --> 00:06:17,807 When beta is equal to 1, the Rf's cancel out, 127 00:06:17,807 --> 00:06:19,640 and the expected rate of return of the asset 128 00:06:19,640 --> 00:06:23,570 is equal to the expected rate of return on the market. 129 00:06:23,570 --> 00:06:25,520 Now, what about if the beta is equal to 0? 130 00:06:25,520 --> 00:06:29,590 If the beta is equal to 0, then you get the risk-free rate. 131 00:06:29,590 --> 00:06:33,010 It's important to realize that if the beta of an asset 132 00:06:33,010 --> 00:06:35,620 is equal to 0, it doesn't mean that the asset has 133 00:06:35,620 --> 00:06:38,670 no volatility. 134 00:06:38,670 --> 00:06:41,490 In the past, when we've looked at mixing 135 00:06:41,490 --> 00:06:45,360 the risk-free asset, T-bills, with the market, 136 00:06:45,360 --> 00:06:48,990 we know that when the risk-free asset is included, 137 00:06:48,990 --> 00:06:51,130 you get that straight line. 138 00:06:51,130 --> 00:06:54,150 And it's because the risk-free asset has no covariance. 139 00:06:54,150 --> 00:06:56,200 It has no risk at all. 140 00:06:56,200 --> 00:07:01,050 But now, with an asset that has a beta of 0, 141 00:07:01,050 --> 00:07:02,850 you're getting the risk-free return, 142 00:07:02,850 --> 00:07:06,990 even though an asset with a beta of 0 143 00:07:06,990 --> 00:07:09,430 still may have some volatility. 144 00:07:09,430 --> 00:07:11,040 It's not the risk-free asset. 145 00:07:11,040 --> 00:07:12,960 It's any asset with a 0 beta. 146 00:07:16,310 --> 00:07:18,290 The third observation that I want to make 147 00:07:18,290 --> 00:07:21,230 is when a beta is negative. 148 00:07:21,230 --> 00:07:24,770 With the beta that's negative, the expected rate of return 149 00:07:24,770 --> 00:07:28,350 is actually less than the risk-free rate. 150 00:07:28,350 --> 00:07:30,260 Now that's really odd. 151 00:07:30,260 --> 00:07:33,130 I've got an asset that is risky. 152 00:07:33,130 --> 00:07:37,810 But just because it has a negative beta, 153 00:07:37,810 --> 00:07:41,360 the expected rate of return is less than the risk-free rate. 154 00:07:41,360 --> 00:07:45,740 That means that you are willing to take a lower expected rate 155 00:07:45,740 --> 00:07:48,920 of return than the risk-free rate for an asset that 156 00:07:48,920 --> 00:07:52,757 has this weird property of negative beta. 157 00:07:52,757 --> 00:07:55,090 And the question I want to answer today is, why is that? 158 00:07:55,090 --> 00:07:58,240 Why is it the case that you might 159 00:07:58,240 --> 00:08:01,540 be willing to take such a low rate of return? 160 00:08:01,540 --> 00:08:04,420 And actually, if the beta is negative enough, 161 00:08:04,420 --> 00:08:06,280 if this beta is negative enough, it 162 00:08:06,280 --> 00:08:10,560 could be the case that the expected rate of return 163 00:08:10,560 --> 00:08:13,060 is negative. 164 00:08:13,060 --> 00:08:16,920 In other words, you might be willing to pay somebody 165 00:08:16,920 --> 00:08:21,300 for the privilege of bearing that risk. 166 00:08:21,300 --> 00:08:23,190 That seems completely counterintuitive. 167 00:08:23,190 --> 00:08:26,760 Why would you be willing to pay to take risk? 168 00:08:26,760 --> 00:08:29,610 You should be getting paid to take risk, right? 169 00:08:29,610 --> 00:08:33,690 That's the standard hypothesis that we 170 00:08:33,690 --> 00:08:36,700 come into the financial markets with. 171 00:08:36,700 --> 00:08:38,695 So yeah, Leah? 172 00:08:38,695 --> 00:08:40,514 AUDIENCE: [INAUDIBLE] 173 00:08:40,514 --> 00:08:41,514 ANDREW LO: That's right. 174 00:08:41,514 --> 00:08:43,789 AUDIENCE: [INAUDIBLE] 175 00:08:43,789 --> 00:08:44,810 ANDREW LO: Exactly. 176 00:08:44,810 --> 00:08:49,070 That's exactly the intuition for all three of these cases. 177 00:08:49,070 --> 00:08:53,240 It turns out that the beta, remember, has 178 00:08:53,240 --> 00:08:56,400 this covariance term in there. 179 00:08:56,400 --> 00:08:59,900 And it is going to turn out that, if you 180 00:08:59,900 --> 00:09:04,910 can find an asset that is negatively correlated 181 00:09:04,910 --> 00:09:09,050 to the tangency portfolio, that is going to be 182 00:09:09,050 --> 00:09:11,080 of tremendous value to you. 183 00:09:11,080 --> 00:09:13,580 It's very, very valuable. 184 00:09:13,580 --> 00:09:14,310 Now, OK. 185 00:09:14,310 --> 00:09:16,280 Let me try to explain the logic behind it. 186 00:09:16,280 --> 00:09:18,420 And we're going to do a few examples. 187 00:09:18,420 --> 00:09:23,270 So let's go through the basic logic of what's going on. 188 00:09:23,270 --> 00:09:26,810 The tangency portfolio plays a central role 189 00:09:26,810 --> 00:09:28,760 in that everybody in the world is 190 00:09:28,760 --> 00:09:31,280 going to want to have a portfolio that's 191 00:09:31,280 --> 00:09:33,020 a combination of the risk-free asset 192 00:09:33,020 --> 00:09:35,360 and the tangency portfolio. 193 00:09:35,360 --> 00:09:37,490 That's fact number one. 194 00:09:37,490 --> 00:09:44,720 Fact number two, the tangency portfolio is a portfolio that 195 00:09:44,720 --> 00:09:50,300 has the aggregate measure of the total amount of risk 196 00:09:50,300 --> 00:09:55,140 in the economy that cannot be diversified beyond that point. 197 00:09:55,140 --> 00:09:59,360 In other words, in order to get lower risk 198 00:09:59,360 --> 00:10:01,730 than this particular portfolio, you 199 00:10:01,730 --> 00:10:06,540 have to decrease your expected rate of return. 200 00:10:06,540 --> 00:10:10,040 There's no way to get lower risk and keep that same level 201 00:10:10,040 --> 00:10:10,940 of expected return. 202 00:10:10,940 --> 00:10:11,856 You can't go this way. 203 00:10:11,856 --> 00:10:13,660 You have to go down this line. 204 00:10:13,660 --> 00:10:14,480 OK? 205 00:10:14,480 --> 00:10:19,610 So if you're going to hold a portfolio of purely 206 00:10:19,610 --> 00:10:22,970 risky securities, then basically this 207 00:10:22,970 --> 00:10:25,220 is the best that you can do. 208 00:10:25,220 --> 00:10:27,380 This is the best trade-off that you can 209 00:10:27,380 --> 00:10:31,140 get in terms of risk-reward. 210 00:10:31,140 --> 00:10:35,210 So right away you know that this market portfolio 211 00:10:35,210 --> 00:10:37,850 plays a very special role. 212 00:10:37,850 --> 00:10:44,630 It is really the representation of the aggregate risk 213 00:10:44,630 --> 00:10:46,680 in the stock market. 214 00:10:46,680 --> 00:10:50,600 And that's why it can serve as a kind of a benchmark for what 215 00:10:50,600 --> 00:10:52,042 the stock market is doing. 216 00:10:52,042 --> 00:10:54,000 We're going to come back to that benchmark idea 217 00:10:54,000 --> 00:10:55,590 in a few minutes. 218 00:10:55,590 --> 00:11:00,890 So, if you have a security that is very highly 219 00:11:00,890 --> 00:11:03,740 correlated to that market return, 220 00:11:03,740 --> 00:11:05,660 then that's not going to help you in terms 221 00:11:05,660 --> 00:11:08,690 of your own diversification. 222 00:11:08,690 --> 00:11:11,930 If, on the other hand, you have a security that is negatively 223 00:11:11,930 --> 00:11:14,510 correlated with that market portfolio, 224 00:11:14,510 --> 00:11:17,290 that's going to help you a lot. 225 00:11:17,290 --> 00:11:20,080 And if it's going to help you a lot, 226 00:11:20,080 --> 00:11:21,929 you're willing to pay for it. 227 00:11:21,929 --> 00:11:24,220 When you're willing to pay for it, what does that mean? 228 00:11:24,220 --> 00:11:27,370 You drive the price today high. 229 00:11:27,370 --> 00:11:30,230 And therefore, the expected rate of return, 230 00:11:30,230 --> 00:11:34,360 which is the return between today and next period, that 231 00:11:34,360 --> 00:11:37,690 becomes lower. 232 00:11:37,690 --> 00:11:41,470 So an asset that helps you hedge what 233 00:11:41,470 --> 00:11:45,550 is essentially unhedgedgeable, in other words, the market 234 00:11:45,550 --> 00:11:49,504 portfolio, that can benefit you a great deal. 235 00:11:49,504 --> 00:11:50,920 As a result, it's going to be very 236 00:11:50,920 --> 00:11:56,740 hard to find negative beta securities or assets. 237 00:11:56,740 --> 00:11:59,470 But in any case, this relationship really 238 00:11:59,470 --> 00:12:04,240 tells you that, given a particular covariance, 239 00:12:04,240 --> 00:12:07,210 you can measure the expected rate of return 240 00:12:07,210 --> 00:12:09,250 that you ought to be getting. 241 00:12:09,250 --> 00:12:11,200 And this relationship is so important 242 00:12:11,200 --> 00:12:12,590 that we give it a separate name. 243 00:12:12,590 --> 00:12:16,780 It's called the security market line, not the capital market 244 00:12:16,780 --> 00:12:19,000 line, but the security market line 245 00:12:19,000 --> 00:12:23,290 because this applies to every single security 246 00:12:23,290 --> 00:12:24,960 in your entire universe. 247 00:12:24,960 --> 00:12:25,960 Yeah, Dennis? 248 00:12:25,960 --> 00:12:27,210 AUDIENCE: You say it's hard to find something 249 00:12:27,210 --> 00:12:28,085 with a negative beta. 250 00:12:28,085 --> 00:12:30,082 But when you short something, does 251 00:12:30,082 --> 00:12:31,790 that mean you're getting a negative beta? 252 00:12:31,790 --> 00:12:33,090 ANDREW LO: It is. 253 00:12:33,090 --> 00:12:34,120 You do. 254 00:12:34,120 --> 00:12:36,250 But the problem with shorting something 255 00:12:36,250 --> 00:12:38,410 where you get a negative beta, you also 256 00:12:38,410 --> 00:12:42,470 get a negative expected rate of return typically. 257 00:12:42,470 --> 00:12:44,560 So what you want to have is an asset that's 258 00:12:44,560 --> 00:12:46,630 got a positive beta-- or negative beta, 259 00:12:46,630 --> 00:12:48,550 but a positive expected rate of return. 260 00:12:48,550 --> 00:12:50,500 That's what's very rare. 261 00:12:50,500 --> 00:12:52,870 But you can manufacture a negative beta security very 262 00:12:52,870 --> 00:12:55,480 easily by just shorting it. 263 00:12:55,480 --> 00:12:57,460 The problem is that when you short a stock, 264 00:12:57,460 --> 00:12:59,710 you're going to also get a very negative expected rate 265 00:12:59,710 --> 00:13:00,364 of return. 266 00:13:00,364 --> 00:13:01,780 And that doesn't help you in terms 267 00:13:01,780 --> 00:13:05,190 of producing an attractive investment opportunity. 268 00:13:05,190 --> 00:13:07,660 Ken, question? 269 00:13:07,660 --> 00:13:12,160 AUDIENCE: So, what's an example of a negative beta security? 270 00:13:12,160 --> 00:13:15,550 ANDREW LO: Well, it's very hard to come by. 271 00:13:15,550 --> 00:13:19,540 But the closest thing that exists in markets today 272 00:13:19,540 --> 00:13:26,770 is stocks that are involved in gold production, gold mining 273 00:13:26,770 --> 00:13:27,970 stocks. 274 00:13:27,970 --> 00:13:31,620 That has a beta of around 0, but sometimes it's negative. 275 00:13:31,620 --> 00:13:32,620 Sometimes it's positive. 276 00:13:32,620 --> 00:13:34,150 But it's small. 277 00:13:34,150 --> 00:13:37,510 So that's an example, but that's about the only example 278 00:13:37,510 --> 00:13:40,330 that we can come up with in the data that 279 00:13:40,330 --> 00:13:42,520 looks slightly negative. 280 00:13:42,520 --> 00:13:47,920 By and large, most of the betas in the data sets are positive. 281 00:13:47,920 --> 00:13:51,130 And they're actually clustered around 1. 282 00:13:51,130 --> 00:13:57,521 So the typical beta is in the neighborhood of 0.5 to 1.5. 283 00:13:57,521 --> 00:13:58,020 All right. 284 00:13:58,020 --> 00:13:59,350 Now, before we start looking at the data-- 285 00:13:59,350 --> 00:14:01,225 I'm going to show you some data in a minute-- 286 00:14:01,225 --> 00:14:05,930 I want to take the security market line and apply it. 287 00:14:05,930 --> 00:14:08,130 So the security market line I did not derive. 288 00:14:08,130 --> 00:14:09,550 I want to make that clear. 289 00:14:09,550 --> 00:14:11,966 And for those of you who are interested in the derivation, 290 00:14:11,966 --> 00:14:14,200 you can take a look at the appendix in the Brealey, 291 00:14:14,200 --> 00:14:14,950 Meyers, and Allen. 292 00:14:14,950 --> 00:14:16,720 They provide the derivation. 293 00:14:16,720 --> 00:14:19,600 It's a little bit messy, but with a little bit 294 00:14:19,600 --> 00:14:23,230 of matrix algebra you can work through it. 295 00:14:23,230 --> 00:14:26,720 But the implications are extremely important, 296 00:14:26,720 --> 00:14:29,390 so I want all of you to know how to use it. 297 00:14:29,390 --> 00:14:32,050 So it may look pretty simple, but I'll 298 00:14:32,050 --> 00:14:35,110 show you a few applications that you might not have thought of. 299 00:14:35,110 --> 00:14:41,970 For example, suppose this is true for every single security. 300 00:14:41,970 --> 00:14:44,880 Well, if it's true for every single security, 301 00:14:44,880 --> 00:14:47,980 it turns out that this works for portfolios as well. 302 00:14:47,980 --> 00:14:49,650 And let me show you why. 303 00:14:49,650 --> 00:14:51,510 Suppose you've got a portfolio that's 304 00:14:51,510 --> 00:14:54,150 a weighted average of the returns 305 00:14:54,150 --> 00:14:57,680 for the individual components securities. 306 00:14:57,680 --> 00:14:59,960 Then if I calculate the covariance 307 00:14:59,960 --> 00:15:03,920 between the portfolio return and the tangency portfolio, 308 00:15:03,920 --> 00:15:08,110 or the market, the covariance is going 309 00:15:08,110 --> 00:15:10,590 to look like this, which is actually 310 00:15:10,590 --> 00:15:12,340 just going to look like a weighted average 311 00:15:12,340 --> 00:15:14,800 of the covariances. 312 00:15:14,800 --> 00:15:19,060 This is a mathematical identity, from here down to here. 313 00:15:19,060 --> 00:15:22,360 And therefore, when I divide both sides 314 00:15:22,360 --> 00:15:26,170 by the variance of the market, I get something pretty neat, 315 00:15:26,170 --> 00:15:29,800 which is that the beta of my portfolio-- 316 00:15:29,800 --> 00:15:32,050 where beta is defined as the covariance 317 00:15:32,050 --> 00:15:36,430 between the portfolio and the market divided 318 00:15:36,430 --> 00:15:39,190 by the variance-- the beta of the portfolio 319 00:15:39,190 --> 00:15:41,710 is just equal to the weighted average of the betas 320 00:15:41,710 --> 00:15:44,440 of my component securities. 321 00:15:44,440 --> 00:15:47,340 That's really neat because what that says 322 00:15:47,340 --> 00:15:50,910 is that, when I want to measure the risk of a collection 323 00:15:50,910 --> 00:15:54,510 of securities, as long as I know the betas 324 00:15:54,510 --> 00:15:58,350 of each individual security, I can 325 00:15:58,350 --> 00:16:00,810 calculate a weighted average of those betas. 326 00:16:00,810 --> 00:16:03,800 And that is the beta of my portfolio. 327 00:16:03,800 --> 00:16:07,200 So if you think of beta as a measure of risk, 328 00:16:07,200 --> 00:16:11,570 this measure of risk is actually linear, 329 00:16:11,570 --> 00:16:17,330 unlike volatility, which is not linear. 330 00:16:17,330 --> 00:16:21,140 The variance of a portfolio is not simply 331 00:16:21,140 --> 00:16:24,020 equal to the sum of the variances weighted 332 00:16:24,020 --> 00:16:25,370 by their portfolio weights. 333 00:16:25,370 --> 00:16:27,650 It's that complicated expression where 334 00:16:27,650 --> 00:16:31,500 you're adding up all of those cross products as well. 335 00:16:31,500 --> 00:16:34,370 So we get an enormous simplification 336 00:16:34,370 --> 00:16:35,960 with the security market line. 337 00:16:35,960 --> 00:16:39,890 It says that we can measure the risk of a portfolio using 338 00:16:39,890 --> 00:16:41,630 this concept called beta. 339 00:16:41,630 --> 00:16:44,090 And beta happens to be linear in the sense 340 00:16:44,090 --> 00:16:46,610 that, when you take a weighted average, 341 00:16:46,610 --> 00:16:48,590 the beta is equal to the weighted average 342 00:16:48,590 --> 00:16:52,160 of the individual asset betas. 343 00:16:52,160 --> 00:16:55,910 So therefore, if you know that the betas are 344 00:16:55,910 --> 00:16:59,660 going to be a weighted average, then, in fact, 345 00:16:59,660 --> 00:17:03,020 the expected rate of return on the portfolio 346 00:17:03,020 --> 00:17:05,210 now is equal to the risk-free rate 347 00:17:05,210 --> 00:17:12,470 plus this weighted average beta times the market risk premium. 348 00:17:12,470 --> 00:17:13,800 Do you see the power of this? 349 00:17:13,800 --> 00:17:17,730 This now allows you to analyze the expected return 350 00:17:17,730 --> 00:17:21,210 on anything, any collection of assets. 351 00:17:21,210 --> 00:17:23,940 If you know what the betas are for the individual components, 352 00:17:23,940 --> 00:17:25,939 you know what the betas are for the whole thing. 353 00:17:29,210 --> 00:17:32,560 So now you can calculate the appropriate rate of return 354 00:17:32,560 --> 00:17:35,260 for virtually anything. 355 00:17:35,260 --> 00:17:37,400 And this is not just limited to stocks. 356 00:17:37,400 --> 00:17:39,650 You can apply this to projects. 357 00:17:39,650 --> 00:17:41,320 For example, if you want to know what 358 00:17:41,320 --> 00:17:44,620 the expected rate of return is on an oil drilling project, 359 00:17:44,620 --> 00:17:49,720 well, measure the beta of oil drilling stocks, use that beta, 360 00:17:49,720 --> 00:17:51,670 and that will be appropriate discount 361 00:17:51,670 --> 00:17:55,260 rate for that particular oil drilling project. 362 00:17:55,260 --> 00:17:59,260 It's a really remarkable result. 363 00:17:59,260 --> 00:18:02,740 So we have an expression for the required rate of return, 364 00:18:02,740 --> 00:18:05,560 opportunity cost of capital, risk-adjusted discount rate, 365 00:18:05,560 --> 00:18:09,130 for all the various different kind of examples and cases 366 00:18:09,130 --> 00:18:12,220 that we looked at up until now. 367 00:18:12,220 --> 00:18:14,980 And the last point I want to make about this equation 368 00:18:14,980 --> 00:18:18,640 is, how do you actually take it out for a spin? 369 00:18:18,640 --> 00:18:20,680 How do you estimate the expected rate of return 370 00:18:20,680 --> 00:18:22,250 on the market and the risk-free rate? 371 00:18:22,250 --> 00:18:24,520 Well, that comes from the data. 372 00:18:24,520 --> 00:18:26,440 That comes from the marketplace. 373 00:18:26,440 --> 00:18:28,720 We observe it in the marketplace. 374 00:18:28,720 --> 00:18:30,870 And we can actually see it. 375 00:18:30,870 --> 00:18:31,480 OK. 376 00:18:31,480 --> 00:18:34,240 So let's do some examples, just to make sure that we all get 377 00:18:34,240 --> 00:18:36,790 this and know how to apply it. 378 00:18:36,790 --> 00:18:39,880 Using returns from 1990 to 2001, we 379 00:18:39,880 --> 00:18:43,690 estimate that Microsoft's beta during that period of time 380 00:18:43,690 --> 00:18:46,180 is 1.49. 381 00:18:46,180 --> 00:18:49,090 And if you do the same thing for Gillette, 382 00:18:49,090 --> 00:18:52,930 you get that Gillette's beta is 0.81. 383 00:18:52,930 --> 00:18:57,430 Now, let's not even look at the next set of numbers 384 00:18:57,430 --> 00:19:00,790 for a moment, and just talk about those two numbers, 1.49 385 00:19:00,790 --> 00:19:01,780 and 0.81. 386 00:19:01,780 --> 00:19:03,310 Does that make sense to you? 387 00:19:03,310 --> 00:19:05,240 Let's think about what that's saying. 388 00:19:05,240 --> 00:19:09,820 1.49 says that the covariance between Microsoft 389 00:19:09,820 --> 00:19:13,510 and the market portfolio is actually 390 00:19:13,510 --> 00:19:20,210 a lot higher than the variance of the market itself. 391 00:19:20,210 --> 00:19:24,210 So let me ask you to think about whether or not 392 00:19:24,210 --> 00:19:26,820 adding Microsoft to your portfolio 393 00:19:26,820 --> 00:19:29,760 is going to make it less risky or more risky. 394 00:19:29,760 --> 00:19:32,790 And here's how I want you to think about it. 395 00:19:32,790 --> 00:19:35,550 Remember what we said about diversification. 396 00:19:35,550 --> 00:19:37,920 When you hold a collection of securities, 397 00:19:37,920 --> 00:19:41,322 what matters more, the variances or the covariances? 398 00:19:41,322 --> 00:19:42,352 AUDIENCE: Covariances. 399 00:19:42,352 --> 00:19:43,060 ANDREW LO: Right. 400 00:19:43,060 --> 00:19:47,590 Why are the covariances more important? 401 00:19:47,590 --> 00:19:51,700 What's a quick and dirty way of arguing that the covariances 402 00:19:51,700 --> 00:19:53,362 matter more? 403 00:19:53,362 --> 00:19:55,290 AUDIENCE: Because there are n squared minus n. 404 00:19:55,290 --> 00:19:55,750 ANDREW LO: Exactly. 405 00:19:55,750 --> 00:19:57,550 There are a heck of a lot more covariances 406 00:19:57,550 --> 00:19:58,591 than there are variances. 407 00:19:58,591 --> 00:20:01,040 You only got n variances to worry about, 408 00:20:01,040 --> 00:20:04,030 but you got n squared minus n covariances. 409 00:20:04,030 --> 00:20:07,150 And if they all line up in the same direction, 410 00:20:07,150 --> 00:20:10,570 you get the subprime crisis problem, right? 411 00:20:10,570 --> 00:20:13,630 So covariances matter more than variances. 412 00:20:13,630 --> 00:20:17,980 Well, if that's the case, then when we look at a stock 413 00:20:17,980 --> 00:20:20,810 and think about bringing it into our portfolio, 414 00:20:20,810 --> 00:20:23,080 we want to ask the question, what 415 00:20:23,080 --> 00:20:29,070 is it doing in terms of adding or subtracting covariances 416 00:20:29,070 --> 00:20:30,690 to our portfolio? 417 00:20:30,690 --> 00:20:32,850 And one way to measure whether or not 418 00:20:32,850 --> 00:20:36,600 it's adding or subtracting is to ask the question, what 419 00:20:36,600 --> 00:20:42,870 is the covariance between Microsoft and my stock 420 00:20:42,870 --> 00:20:43,800 holdings? 421 00:20:43,800 --> 00:20:46,170 Now what are your stock holdings? 422 00:20:46,170 --> 00:20:48,750 If everybody is a rational investor-- 423 00:20:48,750 --> 00:20:52,020 by rational I mean you like return 424 00:20:52,020 --> 00:20:53,700 and you don't like risk-- 425 00:20:53,700 --> 00:20:56,550 then you know you're going to be holding the risk-free rate 426 00:20:56,550 --> 00:20:57,690 and the market portfolio. 427 00:20:57,690 --> 00:21:00,396 You're going to be on that capital market line. 428 00:21:00,396 --> 00:21:01,770 So if you're a rational investor, 429 00:21:01,770 --> 00:21:04,565 the only stock holding you have is that mutual fund, 430 00:21:04,565 --> 00:21:07,230 m, the tangency portfolio. 431 00:21:07,230 --> 00:21:10,269 So therefore, the most important thing in your mind 432 00:21:10,269 --> 00:21:12,060 is, when you think about buying a new stock 433 00:21:12,060 --> 00:21:14,880 and putting into your portfolio, is this 434 00:21:14,880 --> 00:21:20,520 going to be highly correlated with my market portfolio? 435 00:21:20,520 --> 00:21:22,530 Well, that's what beta measures. 436 00:21:22,530 --> 00:21:27,180 Beta is a relative measure that says, OK, the total variance 437 00:21:27,180 --> 00:21:29,390 that you're holding in risky securities, that's 438 00:21:29,390 --> 00:21:30,750 sigma m squared. 439 00:21:30,750 --> 00:21:35,070 That's the variance of the market portfolio. 440 00:21:35,070 --> 00:21:39,200 How does Microsoft compare to that 441 00:21:39,200 --> 00:21:42,230 in terms of what it will contribute, 442 00:21:42,230 --> 00:21:45,260 in terms of its covariance with your holding? 443 00:21:45,260 --> 00:21:47,039 So you're holding one mutual fund, 444 00:21:47,039 --> 00:21:48,830 and you're thinking about adding Microsoft. 445 00:21:48,830 --> 00:21:50,750 The only covariance that you should care about 446 00:21:50,750 --> 00:21:52,700 is the covariance between Microsoft 447 00:21:52,700 --> 00:21:54,810 and what you're holding. 448 00:21:54,810 --> 00:21:56,380 Well, that's what beta measures. 449 00:21:56,380 --> 00:21:58,570 If the number is greater than 1, what it's saying 450 00:21:58,570 --> 00:22:01,750 is that, when you bring Microsoft into your portfolio, 451 00:22:01,750 --> 00:22:04,480 you're going to be increasing the variance 452 00:22:04,480 --> 00:22:08,470 because the covariance, which is what we care about, 453 00:22:08,470 --> 00:22:12,580 is greater than the variance of what you're holding. 454 00:22:12,580 --> 00:22:15,970 If, on the other hand, the beta is less than 1, 455 00:22:15,970 --> 00:22:19,120 then, presumably, that's helping you 456 00:22:19,120 --> 00:22:23,260 because that's lowering the variance relative to what 457 00:22:23,260 --> 00:22:24,280 you're holding. 458 00:22:24,280 --> 00:22:27,550 But helping or hurting, that only 459 00:22:27,550 --> 00:22:30,340 can be answered directly if you explain 460 00:22:30,340 --> 00:22:34,130 what you're getting in terms of the expected rate of return. 461 00:22:34,130 --> 00:22:37,540 So looking at beta by itself is not enough. 462 00:22:37,540 --> 00:22:39,880 Beta is a measure of risk. 463 00:22:39,880 --> 00:22:41,860 It measures this covariance divided 464 00:22:41,860 --> 00:22:45,280 by the variance, or covariance per unit 465 00:22:45,280 --> 00:22:46,732 variance in the marketplace. 466 00:22:46,732 --> 00:22:48,940 But you want to know what the expected rate of return 467 00:22:48,940 --> 00:22:49,440 is as well. 468 00:22:49,440 --> 00:22:52,070 That's what the security market line gives you. 469 00:22:52,070 --> 00:22:52,570 OK. 470 00:22:52,570 --> 00:22:54,490 Now let's get back to the example. 471 00:22:54,490 --> 00:22:58,180 Microsoft is a lot more risky than the market. 472 00:22:58,180 --> 00:23:02,120 It's about 49% more risky according to this measure. 473 00:23:02,120 --> 00:23:04,120 On the other hand, Gillette is actually 474 00:23:04,120 --> 00:23:06,950 less risky than the market. 475 00:23:06,950 --> 00:23:09,050 Now do you guys buy that? 476 00:23:09,050 --> 00:23:10,935 Does that pass the smell test? 477 00:23:10,935 --> 00:23:11,810 Does that make sense? 478 00:23:11,810 --> 00:23:13,180 Why? 479 00:23:13,180 --> 00:23:17,125 What's the intuition for that? 480 00:23:17,125 --> 00:23:17,625 Courtney? 481 00:23:17,625 --> 00:23:19,958 AUDIENCE: Well, people don't necessarily need computers. 482 00:23:19,958 --> 00:23:23,970 And the technology is variable, but Gillette sells razor 483 00:23:23,970 --> 00:23:26,949 products and deodorant, which is kind of a staple in a lot 484 00:23:26,949 --> 00:23:27,490 of people's-- 485 00:23:27,490 --> 00:23:28,281 ANDREW LO: Exactly. 486 00:23:28,281 --> 00:23:28,880 That's right. 487 00:23:28,880 --> 00:23:34,080 If you make the argument that, from 1990 to 2001, if there 488 00:23:34,080 --> 00:23:36,660 are economic downturns, what's the first 489 00:23:36,660 --> 00:23:39,840 to go, razorblades or Windows? 490 00:23:39,840 --> 00:23:40,800 Thankfully Windows. 491 00:23:40,800 --> 00:23:42,100 [LAUGHTER] 492 00:23:42,100 --> 00:23:45,390 Nowadays, I don't know the answer to that actually. 493 00:23:45,390 --> 00:23:49,470 Because nowadays, we depend so much on the internet, 494 00:23:49,470 --> 00:23:51,210 that actually it could be different. 495 00:23:51,210 --> 00:23:52,680 So I haven't updated this analysis 496 00:23:52,680 --> 00:23:56,940 to see what the beta is from 2001 to 2008, 497 00:23:56,940 --> 00:23:59,170 but it could be different. 498 00:23:59,170 --> 00:24:00,900 So now we may have unshaven geeks 499 00:24:00,900 --> 00:24:03,090 that, you know, during downturns-- 500 00:24:03,090 --> 00:24:04,770 and maybe it's flipped around. 501 00:24:04,770 --> 00:24:06,592 Eduard? 502 00:24:06,592 --> 00:24:08,300 AUDIENCE: Could you give us an intuition? 503 00:24:08,300 --> 00:24:11,040 Because beta allows us to compute 504 00:24:11,040 --> 00:24:15,890 the appropriate return for a certain risk. 505 00:24:15,890 --> 00:24:16,840 ANDREW LO: Yes. 506 00:24:16,840 --> 00:24:19,010 AUDIENCE: But what is the intuition of, 507 00:24:19,010 --> 00:24:23,147 how far away am I from the efficiency portfolio? 508 00:24:23,147 --> 00:24:28,380 So, how bad is this portfolio compared to the efficient one? 509 00:24:28,380 --> 00:24:29,450 ANDREW LO: Yeah. 510 00:24:29,450 --> 00:24:31,401 So, that's a good question. 511 00:24:31,401 --> 00:24:33,650 Let me go back to this equation and take a look at it, 512 00:24:33,650 --> 00:24:36,020 and try to provide even more intuition for this 513 00:24:36,020 --> 00:24:37,490 before we go on. 514 00:24:37,490 --> 00:24:39,800 So the idea behind this equation is 515 00:24:39,800 --> 00:24:42,200 that it tells you that this is the rate of return 516 00:24:42,200 --> 00:24:46,570 that you should have if you have a certain beta. 517 00:24:46,570 --> 00:24:50,130 Now you can actually measure the deviation from that 518 00:24:50,130 --> 00:24:52,050 very simply by asking the question. 519 00:24:52,050 --> 00:24:55,066 For a portfolio manager or an investment project 520 00:24:55,066 --> 00:24:56,940 that yields an expected rate of return that's 521 00:24:56,940 --> 00:25:00,220 different from this, that difference 522 00:25:00,220 --> 00:25:03,260 is actually what we call alpha. 523 00:25:03,260 --> 00:25:05,550 And alpha could be positive or negative. 524 00:25:05,550 --> 00:25:09,890 So when you say, how far away are you from efficiency? 525 00:25:09,890 --> 00:25:12,487 This gives you a direct measure of how far away you are. 526 00:25:12,487 --> 00:25:14,570 It's basically the difference between the expected 527 00:25:14,570 --> 00:25:16,760 rate of return you have versus what 528 00:25:16,760 --> 00:25:20,900 you're supposed to have given the beta of the security. 529 00:25:20,900 --> 00:25:22,740 But let me add one more thing to that, 530 00:25:22,740 --> 00:25:28,010 which is that beta is a measure of a particular kind of risk 531 00:25:28,010 --> 00:25:31,520 that a particular security has. 532 00:25:31,520 --> 00:25:34,310 And the kind of risk, as I said before, 533 00:25:34,310 --> 00:25:36,410 is this covariance between the rate 534 00:25:36,410 --> 00:25:41,240 of return on a particular asset and the rate of return 535 00:25:41,240 --> 00:25:43,190 on the market portfolio. 536 00:25:43,190 --> 00:25:46,760 This kind of risk is not the total risk 537 00:25:46,760 --> 00:25:48,770 of a particular security. 538 00:25:48,770 --> 00:25:52,990 In fact, it is called the systematic risk. 539 00:25:52,990 --> 00:25:55,730 The systematic risk is the portion 540 00:25:55,730 --> 00:25:59,790 of the risk that is related to the market portfolio. 541 00:25:59,790 --> 00:26:03,470 So how far away you are from efficiency really 542 00:26:03,470 --> 00:26:08,660 depends upon how much risk you have that is not 543 00:26:08,660 --> 00:26:11,270 necessarily systematic risk. 544 00:26:11,270 --> 00:26:13,504 Now, I don't expect you to understand all of it 545 00:26:13,504 --> 00:26:15,920 yet because I need to develop a little bit more machinery. 546 00:26:15,920 --> 00:26:17,720 But I'm going to get back to that intuition 547 00:26:17,720 --> 00:26:19,190 in just a few minutes, OK? 548 00:26:19,190 --> 00:26:20,060 So I'm going to give you a better 549 00:26:20,060 --> 00:26:22,490 answer to your question than what I just did because I'll 550 00:26:22,490 --> 00:26:25,220 explain the difference between systematic risk 551 00:26:25,220 --> 00:26:26,790 and idiosyncratic risk. 552 00:26:26,790 --> 00:26:29,780 And I think then it'll make this completely transparent. 553 00:26:29,780 --> 00:26:31,650 So give me another 15 minutes. 554 00:26:31,650 --> 00:26:32,180 Yeah? 555 00:26:32,180 --> 00:26:34,820 AUDIENCE: So you mentioned that gold stocks 556 00:26:34,820 --> 00:26:36,496 can reduce the volatility. 557 00:26:36,496 --> 00:26:37,339 They may have-- 558 00:26:37,339 --> 00:26:38,630 ANDREW LO: Historically it has. 559 00:26:38,630 --> 00:26:39,390 AUDIENCE: Yeah. 560 00:26:39,390 --> 00:26:40,880 So there are some currencies that 561 00:26:40,880 --> 00:26:43,250 are indexed to gold prices. 562 00:26:43,250 --> 00:26:44,730 So let's say you're company x. 563 00:26:44,730 --> 00:26:48,480 If you are listed in the Dow Jones versus this country, 564 00:26:48,480 --> 00:26:50,930 whose currency is indexed to gold, 565 00:26:50,930 --> 00:26:54,080 do you expect the company that's listed in the gold index 566 00:26:54,080 --> 00:26:57,407 currency to have a lower beta? 567 00:26:57,407 --> 00:26:58,490 ANDREW LO: Well, it could. 568 00:26:58,490 --> 00:27:00,140 But on the other hand, the question 569 00:27:00,140 --> 00:27:02,900 is, what are they doing to try to hedge that currency 570 00:27:02,900 --> 00:27:03,990 exposure? 571 00:27:03,990 --> 00:27:06,530 In other words, if they end up hedging all of that exposure, 572 00:27:06,530 --> 00:27:09,260 then it doesn't matter anymore, right? 573 00:27:09,260 --> 00:27:10,700 So it depends. 574 00:27:10,700 --> 00:27:15,740 But the idea is that, if it has exposure to a 0 beta asset, 575 00:27:15,740 --> 00:27:18,770 then you will find that the ultimate fluctuations are 576 00:27:18,770 --> 00:27:21,830 going to have less correlation to the market portfolio. 577 00:27:21,830 --> 00:27:22,760 Slomi? 578 00:27:22,760 --> 00:27:24,620 AUDIENCE: Maybe Microsoft has a bigger beta 579 00:27:24,620 --> 00:27:28,370 because during this period, the 10 years, 580 00:27:28,370 --> 00:27:32,410 Microsoft was a [? growth ?] company, and [INAUDIBLE].. 581 00:27:32,410 --> 00:27:35,819 So this is the reason why it has a bigger beta. 582 00:27:35,819 --> 00:27:37,360 ANDREW LO: You know, that's possible. 583 00:27:37,360 --> 00:27:39,700 But remember that when we estimate the beta, 584 00:27:39,700 --> 00:27:42,370 we're estimating it using monthly returns. 585 00:27:42,370 --> 00:27:44,050 And so we're measuring the covariance 586 00:27:44,050 --> 00:27:46,570 on a month-to-month basis, not just the trend. 587 00:27:46,570 --> 00:27:50,240 We're measuring fluctuations around that trend. 588 00:27:50,240 --> 00:27:53,710 So the trend alone won't necessarily explain all of it. 589 00:27:53,710 --> 00:27:56,980 It has to also be the fluctuations are actually 590 00:27:56,980 --> 00:28:01,570 going both up and down, higher than the variability 591 00:28:01,570 --> 00:28:04,540 of the market portfolio. 592 00:28:04,540 --> 00:28:06,100 Let me continue on with the example. 593 00:28:06,100 --> 00:28:06,810 And we're going to come back. 594 00:28:06,810 --> 00:28:08,435 I'm going to show how to estimate this, 595 00:28:08,435 --> 00:28:10,570 and then you'll develop more intuition from it. 596 00:28:10,570 --> 00:28:14,170 So this makes sense from the smell test in the sense 597 00:28:14,170 --> 00:28:17,226 that Microsoft, at least during that period of time, 598 00:28:17,226 --> 00:28:19,600 was not necessarily something that you would expect would 599 00:28:19,600 --> 00:28:21,610 do well in good times and bad. 600 00:28:21,610 --> 00:28:25,000 But something like razor blades and shaving cream 601 00:28:25,000 --> 00:28:26,650 we need to use regardless. 602 00:28:26,650 --> 00:28:31,020 So that sort of tells us that these betas look about right. 603 00:28:31,020 --> 00:28:31,600 OK. 604 00:28:31,600 --> 00:28:34,030 If you agree with the betas, then it 605 00:28:34,030 --> 00:28:36,460 turns out that we can actually calculate 606 00:28:36,460 --> 00:28:40,070 the required rate of return for each of these two stocks. 607 00:28:40,070 --> 00:28:43,820 So if you assume that the risk-free rate is 5%, 608 00:28:43,820 --> 00:28:47,170 which is what it was about in that period-- 609 00:28:47,170 --> 00:28:51,520 not today obviously, but back in that period, so about 5%. 610 00:28:51,520 --> 00:28:53,560 And if, historically, the risk premium, 611 00:28:53,560 --> 00:28:55,930 as I told you last time, is about 6%, 612 00:28:55,930 --> 00:28:58,810 then when you do the calculations using the security 613 00:28:58,810 --> 00:29:01,570 market line, you get a very sharp answer 614 00:29:01,570 --> 00:29:04,480 to the question, what are the appropriate discount rates 615 00:29:04,480 --> 00:29:06,940 or costs of capital for these two companies? 616 00:29:06,940 --> 00:29:11,560 The answer, for Gillette, it's about 9.86%, for Microsoft, 617 00:29:11,560 --> 00:29:14,620 13.94%. 618 00:29:14,620 --> 00:29:18,329 So now if you're sitting in these companies 619 00:29:18,329 --> 00:29:19,870 and you're asking the question, we're 620 00:29:19,870 --> 00:29:23,450 going to expand our operations, but in order to do that, 621 00:29:23,450 --> 00:29:26,800 we have to do an NPV calculation to see whether it's worthwhile. 622 00:29:26,800 --> 00:29:30,937 We have to compute the expected net present value of expansion. 623 00:29:30,937 --> 00:29:32,770 And in order to do that, we've got estimates 624 00:29:32,770 --> 00:29:36,040 of what our cash flows are going to be for our expansion, 625 00:29:36,040 --> 00:29:38,559 but we don't know what the cost of capital is. 626 00:29:38,559 --> 00:29:39,850 Well here's the answer for you. 627 00:29:39,850 --> 00:29:43,000 You've actually got hard numbers to plug in to your NPV 628 00:29:43,000 --> 00:29:46,000 calculations now. 629 00:29:46,000 --> 00:29:49,375 Now, there are a bunch of assumptions that we've made. 630 00:29:49,375 --> 00:29:51,250 So we're going to have to go back and justify 631 00:29:51,250 --> 00:29:55,810 those assumptions each and every time you use this technology. 632 00:29:55,810 --> 00:29:57,400 It's not physics. 633 00:29:57,400 --> 00:29:59,110 This is not mathematics. 634 00:29:59,110 --> 00:30:01,930 You're applying a set of theories and approximations 635 00:30:01,930 --> 00:30:03,952 to a much, much more complex reality. 636 00:30:03,952 --> 00:30:05,410 Every time you apply it, you've got 637 00:30:05,410 --> 00:30:08,800 to go back and ask the question, does it make sense? 638 00:30:08,800 --> 00:30:10,510 Do these assumptions hold? 639 00:30:10,510 --> 00:30:12,380 And if so, great, go ahead and use it. 640 00:30:12,380 --> 00:30:15,430 If not, you've got to go back and rederive 641 00:30:15,430 --> 00:30:17,470 some of these analytics. 642 00:30:17,470 --> 00:30:21,220 OK, so the security market line is now 643 00:30:21,220 --> 00:30:24,230 a line that describes the expected return, 644 00:30:24,230 --> 00:30:27,880 or required rate of return, on an asset or a project 645 00:30:27,880 --> 00:30:31,180 as a function of the riskiness, where the riskiness is now 646 00:30:31,180 --> 00:30:33,640 measured by beta, not by sigma. 647 00:30:33,640 --> 00:30:36,550 It's not variance or standard deviation 648 00:30:36,550 --> 00:30:42,510 that measures the appropriate risk for most projects. 649 00:30:42,510 --> 00:30:45,390 Most projects, the way you measure their risk 650 00:30:45,390 --> 00:30:47,900 is not by sigma. 651 00:30:47,900 --> 00:30:50,180 It turns out that the way you measure their risk, 652 00:30:50,180 --> 00:30:54,410 for the purposes of calculating the required rate of return, 653 00:30:54,410 --> 00:30:58,010 you measure it by beta. 654 00:30:58,010 --> 00:30:59,240 OK? 655 00:30:59,240 --> 00:31:01,970 That's a very deep insight. 656 00:31:01,970 --> 00:31:04,580 It changes the way we think about risk 657 00:31:04,580 --> 00:31:05,900 and expected rate of return. 658 00:31:05,900 --> 00:31:09,175 It's not to say that risk, in terms of volatility, 659 00:31:09,175 --> 00:31:09,800 doesn't matter. 660 00:31:09,800 --> 00:31:11,000 Of course it does. 661 00:31:11,000 --> 00:31:13,460 That is the basis of this entire framework. 662 00:31:13,460 --> 00:31:16,400 We started out by saying that people don't like sigma, 663 00:31:16,400 --> 00:31:18,350 and they do like mu. 664 00:31:18,350 --> 00:31:19,400 They don't like variants. 665 00:31:19,400 --> 00:31:21,320 They do like expected rate of return. 666 00:31:21,320 --> 00:31:22,850 That still holds. 667 00:31:22,850 --> 00:31:26,900 But in doing so, when we derive all of these implications, what 668 00:31:26,900 --> 00:31:30,680 we find is that, as an investor, you 669 00:31:30,680 --> 00:31:34,970 don't get rewarded for taking larger and larger amounts 670 00:31:34,970 --> 00:31:38,000 of volatility necessarily. 671 00:31:38,000 --> 00:31:42,260 You do get rewarded for taking larger and larger amounts 672 00:31:42,260 --> 00:31:43,700 of beta. 673 00:31:43,700 --> 00:31:48,200 That's the sense in which beta is a better measure of risk. 674 00:31:48,200 --> 00:31:52,010 For the purposes of computing the required rate of return, 675 00:31:52,010 --> 00:31:54,980 beta is the right measurement, not sigma. 676 00:31:54,980 --> 00:31:59,120 The only cases where sigma is the right measure of risk-- 677 00:31:59,120 --> 00:32:03,620 when I say right, I mean where increases in sigma must imply 678 00:32:03,620 --> 00:32:07,020 increases in the required rate of return-- 679 00:32:07,020 --> 00:32:09,580 is when? 680 00:32:09,580 --> 00:32:11,990 When is sigma the right measure of risk 681 00:32:11,990 --> 00:32:16,920 for the purposes of computing the required rate of return? 682 00:32:16,920 --> 00:32:19,620 For what kind of securities or portfolios? 683 00:32:22,450 --> 00:32:22,962 Yeah? 684 00:32:22,962 --> 00:32:24,670 AUDIENCE: Is it for efficient portfolios? 685 00:32:24,670 --> 00:32:25,461 ANDREW LO: Exactly. 686 00:32:25,461 --> 00:32:28,000 For efficient portfolios only. 687 00:32:28,000 --> 00:32:33,130 Efficient portfolios meaning these guys, meaning these guys. 688 00:32:33,130 --> 00:32:37,600 Anything on this line, then sigma is the right measure. 689 00:32:37,600 --> 00:32:44,700 Sigma p over sigma m, that is the right measure for any kind 690 00:32:44,700 --> 00:32:47,640 of portfolio that is efficient. 691 00:32:47,640 --> 00:32:49,760 But we know that the typical security, 692 00:32:49,760 --> 00:32:54,650 the typical project, the typical division, is not efficient. 693 00:32:54,650 --> 00:32:57,870 Efficient, again, meaning you can get the-- 694 00:32:57,870 --> 00:33:00,660 you can't get any better expected rate of return 695 00:33:00,660 --> 00:33:04,320 for the same risk, or you can't get a lower amount of risk 696 00:33:04,320 --> 00:33:06,460 for the same expected rate of return. 697 00:33:06,460 --> 00:33:10,740 So for all of the inefficient securities, portfolios, 698 00:33:10,740 --> 00:33:13,770 or projects, you've got to use this relationship, 699 00:33:13,770 --> 00:33:16,690 and this relationship tells you beta is what matters, 700 00:33:16,690 --> 00:33:17,700 not sigma. 701 00:33:17,700 --> 00:33:21,000 Sigma is not the same as beta, except if you happen 702 00:33:21,000 --> 00:33:24,910 to be an efficient portfolio. 703 00:33:24,910 --> 00:33:25,654 OK. 704 00:33:25,654 --> 00:33:27,070 Question-- do you have a question? 705 00:33:27,070 --> 00:33:27,569 No? 706 00:33:27,569 --> 00:33:28,520 OK. 707 00:33:28,520 --> 00:33:29,820 All right. 708 00:33:29,820 --> 00:33:34,470 So here's an example of the security market line at work. 709 00:33:34,470 --> 00:33:37,530 And the slope of this security market line 710 00:33:37,530 --> 00:33:40,050 is, of course, the expected rate of return on the market 711 00:33:40,050 --> 00:33:41,640 minus the risk-free rate. 712 00:33:41,640 --> 00:33:44,160 And the idea behind the security market line 713 00:33:44,160 --> 00:33:48,480 is that, no matter what your beta is, 714 00:33:48,480 --> 00:33:50,790 you've got a required rate of return that's 715 00:33:50,790 --> 00:33:52,740 determined by this slope. 716 00:33:52,740 --> 00:33:56,670 And now, to answer Eduard's question about deviations 717 00:33:56,670 --> 00:33:59,610 and how far away you are from efficiency 718 00:33:59,610 --> 00:34:04,320 if you deviate from this line, then the vertical distance 719 00:34:04,320 --> 00:34:10,699 is the alpha of your portfolio or project or investment 720 00:34:10,699 --> 00:34:12,260 opportunity. 721 00:34:12,260 --> 00:34:15,920 If markets are working exactly the way they should, 722 00:34:15,920 --> 00:34:17,600 then you're on this line. 723 00:34:17,600 --> 00:34:19,900 You're always on this line. 724 00:34:19,900 --> 00:34:23,800 And if you're Warren Buffett, you're off of this line. 725 00:34:23,800 --> 00:34:26,449 You've got a very large, positive alpha. 726 00:34:26,449 --> 00:34:29,650 So if you've got skill, if you can forecast markets, 727 00:34:29,650 --> 00:34:32,449 then you will do better than this. 728 00:34:32,449 --> 00:34:35,650 But what this framework tells you is that even if you cannot 729 00:34:35,650 --> 00:34:38,230 forecast markets, even if you don't know what's going 730 00:34:38,230 --> 00:34:41,900 to happen next year to stock prices, 731 00:34:41,900 --> 00:34:47,980 you should still do as well as what this line suggests that 732 00:34:47,980 --> 00:34:48,980 you can do. 733 00:34:48,980 --> 00:34:49,480 OK? 734 00:34:49,480 --> 00:34:54,489 On average, this line should be achievable by everybody 735 00:34:54,489 --> 00:34:58,190 that understands the basics of portfolio theory. 736 00:34:58,190 --> 00:35:03,290 Now, as I said, the performance evaluation approach 737 00:35:03,290 --> 00:35:05,720 to using the security market line 738 00:35:05,720 --> 00:35:07,760 is just a measure of the vertical distances. 739 00:35:07,760 --> 00:35:11,100 And it can lead to some interesting results. 740 00:35:11,100 --> 00:35:14,480 For example, here are three managers. 741 00:35:14,480 --> 00:35:18,900 All three of these managers have a 15% expected rate of return. 742 00:35:22,020 --> 00:35:25,130 But they have different betas. 743 00:35:25,130 --> 00:35:26,900 And so the question is, if you had 744 00:35:26,900 --> 00:35:28,680 money to put into these managers, 745 00:35:28,680 --> 00:35:30,240 which would you choose? 746 00:35:30,240 --> 00:35:34,010 Well, clearly you would choose manager A 747 00:35:34,010 --> 00:35:35,720 because the manager is only supposed 748 00:35:35,720 --> 00:35:40,790 to have a 6% rate of return, but, in fact, he's offering 15 749 00:35:40,790 --> 00:35:42,350 for that level of risk. 750 00:35:42,350 --> 00:35:46,370 Manager B is just basically doing 751 00:35:46,370 --> 00:35:49,310 what you would expect the manager should be doing. 752 00:35:49,310 --> 00:35:53,180 And manager C is actually underperforming. 753 00:35:53,180 --> 00:35:56,720 Given the risk that manager C is exposing you to, 754 00:35:56,720 --> 00:35:59,570 manager C should be doing much better than he is. 755 00:36:03,280 --> 00:36:06,070 And by the way, notice that I've said that the same-- 756 00:36:06,070 --> 00:36:10,030 all three managers have the same volatility, 20%. 757 00:36:10,030 --> 00:36:14,290 You can have the same volatility but have different betas. 758 00:36:14,290 --> 00:36:19,390 Betas and volatilities do not necessarily go hand in hand. 759 00:36:19,390 --> 00:36:23,110 There is actually a relationship between beta and volatility. 760 00:36:23,110 --> 00:36:25,580 We'll talk about that in a little while. 761 00:36:25,580 --> 00:36:29,279 But that relationship is not nearly as straightforward 762 00:36:29,279 --> 00:36:30,070 as you might think. 763 00:36:30,070 --> 00:36:30,570 Ingrid? 764 00:36:33,630 --> 00:36:37,750 AUDIENCE: Can you estimate a future return of a mutual fund 765 00:36:37,750 --> 00:36:40,484 by [INAUDIBLE]. 766 00:36:40,484 --> 00:36:42,400 I mean, I understand it's the best you can do, 767 00:36:42,400 --> 00:36:44,260 but how realistic is it? 768 00:36:44,260 --> 00:36:48,430 ANDREW LO: Well, so it depends on who you are. 769 00:36:48,430 --> 00:36:52,900 If you are a typical index fund manager, 770 00:36:52,900 --> 00:36:56,590 you would argue that mutual funds are basically 771 00:36:56,590 --> 00:37:02,200 going to provide you with a relatively stable expected rate 772 00:37:02,200 --> 00:37:03,644 of return over time. 773 00:37:03,644 --> 00:37:05,560 So in other words, it'll fluctuate up and down 774 00:37:05,560 --> 00:37:07,390 because it's got some variance, but there 775 00:37:07,390 --> 00:37:09,760 is a baseline expected rate of return 776 00:37:09,760 --> 00:37:11,620 that a mutual fund offers you. 777 00:37:11,620 --> 00:37:13,300 And that's what people are buying. 778 00:37:13,300 --> 00:37:15,640 When you put your money in an emerging market 779 00:37:15,640 --> 00:37:18,040 equity mutual fund, you're going to have a higher 780 00:37:18,040 --> 00:37:22,660 return on average, on average, than if you put your money 781 00:37:22,660 --> 00:37:25,659 in a S&P 500 index fund. 782 00:37:25,659 --> 00:37:27,700 Why are you going to have a higher rate of return 783 00:37:27,700 --> 00:37:28,270 on average? 784 00:37:28,270 --> 00:37:31,810 Because you're going be bearing more risk on average. 785 00:37:31,810 --> 00:37:34,750 The only way to convince you to put your money in an emerging 786 00:37:34,750 --> 00:37:38,500 market fund is if it does have that higher expected rate 787 00:37:38,500 --> 00:37:40,660 of return on average. 788 00:37:40,660 --> 00:37:45,190 So what you're basing these kinds of calculations on 789 00:37:45,190 --> 00:37:48,370 is not that I can forecast what mutual funds are going 790 00:37:48,370 --> 00:37:50,860 to do next year, but rather, mutual funds 791 00:37:50,860 --> 00:37:54,440 offer expected rate of returns that are stable over time. 792 00:37:54,440 --> 00:37:56,920 So what happened last year and the year before and the year 793 00:37:56,920 --> 00:37:59,210 before that, when you average it all together, 794 00:37:59,210 --> 00:38:03,300 it's about what you're going to get over the next five years. 795 00:38:03,300 --> 00:38:03,800 That's it. 796 00:38:03,800 --> 00:38:04,580 That's the argument. 797 00:38:04,580 --> 00:38:05,454 AUDIENCE: [INAUDIBLE] 798 00:38:05,454 --> 00:38:06,139 ANDREW LO: Yes. 799 00:38:06,139 --> 00:38:07,430 We don't know-- right, exactly. 800 00:38:07,430 --> 00:38:12,440 So there is a very large idiosyncratic component 801 00:38:12,440 --> 00:38:15,950 that fluctuates year by year, and who 802 00:38:15,950 --> 00:38:18,510 knows what that could be. 803 00:38:18,510 --> 00:38:20,050 OK. 804 00:38:20,050 --> 00:38:20,777 Yes? 805 00:38:20,777 --> 00:38:22,685 AUDIENCE: Last time, when you were 806 00:38:22,685 --> 00:38:24,600 describing more [INAUDIBLE]. 807 00:38:24,600 --> 00:38:25,230 ANDREW LO: Yes. 808 00:38:25,230 --> 00:38:29,810 AUDIENCE: You had mentioned that for more risk people 809 00:38:29,810 --> 00:38:32,880 will expect more return, but not necessarily 810 00:38:32,880 --> 00:38:34,930 proportional to the-- 811 00:38:34,930 --> 00:38:40,634 so you end up having a line that just goes up exponentially, 812 00:38:40,634 --> 00:38:41,134 right? 813 00:38:41,134 --> 00:38:45,060 Because you had given the analogy that, OK, 814 00:38:45,060 --> 00:38:47,480 now to get investors to be in more risk, 815 00:38:47,480 --> 00:38:52,310 to take on more risk, you have to offer a lot more than just 816 00:38:52,310 --> 00:38:54,050 [INAUDIBLE]. 817 00:38:54,050 --> 00:38:55,520 ANDREW LO: Well, you may. 818 00:38:55,520 --> 00:38:58,760 But the equilibrium theory that we've argued 819 00:38:58,760 --> 00:39:03,050 has to hold actually says that the risk-reward trade-off 820 00:39:03,050 --> 00:39:06,410 is, in fact, linear for efficient portfolios. 821 00:39:06,410 --> 00:39:11,010 If it's not for efficient portfolios, then who knows? 822 00:39:11,010 --> 00:39:13,640 But the theory of the capital asset pricing 823 00:39:13,640 --> 00:39:15,830 model, or the security market line, which 824 00:39:15,830 --> 00:39:18,920 is what we derive-- what we what we talked about today, 825 00:39:18,920 --> 00:39:22,150 this says that, in fact, it is linear. 826 00:39:22,150 --> 00:39:24,070 So in other words, this result, as I told you, 827 00:39:24,070 --> 00:39:26,640 we didn't derive it, but it's a major result 828 00:39:26,640 --> 00:39:30,150 that shows that the relationship between risk and expected 829 00:39:30,150 --> 00:39:37,170 return, where risk is measured by beta now, is linear. 830 00:39:37,170 --> 00:39:39,370 This is a linear relationship. 831 00:39:39,370 --> 00:39:43,440 So this is a major advance that we didn't expect. 832 00:39:43,440 --> 00:39:47,410 And, in fact, so what I showed before was the preferences. 833 00:39:47,410 --> 00:39:50,880 So in other words, we talked last time about the situation 834 00:39:50,880 --> 00:39:54,630 where, suppose that you're an investor, 835 00:39:54,630 --> 00:39:57,990 and I start you off at a point like this. 836 00:39:57,990 --> 00:40:00,570 And I ask the question, if I want 837 00:40:00,570 --> 00:40:05,580 you to tell me where you're going to be such 838 00:40:05,580 --> 00:40:07,580 that you're just as well off. 839 00:40:07,580 --> 00:40:10,250 You have the same level of utility. 840 00:40:10,250 --> 00:40:12,270 That curve, that indifference curve, 841 00:40:12,270 --> 00:40:15,870 is going to look something like this. 842 00:40:15,870 --> 00:40:17,520 That's going to be curved. 843 00:40:17,520 --> 00:40:19,580 That's what you're talking about. 844 00:40:19,580 --> 00:40:23,720 But that's the behavior of one individual. 845 00:40:23,720 --> 00:40:25,380 The point about the CAPM is that if you 846 00:40:25,380 --> 00:40:29,820 aggregate all of the individuals together and ask the question, 847 00:40:29,820 --> 00:40:33,120 what does the expected rate of return and volatility 848 00:40:33,120 --> 00:40:35,850 or expected rate of return and beta look like? 849 00:40:35,850 --> 00:40:37,270 How are they related? 850 00:40:37,270 --> 00:40:41,280 In fact, it's magical that it actually is linear. 851 00:40:41,280 --> 00:40:45,360 So it's exactly the fact that we didn't expect linearity. 852 00:40:45,360 --> 00:40:48,120 Given that there are diminishing marginal returns 853 00:40:48,120 --> 00:40:51,930 to risk and reward, you wouldn't expect linearity. 854 00:40:51,930 --> 00:40:53,850 But, in fact, it drops out. 855 00:40:53,850 --> 00:40:58,320 I mean, this drops out of this tangency portfolio argument, 856 00:40:58,320 --> 00:40:59,660 right? 857 00:40:59,660 --> 00:41:01,410 Nothing up my sleeve, this was an argument 858 00:41:01,410 --> 00:41:02,460 that we all did together. 859 00:41:02,460 --> 00:41:05,790 And we derived this curve from first principles. 860 00:41:05,790 --> 00:41:10,230 So this is really an astounding result, 861 00:41:10,230 --> 00:41:12,180 but it's even more astonishing that you 862 00:41:12,180 --> 00:41:14,370 get this result for all securities, 863 00:41:14,370 --> 00:41:18,570 not just for efficient portfolios. 864 00:41:18,570 --> 00:41:22,170 OK, other questions? 865 00:41:22,170 --> 00:41:22,980 All right. 866 00:41:22,980 --> 00:41:24,970 Let's do another example. 867 00:41:24,970 --> 00:41:30,010 So here I want to show you how you can use the security market 868 00:41:30,010 --> 00:41:33,950 line, also called the CAPM, C-A-P-M, 869 00:41:33,950 --> 00:41:36,339 for Capital Asset Pricing Model. 870 00:41:36,339 --> 00:41:37,880 I want to show you how you can use it 871 00:41:37,880 --> 00:41:39,900 to do performance attribution. 872 00:41:39,900 --> 00:41:43,460 This is the data from a real live hedge fund 873 00:41:43,460 --> 00:41:46,250 manager, who will go nameless since I don't want to get 874 00:41:46,250 --> 00:41:48,680 sued by him for any reason. 875 00:41:48,680 --> 00:41:52,520 Hedge fund managers are both very wealthy, typically, 876 00:41:52,520 --> 00:41:55,610 and also very litigious, so you want 877 00:41:55,610 --> 00:41:58,520 to be careful when you talk about them in public. 878 00:41:58,520 --> 00:42:02,960 Hedge fund XYZ had an average annualized return of 12.5% 879 00:42:02,960 --> 00:42:06,080 and a return standard deviation of 5.5% from January 880 00:42:06,080 --> 00:42:11,660 '85 to December 2002, and the estimated beta over this period 881 00:42:11,660 --> 00:42:13,840 was minus 0.028. 882 00:42:13,840 --> 00:42:15,590 Now, somebody asked about a negative beta. 883 00:42:15,590 --> 00:42:19,540 Well here's an example of a negative beta asset. 884 00:42:19,540 --> 00:42:23,960 Positive expected rate of return, negative beta. 885 00:42:23,960 --> 00:42:25,900 So if it's got a positive expected return 886 00:42:25,900 --> 00:42:28,270 and a negative beta, you know something can't exactly 887 00:42:28,270 --> 00:42:31,840 be right because that doesn't sound like it makes sense 888 00:42:31,840 --> 00:42:34,440 in terms of the CAPM framework. 889 00:42:34,440 --> 00:42:35,940 And, in fact, it doesn't. 890 00:42:35,940 --> 00:42:37,390 It doesn't make sense. 891 00:42:37,390 --> 00:42:39,510 Well, let's do the math. 892 00:42:39,510 --> 00:42:41,370 The expected the rate of return is 893 00:42:41,370 --> 00:42:45,000 equal to Rf plus beta times the market risk premium. 894 00:42:45,000 --> 00:42:48,300 Market risk premium of 6%, risk-free rate of 5%, 895 00:42:48,300 --> 00:42:50,430 plug that in with the beta of minus 0.028, 896 00:42:50,430 --> 00:42:53,730 and you get that this manager should 897 00:42:53,730 --> 00:42:57,940 have earned 4.83% per year. 898 00:42:57,940 --> 00:43:01,560 That's what the manager should have earned. 899 00:43:01,560 --> 00:43:07,380 In fact, the manager earned a rate of return of 12.% 900 00:43:07,380 --> 00:43:09,040 per year. 901 00:43:09,040 --> 00:43:10,590 So that's an alpha. 902 00:43:10,590 --> 00:43:14,880 If you define the alpha as what the manager did earn minus 903 00:43:14,880 --> 00:43:17,520 what the manager should have earned, 904 00:43:17,520 --> 00:43:23,230 you've got an alpha of 771 basis points per year. 905 00:43:23,230 --> 00:43:26,470 That's a humongous alpha. 906 00:43:26,470 --> 00:43:31,420 Very, very big amount of excess performance. 907 00:43:31,420 --> 00:43:34,010 This is why people are excited about hedge funds. 908 00:43:34,010 --> 00:43:37,120 Now, we're not going to talk in great detail about it 909 00:43:37,120 --> 00:43:40,780 in this course because it goes beyond the scope of Finance 910 00:43:40,780 --> 00:43:42,520 401. 911 00:43:42,520 --> 00:43:45,999 But in an investments course, the next level 912 00:43:45,999 --> 00:43:48,040 of sophistication would be to take a look at this 913 00:43:48,040 --> 00:43:51,940 and say, OK, is this alpha really alpha, 914 00:43:51,940 --> 00:43:57,331 or is it due to other factors, other risks that we're not 915 00:43:57,331 --> 00:43:57,830 measuring? 916 00:43:57,830 --> 00:44:00,200 Right now the only risk we're measuring 917 00:44:00,200 --> 00:44:06,070 is this tangency portfolio risk, this beta risk. 918 00:44:06,070 --> 00:44:08,360 But maybe there are multiple betas out there. 919 00:44:08,360 --> 00:44:10,360 We're not going to talk about it in this course, 920 00:44:10,360 --> 00:44:11,960 but in 433 you will discuss it. 921 00:44:11,960 --> 00:44:13,940 And it will turn out that hedge funds actually 922 00:44:13,940 --> 00:44:15,719 do have multiple betas. 923 00:44:15,719 --> 00:44:18,260 So you shouldn't go out and put all your money in hedge funds 924 00:44:18,260 --> 00:44:21,320 right away because this extra performance, some of it 925 00:44:21,320 --> 00:44:28,207 is due to true genius and insight and unique skill. 926 00:44:28,207 --> 00:44:29,790 But part of it is also due to the fact 927 00:44:29,790 --> 00:44:33,570 that you're bearing risks that you had no idea you're bearing. 928 00:44:33,570 --> 00:44:36,360 And so you've got to be careful about getting on the bandwagon 929 00:44:36,360 --> 00:44:38,190 and saying, yeah, give me some hedge funds. 930 00:44:38,190 --> 00:44:39,670 I want some of this alpha. 931 00:44:39,670 --> 00:44:41,439 Anon? 932 00:44:41,439 --> 00:44:46,891 AUDIENCE: [INAUDIBLE] But how do we know 933 00:44:46,891 --> 00:44:48,210 this is good for the investor? 934 00:44:48,210 --> 00:44:52,174 Because they could have invested in the asset [INAUDIBLE].. 935 00:44:52,174 --> 00:44:53,840 ANDREW LO: So the question is, how do we 936 00:44:53,840 --> 00:44:56,120 know that this is actually good for the investor? 937 00:44:56,120 --> 00:45:00,470 Because they could have gotten some returns from the S&P. 938 00:45:00,470 --> 00:45:03,210 The way we know that is because we're 939 00:45:03,210 --> 00:45:08,860 measuring the expected rate of return relative to the S&P. 940 00:45:08,860 --> 00:45:11,310 So in other words, the way I got this number, 941 00:45:11,310 --> 00:45:14,190 this is the excess return on the S&P. 942 00:45:14,190 --> 00:45:16,440 That's what the market risk premium is. 943 00:45:16,440 --> 00:45:21,790 So in fact, given the beta of this manager, 944 00:45:21,790 --> 00:45:25,960 it should have only given you 4.83% 945 00:45:25,960 --> 00:45:29,590 return relative to what the S&P would have given you, 946 00:45:29,590 --> 00:45:33,290 which is a 6% excess rate of return. 947 00:45:33,290 --> 00:45:37,820 And, in fact, what we see is that this manager produced 948 00:45:37,820 --> 00:45:41,450 a 12% rate of return, or 7% above 949 00:45:41,450 --> 00:45:44,990 and beyond what it was supposed to have done. 950 00:45:44,990 --> 00:45:46,796 So this takes that into account. 951 00:45:46,796 --> 00:45:48,170 What it doesn't take into account 952 00:45:48,170 --> 00:45:51,650 is how much liquidity risk the hedge fund manager is taking, 953 00:45:51,650 --> 00:45:55,770 how much currency risk, how much commodity risk, 954 00:45:55,770 --> 00:45:58,530 and a bunch of other risks that are not represented 955 00:45:58,530 --> 00:46:01,060 by the tangency portfolio. 956 00:46:01,060 --> 00:46:02,771 Megan? 957 00:46:02,771 --> 00:46:05,256 AUDIENCE: [? When you hear about ?] 958 00:46:05,256 --> 00:46:07,490 looking out for beta dressed up as alpha, 959 00:46:07,490 --> 00:46:10,877 it's really because there are multiple sources of beta 960 00:46:10,877 --> 00:46:12,460 that aren't getting wrapped into that. 961 00:46:12,460 --> 00:46:13,330 ANDREW LO: Exactly. 962 00:46:13,330 --> 00:46:14,440 That's exactly right. 963 00:46:14,440 --> 00:46:16,570 Recently, a lot of institutional investors 964 00:46:16,570 --> 00:46:18,220 have become skeptical of hedge funds 965 00:46:18,220 --> 00:46:21,760 because they say, hedge funds alpha 966 00:46:21,760 --> 00:46:24,110 is really dressed up data. 967 00:46:24,110 --> 00:46:25,870 In other words, hedge fund managers 968 00:46:25,870 --> 00:46:27,820 are taking risks that are not captured 969 00:46:27,820 --> 00:46:29,546 by this very simple framework. 970 00:46:29,546 --> 00:46:31,420 And so when you run these kind of regressions 971 00:46:31,420 --> 00:46:34,210 and do this analysis, you're getting tremendous alpha, 972 00:46:34,210 --> 00:46:36,630 but in fact, it's not all alpha. 973 00:46:36,630 --> 00:46:40,040 There's other kinds of betas in there. 974 00:46:40,040 --> 00:46:41,620 And so there's a whole literature 975 00:46:41,620 --> 00:46:44,020 that has developed about multiple, 976 00:46:44,020 --> 00:46:47,020 what are called exotic, betas or alternative betas. 977 00:46:47,020 --> 00:46:49,750 Again, not part of the scope of introductory 978 00:46:49,750 --> 00:46:53,193 finance, but it is something that's covered in investments. 979 00:46:57,060 --> 00:47:01,950 Just another illustration of what this hedge fund has done. 980 00:47:01,950 --> 00:47:04,950 Take a look at the growth of $1 invested 981 00:47:04,950 --> 00:47:08,760 in the hedge fund over the last 20 years, 982 00:47:08,760 --> 00:47:11,130 and you'll see that the blue line is the hedge fund. 983 00:47:11,130 --> 00:47:13,270 The red line is the S&P 500. 984 00:47:13,270 --> 00:47:18,224 So to your point, Anon, the S&P 500 gave you a wild ride. 985 00:47:18,224 --> 00:47:19,890 And so for a while you were doing better 986 00:47:19,890 --> 00:47:23,100 than the hedge fund, but, in fact, now this hedge fund 987 00:47:23,100 --> 00:47:24,660 has done quite a bit better. 988 00:47:24,660 --> 00:47:27,744 Now this ends in 2002. 989 00:47:27,744 --> 00:47:29,410 I'll give you a little bit of an update. 990 00:47:29,410 --> 00:47:31,400 I don't have it here in the graph, 991 00:47:31,400 --> 00:47:34,420 but you can use your imagination. 992 00:47:34,420 --> 00:47:38,290 It turns out that up to 2007, the blue line 993 00:47:38,290 --> 00:47:40,030 is way ahead of the red line. 994 00:47:42,890 --> 00:47:45,870 That's actually changed in 2008. 995 00:47:45,870 --> 00:47:49,160 This hedge fund has done very badly this year. 996 00:47:49,160 --> 00:47:52,620 Of course, the S&P has done even worse. 997 00:47:52,620 --> 00:47:55,130 So the gap is not as wide as it used to be. 998 00:47:55,130 --> 00:47:59,110 There's still a gap, but the gap is actually narrowed a bit. 999 00:47:59,110 --> 00:48:00,060 Yeah? 1000 00:48:00,060 --> 00:48:04,335 AUDIENCE: [INAUDIBLE] The risk-free rate is changing. 1001 00:48:04,335 --> 00:48:07,737 The market rate is changing, so-- 1002 00:48:07,737 --> 00:48:08,320 ANDREW LO: No. 1003 00:48:08,320 --> 00:48:10,280 In fact, everything is changing. 1004 00:48:10,280 --> 00:48:12,931 So if you want to take seriously change, 1005 00:48:12,931 --> 00:48:15,430 you've basically got to figure out how the risk-free rate is 1006 00:48:15,430 --> 00:48:17,920 changing, the expected rate of return is changing, 1007 00:48:17,920 --> 00:48:21,424 and the betas actually are also changing. 1008 00:48:21,424 --> 00:48:23,590 But what I'm trying to do with a simple illustration 1009 00:48:23,590 --> 00:48:26,850 is use a long period and say, over that entire period, 1010 00:48:26,850 --> 00:48:29,270 let's average across all of these changes. 1011 00:48:29,270 --> 00:48:30,008 Justin? 1012 00:48:30,008 --> 00:48:35,424 AUDIENCE: [INAUDIBLE] If you look at the graph 1013 00:48:35,424 --> 00:48:38,612 and it seems like the differences of the graph 1014 00:48:38,612 --> 00:48:40,540 were just higher with the market. 1015 00:48:40,540 --> 00:48:43,660 ANDREW LO: It is, but you don't adjust for the beta. 1016 00:48:43,660 --> 00:48:45,460 That's the key, right? 1017 00:48:45,460 --> 00:48:47,930 The S&P has a beta of 1. 1018 00:48:47,930 --> 00:48:49,910 This guy, this hedge fund manager, 1019 00:48:49,910 --> 00:48:53,150 has a beta of 0 or slightly negative. 1020 00:48:53,150 --> 00:48:54,680 That's the difference. 1021 00:48:54,680 --> 00:48:58,190 That's why looking at volatility can be misleading. 1022 00:48:58,190 --> 00:48:59,750 If you look at volatility, you'd say, 1023 00:48:59,750 --> 00:49:03,000 well, you know, obviously the S&P has done better. 1024 00:49:03,000 --> 00:49:08,750 But keep in mind that look how smooth the blue line is. 1025 00:49:08,750 --> 00:49:13,670 And the lesson of the CAPM is that investors 1026 00:49:13,670 --> 00:49:17,930 pay for smoothness, but only a certain kind of smoothness. 1027 00:49:17,930 --> 00:49:21,290 In other words, smoothness means low volatility, right? 1028 00:49:21,290 --> 00:49:23,690 The smoothest line, of course, is T-bills. 1029 00:49:23,690 --> 00:49:24,830 That's a straight line. 1030 00:49:24,830 --> 00:49:28,340 That will go sort of like this. 1031 00:49:28,340 --> 00:49:30,680 And investors are not going to pay a lot for that 1032 00:49:30,680 --> 00:49:34,280 because that doesn't really help them generate 1033 00:49:34,280 --> 00:49:36,020 expected rate of return. 1034 00:49:36,020 --> 00:49:39,290 If you've got expected rate of return and smoothness together, 1035 00:49:39,290 --> 00:49:42,270 you get a really big, big alpha. 1036 00:49:42,270 --> 00:49:45,620 And that's exactly what we see here, an alpha of 771 basis 1037 00:49:45,620 --> 00:49:46,120 points. 1038 00:49:48,950 --> 00:49:51,580 Now, here I talk about these multiple sources 1039 00:49:51,580 --> 00:49:53,410 of systematic risk. 1040 00:49:53,410 --> 00:49:55,630 I don't want to focus on that for this course 1041 00:49:55,630 --> 00:49:58,360 because, as I said, it's going to be much more complicated 1042 00:49:58,360 --> 00:50:00,710 and requires more machinery. 1043 00:50:00,710 --> 00:50:03,730 But the basic intuition is the same. 1044 00:50:03,730 --> 00:50:08,270 Instead of just one source of systematic risk, 1045 00:50:08,270 --> 00:50:09,554 you may have multiple sources. 1046 00:50:09,554 --> 00:50:11,720 And so therefore, you're going to have multiple risk 1047 00:50:11,720 --> 00:50:14,550 premia as opposed to just one. 1048 00:50:14,550 --> 00:50:17,450 But for now, let's not focus on that. 1049 00:50:17,450 --> 00:50:19,310 And we're going to focus our attention just 1050 00:50:19,310 --> 00:50:22,289 on this simple equation, and make sure we understand it 1051 00:50:22,289 --> 00:50:23,330 and know how to apply it. 1052 00:50:26,290 --> 00:50:27,690 Now, I want to go-- 1053 00:50:27,690 --> 00:50:32,320 I want to give you one more intuition for why 1054 00:50:32,320 --> 00:50:36,670 it is that beta is the appropriate measure of risk, 1055 00:50:36,670 --> 00:50:41,500 and not sigma, for arbitrary inefficient portfolios. 1056 00:50:41,500 --> 00:50:44,470 And the idea is actually pretty simple. 1057 00:50:44,470 --> 00:50:46,990 When you think of an investment like Microsoft 1058 00:50:46,990 --> 00:50:51,280 or like Gillette, you can think of the risk of that portfolio 1059 00:50:51,280 --> 00:50:52,270 as being-- 1060 00:50:52,270 --> 00:50:55,690 the risk of that investment in those individual securities 1061 00:50:55,690 --> 00:50:57,650 as having two components. 1062 00:50:57,650 --> 00:51:00,580 So when you think of the volatility of Gillette, 1063 00:51:00,580 --> 00:51:02,890 you can think of the volatility of Gillette 1064 00:51:02,890 --> 00:51:05,730 coming from two sources. 1065 00:51:05,730 --> 00:51:15,340 One source is the aggregate risk that affects all companies. 1066 00:51:15,340 --> 00:51:17,380 And the second source of risk is the risk 1067 00:51:17,380 --> 00:51:19,630 unique to Gillette, the fact that they've 1068 00:51:19,630 --> 00:51:22,750 got a particular manufacturing plant in a particular location 1069 00:51:22,750 --> 00:51:24,310 of the country, the fact that they've 1070 00:51:24,310 --> 00:51:27,880 got a specific set of managers that are either good or bad, 1071 00:51:27,880 --> 00:51:29,680 the fact that they are subject to a very 1072 00:51:29,680 --> 00:51:33,310 specific set of requirements for producing their blades, 1073 00:51:33,310 --> 00:51:37,100 who knows, but very specific to that company. 1074 00:51:37,100 --> 00:51:41,900 When you think about that kind of risk, 1075 00:51:41,900 --> 00:51:45,620 let me ask you a question from a purely business perspective. 1076 00:51:45,620 --> 00:51:46,790 You're the investor. 1077 00:51:46,790 --> 00:51:48,500 I'm a representative of Gillette. 1078 00:51:48,500 --> 00:51:50,810 I'm trying to sell you my company's stock. 1079 00:51:50,810 --> 00:51:54,600 I want you to invest in my company. 1080 00:51:54,600 --> 00:52:00,850 And therefore, I have to pay you to take the risk of Gillette. 1081 00:52:00,850 --> 00:52:04,490 If I tell you that Gillette has these two pieces of risk-- 1082 00:52:04,490 --> 00:52:08,380 so I'm the representative from Gillette and I tell you that 1083 00:52:08,380 --> 00:52:12,190 our company is subject to economy-wide fluctuations that 1084 00:52:12,190 --> 00:52:17,350 will help or hurt our business and unique fluctuations that 1085 00:52:17,350 --> 00:52:22,490 are specific and special to Gillette-- 1086 00:52:22,490 --> 00:52:25,100 which of these two risks are you going 1087 00:52:25,100 --> 00:52:29,000 to be more concerned about from your investment portfolio 1088 00:52:29,000 --> 00:52:31,050 perspective? 1089 00:52:31,050 --> 00:52:31,550 Rami? 1090 00:52:31,550 --> 00:52:34,310 AUDIENCE: I think you'd be more concerned about-- 1091 00:52:34,310 --> 00:52:36,610 as a portfolio as a whole, you look at the economy, 1092 00:52:36,610 --> 00:52:38,611 but I think, for this specific purpose, 1093 00:52:38,611 --> 00:52:41,710 [INAUDIBLE] you obviously will pick Gillette-specific-- 1094 00:52:41,710 --> 00:52:42,640 ANDREW LO: OK. 1095 00:52:42,640 --> 00:52:45,110 But I want-- you hurried through the first point, 1096 00:52:45,110 --> 00:52:47,180 and I want you to expand on that a little bit. 1097 00:52:47,180 --> 00:52:50,480 You said that if you're worried about your portfolio, then 1098 00:52:50,480 --> 00:52:52,190 obviously the economy-wide risk. 1099 00:52:52,190 --> 00:52:53,162 AUDIENCE: Absolutely. 1100 00:52:53,162 --> 00:52:56,564 If you're worried about the economy-wide risk, 1101 00:52:56,564 --> 00:52:58,994 and for example, over the next two, three years, 1102 00:52:58,994 --> 00:53:01,157 you don't think the economy is going to recover, 1103 00:53:01,157 --> 00:53:03,900 then you're going to just avoid that type of investment 1104 00:53:03,900 --> 00:53:04,440 as a whole. 1105 00:53:04,440 --> 00:53:05,790 ANDREW LO: OK. 1106 00:53:05,790 --> 00:53:06,834 OK, fine. 1107 00:53:06,834 --> 00:53:09,000 But on the other hand, you also said something else, 1108 00:53:09,000 --> 00:53:11,730 which is that if you're comparing between two stocks, 1109 00:53:11,730 --> 00:53:13,950 then what you're focusing on is the risks that 1110 00:53:13,950 --> 00:53:15,756 are unique to Gillette. 1111 00:53:15,756 --> 00:53:20,193 AUDIENCE: You also might look at how much the economic downturn 1112 00:53:20,193 --> 00:53:22,350 would affect a company like Gillette. 1113 00:53:22,350 --> 00:53:23,066 ANDREW LO: Right. 1114 00:53:23,066 --> 00:53:25,482 AUDIENCE: So if the economic downturn, as you said before, 1115 00:53:25,482 --> 00:53:28,815 affects Microsoft greater than it would Gillette, 1116 00:53:28,815 --> 00:53:30,689 and you suspect something is going to happen, 1117 00:53:30,689 --> 00:53:32,154 you'd go for Gillette. 1118 00:53:32,154 --> 00:53:34,112 If, on the other hand, you didn't suspect that, 1119 00:53:34,112 --> 00:53:35,590 you might go for-- 1120 00:53:35,590 --> 00:53:36,210 ANDREW LO: OK. 1121 00:53:36,210 --> 00:53:38,670 But let's now talk about the negotiations 1122 00:53:38,670 --> 00:53:39,780 between you and me. 1123 00:53:39,780 --> 00:53:41,160 I'm a representative of Gillette. 1124 00:53:41,160 --> 00:53:43,370 I'm trying to get you to invest with us. 1125 00:53:43,370 --> 00:53:45,330 And I've got two sources of risk that you 1126 00:53:45,330 --> 00:53:51,500 might be concerned about, market risk or Gillette-specific risk. 1127 00:53:51,500 --> 00:53:53,990 From your portfolio perspective, since you just 1128 00:53:53,990 --> 00:53:57,271 care about maximizing the value of your portfolio, 1129 00:53:57,271 --> 00:53:59,270 you're not worried about Gillette in particular. 1130 00:53:59,270 --> 00:54:00,290 You're not management. 1131 00:54:00,290 --> 00:54:01,250 You're an investor. 1132 00:54:01,250 --> 00:54:02,210 I'm management. 1133 00:54:02,210 --> 00:54:03,410 I'm worried about Gillette. 1134 00:54:03,410 --> 00:54:06,380 I couldn't care less about your portfolio, I'm sorry to say. 1135 00:54:06,380 --> 00:54:09,680 What I care about is my company, but what you care about 1136 00:54:09,680 --> 00:54:10,910 is your portfolio. 1137 00:54:10,910 --> 00:54:13,340 From your portfolio perspective, what 1138 00:54:13,340 --> 00:54:17,030 are you going to care more about, Gillette-specific risk 1139 00:54:17,030 --> 00:54:22,495 or the macroeconomic risk that I represent to your portfolio? 1140 00:54:22,495 --> 00:54:23,950 AUDIENCE: When I'm talking to you, 1141 00:54:23,950 --> 00:54:26,380 I care more about your specific risks. 1142 00:54:26,380 --> 00:54:28,840 ANDREW LO: Well, I'm asking a question though 1143 00:54:28,840 --> 00:54:29,927 about your portfolio. 1144 00:54:29,927 --> 00:54:31,510 What you care about is your portfolio. 1145 00:54:31,510 --> 00:54:33,070 I understand that when you're talking to me, 1146 00:54:33,070 --> 00:54:35,528 you're going to be asking me about my company-specific risk 1147 00:54:35,528 --> 00:54:36,940 to try to get a handle on it. 1148 00:54:36,940 --> 00:54:38,920 But is that what you ultimately are 1149 00:54:38,920 --> 00:54:40,151 going to be concerned about? 1150 00:54:40,151 --> 00:54:42,150 AUDIENCE: I would be concerned about, obviously, 1151 00:54:42,150 --> 00:54:46,237 the macro portion of it and how you fit into that. 1152 00:54:46,237 --> 00:54:49,109 But I'd look at your beta and see-- 1153 00:54:49,109 --> 00:54:50,900 ANDREW LO: You don't know the CAPM, though. 1154 00:54:50,900 --> 00:54:55,460 So now you're cheating because you now know the CAPM. 1155 00:54:55,460 --> 00:54:56,630 But suppose you didn't. 1156 00:54:56,630 --> 00:54:58,450 What I'm trying to get at is the intuition, 1157 00:54:58,450 --> 00:55:00,890 a businessman's intuition, for what 1158 00:55:00,890 --> 00:55:03,110 you would care about more in terms 1159 00:55:03,110 --> 00:55:05,810 of what I do to your portfolio. 1160 00:55:05,810 --> 00:55:06,530 Yeah, Sema? 1161 00:55:06,530 --> 00:55:08,362 AUDIENCE: Didn't you say, two lectures ago, 1162 00:55:08,362 --> 00:55:11,570 that the idiosyncratic risk is [? their survival? ?] 1163 00:55:11,570 --> 00:55:12,305 ANDREW LO: Yes. 1164 00:55:12,305 --> 00:55:14,430 AUDIENCE: So, you care more about systematic risk-- 1165 00:55:14,430 --> 00:55:14,790 ANDREW LO: Why? 1166 00:55:14,790 --> 00:55:16,910 AUDIENCE: Because only one [INAUDIBLE] in my portfolio. 1167 00:55:16,910 --> 00:55:18,350 ANDREW LO: That's exactly right. 1168 00:55:18,350 --> 00:55:21,860 The idea is that if it's Gillette-specific 1169 00:55:21,860 --> 00:55:24,980 risk, then by definition, if you're 1170 00:55:24,980 --> 00:55:28,150 holding a well-diversified portfolio, 1171 00:55:28,150 --> 00:55:30,760 then you're not going to care about that because that's going 1172 00:55:30,760 --> 00:55:33,100 to average out to nothing. 1173 00:55:33,100 --> 00:55:36,040 Now, of course, we have to think about the case 1174 00:55:36,040 --> 00:55:38,260 where you're not holding a diversified portfolio, 1175 00:55:38,260 --> 00:55:40,390 but let me get back to that in a minute. 1176 00:55:40,390 --> 00:55:42,849 I'm assuming that all of you are good business folks, which 1177 00:55:42,849 --> 00:55:44,390 means that you're going to be holding 1178 00:55:44,390 --> 00:55:45,500 a diversified portfolio. 1179 00:55:45,500 --> 00:55:47,770 You're not going to concentrate all your bets 1180 00:55:47,770 --> 00:55:52,150 on one particular kind of investment, right? 1181 00:55:52,150 --> 00:55:55,060 So if you are already holding a very well-diversified 1182 00:55:55,060 --> 00:55:57,970 portfolio, then when you interview me 1183 00:55:57,970 --> 00:56:01,960 as a potential investment opportunity, 1184 00:56:01,960 --> 00:56:04,870 do you really care about the idiosyncratic risk? 1185 00:56:04,870 --> 00:56:07,360 Because that risk is going to be diversified away. 1186 00:56:07,360 --> 00:56:09,760 What you care about from a portfolio perspective is, 1187 00:56:09,760 --> 00:56:12,250 how much am I going to be contributing 1188 00:56:12,250 --> 00:56:14,140 to your overall risk? 1189 00:56:14,140 --> 00:56:18,520 And now that you know the CAPM, you understand the logic of it. 1190 00:56:18,520 --> 00:56:23,080 It says, you care about my beta because my beta is a measure 1191 00:56:23,080 --> 00:56:26,320 of the amount of risk I'm going to be adding to your portfolio 1192 00:56:26,320 --> 00:56:28,180 that you cannot get rid of. 1193 00:56:28,180 --> 00:56:30,910 How do you know you cannot get rid of it? 1194 00:56:30,910 --> 00:56:33,840 Well, by definition it's the market portfolio. 1195 00:56:33,840 --> 00:56:34,950 Everybody's holding it. 1196 00:56:34,950 --> 00:56:37,480 Nobody wants to get rid of it completely. 1197 00:56:37,480 --> 00:56:40,170 You're on the capital market's line. 1198 00:56:40,170 --> 00:56:41,910 That's the best you can do. 1199 00:56:41,910 --> 00:56:47,100 So this notion of firm-specific risk 1200 00:56:47,100 --> 00:56:50,100 versus economy-wide risk, that distinction 1201 00:56:50,100 --> 00:56:51,690 is a really important one. 1202 00:56:51,690 --> 00:56:54,190 And I'll show you the mathematics of it in a minute, 1203 00:56:54,190 --> 00:56:56,410 but I want to give you the intuition. 1204 00:56:56,410 --> 00:56:59,490 As a result, think about this conversation 1205 00:56:59,490 --> 00:57:02,100 happening not just for Gillette, but for every company 1206 00:57:02,100 --> 00:57:03,720 in the economy. 1207 00:57:03,720 --> 00:57:07,680 If it's the case that portfolio managers that are buying stocks 1208 00:57:07,680 --> 00:57:12,490 only care about the systematic risk, about the market risk, 1209 00:57:12,490 --> 00:57:15,640 about the risk that they cannot get rid of, and then you have 1210 00:57:15,640 --> 00:57:18,850 to reward them for that, then what that means is that you 1211 00:57:18,850 --> 00:57:23,850 don't have to reward them for idiosyncratic risk. 1212 00:57:23,850 --> 00:57:24,480 Why? 1213 00:57:24,480 --> 00:57:26,934 Because that's not risk that you are forced to bear. 1214 00:57:26,934 --> 00:57:28,350 There's nothing that says you have 1215 00:57:28,350 --> 00:57:30,672 to bear idiosyncratic risk. 1216 00:57:30,672 --> 00:57:32,130 How do you get rid of idiosyncratic 1217 00:57:32,130 --> 00:57:35,160 risk if you don't want to bear it? 1218 00:57:35,160 --> 00:57:35,790 Diversify. 1219 00:57:35,790 --> 00:57:36,660 Exactly. 1220 00:57:36,660 --> 00:57:38,610 Just buy 10 stocks instead of one, 1221 00:57:38,610 --> 00:57:39,830 and then you're diversified. 1222 00:57:39,830 --> 00:57:41,940 20 stocks is better than 10. 1223 00:57:41,940 --> 00:57:45,390 And mathematically, after 50 stocks, 1224 00:57:45,390 --> 00:57:47,040 you're basically diversified. 1225 00:57:47,040 --> 00:57:48,600 You're done. 1226 00:57:48,600 --> 00:57:53,190 So nobody should be holding two or three stocks. 1227 00:57:53,190 --> 00:57:58,855 Or if they do, they are bearing risk that they need not bear. 1228 00:57:58,855 --> 00:58:00,730 And they may want to do it for other reasons. 1229 00:58:00,730 --> 00:58:03,900 For example, as a manager of Gillette, 1230 00:58:03,900 --> 00:58:05,730 I believe in the company. 1231 00:58:05,730 --> 00:58:07,530 I want to demonstrate to my shareholders 1232 00:58:07,530 --> 00:58:09,600 that I'm tied to the company, so I'm 1233 00:58:09,600 --> 00:58:12,090 going to hold a lot of my wealth in Gillette stock. 1234 00:58:12,090 --> 00:58:13,740 That's not well diversified. 1235 00:58:13,740 --> 00:58:17,310 I'm holding a lot of Gillette-specific risk. 1236 00:58:17,310 --> 00:58:19,530 That's not a smart thing to do from an investment 1237 00:58:19,530 --> 00:58:21,300 point of view, but that is a smart thing 1238 00:58:21,300 --> 00:58:23,430 to do from a management point of view 1239 00:58:23,430 --> 00:58:28,480 because I'm tying my fate to the fate of the company. 1240 00:58:28,480 --> 00:58:32,130 It's definitely not a smart thing from an investments 1241 00:58:32,130 --> 00:58:33,330 perspective. 1242 00:58:33,330 --> 00:58:35,100 If you're in a financial services sector, 1243 00:58:35,100 --> 00:58:38,096 you should not be buying financial services stocks. 1244 00:58:38,096 --> 00:58:39,720 If you're in the pharmaceutical sector, 1245 00:58:39,720 --> 00:58:42,090 you should not be buying biotech stocks. 1246 00:58:42,090 --> 00:58:47,220 And yet we do that for reasons other than portfolio 1247 00:58:47,220 --> 00:58:48,600 management. 1248 00:58:48,600 --> 00:58:51,454 But given that I'm teaching you about portfolio management, 1249 00:58:51,454 --> 00:58:53,370 I'm not going to focus on those other reasons. 1250 00:58:53,370 --> 00:58:56,062 If this were an organizational studies course, 1251 00:58:56,062 --> 00:58:57,770 you'd be getting a different perspective. 1252 00:58:57,770 --> 00:58:59,740 And you should get a different perspective. 1253 00:58:59,740 --> 00:59:02,250 But for the purposes of building financial wealth, what 1254 00:59:02,250 --> 00:59:04,500 you want to do is to focus on how 1255 00:59:04,500 --> 00:59:07,950 much the systematic component is contributing to your risk, 1256 00:59:07,950 --> 00:59:10,290 because the idiosyncratic component 1257 00:59:10,290 --> 00:59:11,970 you don't have to bear. 1258 00:59:11,970 --> 00:59:12,977 Yeah? 1259 00:59:12,977 --> 00:59:15,101 AUDIENCE: So like an employee purchase plan, where, 1260 00:59:15,101 --> 00:59:15,737 if you're in financial services, you're 1261 00:59:15,737 --> 00:59:17,153 working for a mutual fund company, 1262 00:59:17,153 --> 00:59:19,800 and they offer you 10%, 15% you put your salary in, 1263 00:59:19,800 --> 00:59:20,855 and you can buy stock-- 1264 00:59:20,855 --> 00:59:21,480 ANDREW LO: Yes. 1265 00:59:21,480 --> 00:59:23,040 AUDIENCE: Would you recommend not doing that? 1266 00:59:23,040 --> 00:59:24,748 ANDREW LO: Well, I recommend not doing it 1267 00:59:24,748 --> 00:59:26,760 from the financial perspective, but I 1268 00:59:26,760 --> 00:59:28,620 may recommend doing it from the management, 1269 00:59:28,620 --> 00:59:30,600 or managerial incentives, perspective. 1270 00:59:30,600 --> 00:59:34,370 The reason that companies do that is very simple. 1271 00:59:34,370 --> 00:59:35,964 They're trying to suck you in. 1272 00:59:35,964 --> 00:59:38,130 They're trying to get you to be more intimately tied 1273 00:59:38,130 --> 00:59:41,670 to the company so you'll act like an owner of the company, 1274 00:59:41,670 --> 00:59:43,880 as opposed to an employee. 1275 00:59:43,880 --> 00:59:45,950 And if you act like an owner, you 1276 00:59:45,950 --> 00:59:48,350 will engage in behavior that is much more 1277 00:59:48,350 --> 00:59:50,990 productive for building the company's wealth, 1278 00:59:50,990 --> 00:59:52,830 rather than as an employee. 1279 00:59:52,830 --> 00:59:55,010 But from your personal perspective, 1280 00:59:55,010 --> 00:59:59,030 you're bearing risk that you don't need to. 1281 00:59:59,030 --> 01:00:01,810 So you know, the analogy that I give-- 1282 01:00:01,810 --> 01:00:03,940 I've given before-- it may work for some of you. 1283 01:00:03,940 --> 01:00:04,510 It may not. 1284 01:00:04,510 --> 01:00:07,000 Let me explain. 1285 01:00:07,000 --> 01:00:13,300 Anybody know how much window washers in midtown Manhattan 1286 01:00:13,300 --> 01:00:14,877 get paid on an annual basis? 1287 01:00:14,877 --> 01:00:16,210 You know what I'm talking about? 1288 01:00:16,210 --> 01:00:19,810 These are the folks that climb up on these two-foot catwalks 1289 01:00:19,810 --> 01:00:22,480 that are 40 stories high, and they wash the windows 1290 01:00:22,480 --> 01:00:23,860 of these skyscrapers. 1291 01:00:23,860 --> 01:00:26,079 That's a pretty risky job. 1292 01:00:26,079 --> 01:00:27,620 Anybody know what their annual salary 1293 01:00:27,620 --> 01:00:28,760 is, when you annualize it? 1294 01:00:28,760 --> 01:00:31,496 I actually decided to find out one day. 1295 01:00:31,496 --> 01:00:33,620 I was kind of curious about that because, you know, 1296 01:00:33,620 --> 01:00:35,210 there's a trade-off of risk and return. 1297 01:00:35,210 --> 01:00:36,060 And that's really risky. 1298 01:00:36,060 --> 01:00:38,476 You know, there was one day when I was staying at a hotel. 1299 01:00:38,476 --> 01:00:41,780 I think it was the Millennium, and I was on the 30th floor, 1300 01:00:41,780 --> 01:00:43,622 and it was a windy winter day. 1301 01:00:43,622 --> 01:00:45,830 And, sure enough, there was somebody there pulling up 1302 01:00:45,830 --> 01:00:48,950 the thing, cleaning the window, and looked happy as can be. 1303 01:00:48,950 --> 01:00:50,420 You know, no problem. 1304 01:00:50,420 --> 01:00:53,600 And I was thinking, boy, this guy's taking a lot of risk, 1305 01:00:53,600 --> 01:00:54,740 you know? 1306 01:00:54,740 --> 01:00:59,070 And I hope he's getting paid for it. 1307 01:00:59,070 --> 01:01:01,700 And these salaries are determined 1308 01:01:01,700 --> 01:01:02,740 by supply and demand. 1309 01:01:02,740 --> 01:01:03,420 What do you think it would be? 1310 01:01:03,420 --> 01:01:04,410 Anybody have a guess? 1311 01:01:04,410 --> 01:01:05,464 Yeah? 1312 01:01:05,464 --> 01:01:06,730 AUDIENCE: About $70,000. 1313 01:01:06,730 --> 01:01:09,860 ANDREW LO: $70,000, OK. 1314 01:01:09,860 --> 01:01:10,500 Anybody else? 1315 01:01:10,500 --> 01:01:11,176 Justin? 1316 01:01:11,176 --> 01:01:12,170 AUDIENCE: $125,000. 1317 01:01:12,170 --> 01:01:13,250 ANDREW LO: $125,000? 1318 01:01:13,250 --> 01:01:14,709 [LAUGHTER] 1319 01:01:14,709 --> 01:01:16,625 That's higher than some NBA starting salaries. 1320 01:01:16,625 --> 01:01:17,900 [LAUGHTER] 1321 01:01:17,900 --> 01:01:18,710 OK. 1322 01:01:18,710 --> 01:01:19,540 Leah? 1323 01:01:19,540 --> 01:01:20,290 AUDIENCE: $30,000. 1324 01:01:20,290 --> 01:01:21,081 ANDREW LO: $30,000. 1325 01:01:21,081 --> 01:01:22,550 AUDIENCE: Do they take interns? 1326 01:01:22,550 --> 01:01:23,620 ANDREW LO: Insurance? 1327 01:01:23,620 --> 01:01:24,560 Interns. 1328 01:01:24,560 --> 01:01:25,061 Interns. 1329 01:01:25,061 --> 01:01:26,060 I don't know about that. 1330 01:01:26,060 --> 01:01:26,620 [LAUGHTER] 1331 01:01:26,620 --> 01:01:29,120 Well, so when I looked last time, which 1332 01:01:29,120 --> 01:01:31,610 is about four years ago, it turns out 1333 01:01:31,610 --> 01:01:35,300 that the typical window washer for these skyscrapers 1334 01:01:35,300 --> 01:01:39,430 gets paid about $60,000 a year, annual salary. 1335 01:01:39,430 --> 01:01:42,040 $60,000. 1336 01:01:42,040 --> 01:01:44,950 Now, you know, I don't know whether you 1337 01:01:44,950 --> 01:01:46,810 think that's a lot or a little. 1338 01:01:46,810 --> 01:01:51,520 But, seems to me that that compensation reflects 1339 01:01:51,520 --> 01:01:54,220 the kind of risk that we're talking about. 1340 01:01:54,220 --> 01:01:56,860 And you know, you have no educational requirements, 1341 01:01:56,860 --> 01:01:58,450 no degrees, no certifications. 1342 01:01:58,450 --> 01:02:01,510 You just show up and, you know, up you go. 1343 01:02:01,510 --> 01:02:03,670 Now let me ask you a question. 1344 01:02:03,670 --> 01:02:07,450 Suppose that a window washer comes 1345 01:02:07,450 --> 01:02:11,560 to the job who happens to really enjoy dancing 1346 01:02:11,560 --> 01:02:13,404 while he washes windows. 1347 01:02:13,404 --> 01:02:15,070 In particular, he dances that, you know, 1348 01:02:15,070 --> 01:02:16,330 the Irish jig or whatever. 1349 01:02:16,330 --> 01:02:17,710 [LAUGHTER] 1350 01:02:17,710 --> 01:02:19,204 You know what I'm talking about? 1351 01:02:19,204 --> 01:02:20,620 You know, that dancing, the very-- 1352 01:02:20,620 --> 01:02:23,590 and he just likes to do that while he's washing windows 1353 01:02:23,590 --> 01:02:25,750 on the 40th floor. 1354 01:02:25,750 --> 01:02:28,899 You agree that that's more risky, right? 1355 01:02:28,899 --> 01:02:30,940 Do you think that that particular individual gets 1356 01:02:30,940 --> 01:02:34,850 paid more than $60,000 a year? 1357 01:02:34,850 --> 01:02:35,350 Why? 1358 01:02:35,350 --> 01:02:37,821 He's taking more risk. 1359 01:02:37,821 --> 01:02:38,320 Why not? 1360 01:02:38,320 --> 01:02:39,611 Why isn't he getting paid more? 1361 01:02:42,000 --> 01:02:43,240 Exactly. 1362 01:02:43,240 --> 01:02:44,830 He doesn't have to take that risk. 1363 01:02:44,830 --> 01:02:46,780 That's not part of the job. 1364 01:02:46,780 --> 01:02:49,420 He can choose to take that risk, but he's not 1365 01:02:49,420 --> 01:02:52,840 going to get compensated for it because it's not necessary. 1366 01:02:52,840 --> 01:02:55,960 And there are 100,000 people behind him waiting in line 1367 01:02:55,960 --> 01:02:58,150 to get that job that won't necessarily 1368 01:02:58,150 --> 01:02:59,826 need to take that risk. 1369 01:02:59,826 --> 01:03:00,522 Yeah? 1370 01:03:00,522 --> 01:03:02,380 AUDIENCE: I thought of it differently. 1371 01:03:02,380 --> 01:03:04,006 If you had a long, short portfolio, 1372 01:03:04,006 --> 01:03:05,380 would it be the other way around? 1373 01:03:05,380 --> 01:03:07,380 Because you wouldn't care about the market risk. 1374 01:03:07,380 --> 01:03:08,590 You can hedge that out. 1375 01:03:08,590 --> 01:03:10,442 You're thinking only about specific risk. 1376 01:03:10,442 --> 01:03:13,800 So like in that case, I would short the guy who likes to jig. 1377 01:03:13,800 --> 01:03:15,602 And I would invest in the guy who didn't. 1378 01:03:15,602 --> 01:03:17,560 ANDREW LO: Well, that depends on whether or not 1379 01:03:17,560 --> 01:03:19,510 doing the Irish jig actually makes 1380 01:03:19,510 --> 01:03:21,580 you wash windows better or worse, 1381 01:03:21,580 --> 01:03:24,190 in other words, where there's an alpha to that risk. 1382 01:03:24,190 --> 01:03:26,260 It may be the case that dancing the Irish jig 1383 01:03:26,260 --> 01:03:28,270 actually helps you scrape off dirt 1384 01:03:28,270 --> 01:03:29,470 that much more effectively. 1385 01:03:29,470 --> 01:03:31,303 In which case, you may not want to short him 1386 01:03:31,303 --> 01:03:34,240 because then he will earn a premium in certain markets. 1387 01:03:34,240 --> 01:03:37,177 Those with lots of pigeon poop on the windows. 1388 01:03:37,177 --> 01:03:38,430 [LAUGHTER] 1389 01:03:38,430 --> 01:03:41,020 So we can get into this analogy more deeply than we should. 1390 01:03:41,020 --> 01:03:42,190 [LAUGHTER] 1391 01:03:42,190 --> 01:03:44,770 But the point is that, when you think about the CAPM, 1392 01:03:44,770 --> 01:03:48,560 all it's saying is that you get what you pay for. 1393 01:03:48,560 --> 01:03:50,150 And you pay for what you get. 1394 01:03:50,150 --> 01:03:52,810 In other words, if there is a certain amount of risk 1395 01:03:52,810 --> 01:03:57,550 in a particular investment that is risk that nobody 1396 01:03:57,550 --> 01:03:59,560 can get rid of easily-- 1397 01:03:59,560 --> 01:04:01,780 in other words, you have to bear it-- 1398 01:04:01,780 --> 01:04:03,430 then you have to pay for it. 1399 01:04:03,430 --> 01:04:05,840 Because otherwise people aren't going to do it. 1400 01:04:05,840 --> 01:04:07,990 However, if there's risk in a particular company 1401 01:04:07,990 --> 01:04:12,280 that you don't have to pay for, that you don't have to take, 1402 01:04:12,280 --> 01:04:14,030 then you don't have to pay for it. 1403 01:04:14,030 --> 01:04:16,810 That's all that the CAPM is saying. 1404 01:04:16,810 --> 01:04:21,370 Beta is a measure of that hard little pellet of risk 1405 01:04:21,370 --> 01:04:23,080 that you can't get rid of. 1406 01:04:23,080 --> 01:04:26,920 And the variance is the measure of the entire risk 1407 01:04:26,920 --> 01:04:29,570 in a particular portfolio. 1408 01:04:29,570 --> 01:04:34,710 The only case where variance and beta are the same 1409 01:04:34,710 --> 01:04:38,050 is for what kind of portfolio? 1410 01:04:38,050 --> 01:04:39,209 An efficient portfolio. 1411 01:04:39,209 --> 01:04:40,500 What is an efficient portfolio? 1412 01:04:40,500 --> 01:04:43,990 It's one that is already maximally diversified. 1413 01:04:43,990 --> 01:04:46,330 By adding more securities, you are not 1414 01:04:46,330 --> 01:04:49,960 going to do any better than that straight line. 1415 01:04:49,960 --> 01:04:55,090 All of these portfolios have been completely diversified. 1416 01:04:55,090 --> 01:04:56,000 How do I know that? 1417 01:04:56,000 --> 01:04:58,510 Because you're at the tangency portfolio. 1418 01:04:58,510 --> 01:05:00,700 There is nowhere to go in the Northwest 1419 01:05:00,700 --> 01:05:02,900 region off of that line. 1420 01:05:02,900 --> 01:05:08,260 So for all of these securities, the sigma and the beta 1421 01:05:08,260 --> 01:05:10,450 are literally numerically identical because there 1422 01:05:10,450 --> 01:05:13,690 is no more extra risk in the portfolio. 1423 01:05:13,690 --> 01:05:15,540 It's been diversified away. 1424 01:05:15,540 --> 01:05:19,190 But for Gillette, for Microsoft, for IBM, General Motors, 1425 01:05:19,190 --> 01:05:22,940 and Motorola, each of these contain both beta risk 1426 01:05:22,940 --> 01:05:25,580 and non-beta risk. 1427 01:05:25,580 --> 01:05:27,500 The non-beta risk is that Irish jig 1428 01:05:27,500 --> 01:05:29,844 that you don't have to do while you're washing windows. 1429 01:05:29,844 --> 01:05:32,260 And you're not going to get paid for it, I'm sorry to say. 1430 01:05:32,260 --> 01:05:36,170 So the relationship that you want to focus on 1431 01:05:36,170 --> 01:05:39,950 is the capital asset pricing model's security market line. 1432 01:05:39,950 --> 01:05:42,200 Measure the stuff that you're going to get paid for. 1433 01:05:42,200 --> 01:05:45,710 And this is what you're going to get paid for it. 1434 01:05:45,710 --> 01:05:47,335 Yeah, Ingrid? 1435 01:05:47,335 --> 01:05:50,185 AUDIENCE: When you go back into the sort of the real world 1436 01:05:50,185 --> 01:05:54,000 and include transaction costs, how do they enter here? 1437 01:05:54,000 --> 01:05:56,750 ANDREW LO: Well, so there have been versions of the CAPM 1438 01:05:56,750 --> 01:05:58,610 with transactions cost. 1439 01:05:58,610 --> 01:06:02,150 And it turns out that it doesn't change things too much. 1440 01:06:02,150 --> 01:06:06,680 If you impose transactions cost on all securities, 1441 01:06:06,680 --> 01:06:08,760 and say that there's a percentage 1442 01:06:08,760 --> 01:06:11,790 cost for going in and out, you can derive a net 1443 01:06:11,790 --> 01:06:13,670 of fee transactions costs. 1444 01:06:13,670 --> 01:06:16,040 It won't affect the pricing necessarily. 1445 01:06:16,040 --> 01:06:19,010 What it will affect is the dynamics, the trading. 1446 01:06:19,010 --> 01:06:21,620 What it will mean is that you will rebalance your portfolios 1447 01:06:21,620 --> 01:06:23,676 less frequently than you otherwise might. 1448 01:06:23,676 --> 01:06:25,550 But there is still going to be a relationship 1449 01:06:25,550 --> 01:06:28,190 between the net of fee transactions 1450 01:06:28,190 --> 01:06:29,940 costs of these securities. 1451 01:06:29,940 --> 01:06:32,450 So you can actually look at the transactions cost 1452 01:06:32,450 --> 01:06:35,600 as a way to deduct the expected rate of return 1453 01:06:35,600 --> 01:06:38,444 from each of these securities. 1454 01:06:38,444 --> 01:06:40,110 So transactions cost is not a big issue, 1455 01:06:40,110 --> 01:06:41,610 but there are other issues that I'll 1456 01:06:41,610 --> 01:06:43,662 come to that will be a problem for this. 1457 01:06:43,662 --> 01:06:47,064 AUDIENCE: Looking at this, [INAUDIBLE] one of the best, 1458 01:06:47,064 --> 01:06:50,466 efficient portfolio that I can have is basically the index. 1459 01:06:50,466 --> 01:06:53,870 If I want to allocate my money globally, 1460 01:06:53,870 --> 01:06:57,008 should I buy indexes according to the market 1461 01:06:57,008 --> 01:06:57,970 capital of the market? 1462 01:06:57,970 --> 01:06:58,765 ANDREW LO: Yeah. 1463 01:06:58,765 --> 01:07:03,026 AUDIENCE: This is the most efficient portfolio I would-- 1464 01:07:03,026 --> 01:07:04,900 ANDREW LO: Right, so that's a great question. 1465 01:07:04,900 --> 01:07:07,530 And we actually have a separate course on international finance 1466 01:07:07,530 --> 01:07:09,238 that deals just with those kind of issues 1467 01:07:09,238 --> 01:07:10,410 because they're so tricky. 1468 01:07:10,410 --> 01:07:12,270 But I'll give you the short answer. 1469 01:07:12,270 --> 01:07:16,590 According to the theory, this tangency portfolio 1470 01:07:16,590 --> 01:07:19,950 is not just for the US stock market. 1471 01:07:19,950 --> 01:07:23,560 It should be for the world stock market, everything. 1472 01:07:23,560 --> 01:07:25,740 So this tangency portfolio should not 1473 01:07:25,740 --> 01:07:28,020 be the S&P 500 or the Russell 2000, 1474 01:07:28,020 --> 01:07:31,230 it should be the MSCI, or EAFE, index 1475 01:07:31,230 --> 01:07:35,460 that has all of the assets in the world weighted 1476 01:07:35,460 --> 01:07:38,490 relative to their market cap in that particular currency 1477 01:07:38,490 --> 01:07:41,200 of the investor that you happen to be. 1478 01:07:41,200 --> 01:07:43,830 So if you're a US investor, it'll be in dollars. 1479 01:07:43,830 --> 01:07:46,680 If you're a Brazilian investor, it'll be in real. 1480 01:07:46,680 --> 01:07:50,073 It'll be in whatever currency you trade in. 1481 01:07:50,073 --> 01:07:54,590 But that presupposes that there's 1482 01:07:54,590 --> 01:07:57,960 capital market integration throughout the world. 1483 01:07:57,960 --> 01:08:01,910 So in other words, if I call this the world portfolio, 1484 01:08:01,910 --> 01:08:04,700 implicitly I'm assuming that you're 1485 01:08:04,700 --> 01:08:09,440 free to trade stocks in any part of the world freely. 1486 01:08:09,440 --> 01:08:11,809 There are no barriers to trading. 1487 01:08:11,809 --> 01:08:13,350 And we know that that's not the case. 1488 01:08:13,350 --> 01:08:14,930 There are barriers, in fact. 1489 01:08:14,930 --> 01:08:17,569 So what that means is that the CAPM, applied 1490 01:08:17,569 --> 01:08:21,020 to international stocks, is an approximation that may actually 1491 01:08:21,020 --> 01:08:24,990 be worse than applying it country by country 1492 01:08:24,990 --> 01:08:28,220 and then looking to see whether there are any distances 1493 01:08:28,220 --> 01:08:31,556 or discrepancies across those different countries. 1494 01:08:31,556 --> 01:08:33,680 But people have come up with international versions 1495 01:08:33,680 --> 01:08:34,939 of the CAPM. 1496 01:08:34,939 --> 01:08:36,410 And they don't work very well. 1497 01:08:36,410 --> 01:08:39,300 At least, they didn't as of 10 years ago. 1498 01:08:39,300 --> 01:08:41,510 Within the last 10 years, a lot has changed. 1499 01:08:41,510 --> 01:08:44,000 So it could be that capital market integration 1500 01:08:44,000 --> 01:08:47,029 has made the world CAPM look a lot better 1501 01:08:47,029 --> 01:08:49,237 in terms of the data. 1502 01:08:49,237 --> 01:08:50,649 OK. 1503 01:08:50,649 --> 01:08:54,221 Other questions? 1504 01:08:54,221 --> 01:08:54,720 All right. 1505 01:08:54,720 --> 01:08:59,580 So now I'm going to talk about implementing it. 1506 01:08:59,580 --> 01:09:01,920 And we're going to deal with all of the messy issues 1507 01:09:01,920 --> 01:09:05,250 that I tried to put off a lecture ago. 1508 01:09:05,250 --> 01:09:07,340 How do you take this thing out for a spin? 1509 01:09:07,340 --> 01:09:10,189 Well, one thing you could do is to try 1510 01:09:10,189 --> 01:09:13,200 to test the CAPM to see if it works. 1511 01:09:13,200 --> 01:09:16,740 And one way to test it is to ask the question, 1512 01:09:16,740 --> 01:09:20,180 if we assume that all securities are priced according 1513 01:09:20,180 --> 01:09:25,479 to this equation, then another way to write the equation that 1514 01:09:25,479 --> 01:09:28,540 doesn't rely on expected returns, but relies 1515 01:09:28,540 --> 01:09:33,130 on realized returns, is to write it as a regression equation, 1516 01:09:33,130 --> 01:09:35,710 as you did in DMD. 1517 01:09:35,710 --> 01:09:39,670 The regression equation is the return, the actual realized 1518 01:09:39,670 --> 01:09:45,640 return on security i, is given by the risk-free rate 1519 01:09:45,640 --> 01:09:49,510 plus beta times the realized return on the market 1520 01:09:49,510 --> 01:09:54,149 minus the risk-free rate plus epsilon. 1521 01:09:54,149 --> 01:10:01,380 Epsilon is the error term, the disturbance, the residual, 1522 01:10:01,380 --> 01:10:04,230 that is giving you the fluctuations 1523 01:10:04,230 --> 01:10:06,700 around the expected value. 1524 01:10:06,700 --> 01:10:09,690 So when we remove the expected values from this equation, 1525 01:10:09,690 --> 01:10:12,120 we have to stick in this epsilon term that 1526 01:10:12,120 --> 01:10:13,290 sort of bounces around. 1527 01:10:16,440 --> 01:10:18,960 By the way, when you look at this equation, 1528 01:10:18,960 --> 01:10:21,690 you now have an explicit representation 1529 01:10:21,690 --> 01:10:27,990 for systematic risk and idiosyncratic risk. 1530 01:10:27,990 --> 01:10:30,960 For a given return, it's comprised 1531 01:10:30,960 --> 01:10:36,480 of three pieces, the risk-free rate, beta times the market 1532 01:10:36,480 --> 01:10:42,050 return that bounces around, and this epsilon is the Irish jig. 1533 01:10:42,050 --> 01:10:45,890 That is the idiosyncratic bouncing around 1534 01:10:45,890 --> 01:10:47,491 that you don't get any reward for. 1535 01:10:47,491 --> 01:10:49,490 How do you know you don't get any reward for it? 1536 01:10:49,490 --> 01:10:53,570 Because on average, the expected value of this is equal to 0. 1537 01:10:53,570 --> 01:10:54,680 How do I know that? 1538 01:10:54,680 --> 01:10:58,550 By definition that's how I got from this equation down here. 1539 01:10:58,550 --> 01:11:01,250 If you take the expected value of this equation, 1540 01:11:01,250 --> 01:11:03,560 the only way that the expected value of this 1541 01:11:03,560 --> 01:11:05,480 gives you this equation on the top 1542 01:11:05,480 --> 01:11:08,240 is if that epsilon has a 0 mean. 1543 01:11:08,240 --> 01:11:13,520 So you don't get paid for bearing epsilon risk. 1544 01:11:13,520 --> 01:11:15,480 It's there. 1545 01:11:15,480 --> 01:11:18,582 And for some stocks it's huge. 1546 01:11:18,582 --> 01:11:20,290 But you don't get paid for it because you 1547 01:11:20,290 --> 01:11:21,520 don't have to bear it. 1548 01:11:21,520 --> 01:11:22,750 And the reason you don't have to bear it 1549 01:11:22,750 --> 01:11:24,220 is, if you take 50 of these stocks 1550 01:11:24,220 --> 01:11:28,400 and stick them in a portfolio, the epsilons average out to 0. 1551 01:11:28,400 --> 01:11:29,730 How do I know that? 1552 01:11:29,730 --> 01:11:32,650 Well, this relies on a piece of mathematics 1553 01:11:32,650 --> 01:11:34,470 that's known as the law of large numbers. 1554 01:11:34,470 --> 01:11:37,160 You may have heard that term used in casual conversation, 1555 01:11:37,160 --> 01:11:38,750 but it's actually a real theorem. 1556 01:11:38,750 --> 01:11:40,670 What it says is that when you have large, 1557 01:11:40,670 --> 01:11:43,730 large numbers of fluctuations that are not 1558 01:11:43,730 --> 01:11:45,890 correlated with each other-- 1559 01:11:45,890 --> 01:11:48,680 and by definition, idiosyncratic risks 1560 01:11:48,680 --> 01:11:51,349 for Gillette and Microsoft and other companies 1561 01:11:51,349 --> 01:11:53,390 are not correlated because they're idiosyncratic. 1562 01:11:53,390 --> 01:11:55,131 They're unique to those firms. 1563 01:11:55,131 --> 01:11:57,380 That when you get a large number of these uncorrelated 1564 01:11:57,380 --> 01:12:01,970 fluctuations, that in the limit, they actually go to 0. 1565 01:12:01,970 --> 01:12:04,250 You can disregard them. 1566 01:12:04,250 --> 01:12:06,140 So the law of large numbers is what 1567 01:12:06,140 --> 01:12:09,380 tells you that this idiosyncratic risk is not 1568 01:12:09,380 --> 01:12:12,380 going to be something you will get paid for. 1569 01:12:12,380 --> 01:12:18,050 So this is the CAPM relationship using actual data. 1570 01:12:18,050 --> 01:12:23,420 And if we stick in an alpha term to represent deviations from 1571 01:12:23,420 --> 01:12:26,480 the CAPM, and I subtract the risk-free rate from both sides, 1572 01:12:26,480 --> 01:12:29,030 just to have everything in excess returns, 1573 01:12:29,030 --> 01:12:35,960 then the CAPM reduces to the hypothesis that the alpha-- 1574 01:12:35,960 --> 01:12:39,680 across all stocks, all managers, all projects, 1575 01:12:39,680 --> 01:12:42,190 the alpha is equal to 0. 1576 01:12:42,190 --> 01:12:44,662 That's what the CAPM says. 1577 01:12:44,662 --> 01:12:48,380 And if you want to formulate it strictly 1578 01:12:48,380 --> 01:12:51,410 in terms of total rates of return, 1579 01:12:51,410 --> 01:12:54,560 it says that the alpha has to be equal to the risk-free rate 1580 01:12:54,560 --> 01:12:55,800 times 1 minus beta. 1581 01:12:55,800 --> 01:12:57,920 This is a different alpha than this alpha. 1582 01:12:57,920 --> 01:13:02,290 This alpha represents the excess rate of return. 1583 01:13:02,290 --> 01:13:05,290 OK, so let's do it. 1584 01:13:05,290 --> 01:13:07,700 Let's see whether or not it's true. 1585 01:13:07,700 --> 01:13:10,600 Let's take a bunch of stocks, subtract the risk-free rate 1586 01:13:10,600 --> 01:13:15,510 from the stock returns, run a regression of that stock's 1587 01:13:15,510 --> 01:13:21,660 return on a constant and the market excess return, 1588 01:13:21,660 --> 01:13:24,940 and let's see whether the intercept is equal to 0. 1589 01:13:24,940 --> 01:13:32,760 Well, if you do this for two stocks, Biogen and Motorola-- 1590 01:13:32,760 --> 01:13:40,940 I've done this from 1988 to I think 2006. 1591 01:13:40,940 --> 01:13:44,210 When you run that regression, here's what you get. 1592 01:13:44,210 --> 01:13:54,130 For Biogen, the beta is 1.43, the intercept 1.61%, 1593 01:13:54,130 --> 01:13:57,850 and the standard error is 1.1%. 1594 01:13:57,850 --> 01:14:02,440 And then Rf times 1 minus beta is minus 2.1%. 1595 01:14:02,440 --> 01:14:08,020 This should be equal to the alpha in that previous equation 1596 01:14:08,020 --> 01:14:10,180 that I gave you. 1597 01:14:10,180 --> 01:14:15,280 So in other words, the alpha that we've estimated for Biogen 1598 01:14:15,280 --> 01:14:19,640 using this CAPM regression is 3.7%, 1599 01:14:19,640 --> 01:14:24,940 or on a monthly basis 45% alpha. 1600 01:14:24,940 --> 01:14:29,620 Biogen is an incredibly good buy according to the CAPM, 1601 01:14:29,620 --> 01:14:31,330 if you believe the CAPM. 1602 01:14:31,330 --> 01:14:32,700 All right. 1603 01:14:32,700 --> 01:14:35,760 Now that's Biogen. What about Motorola? 1604 01:14:35,760 --> 01:14:38,040 During the same period, when you estimate Motorola, 1605 01:14:38,040 --> 01:14:40,500 it's got a beta of 1.42. 1606 01:14:40,500 --> 01:14:45,630 And we're estimating an alpha not quite as big, but 23.5% 1607 01:14:45,630 --> 01:14:47,550 percent on an annualized basis. 1608 01:14:47,550 --> 01:14:50,560 That's still pretty big. 1609 01:14:50,560 --> 01:14:54,310 So if you run this regression and analyze it, 1610 01:14:54,310 --> 01:14:58,120 this is what you would conclude, that these two stocks 1611 01:14:58,120 --> 01:15:00,410 are wonderful buys. 1612 01:15:00,410 --> 01:15:02,260 What we're going to talk about next time 1613 01:15:02,260 --> 01:15:04,990 is whether this interpretation really makes sense, 1614 01:15:04,990 --> 01:15:07,076 or whether we've got some missing factors, 1615 01:15:07,076 --> 01:15:08,950 or whether we're measuring things improperly. 1616 01:15:08,950 --> 01:15:10,700 We're going to need to do a bit more work. 1617 01:15:10,700 --> 01:15:13,180 But we're very close to being able to figure out 1618 01:15:13,180 --> 01:15:15,340 exactly how all of these pricing models 1619 01:15:15,340 --> 01:15:19,360 work in tandem with the kinds of risk budgeting calculations 1620 01:15:19,360 --> 01:15:22,100 that we're going to need to do for the rest of the course. 1621 01:15:22,100 --> 01:15:24,120 So I'll see you on Monday.