1 00:00:00,090 --> 00:00:02,430 The following content is provided under a Creative 2 00:00:02,430 --> 00:00:03,820 Commons license. 3 00:00:03,820 --> 00:00:06,030 Your support will help MIT OpenCourseWare 4 00:00:06,030 --> 00:00:10,120 continue to offer high quality educational resources for free. 5 00:00:10,120 --> 00:00:12,690 To make a donation or to view additional materials 6 00:00:12,690 --> 00:00:16,620 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:16,620 --> 00:00:17,830 at ocw.mit.edu. 8 00:00:21,630 --> 00:00:25,120 ANDREW LO: I hope you all had a good Columbus Day weekend. 9 00:00:25,120 --> 00:00:26,450 The stock market certainly did. 10 00:00:30,090 --> 00:00:31,790 Any questions from last time? 11 00:00:35,774 --> 00:00:36,280 No? 12 00:00:36,280 --> 00:00:37,540 OK. 13 00:00:37,540 --> 00:00:40,420 So what I want to do today is to continue 14 00:00:40,420 --> 00:00:44,260 talking about futures and forward contracts. 15 00:00:44,260 --> 00:00:46,990 Today we're going to finish up on these interesting 16 00:00:46,990 --> 00:00:49,480 instruments, with a couple of examples, 17 00:00:49,480 --> 00:00:54,970 and then with a specific method for pricing forward and futures 18 00:00:54,970 --> 00:00:56,720 contracts. 19 00:00:56,720 --> 00:01:00,400 So let me refresh your memory, it's been a week, so I know. 20 00:01:00,400 --> 00:01:06,140 So we're going to go back and look at a specific futures 21 00:01:06,140 --> 00:01:07,640 contract. 22 00:01:07,640 --> 00:01:09,710 And I'm going to take this contract 23 00:01:09,710 --> 00:01:14,150 and then try to talk a bit about how you might use contracts 24 00:01:14,150 --> 00:01:18,050 like this in hedging your risks, as well 25 00:01:18,050 --> 00:01:23,150 as in making certain kinds of bets, if you will. 26 00:01:23,150 --> 00:01:28,550 So remember that this contract is a contract that 27 00:01:28,550 --> 00:01:33,710 was issued on July 27, 2007-- 28 00:01:33,710 --> 00:01:35,940 so it was the middle of the summer-- 29 00:01:35,940 --> 00:01:40,890 for oil to be delivered in December. 30 00:01:40,890 --> 00:01:44,610 And there's a specific date in December 31 00:01:44,610 --> 00:01:50,190 where all oil futures contracts of this type will settle-- 32 00:01:50,190 --> 00:01:52,410 that is will come to maturity-- where 33 00:01:52,410 --> 00:01:55,290 the date is going to be specified in advance 34 00:01:55,290 --> 00:01:56,970 and everybody knows it. 35 00:01:56,970 --> 00:02:00,150 And so in July, when you buy this contract 36 00:02:00,150 --> 00:02:05,520 at a price of $75.06 per barrel, and each contract 37 00:02:05,520 --> 00:02:07,650 is for 1,000 barrels. 38 00:02:07,650 --> 00:02:10,680 When you quote "buy the contract," 39 00:02:10,680 --> 00:02:15,840 what that means is that you are agreeing today, July 27-- 40 00:02:15,840 --> 00:02:19,050 you are agreeing today, that come 41 00:02:19,050 --> 00:02:24,540 December you are going to buy 1,000 barrels at a price 42 00:02:24,540 --> 00:02:29,010 of $75.06 per barrel. 43 00:02:29,010 --> 00:02:31,380 So that's the agreement. 44 00:02:31,380 --> 00:02:36,330 And the party who is selling you the contract, the counterparty, 45 00:02:36,330 --> 00:02:39,570 is agreeing to provide you with that oil 46 00:02:39,570 --> 00:02:42,730 at that price in December. 47 00:02:42,730 --> 00:02:46,050 So the futures price is $75.06. 48 00:02:46,050 --> 00:02:49,620 And as we said last time, the current market 49 00:02:49,620 --> 00:02:55,540 price on July 27, 2007, that's called the spot price. 50 00:02:55,540 --> 00:02:59,850 The spot price may be higher or lower than the futures price, 51 00:02:59,850 --> 00:03:03,720 depending on what expectations are 52 00:03:03,720 --> 00:03:07,650 for what's going to happen with oil over the subsequent six 53 00:03:07,650 --> 00:03:10,870 month period. 54 00:03:10,870 --> 00:03:14,410 Now the initial margin, as I mentioned last time, 55 00:03:14,410 --> 00:03:16,870 was $4,050. 56 00:03:16,870 --> 00:03:19,270 The maintenance margin, the margin 57 00:03:19,270 --> 00:03:21,790 that you need to maintain. 58 00:03:21,790 --> 00:03:26,020 So that if the initial margin goes down in value, 59 00:03:26,020 --> 00:03:28,630 you have to actually put money back into your brokerage 60 00:03:28,630 --> 00:03:31,120 account, your margin account. 61 00:03:31,120 --> 00:03:35,600 And if you fall below that $3,000 threshold, 62 00:03:35,600 --> 00:03:40,980 you'll get a phone call, which is known as a margin call. 63 00:03:40,980 --> 00:03:43,890 Several weeks ago, somebody told me 64 00:03:43,890 --> 00:03:47,180 that they've been getting lots of phone calls 65 00:03:47,180 --> 00:03:50,710 all from the same person, a person called margin. 66 00:03:50,710 --> 00:03:56,070 And you know that can happen when markets go awry. 67 00:03:56,070 --> 00:04:01,290 Now again no cash changes hands today, 68 00:04:01,290 --> 00:04:05,220 because the value of the contract when it's struck 69 00:04:05,220 --> 00:04:10,150 is a zero NPV transaction. 70 00:04:10,150 --> 00:04:12,310 And how do you know it's zero NPV? 71 00:04:12,310 --> 00:04:16,360 Again, because if it's positive for one party, 72 00:04:16,360 --> 00:04:18,470 it's coming from the other party. 73 00:04:18,470 --> 00:04:20,320 So which party would you like to be? 74 00:04:20,320 --> 00:04:22,960 You'd like to be the party receiving that positive NPV, 75 00:04:22,960 --> 00:04:27,290 nobody wants to be the party that is losing the NPV. 76 00:04:27,290 --> 00:04:30,310 So the futures price will adjust, in order 77 00:04:30,310 --> 00:04:32,260 to make it zero NPV. 78 00:04:32,260 --> 00:04:36,250 In fact, that's what we mean when we say that it's zero NPV. 79 00:04:36,250 --> 00:04:41,781 It is the futures price that makes it so. 80 00:04:41,781 --> 00:04:44,240 So I'll give me an example. 81 00:04:44,240 --> 00:04:48,860 If it turns out that somebody suggests a futures price 82 00:04:48,860 --> 00:04:53,560 of $60 a barrel on that day. 83 00:04:53,560 --> 00:04:55,450 Lots and lots of people are going 84 00:04:55,450 --> 00:04:58,060 to want to buy that contract, because that's 85 00:04:58,060 --> 00:05:01,960 a good deal relative to where oil really should be. 86 00:05:01,960 --> 00:05:05,560 And that means lots of people are going to want to buy, 87 00:05:05,560 --> 00:05:11,231 but nobody's going to want to sell at that price of $60. 88 00:05:11,231 --> 00:05:13,480 So if everybody wants to buy and nobody wants to sell, 89 00:05:13,480 --> 00:05:16,080 what has to happen to the price? 90 00:05:16,080 --> 00:05:17,290 Exactly, it goes up. 91 00:05:17,290 --> 00:05:20,650 And it keeps going up until the number of buyers 92 00:05:20,650 --> 00:05:22,000 equals the number of sellers. 93 00:05:22,000 --> 00:05:28,180 That's the point at which it's a zero NPV transaction. 94 00:05:28,180 --> 00:05:31,450 Now let's take a look at what the payoff is 95 00:05:31,450 --> 00:05:38,320 of such a contract on day zero, in this case July 27, 2007, 96 00:05:38,320 --> 00:05:40,660 the contract is worth nothing. 97 00:05:40,660 --> 00:05:46,730 But if the futures price moves tomorrow, 98 00:05:46,730 --> 00:05:49,390 then the contract could actually have value. 99 00:05:49,390 --> 00:05:55,150 And a diagram of how that works is something like this. 100 00:05:55,150 --> 00:05:58,000 If the futures price-- 101 00:05:58,000 --> 00:06:01,434 not the spot-- the spot obviously will move also. 102 00:06:01,434 --> 00:06:03,100 But I'm talking about the futures price, 103 00:06:03,100 --> 00:06:07,150 because the futures contract is specified 104 00:06:07,150 --> 00:06:13,630 so that every day's worth of gains or losses in the futures 105 00:06:13,630 --> 00:06:17,740 contract relative to its price, you 106 00:06:17,740 --> 00:06:22,030 will have to either get paid, or you will have to pay. 107 00:06:22,030 --> 00:06:25,900 So this blue line shows you the payoff 108 00:06:25,900 --> 00:06:29,590 if you're holding a long position in one 109 00:06:29,590 --> 00:06:33,460 of these contracts-- if you bought a contract. 110 00:06:33,460 --> 00:06:36,490 If you sold the contract, then your payoff diagram 111 00:06:36,490 --> 00:06:38,500 is the dotted line. 112 00:06:38,500 --> 00:06:40,870 Now the blue line basically says that if the futures 113 00:06:40,870 --> 00:06:46,480 price goes above $75.06, then you make money. 114 00:06:46,480 --> 00:06:51,830 If the futures price goes below $75.06, you lose money. 115 00:06:51,830 --> 00:06:56,200 So when you buy a contract like this, 116 00:06:56,200 --> 00:07:01,680 it is as if you actually bought the oil. 117 00:07:01,680 --> 00:07:03,330 But you haven't really bought the oil, 118 00:07:03,330 --> 00:07:07,410 all you've done is to buy the right 119 00:07:07,410 --> 00:07:10,635 and obligation to purchase the oil in the future. 120 00:07:14,040 --> 00:07:16,120 Let me let me give you another example that will 121 00:07:16,120 --> 00:07:18,310 make this even more concrete. 122 00:07:18,310 --> 00:07:20,020 The only way to understand this-- 123 00:07:20,020 --> 00:07:24,580 because this is not a natural security for most of us-- 124 00:07:24,580 --> 00:07:28,030 stocks and bonds you might find natural, 125 00:07:28,030 --> 00:07:31,960 futures contracts are weird in that they 126 00:07:31,960 --> 00:07:36,500 have zero investment today, and so they're worthless today. 127 00:07:36,500 --> 00:07:39,850 But they're not worthless after the initial date when 128 00:07:39,850 --> 00:07:41,150 you enter into that agreement. 129 00:07:41,150 --> 00:07:45,550 So let's do an example Yesterday, 130 00:07:45,550 --> 00:07:50,920 you bought 10 December live cattle contracts on the Chicago 131 00:07:50,920 --> 00:07:56,260 Mercantile Exchange at a price of $0.7455 per pound. 132 00:07:56,260 --> 00:07:59,950 OK, so you basically bought some cows. 133 00:07:59,950 --> 00:08:05,074 And the contract size is 40,000 pounds of cow. 134 00:08:05,074 --> 00:08:06,490 I don't know how much cow that is, 135 00:08:06,490 --> 00:08:09,270 but even if you're on the Atkins diet that's plenty of cow. 136 00:08:09,270 --> 00:08:14,560 [LAUGHTER] And so what you have though in this contract 137 00:08:14,560 --> 00:08:19,240 is not the cows, but rather you have the obligation 138 00:08:19,240 --> 00:08:25,970 to buy the cows in December for a price of $0.7455 per pound, 139 00:08:25,970 --> 00:08:28,270 and there is 40,000 pounds of it. 140 00:08:28,270 --> 00:08:37,270 So the value of your position is the size 141 00:08:37,270 --> 00:08:40,120 of the contract, multiplied by the futures price, 142 00:08:40,120 --> 00:08:41,850 multiplied by the number of contracts. 143 00:08:41,850 --> 00:08:46,400 So it's $298,200. 144 00:08:46,400 --> 00:08:48,990 That's the size of your position, 145 00:08:48,990 --> 00:08:52,440 or sometimes that's also called the notional size. 146 00:08:52,440 --> 00:08:55,410 You've heard that term over the last few weeks-- notional. 147 00:08:55,410 --> 00:08:58,080 Well, this is an example of a notional. 148 00:08:58,080 --> 00:09:03,510 So you don't actually own $298,200 of anything, 149 00:09:03,510 --> 00:09:07,110 because of course, we've said that the contract is zero 150 00:09:07,110 --> 00:09:09,120 NPV when you enter into it. 151 00:09:09,120 --> 00:09:15,750 All you've done is to agree to buy 40,000 pounds of cow 152 00:09:15,750 --> 00:09:18,420 in December at a particular price. 153 00:09:18,420 --> 00:09:24,630 So the idea is that you control the notional amount 154 00:09:24,630 --> 00:09:29,790 of $298,200, and what you do specifically 155 00:09:29,790 --> 00:09:36,010 get is the profits and losses from that notional. 156 00:09:36,010 --> 00:09:37,600 So let's do an example. 157 00:09:37,600 --> 00:09:39,280 That was the position yesterday. 158 00:09:39,280 --> 00:09:41,110 No money changed hands. 159 00:09:41,110 --> 00:09:43,590 You got some initial margin that you had to put down, 160 00:09:43,590 --> 00:09:46,720 but that's really your money in a brokerage account. 161 00:09:46,720 --> 00:09:48,430 You're not giving it to anybody. 162 00:09:48,430 --> 00:09:51,670 It's safety money, it's collateral. 163 00:09:51,670 --> 00:09:53,310 Now today what happens? 164 00:09:53,310 --> 00:09:55,060 Let's suppose that today the futures price 165 00:09:55,060 --> 00:09:58,360 closes at $0.7435. 166 00:09:58,360 --> 00:10:03,750 All right, it's just gone down by 2/10 of a cent. 167 00:10:06,880 --> 00:10:10,060 The value of cattle has gone down. 168 00:10:10,060 --> 00:10:14,320 Your holding long this cattle contract, 169 00:10:14,320 --> 00:10:20,350 maybe you're a restaurateur, you have a chain of steakhouses, 170 00:10:20,350 --> 00:10:23,390 and so you need to buy cattle on a regular basis. 171 00:10:23,390 --> 00:10:26,770 So the price of cattle just went down. 172 00:10:26,770 --> 00:10:29,051 Did you make money or lose money? 173 00:10:29,051 --> 00:10:31,540 Yeah, you lost, if you're long. 174 00:10:31,540 --> 00:10:33,880 On the other hand, if you're a cattle farmer 175 00:10:33,880 --> 00:10:37,180 and you sold the contract, you did a good thing, 176 00:10:37,180 --> 00:10:41,170 because you locked in the price of $0.7455, 177 00:10:41,170 --> 00:10:42,610 and now the price went down. 178 00:10:42,610 --> 00:10:46,480 So let's calculate what the value of the notional size 179 00:10:46,480 --> 00:10:47,410 of the position is. 180 00:10:47,410 --> 00:10:51,130 It's $297,400. 181 00:10:51,130 --> 00:10:55,280 That yields a loss of $800. 182 00:10:55,280 --> 00:10:56,990 So you know what happens today? 183 00:10:56,990 --> 00:11:01,880 Today, your broker will deduct $800 from your account, 184 00:11:01,880 --> 00:11:06,380 from your margin account, and take that $800 185 00:11:06,380 --> 00:11:10,250 and put it into the cattle farmer's account. 186 00:11:10,250 --> 00:11:14,400 So now he has the $800. 187 00:11:14,400 --> 00:11:18,600 Now, if the day after, if tomorrow, it 188 00:11:18,600 --> 00:11:20,100 turns out that the price of cattle 189 00:11:20,100 --> 00:11:24,360 goes up by 2/10 of a cent, it goes back to $0.7455. 190 00:11:24,360 --> 00:11:26,600 You know what happens? 191 00:11:26,600 --> 00:11:28,280 You get $800 back. 192 00:11:28,280 --> 00:11:34,600 Now the cattle farmer loses that $800 and gives it back to you. 193 00:11:34,600 --> 00:11:41,520 You see this way you always settle up every day. 194 00:11:41,520 --> 00:11:46,500 So if for some reason the cattle farmer ends up going bankrupt, 195 00:11:46,500 --> 00:11:50,070 and isn't able to deliver any cattle to you, 196 00:11:50,070 --> 00:11:56,940 then you're at out at most one day's worth of movements. 197 00:11:56,940 --> 00:12:00,480 And that's one of the reasons why futures markets and futures 198 00:12:00,480 --> 00:12:04,140 brokers are so careful about closing down 199 00:12:04,140 --> 00:12:07,430 accounts that don't meet their margin requirements. 200 00:12:07,430 --> 00:12:11,130 It's because they don't want to have credit risk lingering, 201 00:12:11,130 --> 00:12:14,670 growing, and unknown. 202 00:12:14,670 --> 00:12:18,450 The first moment that you do not make a margin call-- 203 00:12:18,450 --> 00:12:21,600 you do not deposit the requisite margin-- the first time 204 00:12:21,600 --> 00:12:24,930 that happens, they have the right, 205 00:12:24,930 --> 00:12:29,400 which they exercise always, to close down your position. 206 00:12:29,400 --> 00:12:32,040 You're out of the game, and that's the end. 207 00:12:32,040 --> 00:12:35,760 So it reduces dramatically, the amount of credit 208 00:12:35,760 --> 00:12:37,950 risk that either counterparty has. 209 00:12:37,950 --> 00:12:40,620 I don't have to trust you that three months from now 210 00:12:40,620 --> 00:12:44,230 you're going to actually have 40,000 pounds of cow for me. 211 00:12:44,230 --> 00:12:48,160 All I need to do is to make sure that this contract settles 212 00:12:48,160 --> 00:12:49,660 every day. 213 00:12:49,660 --> 00:12:54,370 And the uncertainty then gets resolved day by day, 214 00:12:54,370 --> 00:13:00,130 but your credit risk is very well managed, and mine is too. 215 00:13:00,130 --> 00:13:03,310 So this is a very important innovation. 216 00:13:03,310 --> 00:13:06,280 It's very different from a forward contract, in the sense 217 00:13:06,280 --> 00:13:10,251 that forward contracts contain enormous amounts of credit risk 218 00:13:10,251 --> 00:13:10,750 right. 219 00:13:10,750 --> 00:13:13,030 Because once we enter into a forward, 220 00:13:13,030 --> 00:13:15,260 that's just like a futures contract, 221 00:13:15,260 --> 00:13:19,810 but the difference is that we don't exchange any money ever 222 00:13:19,810 --> 00:13:22,120 until the settlement date. 223 00:13:22,120 --> 00:13:26,350 And by that point you could be so far out of the money, 224 00:13:26,350 --> 00:13:30,670 you could be so far in debt to me, 225 00:13:30,670 --> 00:13:33,100 as well as to other creditors, that you just 226 00:13:33,100 --> 00:13:34,510 can't afford to pay. 227 00:13:34,510 --> 00:13:36,760 And so I'm stuck with this piece of paper that 228 00:13:36,760 --> 00:13:39,520 says you're going to give me 40,000 pounds of cattle, 229 00:13:39,520 --> 00:13:42,820 and you can't even afford to buy me a steak dinner. 230 00:13:42,820 --> 00:13:45,400 That's a problem. 231 00:13:45,400 --> 00:13:50,090 So this futures exchange is a beautiful thing. 232 00:13:50,090 --> 00:13:52,280 It reduces credit risk. 233 00:13:52,280 --> 00:13:56,390 It also encourages liquidity, it encourages trading. 234 00:13:56,390 --> 00:13:57,010 Why? 235 00:13:57,010 --> 00:14:01,360 Because at any point in time, on any given day between now 236 00:14:01,360 --> 00:14:03,291 and December, if you decide that you 237 00:14:03,291 --> 00:14:05,040 want to get out of the restaurant business 238 00:14:05,040 --> 00:14:07,804 and you don't want this contract any more, 239 00:14:07,804 --> 00:14:08,720 you can get out of it. 240 00:14:08,720 --> 00:14:09,560 Poof. 241 00:14:09,560 --> 00:14:13,500 You just get out of it by doing an opposite transaction. 242 00:14:13,500 --> 00:14:16,154 So if you bought a contract for December, 243 00:14:16,154 --> 00:14:18,320 you know what you do when you want to get out of it? 244 00:14:18,320 --> 00:14:20,390 You sell a contract for December. 245 00:14:20,390 --> 00:14:21,750 You literally sell. 246 00:14:21,750 --> 00:14:25,160 So it's actually duplicated transaction, 247 00:14:25,160 --> 00:14:27,080 but it's of the opposite sign. 248 00:14:27,080 --> 00:14:30,620 And so they cancel out, because you're going to get delivery, 249 00:14:30,620 --> 00:14:34,460 and you will provide delivery, and those will cancel out. 250 00:14:34,460 --> 00:14:37,300 Yeah, Justin. 251 00:14:37,300 --> 00:14:40,180 AUDIENCE: The price of oil has been going down lately. 252 00:14:40,180 --> 00:14:42,420 So let's say I had a long position in oil, 253 00:14:42,420 --> 00:14:45,320 and then I found out that I was going to really lose 254 00:14:45,320 --> 00:14:47,650 half of that money, and I decided just 255 00:14:47,650 --> 00:14:50,532 to forego my margin. 256 00:14:50,532 --> 00:14:52,460 What else would I have to pay? 257 00:14:52,460 --> 00:14:56,660 ANDREW LO: Well, first of all, you 258 00:14:56,660 --> 00:15:00,860 are liable for all of the losses, not just the margin. 259 00:15:00,860 --> 00:15:03,440 So the margin account is not meant 260 00:15:03,440 --> 00:15:05,420 to be a non-recourse loan. 261 00:15:05,420 --> 00:15:07,340 They will go after your assets. 262 00:15:07,340 --> 00:15:09,230 Now you could declare bankruptcy, 263 00:15:09,230 --> 00:15:13,670 personal bankruptcy, and get protection under Chapter 7. 264 00:15:13,670 --> 00:15:16,520 But that will hurt your credit ratings 265 00:15:16,520 --> 00:15:19,550 and all other nasty things will happen to you if that occurs. 266 00:15:19,550 --> 00:15:21,710 AUDIENCE: So when you're saying that they close out 267 00:15:21,710 --> 00:15:26,930 your account, when your margins down. 268 00:15:26,930 --> 00:15:29,450 So they close it out, but if your losses 269 00:15:29,450 --> 00:15:31,860 are higher than your margin was anyway, 270 00:15:31,860 --> 00:15:35,450 so you're still liable for those in addition to [INAUDIBLE].. 271 00:15:35,450 --> 00:15:37,820 ANDREW LO: So you make a good point. 272 00:15:37,820 --> 00:15:40,670 Is it generally possible that your losses are greater 273 00:15:40,670 --> 00:15:41,970 than the amount of margin? 274 00:15:41,970 --> 00:15:44,270 So in that case, who gets left holding the bag? 275 00:15:44,270 --> 00:15:45,920 You know who gets left holding the bag? 276 00:15:45,920 --> 00:15:48,650 That blue box in the middle, the Futures Clearing corporation. 277 00:15:48,650 --> 00:15:52,160 But the reason that they establish a particular level 278 00:15:52,160 --> 00:15:56,750 of margin is to be able to ensure that that's 279 00:15:56,750 --> 00:15:58,400 a very unlikely event. 280 00:15:58,400 --> 00:16:03,080 And it goes back to what are the likely daily swings 281 00:16:03,080 --> 00:16:04,610 in the futures price. 282 00:16:04,610 --> 00:16:06,980 If you put enough margin in your account, 283 00:16:06,980 --> 00:16:10,910 so that I can be sure that 99% of the time you 284 00:16:10,910 --> 00:16:15,030 can cover the daily swing, then I don't have to worry. 285 00:16:15,030 --> 00:16:18,800 Now, of course, if we had a day like last Friday, or on Monday, 286 00:16:18,800 --> 00:16:21,660 you know that's pretty outrageous. 287 00:16:21,660 --> 00:16:24,560 That's one of the reasons why a number of futures exchanges 288 00:16:24,560 --> 00:16:26,080 have increased their margin levels. 289 00:16:26,080 --> 00:16:28,880 It's because the daily swings have gotten much bigger. 290 00:16:28,880 --> 00:16:31,130 But as long as they can cover the one day movement, 291 00:16:31,130 --> 00:16:34,689 they don't have to go after your home or your other assets. 292 00:16:34,689 --> 00:16:35,230 Yeah, Dennis. 293 00:16:35,230 --> 00:16:37,146 AUDIENCE: You said if I bought a contract now, 294 00:16:37,146 --> 00:16:39,230 then I just have to sit on the same contract. 295 00:16:39,230 --> 00:16:41,730 What happens if I bought at a $1.00, it's at $0.50 now, 296 00:16:41,730 --> 00:16:43,641 I can't sell at a $1.00. 297 00:16:43,641 --> 00:16:44,390 ANDREW LO: Oh, no. 298 00:16:44,390 --> 00:16:46,017 You certainly cannot sell at the $1.00, 299 00:16:46,017 --> 00:16:47,100 you have to sell at $0.50. 300 00:16:47,100 --> 00:16:47,943 Says 301 00:16:47,943 --> 00:16:49,980 AUDIENCE: So I'm not really out of the position. 302 00:16:49,980 --> 00:16:51,605 ANDREW LO: You are out of the position, 303 00:16:51,605 --> 00:16:55,100 because you don't have a claim, or you 304 00:16:55,100 --> 00:17:00,105 don't have a commitment to enter into that trade in December. 305 00:17:00,105 --> 00:17:02,480 That's what I mean when I say you're out of the position. 306 00:17:02,480 --> 00:17:04,909 You also happen to be out of money in your example. 307 00:17:04,909 --> 00:17:07,460 [LAUGHTER] In other words, you lost $0.50. 308 00:17:07,460 --> 00:17:09,980 That's not coming back. 309 00:17:09,980 --> 00:17:12,680 But what it means to sell is that you 310 00:17:12,680 --> 00:17:15,440 bought a contract that says in December you're 311 00:17:15,440 --> 00:17:19,109 going to buy 40,000 of cattle-- 312 00:17:19,109 --> 00:17:20,910 you're committed to doing that. 313 00:17:20,910 --> 00:17:23,980 Now if on the other hand, the next day 314 00:17:23,980 --> 00:17:26,357 you decide you want to get out of that commitment-- 315 00:17:26,357 --> 00:17:27,940 the way to get out of it is not to try 316 00:17:27,940 --> 00:17:29,440 to contact the counterparty and say, 317 00:17:29,440 --> 00:17:31,300 would you mind canceling my trade. 318 00:17:31,300 --> 00:17:35,150 The way to do it is to simply sell a commitment at 40,000 319 00:17:35,150 --> 00:17:37,520 pounds of cattle for December. 320 00:17:37,520 --> 00:17:39,490 So your commitment to buy and your commitment 321 00:17:39,490 --> 00:17:41,680 to sell, basically cancel each other out. 322 00:17:41,680 --> 00:17:44,710 So on settlement date, the Futures Clearing corporation 323 00:17:44,710 --> 00:17:48,550 will net out all of these buys and sells, 324 00:17:48,550 --> 00:17:51,070 and the net amount will be transacted 325 00:17:51,070 --> 00:17:53,612 between the providers of the cattle 326 00:17:53,612 --> 00:17:54,820 and the buyers of the cattle. 327 00:17:54,820 --> 00:17:56,320 AUDIENCE: So this means that there's 328 00:17:56,320 --> 00:17:57,430 no physical delivery then. 329 00:17:57,430 --> 00:17:58,680 ANDREW LO: That's right. 330 00:17:58,680 --> 00:18:01,120 So that's an example where if you bought and sold, 331 00:18:01,120 --> 00:18:03,040 then you would be netted out and you would not 332 00:18:03,040 --> 00:18:05,270 have a physical delivery. 333 00:18:05,270 --> 00:18:06,376 Yeah, [INAUDIBLE]. 334 00:18:06,376 --> 00:18:10,120 AUDIENCE: So if the margin is just 335 00:18:10,120 --> 00:18:12,470 a fund for exchanging commodities, 336 00:18:12,470 --> 00:18:15,175 what does the Futures Clearing corp-- what do they make? 337 00:18:15,175 --> 00:18:17,147 Is it a percentage of-- 338 00:18:17,147 --> 00:18:19,120 how do they make money? 339 00:18:19,120 --> 00:18:21,610 ANDREW LO: Well, their job is really not to make money, 340 00:18:21,610 --> 00:18:25,090 but to create an exchange for its members. 341 00:18:25,090 --> 00:18:28,070 So many exchanges are not for profit. 342 00:18:28,070 --> 00:18:30,640 Some of them are for profit, but the objective 343 00:18:30,640 --> 00:18:32,110 of the Futures Clearing corporation 344 00:18:32,110 --> 00:18:33,970 is really not to make a lot of money. 345 00:18:33,970 --> 00:18:36,310 What they're trying to do is just create a market 346 00:18:36,310 --> 00:18:39,220 and let people who want to trade with each other, 347 00:18:39,220 --> 00:18:42,340 trade freely and efficiently. 348 00:18:42,340 --> 00:18:44,980 They will charge perhaps a small transaction 349 00:18:44,980 --> 00:18:46,750 fee, that you have to pay in order 350 00:18:46,750 --> 00:18:48,550 to support the operations. 351 00:18:48,550 --> 00:18:51,040 But they're not trying to make tons of profits off of that 352 00:18:51,040 --> 00:18:52,090 necessarily. 353 00:18:52,090 --> 00:18:54,070 Now they may be trying to make profits off 354 00:18:54,070 --> 00:18:57,640 of other activities, but the objective of the Clearing 355 00:18:57,640 --> 00:19:00,380 Corporation itself is not to make tons of profit, 356 00:19:00,380 --> 00:19:02,380 It's really just to provide a stable environment 357 00:19:02,380 --> 00:19:03,940 where people can transact. 358 00:19:03,940 --> 00:19:07,870 And in some cases, the members of the exchange 359 00:19:07,870 --> 00:19:09,850 own the Clearing Corporation. 360 00:19:09,850 --> 00:19:12,790 So it's their own dollars that support 361 00:19:12,790 --> 00:19:15,865 the actual physical operations of the organization. 362 00:19:15,865 --> 00:19:17,656 AUDIENCE: And just going back to that point 363 00:19:17,656 --> 00:19:20,400 you had about no physical delivery. 364 00:19:20,400 --> 00:19:22,105 Two or three weeks ago, the price 365 00:19:22,105 --> 00:19:25,340 of oil spiked, [INAUDIBLE] I think 366 00:19:25,340 --> 00:19:27,152 the way I read in the papers, was people 367 00:19:27,152 --> 00:19:30,225 were trying to sell it, not buy it, because otherwise they 368 00:19:30,225 --> 00:19:31,420 would get physical delivery. 369 00:19:31,420 --> 00:19:35,250 So do you recall that? 370 00:19:35,250 --> 00:19:37,220 ANDREW LO: I recall the spike. 371 00:19:37,220 --> 00:19:40,620 I certainly don't recall the logic about physical delivery. 372 00:19:40,620 --> 00:19:43,710 I mean it could be that there are a number of people 373 00:19:43,710 --> 00:19:47,180 who are long the oil contracts that basically 374 00:19:47,180 --> 00:19:48,710 want it to be cash settled. 375 00:19:48,710 --> 00:19:50,460 And the way that they have it cash settled 376 00:19:50,460 --> 00:19:53,400 at a particular point in time, before settlement date, 377 00:19:53,400 --> 00:19:55,357 is they close out their positions. 378 00:19:55,357 --> 00:19:56,940 And so by closing out their positions, 379 00:19:56,940 --> 00:19:58,680 they basically reverse the trade, 380 00:19:58,680 --> 00:20:03,402 and that would actually push down the oil price. 381 00:20:03,402 --> 00:20:05,610 So maybe the reverse argument, a lot of short sellers 382 00:20:05,610 --> 00:20:08,670 were trying to argue that oil was going to go down, 383 00:20:08,670 --> 00:20:11,810 and they wanted to cover their position, so they bought. 384 00:20:11,810 --> 00:20:14,820 In any case, you don't have to take physical delivery 385 00:20:14,820 --> 00:20:17,730 if you specify to your broker that you want all of this 386 00:20:17,730 --> 00:20:19,482 to be cash settled. 387 00:20:19,482 --> 00:20:20,364 Yeah? 388 00:20:20,364 --> 00:20:21,700 AUDIENCE: Two part question. 389 00:20:21,700 --> 00:20:23,500 Would you say that the credit risk involved 390 00:20:23,500 --> 00:20:26,440 in a forward contract is somewhat similar to the credit 391 00:20:26,440 --> 00:20:29,530 risk in credit default swaps? 392 00:20:29,530 --> 00:20:32,590 And if so, is there something analogous to a credit default 393 00:20:32,590 --> 00:20:35,702 swap that's similar to a futures contract? 394 00:20:35,702 --> 00:20:37,660 ANDREW LO: So the answer to your first question 395 00:20:37,660 --> 00:20:42,280 is yes, because a credit default swap contract is basically 396 00:20:42,280 --> 00:20:44,320 a kind of a forward contract. 397 00:20:44,320 --> 00:20:46,690 It does involve intermediate payments, 398 00:20:46,690 --> 00:20:51,064 but if it turns out that the credit changes dramatically, 399 00:20:51,064 --> 00:20:52,480 those intermediate payments either 400 00:20:52,480 --> 00:20:55,120 may be too much or not enough to cover the underlying 401 00:20:55,120 --> 00:20:56,390 value of the contract. 402 00:20:56,390 --> 00:20:58,420 And after you strike a credit default swap, 403 00:20:58,420 --> 00:21:01,330 it will take on value. 404 00:21:01,330 --> 00:21:05,230 As for an exchange, what a wonderful idea. 405 00:21:05,230 --> 00:21:07,660 That is exactly what's being proposed now. 406 00:21:07,660 --> 00:21:09,880 It hasn't been done yet, but there 407 00:21:09,880 --> 00:21:11,710 have been a number of proposals to set up 408 00:21:11,710 --> 00:21:15,580 exactly a structure like this for credit default swaps. 409 00:21:15,580 --> 00:21:20,380 In order to do that, you have to standardize those contracts, 410 00:21:20,380 --> 00:21:23,440 and you have to be able to do the paperwork in a relatively 411 00:21:23,440 --> 00:21:24,640 efficient manner. 412 00:21:24,640 --> 00:21:27,910 And so that's actually being discussed, debated, 413 00:21:27,910 --> 00:21:30,250 and I think that there's a proposal by the Chicago 414 00:21:30,250 --> 00:21:32,950 Mercantile Exchange to start doing that. 415 00:21:32,950 --> 00:21:36,070 If you do start doing that, you will see that market growing 416 00:21:36,070 --> 00:21:39,610 even bigger than it is today, and at the same time, 417 00:21:39,610 --> 00:21:42,280 the risks are actually going to decrease. 418 00:21:42,280 --> 00:21:45,400 Because with daily settlement of credit default swaps, 419 00:21:45,400 --> 00:21:47,860 just like with futures contracts, all you need 420 00:21:47,860 --> 00:21:55,280 is one day margin in order to eliminate 99% of the problems. 421 00:21:55,280 --> 00:22:05,534 AUDIENCE: [INAUDIBLE] 422 00:22:05,534 --> 00:22:07,450 ANDREW LO: So let me-- that's a good question. 423 00:22:07,450 --> 00:22:09,850 Let me now talk about how to price futures 424 00:22:09,850 --> 00:22:12,850 and we'll take in interest rates explicitly. 425 00:22:12,850 --> 00:22:17,490 So the question is what determines either a forward 426 00:22:17,490 --> 00:22:19,620 or a futures price? 427 00:22:19,620 --> 00:22:21,750 You now know what a futures price is, right? 428 00:22:21,750 --> 00:22:25,080 It's the price at which you're willing to do 429 00:22:25,080 --> 00:22:27,286 a future transaction. 430 00:22:27,286 --> 00:22:28,410 What determines that price? 431 00:22:28,410 --> 00:22:30,750 We say supply and demand and the market, 432 00:22:30,750 --> 00:22:34,750 but is there some logic that we can give to this process? 433 00:22:34,750 --> 00:22:36,240 And the answer is yes, we're going 434 00:22:36,240 --> 00:22:38,040 to use the exact same argument that we use 435 00:22:38,040 --> 00:22:39,900 for pricing everything else. 436 00:22:39,900 --> 00:22:44,160 We're going to come up with two identical cash flows. 437 00:22:44,160 --> 00:22:48,450 And two assets that have identical cash flows 438 00:22:48,450 --> 00:22:51,246 have to have the same what? 439 00:22:51,246 --> 00:22:52,070 AUDIENCE: Price. 440 00:22:52,070 --> 00:22:55,430 ANDREW LO: Price, value, right. 441 00:22:55,430 --> 00:23:00,110 So for now, I'm going to actually ignore the difference 442 00:23:00,110 --> 00:23:02,030 between futures and forwards. 443 00:23:02,030 --> 00:23:06,530 The only difference is the back and forth amount of money 444 00:23:06,530 --> 00:23:08,810 that we give to each other, and therefore, 445 00:23:08,810 --> 00:23:12,410 the accumulated interest or foregone interest 446 00:23:12,410 --> 00:23:16,040 that we pay when we put our money back and forth 447 00:23:16,040 --> 00:23:17,870 into each other's accounts. 448 00:23:17,870 --> 00:23:19,799 So let me abstract from that and-- you 449 00:23:19,799 --> 00:23:21,590 know if you're interested, you can actually 450 00:23:21,590 --> 00:23:25,250 see the derivation of that in recitation. 451 00:23:25,250 --> 00:23:27,740 I want to focus on the bigger question 452 00:23:27,740 --> 00:23:33,140 of how these things are priced with respect to other prices. 453 00:23:33,140 --> 00:23:36,350 So let me start with some notation. 454 00:23:36,350 --> 00:23:39,335 I've got a particular contract, let's say a futures 455 00:23:39,335 --> 00:23:41,240 or a forward contract. 456 00:23:41,240 --> 00:23:44,780 And I've also got the spot price of the asset 457 00:23:44,780 --> 00:23:46,170 at a point in time. 458 00:23:46,170 --> 00:23:49,220 So I'm going to let St denote my spot price. 459 00:23:49,220 --> 00:23:53,470 I'm going to let F of little t big T 460 00:23:53,470 --> 00:23:55,610 determine the forward price. 461 00:23:55,610 --> 00:23:59,619 And H of little t big T, the futures price. 462 00:23:59,619 --> 00:24:01,160 And for now, I'm going to just assume 463 00:24:01,160 --> 00:24:03,860 that H and F are pretty close. 464 00:24:03,860 --> 00:24:06,700 Now notice that when I write down 465 00:24:06,700 --> 00:24:08,960 a futures price or a forward price, 466 00:24:08,960 --> 00:24:11,360 I've got two sub-indexes. 467 00:24:11,360 --> 00:24:13,160 I've got little t and big T. The reason 468 00:24:13,160 --> 00:24:17,780 I need two is that for every forward or futures contract, 469 00:24:17,780 --> 00:24:20,600 there are two dates you need to worry about. 470 00:24:20,600 --> 00:24:24,410 The date at which you are pricing the contract, namely 471 00:24:24,410 --> 00:24:27,620 today, and the settlement date. 472 00:24:27,620 --> 00:24:29,460 So you need to have those two indexes. 473 00:24:29,460 --> 00:24:32,180 So right away we know that this contract 474 00:24:32,180 --> 00:24:35,450 is a little bit more complicated than say a stock, 475 00:24:35,450 --> 00:24:38,000 where there is no settlement date. 476 00:24:41,150 --> 00:24:42,914 So I want to go back to a comment that 477 00:24:42,914 --> 00:24:45,080 was made by one of you when we first started talking 478 00:24:45,080 --> 00:24:46,370 about futures and forwards. 479 00:24:46,370 --> 00:24:49,310 And the comment was why go to the trouble of using 480 00:24:49,310 --> 00:24:50,810 these contracts, when you could just 481 00:24:50,810 --> 00:24:53,810 buy the asset itself and hold onto it. 482 00:24:53,810 --> 00:24:56,600 If you need oil in December, in order 483 00:24:56,600 --> 00:24:58,550 to make sure you have oil in December, 484 00:24:58,550 --> 00:25:00,560 why don't you just buy it in October 485 00:25:00,560 --> 00:25:01,810 and hold it for two months. 486 00:25:01,810 --> 00:25:03,950 Then you have it in December. 487 00:25:03,950 --> 00:25:06,650 And in fact, that's exactly what we're 488 00:25:06,650 --> 00:25:10,820 going to do to figure out what the appropriate price is 489 00:25:10,820 --> 00:25:14,250 of the specific futures or forward contract. 490 00:25:14,250 --> 00:25:15,680 So here we go. 491 00:25:15,680 --> 00:25:18,170 I'm going to do my exact same analysis 492 00:25:18,170 --> 00:25:20,300 that I've done many times before, 493 00:25:20,300 --> 00:25:23,660 when we tried to price bonds, and stocks, 494 00:25:23,660 --> 00:25:27,380 and other basic securities. 495 00:25:27,380 --> 00:25:29,690 The left hand column here is going 496 00:25:29,690 --> 00:25:33,400 to be the cash flows associated with 497 00:25:33,400 --> 00:25:36,140 a typical forward contract. 498 00:25:36,140 --> 00:25:37,760 So a forward contract is one way. 499 00:25:37,760 --> 00:25:41,330 You enter into the contract, let's say at date zero. 500 00:25:41,330 --> 00:25:43,540 And you pay nothing for the contract right, 501 00:25:43,540 --> 00:25:46,070 this is a zero NPV transaction. 502 00:25:46,070 --> 00:25:49,820 And you are long the forward contract, 503 00:25:49,820 --> 00:25:55,220 with the forward price F of 0,T. 504 00:25:55,220 --> 00:25:58,280 The only cash flow that occurs with a forward contract 505 00:25:58,280 --> 00:26:00,350 is on settlement date. 506 00:26:00,350 --> 00:26:05,690 And on settlement date, you've agreed to pay F of 0,T 507 00:26:05,690 --> 00:26:08,840 for delivery of whatever it is that you bought the forward 508 00:26:08,840 --> 00:26:09,620 contract on. 509 00:26:12,830 --> 00:26:18,080 So the only cash flow that comes out of a forward contract 510 00:26:18,080 --> 00:26:21,730 is this F right here. 511 00:26:21,730 --> 00:26:23,800 Everybody see that? 512 00:26:23,800 --> 00:26:29,860 Nothing up my sleeve, it's very simple calculation. 513 00:26:29,860 --> 00:26:32,290 Now, I want you to look at the right hand column, which 514 00:26:32,290 --> 00:26:34,540 is going to be less simple. 515 00:26:34,540 --> 00:26:36,820 The right hand column, I want you 516 00:26:36,820 --> 00:26:40,420 to imagine doing the following. 517 00:26:40,420 --> 00:26:45,430 I want you to imagine buying the commodity at date zero. 518 00:26:45,430 --> 00:26:49,490 However, I don't want you to use any money. 519 00:26:49,490 --> 00:26:52,330 I want you to buy it with no money down. 520 00:26:52,330 --> 00:26:56,720 That's the start of a scam, it sounds like it, 521 00:26:56,720 --> 00:26:59,360 but I promise you it's not. 522 00:26:59,360 --> 00:27:02,135 So the way you're going to buy the commodity 523 00:27:02,135 --> 00:27:05,750 is you have to pay the price, the spot price. 524 00:27:05,750 --> 00:27:08,150 And the spot prices is S sub 0 You don't 525 00:27:08,150 --> 00:27:12,980 have S sub 0, so borrow it. 526 00:27:12,980 --> 00:27:14,900 Now, I'm going to abstract from credit 527 00:27:14,900 --> 00:27:17,862 risk, which I know is on everybody's minds today. 528 00:27:17,862 --> 00:27:19,820 But let's suppose that you're all good credits, 529 00:27:19,820 --> 00:27:23,420 so I'm not worried about loaning you the money at the risk 530 00:27:23,420 --> 00:27:25,560 free rate. 531 00:27:25,560 --> 00:27:28,820 So now you've borrowed S sub 0 dollars, 532 00:27:28,820 --> 00:27:33,800 and then you spent it right away buying the asset. 533 00:27:33,800 --> 00:27:40,730 So as of date zero, in the right hand column, you own the asset. 534 00:27:40,730 --> 00:27:49,810 Now you have to wait T periods, and while you wait 535 00:27:49,810 --> 00:27:51,370 you may have some costs. 536 00:27:51,370 --> 00:27:56,000 For example, if the asset that you bought is gasoline, 537 00:27:56,000 --> 00:27:59,206 well you've got to store it in just the right way. 538 00:27:59,206 --> 00:28:00,580 You probably don't want to put it 539 00:28:00,580 --> 00:28:02,980 next to your furnace in the basement. 540 00:28:02,980 --> 00:28:05,830 You probably want to put it in a cool place, isolated, 541 00:28:05,830 --> 00:28:07,550 and so on and so forth. 542 00:28:07,550 --> 00:28:11,440 On the other hand, if what you bought is pork bellies, 543 00:28:11,440 --> 00:28:14,890 you probably want to put that in a freezer compartment, as 544 00:28:14,890 --> 00:28:18,280 opposed to in your garage. 545 00:28:18,280 --> 00:28:22,900 So you might have to pay costs for storing. 546 00:28:22,900 --> 00:28:26,530 And at the end of that time T, you 547 00:28:26,530 --> 00:28:29,000 have to pay interest on your loan. 548 00:28:29,000 --> 00:28:31,149 So you borrowed S sub 0 dollars, you 549 00:28:31,149 --> 00:28:33,440 don't get that for free, you got to pay interest on it. 550 00:28:33,440 --> 00:28:34,856 This is a question about interest, 551 00:28:34,856 --> 00:28:37,910 so you've got to pay interest on that money. 552 00:28:37,910 --> 00:28:42,355 And so you have to pay back at this point T-- 553 00:28:42,355 --> 00:28:44,230 you have to pay back the money you borrowed-- 554 00:28:44,230 --> 00:28:47,830 S sub 0, 1 plus R to the capital T, 555 00:28:47,830 --> 00:28:50,150 plus whatever your storage costs are. 556 00:28:50,150 --> 00:28:54,220 But I'm going to allow that having the asset 557 00:28:54,220 --> 00:28:57,700 around might be kind of convenient. 558 00:28:57,700 --> 00:29:01,090 There might be a benefit to having the asset around-- 559 00:29:01,090 --> 00:29:02,530 a convenience yield. 560 00:29:02,530 --> 00:29:05,440 Maybe if you need to use it sooner, you have it there. 561 00:29:05,440 --> 00:29:11,290 And having it there saves you a little bit of trouble in order 562 00:29:11,290 --> 00:29:13,060 to be able to get whatever it is you 563 00:29:13,060 --> 00:29:15,820 need to get done with that underlying asset. 564 00:29:15,820 --> 00:29:20,740 So I'm going to deduct from my cumulative storage costs 565 00:29:20,740 --> 00:29:23,260 any convenience yield-- 566 00:29:23,260 --> 00:29:27,310 that's future speak for any kind of benefits 567 00:29:27,310 --> 00:29:31,150 that you get from holding onto the physical asset. 568 00:29:31,150 --> 00:29:35,020 So your net storage costs are given here-- 569 00:29:35,020 --> 00:29:37,705 that's what you pay at the end of T periods. 570 00:29:40,420 --> 00:29:45,610 I argue that these two cash flows give you 571 00:29:45,610 --> 00:29:50,120 the exact same value of the asset. 572 00:29:50,120 --> 00:29:52,900 In other words, in both cases you 573 00:29:52,900 --> 00:29:56,570 happen to have the asset at the time T. 574 00:29:56,570 --> 00:30:02,140 So these two contracts have to have the same value 575 00:30:02,140 --> 00:30:07,660 because they offer the same set of cash flows, 576 00:30:07,660 --> 00:30:10,960 in terms of the underlying commodity. 577 00:30:10,960 --> 00:30:14,550 You get the commodity in both cases. 578 00:30:14,550 --> 00:30:17,930 So another way of thinking about it is if your objective is 579 00:30:17,930 --> 00:30:23,450 to have 40,000 pounds of cattle in December, both of these 580 00:30:23,450 --> 00:30:26,270 will get you to the exact same point. 581 00:30:26,270 --> 00:30:32,110 Both of these costs you nothing on date zero. 582 00:30:32,110 --> 00:30:35,950 And therefore, if they cost you nothing, 583 00:30:35,950 --> 00:30:40,490 and they give you the same outcome at the end, 584 00:30:40,490 --> 00:30:43,390 they've got to sell for the same price. 585 00:30:43,390 --> 00:30:49,101 So this has to equal this. 586 00:30:49,101 --> 00:30:49,600 That's it. 587 00:30:49,600 --> 00:30:51,220 That's the simple argument. 588 00:30:51,220 --> 00:30:57,020 And the counter argument or proof that this has to be true 589 00:30:57,020 --> 00:30:59,030 is-- let's assume it's not. 590 00:30:59,030 --> 00:31:02,660 Let's assume that this is a lot bigger than this. 591 00:31:02,660 --> 00:31:07,512 Well, if this is bigger than this, then what should you do? 592 00:31:07,512 --> 00:31:08,012 What? 593 00:31:08,012 --> 00:31:12,112 AUDIENCE: [INAUDIBLE] 594 00:31:12,112 --> 00:31:12,820 ANDREW LO: Right. 595 00:31:12,820 --> 00:31:14,410 Which one? 596 00:31:14,410 --> 00:31:16,360 Which one? 597 00:31:16,360 --> 00:31:19,360 Sell the forward contract, and then 598 00:31:19,360 --> 00:31:22,892 buy this thing, whatever it is, do this. 599 00:31:22,892 --> 00:31:24,100 Now what if it's the reverse? 600 00:31:24,100 --> 00:31:26,260 What if this is bigger than this? 601 00:31:26,260 --> 00:31:32,320 Then buy the forward, and then do the opposite of this. 602 00:31:32,320 --> 00:31:33,460 Flip it around. 603 00:31:33,460 --> 00:31:38,050 Short sell the asset if you can, and then take the money 604 00:31:38,050 --> 00:31:42,040 and lend it out at interest rate r, and dot dot dot, 605 00:31:42,040 --> 00:31:44,980 you follow the logic. 606 00:31:44,980 --> 00:31:50,170 So that gives us a relationship between the forward price 607 00:31:50,170 --> 00:31:51,920 and other stuff. 608 00:31:51,920 --> 00:31:53,320 And what is the other stuff? 609 00:31:53,320 --> 00:31:56,680 The forward price has to be related 610 00:31:56,680 --> 00:32:02,560 to the spot price, the interest rate, the time to settlement, 611 00:32:02,560 --> 00:32:07,030 and any other weird things about the commodity that 612 00:32:07,030 --> 00:32:08,740 may affect the value of it. 613 00:32:08,740 --> 00:32:14,436 Like the storage costs or the convenience yield-- 614 00:32:14,436 --> 00:32:17,760 you've got to factor that in. 615 00:32:17,760 --> 00:32:19,980 So this is the relationship that tells you how 616 00:32:19,980 --> 00:32:22,140 to price a forward contract. 617 00:32:22,140 --> 00:32:25,470 Now a futures contract is almost like a forward. 618 00:32:25,470 --> 00:32:28,450 The only difference is the interest differential 619 00:32:28,450 --> 00:32:32,190 on a daily basis, where you actually are moving money back 620 00:32:32,190 --> 00:32:34,230 and forth into our accounts. 621 00:32:34,230 --> 00:32:37,470 But the cumulative sum is going to end up 622 00:32:37,470 --> 00:32:39,270 being approximately the same. 623 00:32:39,270 --> 00:32:41,500 So for the purposes of this class, 624 00:32:41,500 --> 00:32:44,760 I'm going to assert that this is approximately the same. 625 00:32:44,760 --> 00:32:46,350 In fact, you can show that there's 626 00:32:46,350 --> 00:32:48,630 another relationship that looks at the interest 627 00:32:48,630 --> 00:32:50,410 rate per period. 628 00:32:50,410 --> 00:32:53,454 And it's a little bit more complicated, but not 629 00:32:53,454 --> 00:32:54,370 much more complicated. 630 00:32:54,370 --> 00:32:57,280 You can see that in your textbook, if you're interested. 631 00:32:57,280 --> 00:33:00,240 But for now, I want to just focus on this relationship. 632 00:33:00,240 --> 00:33:06,070 This relationship tells us how to price futures and forwards. 633 00:33:06,070 --> 00:33:11,760 And now if I divide by 1 plus r, f to the T, then what I've got 634 00:33:11,760 --> 00:33:16,890 is that the forward price divided by the interest rate, 635 00:33:16,890 --> 00:33:22,140 that calculates the current value of that forward price, 636 00:33:22,140 --> 00:33:25,680 has got to equal the spot price plus the present value 637 00:33:25,680 --> 00:33:27,702 of the net storage costs. 638 00:33:27,702 --> 00:33:29,910 This is the relationship that we've been looking for, 639 00:33:29,910 --> 00:33:33,270 and you guys have been struggling for the last couple 640 00:33:33,270 --> 00:33:33,810 of lectures. 641 00:33:33,810 --> 00:33:35,520 You've been asking well, gee, doesn't the interest 642 00:33:35,520 --> 00:33:37,880 rate belong in there, and what about having the asset, 643 00:33:37,880 --> 00:33:40,420 wouldn't it be nice to have it, and so on and so forth. 644 00:33:40,420 --> 00:33:43,020 All of those considerations are summed up 645 00:33:43,020 --> 00:33:44,870 in this one expression. 646 00:33:44,870 --> 00:33:46,830 A very nice expression. 647 00:33:46,830 --> 00:33:48,930 Very intuitive. 648 00:33:48,930 --> 00:33:54,160 What you pay at date T, when you take the present value of it, 649 00:33:54,160 --> 00:33:59,500 that has to be equal to what the thing is worth today 650 00:33:59,500 --> 00:34:05,230 plus any benefits for having the thing, as opposed 651 00:34:05,230 --> 00:34:09,600 to not having the thing between now and settlement. 652 00:34:09,600 --> 00:34:11,090 That's it. 653 00:34:11,090 --> 00:34:13,300 Now this is for the very beginning 654 00:34:13,300 --> 00:34:15,949 when you strike the contract. 655 00:34:15,949 --> 00:34:20,659 What about at an arbitrary point in time between 0 and T? 656 00:34:20,659 --> 00:34:24,530 Well, all of these arguments work exactly the same way 657 00:34:24,530 --> 00:34:30,830 when you're looking at two dates t and T, as opposed to 0 and T. 658 00:34:30,830 --> 00:34:32,836 So the relationship that I showed you, 659 00:34:32,836 --> 00:34:34,460 it's a little bit more complicated now, 660 00:34:34,460 --> 00:34:37,550 because you've got to take into account the fact that the time 661 00:34:37,550 --> 00:34:39,889 to settlement is not capital T, it's 662 00:34:39,889 --> 00:34:43,310 capital T minus where you are today. 663 00:34:43,310 --> 00:34:45,050 But that's the only change. 664 00:34:45,050 --> 00:34:48,020 Other than that, everything is the same. 665 00:34:51,969 --> 00:34:55,330 And you have to make sure that you accumulate 666 00:34:55,330 --> 00:34:58,840 the future value of all the net storage costs, 667 00:34:58,840 --> 00:35:01,750 so that you actually move all of the costs to the end, 668 00:35:01,750 --> 00:35:06,340 and then you bring it back to time T. 669 00:35:06,340 --> 00:35:08,380 Now, let's take this out for a spin. 670 00:35:08,380 --> 00:35:10,070 Let's see how this works. 671 00:35:10,070 --> 00:35:12,250 Let's take a look at gold. 672 00:35:14,800 --> 00:35:19,170 Gold is easy to store. 673 00:35:19,170 --> 00:35:22,470 There's no storage costs really. 674 00:35:22,470 --> 00:35:25,010 I mean gold is relatively compact, a little heavy, 675 00:35:25,010 --> 00:35:27,510 so you're going to have to lift it and put it in your vault, 676 00:35:27,510 --> 00:35:29,385 as some of you, I'm sure, are doing nowadays. 677 00:35:29,385 --> 00:35:35,490 [LAUGHTER] But the bottom line is that the storage costs 678 00:35:35,490 --> 00:35:37,320 are negligible. 679 00:35:37,320 --> 00:35:38,400 There are no dividends. 680 00:35:38,400 --> 00:35:41,640 Gold does not pay out dividends. 681 00:35:41,640 --> 00:35:44,040 There are no real benefits either, 682 00:35:44,040 --> 00:35:45,765 there is no convenience yield. 683 00:35:45,765 --> 00:35:48,480 It's not like you need a little piece of gold 684 00:35:48,480 --> 00:35:50,500 every once in a while for your pleasure, 685 00:35:50,500 --> 00:35:52,500 and so you want to scrape that off and enjoy it. 686 00:35:52,500 --> 00:35:55,120 [LAUGHTER] It just sort of sits there. 687 00:35:55,120 --> 00:35:57,810 So if that's the case, you factor that 688 00:35:57,810 --> 00:35:59,640 into that relationship that I showed you, 689 00:35:59,640 --> 00:36:04,980 and that last term, the PV of net storage costs is nothing. 690 00:36:04,980 --> 00:36:08,720 And so the relationship is really simple. 691 00:36:08,720 --> 00:36:14,390 The forward slash futures price today 692 00:36:14,390 --> 00:36:17,930 is just equal to what the current spot 693 00:36:17,930 --> 00:36:22,730 price is multiplied by 1 plus the risk free rate of interest 694 00:36:22,730 --> 00:36:27,090 between today and a settlement date. 695 00:36:27,090 --> 00:36:29,340 If this relationship is violated-- 696 00:36:29,340 --> 00:36:33,210 when you look at gold futures, and gold spot, 697 00:36:33,210 --> 00:36:37,140 and you see that this relationship was violated, 698 00:36:37,140 --> 00:36:39,300 that's a sign that there's an arbitrage. 699 00:36:39,300 --> 00:36:41,380 You can make money off of that. 700 00:36:41,380 --> 00:36:43,890 So that really is the way to make a million dollars 701 00:36:43,890 --> 00:36:45,350 with no money down-- 702 00:36:45,350 --> 00:36:50,160 is to try to find violations of this arbitrage relationship. 703 00:36:50,160 --> 00:36:52,770 It's going to be hard, because there are a lot of people that 704 00:36:52,770 --> 00:36:55,080 are looking at it all the time. 705 00:36:55,080 --> 00:36:58,150 And so when there is an inequality of some sort, 706 00:36:58,150 --> 00:36:59,820 it's probably not going to be very big, 707 00:36:59,820 --> 00:37:01,770 and it probably won't last very long. 708 00:37:01,770 --> 00:37:04,590 But to the person who found it first, 709 00:37:04,590 --> 00:37:07,020 they might actually be able to make a little bit off 710 00:37:07,020 --> 00:37:10,920 of that discrepancy, by either buying or selling gold, 711 00:37:10,920 --> 00:37:13,860 and transacting these markets quickly. 712 00:37:13,860 --> 00:37:15,160 Let me do another example. 713 00:37:15,160 --> 00:37:16,140 So this is gold. 714 00:37:16,140 --> 00:37:18,370 What about gasoline? 715 00:37:18,370 --> 00:37:20,850 Gasoline it turns out, is very different from gold. 716 00:37:20,850 --> 00:37:24,910 First of all, it's a pain in the neck to store safely. 717 00:37:24,910 --> 00:37:27,300 So if you don't want to be blown up in the middle-- 718 00:37:27,300 --> 00:37:31,590 and this is what I really mean by blowing up right, gasoline-- 719 00:37:31,590 --> 00:37:33,610 you want to prevent that from happening, 720 00:37:33,610 --> 00:37:35,310 you've got to pay a storage cost. 721 00:37:35,310 --> 00:37:37,310 On the other hand, there is a convenience yield. 722 00:37:37,310 --> 00:37:39,810 If you've got the gasoline, you can actually 723 00:37:39,810 --> 00:37:41,244 use it along the way. 724 00:37:41,244 --> 00:37:42,660 You have to replenish it, in order 725 00:37:42,660 --> 00:37:45,930 to get the same level of stock at the end, 726 00:37:45,930 --> 00:37:48,420 but it's convenient that you have it, 727 00:37:48,420 --> 00:37:50,010 instead of having to go get it. 728 00:37:50,010 --> 00:37:54,150 Because getting it involves trouble and costs. 729 00:37:54,150 --> 00:37:56,850 So that's the convenience yield. 730 00:37:56,850 --> 00:38:02,360 So if you factor that in, then what you get is the futures 731 00:38:02,360 --> 00:38:13,470 or forward price is equal to 1 plus r,f plus a plus a storage 732 00:38:13,470 --> 00:38:17,370 cost per period, minus a convenience yield per period, 733 00:38:17,370 --> 00:38:20,790 and then raised to the T minus t power, 734 00:38:20,790 --> 00:38:24,720 multiplied by the current spot price. 735 00:38:24,720 --> 00:38:27,570 If this is violated, then you're going 736 00:38:27,570 --> 00:38:29,244 to want to do one of two things. 737 00:38:29,244 --> 00:38:31,410 Either you're going to want to buy your own gasoline 738 00:38:31,410 --> 00:38:35,370 and store it, or you're going to want to short it and do 739 00:38:35,370 --> 00:38:37,650 the opposite. 740 00:38:37,650 --> 00:38:40,440 After Hurricane Katrina hit, we had 741 00:38:40,440 --> 00:38:45,750 violations from this for a period of time, which suggested 742 00:38:45,750 --> 00:38:47,880 that it was actually worthwhile for you 743 00:38:47,880 --> 00:38:51,060 to go out and build your own storage facilities, 744 00:38:51,060 --> 00:38:53,760 because the storage facilities were destroyed. 745 00:38:53,760 --> 00:38:55,520 Now it's only if you had the technology 746 00:38:55,520 --> 00:38:57,270 to build those storage facilities that you 747 00:38:57,270 --> 00:38:59,660 could actually profit from it. 748 00:38:59,660 --> 00:39:04,160 But there are periods of time where market dislocation can 749 00:39:04,160 --> 00:39:10,190 occur, and the discrepancy between futures prices and spot 750 00:39:10,190 --> 00:39:11,240 prices-- 751 00:39:11,240 --> 00:39:13,160 that gives you valuable information 752 00:39:13,160 --> 00:39:16,920 about what's happening in markets, and in some cases, 753 00:39:16,920 --> 00:39:20,300 in non-financial contexts, like commodities. 754 00:39:20,300 --> 00:39:23,480 Whether there's a shortage or whether there's a glut. 755 00:39:23,480 --> 00:39:27,110 Weather impacts these commodities. 756 00:39:27,110 --> 00:39:28,910 And so by looking at this relationship 757 00:39:28,910 --> 00:39:32,990 you gather very valuable information. 758 00:39:32,990 --> 00:39:34,340 Here's another example. 759 00:39:34,340 --> 00:39:36,110 Another example is financials. 760 00:39:36,110 --> 00:39:38,684 I'm going to take this example as the last one 761 00:39:38,684 --> 00:39:40,100 that I want to focus on, because I 762 00:39:40,100 --> 00:39:46,940 want to now talk about how to use this for your own purposes. 763 00:39:46,940 --> 00:39:52,100 A financial future is a futures contract 764 00:39:52,100 --> 00:39:55,200 on an index like the S&P 500. 765 00:39:55,200 --> 00:39:59,810 So there, all of those contracts are cash settled, 766 00:39:59,810 --> 00:40:01,270 there is no physical delivery. 767 00:40:01,270 --> 00:40:03,890 Although, you can easily imagine a situation where 768 00:40:03,890 --> 00:40:05,310 you could have physical delivery. 769 00:40:05,310 --> 00:40:08,240 Somebody literally delivers 500 shares 770 00:40:08,240 --> 00:40:13,430 of stocks, 500 stocks with a certain number of shares 771 00:40:13,430 --> 00:40:17,140 for each, in order to get the S&P 500. 772 00:40:17,140 --> 00:40:19,330 But that's a pain, and that defeats 773 00:40:19,330 --> 00:40:20,849 the purpose of the futures market, 774 00:40:20,849 --> 00:40:22,390 which is to try to make things simple 775 00:40:22,390 --> 00:40:25,340 and to make it more efficient. 776 00:40:25,340 --> 00:40:29,830 So a stock index future is really a pure bet 777 00:40:29,830 --> 00:40:32,770 on an underlying index. 778 00:40:32,770 --> 00:40:36,550 And it gives you, the investor or the hedger, 779 00:40:36,550 --> 00:40:40,570 a way to get exposure or get out of exposure of that underlying 780 00:40:40,570 --> 00:40:41,950 in a very direct way. 781 00:40:41,950 --> 00:40:47,395 Now in this case, there's no real convenience yield, 782 00:40:47,395 --> 00:40:50,170 but there is a dividend that gets 783 00:40:50,170 --> 00:40:54,670 paid by the particular set of securities. 784 00:40:54,670 --> 00:40:59,090 So if you're holding the S&P 500 portfolio, 785 00:40:59,090 --> 00:41:02,060 then you're going to be getting paid dividends 786 00:41:02,060 --> 00:41:05,970 for individual stocks in that portfolio. 787 00:41:05,970 --> 00:41:10,850 And so you'd want to factor in in your futures arbitrage 788 00:41:10,850 --> 00:41:15,560 relationship the fact that you're getting a benefit, 789 00:41:15,560 --> 00:41:19,850 like a convenience yield, that you have to subtract off 790 00:41:19,850 --> 00:41:21,830 of this relationship. 791 00:41:21,830 --> 00:41:24,470 So you don't have a cost of storage, 792 00:41:24,470 --> 00:41:26,330 because this is a financial futures, 793 00:41:26,330 --> 00:41:29,960 but you do have a convenience yield, in terms of a payment 794 00:41:29,960 --> 00:41:34,492 if you held the physical shares of the S&P 500. 795 00:41:34,492 --> 00:41:36,200 So that's the difference between futures. 796 00:41:36,200 --> 00:41:37,850 Futures, you don't get that dividend, 797 00:41:37,850 --> 00:41:42,190 so you got to take that out in order to do the calculation. 798 00:41:42,190 --> 00:41:47,180 That tells you what the futures price is relative to the spot. 799 00:41:47,180 --> 00:41:51,430 So now if I give you an exam question that says, 800 00:41:51,430 --> 00:41:54,220 today's spot price is such and such, 801 00:41:54,220 --> 00:41:57,340 and the risk free interest rate over the next three month 802 00:41:57,340 --> 00:42:00,080 period is such and such, you should 803 00:42:00,080 --> 00:42:04,670 be able to tell me what the no arbitrage futures price should 804 00:42:04,670 --> 00:42:06,560 be today. 805 00:42:06,560 --> 00:42:09,832 Or vice versa, if I told you what the futures price is, 806 00:42:09,832 --> 00:42:11,540 and I told you what the interest rate is, 807 00:42:11,540 --> 00:42:13,940 you should be able to infer from that what 808 00:42:13,940 --> 00:42:16,280 the spot price is going to be. 809 00:42:16,280 --> 00:42:22,550 On October 19, 1987, the morning before the New York Stock 810 00:42:22,550 --> 00:42:25,940 Exchange opened, there was a very big discrepancy 811 00:42:25,940 --> 00:42:28,880 between the spot price and the futures price. 812 00:42:31,440 --> 00:42:35,460 That discrepancy caused arbitrageurs to rub their hands 813 00:42:35,460 --> 00:42:38,580 and say, oh my god, this is Christmas coming early, 814 00:42:38,580 --> 00:42:40,450 I'm going to take advantage of this. 815 00:42:40,450 --> 00:42:41,990 And so what they ended up doing-- 816 00:42:41,990 --> 00:42:43,740 it turned out because the relationship was 817 00:42:43,740 --> 00:42:46,840 violated in one specific way-- 818 00:42:46,840 --> 00:42:51,880 they ended up buying the futures and shorting the stocks. 819 00:42:51,880 --> 00:42:56,170 That was the beginning of the October, 1987 crash, 820 00:42:56,170 --> 00:42:59,109 that within a day dropped the market by about 20%. 821 00:42:59,109 --> 00:43:01,150 Nowadays, that's no big deal, we're used to that. 822 00:43:01,150 --> 00:43:06,030 [LAUGHTER] But back then, it was really something. 823 00:43:06,030 --> 00:43:10,620 So now that you have examples of how these prices are 824 00:43:10,620 --> 00:43:15,115 determined, let me take this out for a different kind of a spin. 825 00:43:15,115 --> 00:43:17,240 I want to show you how you use one of these things. 826 00:43:19,910 --> 00:43:27,830 And the way I'm going to do that is with the S&P 500. 827 00:43:27,830 --> 00:43:30,140 What I skipped were more numerical examples 828 00:43:30,140 --> 00:43:34,350 that I would encourage you to go through on your own. 829 00:43:34,350 --> 00:43:36,330 But this is an example that's important, 830 00:43:36,330 --> 00:43:38,330 so I want to take you through it carefully, make 831 00:43:38,330 --> 00:43:40,430 sure everybody understands. 832 00:43:40,430 --> 00:43:42,560 Suppose that you've got $1 million 833 00:43:42,560 --> 00:43:45,770 to invest in the stock market, and you've 834 00:43:45,770 --> 00:43:48,360 decided that you want to invest it in the S&P 500. 835 00:43:48,360 --> 00:43:51,650 You don't want to invest it in any other individual stocks. 836 00:43:51,650 --> 00:43:54,770 You want a broadly diversified investment, 837 00:43:54,770 --> 00:43:58,520 and the S&P looks like a pretty good thing. 838 00:43:58,520 --> 00:44:01,380 So there are several ways of doing this, 839 00:44:01,380 --> 00:44:03,150 I'm going to focus just on two. 840 00:44:03,150 --> 00:44:06,380 One of them is you could put your money 841 00:44:06,380 --> 00:44:10,240 in 500 different stocks. 842 00:44:10,240 --> 00:44:12,534 And you have to spend a little bit of time figuring out 843 00:44:12,534 --> 00:44:14,200 what the proportions are, because if you 844 00:44:14,200 --> 00:44:17,761 want to replicate the S&P, the S&P is a value weighted index, 845 00:44:17,761 --> 00:44:18,760 it's not equal weighted. 846 00:44:18,760 --> 00:44:21,045 It's weighted by market capitalization. 847 00:44:21,045 --> 00:44:23,170 So you've got to actually go through and figure out 848 00:44:23,170 --> 00:44:25,870 how big each company the S&P is, and then 849 00:44:25,870 --> 00:44:27,910 calculate those weights. 850 00:44:27,910 --> 00:44:30,190 And then you've got to give this order to your broker, 851 00:44:30,190 --> 00:44:32,360 and $1 million dollars isn't what it used to be, 852 00:44:32,360 --> 00:44:34,060 so I suspect that that would generate 853 00:44:34,060 --> 00:44:35,380 some pretty tiny trades. 854 00:44:35,380 --> 00:44:37,600 You got 500 securities, and you've 855 00:44:37,600 --> 00:44:39,820 got a bunch of different odd lot trades. 856 00:44:39,820 --> 00:44:41,260 Good luck finding a broker that's 857 00:44:41,260 --> 00:44:42,940 willing to do it at a reasonable price. 858 00:44:42,940 --> 00:44:45,760 It's a pretty long list. 859 00:44:45,760 --> 00:44:50,630 Or you can buy a futures contract. 860 00:44:50,630 --> 00:44:53,330 In particular, you can buy a contract 861 00:44:53,330 --> 00:44:55,370 on the S&P 500 futures. 862 00:44:55,370 --> 00:44:59,090 So I want to go through and show you what that involves. 863 00:44:59,090 --> 00:45:01,855 Now let's take your $1 million and let's deposit 864 00:45:01,855 --> 00:45:06,050 it at the Futures Brokerage account. 865 00:45:06,050 --> 00:45:08,810 So the money is sitting there, earning whatever interest they 866 00:45:08,810 --> 00:45:10,350 pay you on that account. 867 00:45:10,350 --> 00:45:16,670 Which is not much, it's probably akin to a money market return. 868 00:45:16,670 --> 00:45:20,540 So what you do is you want to buy futures contracts 869 00:45:20,540 --> 00:45:22,460 and you want to have the equivalent 870 00:45:22,460 --> 00:45:29,270 exposure of $1 million invested in the S&P 500. 871 00:45:29,270 --> 00:45:32,900 Now the way that the S&P 500 futures contract works, 872 00:45:32,900 --> 00:45:37,580 is that the value of the contract, the notional amount 873 00:45:37,580 --> 00:45:43,020 of the contract, is 250 times the index. 874 00:45:43,020 --> 00:45:46,400 Whatever the index is worth, they just make up a number, 875 00:45:46,400 --> 00:45:49,670 like I don't know 250, and multiply that 876 00:45:49,670 --> 00:45:50,930 by the value of the index. 877 00:45:50,930 --> 00:45:57,014 And they say that is what your exposure is for one contract. 878 00:45:57,014 --> 00:45:57,680 So what is that? 879 00:45:57,680 --> 00:46:06,050 Let's suppose the the S&P index is now at a 1,000. 880 00:46:06,050 --> 00:46:09,140 So the value of the futures contract is 250 times 881 00:46:09,140 --> 00:46:16,910 that and that's going to be $250,000. 882 00:46:16,910 --> 00:46:19,520 In order for you to have the equivalent of $1 million 883 00:46:19,520 --> 00:46:24,990 in the S&P, you need four of those contracts. 884 00:46:24,990 --> 00:46:30,120 Four times a notional of 250 is equal to $1 million. 885 00:46:30,120 --> 00:46:31,230 Now what does this say? 886 00:46:31,230 --> 00:46:33,810 This says that you are essentially 887 00:46:33,810 --> 00:46:40,440 agreeing that you're going to buy the S&P 500 whenever 888 00:46:40,440 --> 00:46:42,060 it settles. 889 00:46:42,060 --> 00:46:43,820 But you're not really buying the S&P 500, 890 00:46:43,820 --> 00:46:50,130 you're buying a pure bet that is equivalent to 250 times 891 00:46:50,130 --> 00:46:53,700 the S&P 500. 892 00:46:53,700 --> 00:46:57,220 So let's take a look at what that means. 893 00:46:57,220 --> 00:47:02,230 Suppose that the S&P index fluctuates, bounces around, 894 00:47:02,230 --> 00:47:07,740 then it turns out that you'll see that your cash portfolio-- 895 00:47:07,740 --> 00:47:11,680 the portfolio fluctuations if you had put $1 million 896 00:47:11,680 --> 00:47:14,260 into the S&P directly-- 897 00:47:14,260 --> 00:47:17,440 it fluctuates in exactly the same way 898 00:47:17,440 --> 00:47:19,480 that your futures portfolio fluctuate. 899 00:47:19,480 --> 00:47:23,920 If the S&P goes down to 900, the notional value 900 00:47:23,920 --> 00:47:28,870 of your portfolio with four contracts is $900,000. 901 00:47:28,870 --> 00:47:31,720 So you've actually lost $100,000, 902 00:47:31,720 --> 00:47:35,580 and that's going to be deducted from your account. 903 00:47:35,580 --> 00:47:41,250 If on the other hand, the S&P goes up by 100, 904 00:47:41,250 --> 00:47:47,790 then your cash portfolio will be worth $1,100,000, 905 00:47:47,790 --> 00:47:50,640 and your futures portfolio will be worth the same. 906 00:47:50,640 --> 00:47:54,660 You will now get $100,000 deposited into your account. 907 00:47:54,660 --> 00:47:56,970 By holding this futures contract, 908 00:47:56,970 --> 00:48:01,860 it's as if you were actually invested in the S&P. 909 00:48:01,860 --> 00:48:05,830 What you're getting is the daily fluctuations. 910 00:48:05,830 --> 00:48:08,360 But you actually don't own the security, 911 00:48:08,360 --> 00:48:14,470 you simply agreed to buy this so-called index on the maturity 912 00:48:14,470 --> 00:48:15,220 date. 913 00:48:15,220 --> 00:48:19,210 And by doing so, and because that contract value 914 00:48:19,210 --> 00:48:22,930 is so closely tied to the S&P 500 index, 915 00:48:22,930 --> 00:48:27,400 it moves in lockstep with the cash portfolio. 916 00:48:30,260 --> 00:48:32,242 Any questions about this? 917 00:48:32,242 --> 00:48:34,572 Yeah. 918 00:48:34,572 --> 00:48:36,660 AUDIENCE: Does someone own those shares 919 00:48:36,660 --> 00:48:38,370 behind you or it's just-- 920 00:48:38,370 --> 00:48:39,010 ANDREW LO: No. 921 00:48:39,010 --> 00:48:41,150 AUDIENCE: --an agreement that we're going to wait on this-- 922 00:48:41,150 --> 00:48:41,960 ANDREW LO: Exactly. 923 00:48:41,960 --> 00:48:42,460 Right. 924 00:48:42,460 --> 00:48:45,860 So you and I, we're just going to agree, we're going to bet. 925 00:48:45,860 --> 00:48:47,660 We're going to bet and we're going 926 00:48:47,660 --> 00:48:52,130 to agree on a particular price for S&P 500 three months 927 00:48:52,130 --> 00:48:53,300 from now. 928 00:48:53,300 --> 00:48:57,170 And if it goes up, and I bought the contract, then I win. 929 00:48:57,170 --> 00:49:01,190 If it goes down, then you sold the contract, then you win. 930 00:49:01,190 --> 00:49:03,564 But it's a pure bet between you and me. 931 00:49:03,564 --> 00:49:05,589 AUDIENCE: In the middle is the Futures-- 932 00:49:05,589 --> 00:49:07,380 ANDREW LO: The Futures Clearing corporation 933 00:49:07,380 --> 00:49:09,963 sits in the middle to make sure that you and I don't run away. 934 00:49:09,963 --> 00:49:11,944 AUDIENCE: Why do they do this? 935 00:49:11,944 --> 00:49:13,235 ANDREW LO: Why do they do this? 936 00:49:13,235 --> 00:49:20,940 AUDIENCE: I mean why do they [INAUDIBLE] days of sunlight. 937 00:49:20,940 --> 00:49:24,650 ANDREW LO: Well, first of all, in some cases they do. 938 00:49:24,650 --> 00:49:27,710 So for example, you could buy a contract 939 00:49:27,710 --> 00:49:34,030 on the number of degree days of a certain amount in Florida. 940 00:49:34,030 --> 00:49:35,960 Now why would you want to do that? 941 00:49:35,960 --> 00:49:41,320 It turns out that one of the largest crops of oranges 942 00:49:41,320 --> 00:49:43,180 are grown in Florida. 943 00:49:43,180 --> 00:49:47,500 And it turns out that the output of oranges groves 944 00:49:47,500 --> 00:49:51,590 is very closely tied to temperature. 945 00:49:51,590 --> 00:49:56,595 So if it goes up to 39 degrees or below 32 degrees, 946 00:49:56,595 --> 00:49:58,720 you can actually have very different kind of crops. 947 00:49:58,720 --> 00:50:01,052 And so you can bet on that, and at some point 948 00:50:01,052 --> 00:50:02,260 you can actually trade on it. 949 00:50:02,260 --> 00:50:03,926 I don't know if you can trade on it now, 950 00:50:03,926 --> 00:50:08,290 but there are markets for some of the wildest things. 951 00:50:08,290 --> 00:50:10,040 And the reason that you have these markets 952 00:50:10,040 --> 00:50:13,670 is because when two mutually consenting adults have 953 00:50:13,670 --> 00:50:17,194 opposite views and they want to express them, then 954 00:50:17,194 --> 00:50:18,860 you want to be able to let them do that, 955 00:50:18,860 --> 00:50:22,700 and allow them to basically either hedge their risks, 956 00:50:22,700 --> 00:50:26,070 or take on risks that they're able to do. 957 00:50:26,070 --> 00:50:27,620 So this is an example of that. 958 00:50:27,620 --> 00:50:28,460 You're an investor. 959 00:50:28,460 --> 00:50:31,310 You want to buy stocks, but you don't 960 00:50:31,310 --> 00:50:34,790 want to buy 500 little stocks one by one. 961 00:50:34,790 --> 00:50:36,834 You want to get the exposure right away. 962 00:50:36,834 --> 00:50:38,750 Now of course, there's another way to do this, 963 00:50:38,750 --> 00:50:40,670 you can put it in a mutual fund. 964 00:50:40,670 --> 00:50:42,170 But the problem with the mutual fund 965 00:50:42,170 --> 00:50:45,980 is that it only gets priced once a day, whereas this thing gets 966 00:50:45,980 --> 00:50:49,460 priced every second of the day when the futures exchange is 967 00:50:49,460 --> 00:50:50,540 open. 968 00:50:50,540 --> 00:50:53,600 Of course, nowadays, you can buy an ETF, an Exchange Traded 969 00:50:53,600 --> 00:50:54,930 Fund. 970 00:50:54,930 --> 00:50:57,180 So that's another way of getting exposure. 971 00:50:57,180 --> 00:51:00,050 But the S&P futures was around long before ETFs 972 00:51:00,050 --> 00:51:04,479 and allowed people to do all sorts of hedging transactions. 973 00:51:04,479 --> 00:51:06,770 Now I'm going to give you a second example that I think 974 00:51:06,770 --> 00:51:08,311 will make it a little bit more clear, 975 00:51:08,311 --> 00:51:12,020 and actually will answer a question that was asked, 976 00:51:12,020 --> 00:51:14,240 I think two lectures ago. 977 00:51:14,240 --> 00:51:15,680 When I first started this lecture, 978 00:51:15,680 --> 00:51:17,450 I said that maybe a company would only 979 00:51:17,450 --> 00:51:19,250 want to hedge 25% of its risk. 980 00:51:19,250 --> 00:51:21,447 And somebody asked well, what does that mean 25%? 981 00:51:21,447 --> 00:51:23,030 And I said, I'll answer that question. 982 00:51:23,030 --> 00:51:25,850 Well, so I'm going to answer that question now. 983 00:51:25,850 --> 00:51:30,440 So suppose now as a different example, 984 00:51:30,440 --> 00:51:34,880 you have a diversified portfolio of large cap stocks 985 00:51:34,880 --> 00:51:36,800 worth $5 million. 986 00:51:36,800 --> 00:51:41,310 So you already own the stocks, and it's currently 987 00:51:41,310 --> 00:51:44,400 worth $5 million, but you don't have any confidence 988 00:51:44,400 --> 00:51:47,160 that the market is going to stay where it is. 989 00:51:47,160 --> 00:51:48,690 You think it's going to go down. 990 00:51:48,690 --> 00:51:51,360 And so you want to hedge some of that risk. 991 00:51:51,360 --> 00:51:52,980 You don't want to hedge all of it, 992 00:51:52,980 --> 00:51:57,540 because you do have faith that over time markets will do well, 993 00:51:57,540 --> 00:52:00,000 but you just want to be able to dampen 994 00:52:00,000 --> 00:52:04,780 a little bit of the downward spiral if it does occur. 995 00:52:04,780 --> 00:52:09,960 So you might consider selling 25% of your portfolio. 996 00:52:09,960 --> 00:52:13,050 Getting rid of 25% of it and putting that in cash. 997 00:52:13,050 --> 00:52:14,710 That's one way to do it. 998 00:52:14,710 --> 00:52:17,160 But the problem as you know is that it's not 999 00:52:17,160 --> 00:52:21,390 that easy to sell 25% of 500 stocks, 1000 00:52:21,390 --> 00:52:24,960 because you have to again, slice the portfolio, stock by stock. 1001 00:52:24,960 --> 00:52:29,280 You're going to have a trade list of 500 stocks, which 1002 00:52:29,280 --> 00:52:32,920 comprise 25% of your portfolio. 1003 00:52:32,920 --> 00:52:34,800 So it's a pain. 1004 00:52:34,800 --> 00:52:37,650 But here's an easier way to do it. 1005 00:52:37,650 --> 00:52:45,170 You can short sell five S&P contracts. 1006 00:52:45,170 --> 00:52:48,230 And I'm arguing that that will do the exact same as 1007 00:52:48,230 --> 00:52:53,530 if you just liquidated 25% of your portfolio. 1008 00:52:53,530 --> 00:52:57,130 Now let's see if that's right. 1009 00:52:57,130 --> 00:52:59,950 So let's go through the exact same table. 1010 00:52:59,950 --> 00:53:01,420 The cash portfolio-- let's see what 1011 00:53:01,420 --> 00:53:05,350 happens to the cash portfolio if the S&P goes up or down by 100 1012 00:53:05,350 --> 00:53:06,730 points. 1013 00:53:06,730 --> 00:53:09,610 If it goes up by 100 points, then you've made money. 1014 00:53:09,610 --> 00:53:11,200 You've got $5.5 million. 1015 00:53:11,200 --> 00:53:13,510 If it goes down by a 100 points, you've lost money. 1016 00:53:13,510 --> 00:53:17,110 You've lost to $4.5 million. 1017 00:53:17,110 --> 00:53:19,510 Now let's see what happens if you don't do anything 1018 00:53:19,510 --> 00:53:22,630 with the cash portfolio, but you simply short sell 1019 00:53:22,630 --> 00:53:26,170 five S&P futures contracts. 1020 00:53:26,170 --> 00:53:30,850 If you do that then obviously if the S&P doesn't change, 1021 00:53:30,850 --> 00:53:33,140 then nothing happens to your portfolio. 1022 00:53:33,140 --> 00:53:35,830 But if the S&P goes up, then you're 1023 00:53:35,830 --> 00:53:38,790 going to make some money. 1024 00:53:38,790 --> 00:53:40,570 Sorry. 1025 00:53:40,570 --> 00:53:42,670 So yeah, if the S&P goes up, you're 1026 00:53:42,670 --> 00:53:47,080 going to lose money in the sense that what's going to happen 1027 00:53:47,080 --> 00:53:53,500 is that your short positions are going to cost you $125,000. 1028 00:53:53,500 --> 00:53:55,149 How did I get $125,000? 1029 00:53:55,149 --> 00:53:56,690 Anybody work through the math for me? 1030 00:54:03,030 --> 00:54:06,310 The S&P 500 goes up by a 100 points. 1031 00:54:06,310 --> 00:54:13,640 The futures price goes up by 250 times 100 points. 1032 00:54:13,640 --> 00:54:16,190 My position, I've got five of these contracts, 1033 00:54:16,190 --> 00:54:19,700 I've just lost $25,000 per contract. 1034 00:54:19,700 --> 00:54:25,460 I've got five of these contracts, I lost $125,000. 1035 00:54:25,460 --> 00:54:27,120 Now what about the downside? 1036 00:54:27,120 --> 00:54:32,090 The downside if the S&P goes down by 100, 1037 00:54:32,090 --> 00:54:38,330 then the price goes down by $25,000. 1038 00:54:38,330 --> 00:54:42,110 I'm short, so I make $25,000 per contract. 1039 00:54:42,110 --> 00:54:46,190 I've got five contracts, I've made $125,000. 1040 00:54:46,190 --> 00:54:48,320 So look what happens. 1041 00:54:48,320 --> 00:54:51,980 In this case, when the S&P goes up, 1042 00:54:51,980 --> 00:54:56,070 I don't make as much, because my hedge works against me. 1043 00:54:56,070 --> 00:54:58,490 On the other hand, when the S&P goes down, 1044 00:54:58,490 --> 00:55:02,030 I don't lose as much, because the hedge is working for me. 1045 00:55:02,030 --> 00:55:06,440 Because I've only taken out 25% of my portfolio 1046 00:55:06,440 --> 00:55:12,190 with this hedge, it's dampening, but not eliminating 1047 00:55:12,190 --> 00:55:13,794 that kind of fluctuation. 1048 00:55:13,794 --> 00:55:15,276 Yeah? 1049 00:55:15,276 --> 00:55:17,808 AUDIENCE: I think that this an obvious question, but why 1050 00:55:17,808 --> 00:55:21,520 do you do that, versus just putting it in cash. 1051 00:55:21,520 --> 00:55:24,516 Because you can make the argument that if you had 25%, 1052 00:55:24,516 --> 00:55:28,241 and had it earning interest, and so you'd still be up too. 1053 00:55:28,241 --> 00:55:29,740 ANDREW LO: Well, that's the argument 1054 00:55:29,740 --> 00:55:31,614 that I gave earlier, which is that you'd have 1055 00:55:31,614 --> 00:55:34,350 to sell 25% of your portfolio. 1056 00:55:34,350 --> 00:55:36,490 This is a way of doing it. 1057 00:55:36,490 --> 00:55:39,450 And not only that, if you did it this way, 1058 00:55:39,450 --> 00:55:42,000 it would be a lot cheaper to implement in the sense 1059 00:55:42,000 --> 00:55:47,100 that you don't have to do 500 transactions, 1060 00:55:47,100 --> 00:55:50,760 you do one transaction. 1061 00:55:50,760 --> 00:55:53,700 So the transactions cost is a lot cheaper, 1062 00:55:53,700 --> 00:55:55,427 and it's also easier to keep track of. 1063 00:55:55,427 --> 00:55:57,510 You don't have to figure out what the price of 500 1064 00:55:57,510 --> 00:55:59,400 securities are. 1065 00:55:59,400 --> 00:56:01,780 You've got the price of just one security to worry about. 1066 00:56:01,780 --> 00:56:02,280 Yeah. 1067 00:56:02,280 --> 00:56:04,560 AUDIENCE: And I think also you're 1068 00:56:04,560 --> 00:56:06,380 not losing out on what you could've 1069 00:56:06,380 --> 00:56:08,120 had in cash in terms of interest, 1070 00:56:08,120 --> 00:56:10,320 because that interest is factored in to the futures. 1071 00:56:10,320 --> 00:56:10,710 ANDREW LO: That's right. 1072 00:56:10,710 --> 00:56:12,540 Remember we used that interest equation 1073 00:56:12,540 --> 00:56:16,850 so all the foregone interest is in there. 1074 00:56:16,850 --> 00:56:21,840 OK, so the meaning of I want to hedge 25% 1075 00:56:21,840 --> 00:56:25,710 means I'm going to use the futures contract, 1076 00:56:25,710 --> 00:56:31,380 so that the notional exposure is 25% of the current value 1077 00:56:31,380 --> 00:56:34,280 of my portfolio. 1078 00:56:34,280 --> 00:56:38,260 So if you're Merck pharmaceutical company that 1079 00:56:38,260 --> 00:56:41,650 has a certain percentage of their revenues 1080 00:56:41,650 --> 00:56:43,870 in foreign denominated currencies, 1081 00:56:43,870 --> 00:56:47,950 you can hedge half of the risk of those exchange rate 1082 00:56:47,950 --> 00:56:51,130 fluctuations by taking half of the revenue stream-- 1083 00:56:51,130 --> 00:56:54,096 let's say it's $10 billion-- 1084 00:56:54,096 --> 00:56:59,080 and buying or selling, depending on which way you're going, 1085 00:56:59,080 --> 00:57:03,190 the amount of futures or forwards to 1086 00:57:03,190 --> 00:57:04,737 get rid of that exposure. 1087 00:57:04,737 --> 00:57:05,551 Yeah. 1088 00:57:05,551 --> 00:57:10,320 AUDIENCE: In this example, we put our million in the margin 1089 00:57:10,320 --> 00:57:15,066 account, but we only should put as much as 1090 00:57:15,066 --> 00:57:15,940 [INTERPOSING VOICES]. 1091 00:57:15,940 --> 00:57:16,979 ANDREW LO: That's right. 1092 00:57:16,979 --> 00:57:19,270 You don't have to put $1 million in the margin account, 1093 00:57:19,270 --> 00:57:21,160 because typically the margin is going 1094 00:57:21,160 --> 00:57:25,300 to be something like in this case 7% or 8% 1095 00:57:25,300 --> 00:57:27,100 of the notional exposure. 1096 00:57:27,100 --> 00:57:30,220 So you could take the rest of that money and go to Las Vegas 1097 00:57:30,220 --> 00:57:31,379 if you like. 1098 00:57:31,379 --> 00:57:33,670 Although, some would say this is better than Las Vegas. 1099 00:57:33,670 --> 00:57:34,115 Yeah. 1100 00:57:34,115 --> 00:57:35,656 AUDIENCE: This is the main reason why 1101 00:57:35,656 --> 00:57:37,656 we buy futures and not ETFs. 1102 00:57:37,656 --> 00:57:40,360 You can leverage your bet as much as you want. 1103 00:57:40,360 --> 00:57:42,850 ANDREW LO: That's right with an ETF, if you want $1 million 1104 00:57:42,850 --> 00:57:47,350 of exposure, you got to put $1 million into the ETF. 1105 00:57:47,350 --> 00:57:50,170 With the futures contract, if you want to put $1 million 1106 00:57:50,170 --> 00:57:53,140 of exposure on, you need 7%. 1107 00:57:53,140 --> 00:57:55,030 And the reason is obvious, it's because 1108 00:57:55,030 --> 00:57:58,220 of that daily mark to market. 1109 00:57:58,220 --> 00:58:01,270 So ETFs have not killed the futures market, 1110 00:58:01,270 --> 00:58:04,180 but it does provide another vehicle for retail investors 1111 00:58:04,180 --> 00:58:07,900 who may not want the leverage, who may not need to leverage, 1112 00:58:07,900 --> 00:58:11,140 to not have to worry about the leverage. 1113 00:58:11,140 --> 00:58:15,650 This leverage-- leverage is a scary thing, as I said before. 1114 00:58:15,650 --> 00:58:18,370 This is the chain saw that you don't want to be giving 1115 00:58:18,370 --> 00:58:20,350 your eight-year-old as a toy. 1116 00:58:20,350 --> 00:58:24,340 Because when prices move quickly, 1117 00:58:24,340 --> 00:58:27,640 you're going to have very big swings in the underlying 1118 00:58:27,640 --> 00:58:30,340 value of your margin account. 1119 00:58:30,340 --> 00:58:35,170 So if you've got only 7% margin in an account, 1120 00:58:35,170 --> 00:58:39,400 think about it, that means that if the prices go down by 7%, 1121 00:58:39,400 --> 00:58:40,540 you are wiped out. 1122 00:58:40,540 --> 00:58:42,790 Your entire margin account is gone. 1123 00:58:42,790 --> 00:58:47,410 When futures brokers take your money, 1124 00:58:47,410 --> 00:58:49,480 they assume that you know what you're doing. 1125 00:58:49,480 --> 00:58:52,960 And so they assume that the margin that you're putting down 1126 00:58:52,960 --> 00:58:56,620 is margin that you can afford to lose, 1127 00:58:56,620 --> 00:58:59,440 and that you understand that what you're getting 1128 00:58:59,440 --> 00:59:02,590 is much bigger exposure that presumably is either 1129 00:59:02,590 --> 00:59:04,240 for speculative purposes, in which case 1130 00:59:04,240 --> 00:59:07,750 you won't over leverage, or for hedging purposes, in which case 1131 00:59:07,750 --> 00:59:10,690 you've got some other assets that are counterbalancing 1132 00:59:10,690 --> 00:59:11,350 these swings. 1133 00:59:11,350 --> 00:59:12,556 Like in this case. 1134 00:59:12,556 --> 00:59:13,930 You know obviously, when you look 1135 00:59:13,930 --> 00:59:17,440 at the fluctuations in your positions, 1136 00:59:17,440 --> 00:59:20,995 they are extraordinarily big relative to the margin. 1137 00:59:23,590 --> 00:59:26,180 Let's do a quick back of the envelope calculation. 1138 00:59:26,180 --> 00:59:27,920 Let me tell you what I mean. 1139 00:59:27,920 --> 00:59:31,640 Suppose that you put 5% margin down. 1140 00:59:31,640 --> 00:59:34,600 You buy a contract, put 5% margin down, 1141 00:59:34,600 --> 00:59:37,810 and let's suppose that the price of the futures contract 1142 00:59:37,810 --> 00:59:40,140 drops by 2.5%. 1143 00:59:43,080 --> 00:59:46,830 What is the rate of return on the amount of money 1144 00:59:46,830 --> 00:59:51,944 you've put down as margin, if that's your initial investment? 1145 00:59:51,944 --> 00:59:53,610 You can think about it as an investment, 1146 00:59:53,610 --> 00:59:56,130 because that's the only way a futures broker will 1147 00:59:56,130 --> 00:59:57,840 let you buy a contract. 1148 00:59:57,840 --> 01:00:04,320 If you put down $100,000 and the futures price goes down 1149 01:00:04,320 --> 01:00:08,218 by $50,000, what's the rate of return on your investment? 1150 01:00:10,910 --> 01:00:14,960 Yeah, it's minus 50%, that's a big move. 1151 01:00:14,960 --> 01:00:18,230 That's a huge move in a day. 1152 01:00:18,230 --> 01:00:20,960 So when you deal with margin, you 1153 01:00:20,960 --> 01:00:22,910 have to be extraordinarily careful. 1154 01:00:22,910 --> 01:00:25,730 You have to have very, very tight risk controls. 1155 01:00:25,730 --> 01:00:29,270 You have to understand what the swings can be, 1156 01:00:29,270 --> 01:00:32,900 and you have to manage that risk very, very carefully, 1157 01:00:32,900 --> 01:00:35,150 on an intradaily basis in some cases, 1158 01:00:35,150 --> 01:00:38,340 because these futures prices can swing a lot even within a day. 1159 01:00:41,330 --> 01:00:44,130 Any other questions? 1160 01:00:44,130 --> 01:00:46,950 Well, that's it for futures and forwards. 1161 01:00:46,950 --> 01:00:49,890 You now know how to price them. 1162 01:00:49,890 --> 01:00:53,290 You now know how to use them for hedging purposes. 1163 01:00:53,290 --> 01:00:55,680 And there are all sorts of other kinds 1164 01:00:55,680 --> 01:00:59,520 of futures and forwards-- interest rate, bond, currency, 1165 01:00:59,520 --> 01:01:02,460 single stock futures now exist. 1166 01:01:02,460 --> 01:01:06,405 In fact, there are even futures contracts on the VIX, 1167 01:01:06,405 --> 01:01:11,805 there's futures contracts on electricity usage, 1168 01:01:11,805 --> 01:01:15,180 there's futures contracts on the presidential election. 1169 01:01:15,180 --> 01:01:18,840 If you go to the Iowa Electronic Markets, the University 1170 01:01:18,840 --> 01:01:21,990 of Iowa, they created a futures exchange 1171 01:01:21,990 --> 01:01:24,300 that has two contracts. 1172 01:01:24,300 --> 01:01:26,700 One that pays $1 if McCain gets elected, 1173 01:01:26,700 --> 01:01:29,460 and the other that pays $1 if Obama gets elected. 1174 01:01:29,460 --> 01:01:31,530 And by looking at the prices, you 1175 01:01:31,530 --> 01:01:34,830 can actually see what the folks that are trading these futures 1176 01:01:34,830 --> 01:01:39,810 contracts are thinking, in terms of who's got the edge. 1177 01:01:39,810 --> 01:01:44,230 So the futures prices contain an enormous amount of information. 1178 01:01:44,230 --> 01:01:50,060 But keep in mind the information is only as good as you are. 1179 01:01:50,060 --> 01:01:52,250 By you, I mean the market. 1180 01:01:52,250 --> 01:01:54,300 If the market is comprised of knuckleheads, 1181 01:01:54,300 --> 01:01:57,660 the prices you get will be knucklehead prices. 1182 01:01:57,660 --> 01:02:00,210 If the market contains really smart 1183 01:02:00,210 --> 01:02:03,060 sharp sophisticated individuals, you'll 1184 01:02:03,060 --> 01:02:05,820 get extremely informative prices. 1185 01:02:05,820 --> 01:02:09,360 So prices, while they are the best thing 1186 01:02:09,360 --> 01:02:12,180 that we have as a guide for the future, 1187 01:02:12,180 --> 01:02:13,890 they're clearly not perfect. 1188 01:02:13,890 --> 01:02:16,740 And there are periods of time when the market prices 1189 01:02:16,740 --> 01:02:18,690 are less perfect than others. 1190 01:02:18,690 --> 01:02:21,540 And as I told you before, for the next three weeks, 1191 01:02:21,540 --> 01:02:24,060 finance theory is going to be on vacation in the US stock 1192 01:02:24,060 --> 01:02:27,120 market, because all the uncertainty that 1193 01:02:27,120 --> 01:02:30,360 has been building up over the last several years 1194 01:02:30,360 --> 01:02:33,060 are now focused on the next three weeks. 1195 01:02:33,060 --> 01:02:36,390 Markets will be swinging back and forth pretty wildly, 1196 01:02:36,390 --> 01:02:38,580 and it's because people are reacting emotionally, 1197 01:02:38,580 --> 01:02:45,680 not necessarily with their full logical capabilities. 1198 01:02:45,680 --> 01:02:48,680 That's it for futures and forwards, 1199 01:02:48,680 --> 01:02:54,860 and now what I'm going to turn to is options. 1200 01:02:54,860 --> 01:02:58,334 These are the last set of securities 1201 01:02:58,334 --> 01:02:59,750 that I want to go through with you 1202 01:02:59,750 --> 01:03:03,275 that are not like the securities that we've done before. 1203 01:03:05,790 --> 01:03:11,605 And let me just pull up the lecture notes for options. 1204 01:03:14,720 --> 01:03:18,170 I want to start with a little bit of an introduction for how 1205 01:03:18,170 --> 01:03:19,370 to motivate options. 1206 01:03:19,370 --> 01:03:22,970 I think most of you know what options are. 1207 01:03:22,970 --> 01:03:25,970 Their name is quite apropos, because they 1208 01:03:25,970 --> 01:03:27,840 do give you options. 1209 01:03:27,840 --> 01:03:32,210 Futures and forwards require you to engage in a transaction, 1210 01:03:32,210 --> 01:03:34,490 but options don't. 1211 01:03:34,490 --> 01:03:38,370 They give you the right, but not the obligation. 1212 01:03:38,370 --> 01:03:41,570 So you have the option of not entering 1213 01:03:41,570 --> 01:03:45,230 into that final transaction at settlement date. 1214 01:03:45,230 --> 01:03:47,210 I'm going to start with some motivation, 1215 01:03:47,210 --> 01:03:49,820 then go through some payoff diagrams, 1216 01:03:49,820 --> 01:03:52,190 go through options strategies, and then I'm 1217 01:03:52,190 --> 01:03:55,100 going to talk very briefly about valuation of options. 1218 01:03:55,100 --> 01:03:57,927 I have to talk to you guys about Black-Scholes. 1219 01:03:57,927 --> 01:04:00,260 You can't leave MIT without hearing about Black-Scholes. 1220 01:04:00,260 --> 01:04:02,360 [LAUGHTER] So I've got to do a little bit of that. 1221 01:04:02,360 --> 01:04:06,080 But really the derivation is quite a bit more sophisticated, 1222 01:04:06,080 --> 01:04:09,920 and that's why you might want to take 15.437 Options 1223 01:04:09,920 --> 01:04:11,930 and Futures, where the entire course is 1224 01:04:11,930 --> 01:04:13,310 devoted to these instruments. 1225 01:04:13,310 --> 01:04:17,880 They are that complex and that important. 1226 01:04:17,880 --> 01:04:21,530 So let me first describe exactly what an option is. 1227 01:04:21,530 --> 01:04:24,530 An option actually is a specific example of something 1228 01:04:24,530 --> 01:04:28,590 that you now know of more generally as a derivative. 1229 01:04:28,590 --> 01:04:31,010 A derivative security gets its name 1230 01:04:31,010 --> 01:04:33,710 because the value of the security 1231 01:04:33,710 --> 01:04:38,750 is derived from yet another security. 1232 01:04:38,750 --> 01:04:44,000 It's derivative, as opposed to I guess fundamental or primary. 1233 01:04:44,000 --> 01:04:49,250 And examples of derivatives are warrants versus options. 1234 01:04:49,250 --> 01:04:51,860 Options are securities that you can 1235 01:04:51,860 --> 01:04:55,460 think of as pure bets between two parties. 1236 01:04:55,460 --> 01:04:58,550 Warrants are options that are issued 1237 01:04:58,550 --> 01:05:01,070 by a company on its own shares. 1238 01:05:01,070 --> 01:05:05,900 So the net supply of options is zero, 1239 01:05:05,900 --> 01:05:09,710 but the net supply of warrants is not zero, 1240 01:05:09,710 --> 01:05:11,810 it's issued by companies. 1241 01:05:11,810 --> 01:05:14,750 And there are two different kinds of options, 1242 01:05:14,750 --> 01:05:15,950 calls and puts. 1243 01:05:15,950 --> 01:05:19,550 A call option is a piece of paper 1244 01:05:19,550 --> 01:05:21,830 that says the holder of this piece of paper 1245 01:05:21,830 --> 01:05:26,930 is allowed to buy a security on or possibly 1246 01:05:26,930 --> 01:05:31,340 before a particular date, usually called the exercise 1247 01:05:31,340 --> 01:05:36,050 date or maturity date. 1248 01:05:36,050 --> 01:05:39,920 And the difference between being able to exercise early 1249 01:05:39,920 --> 01:05:42,890 versus exercising at the maturity only, 1250 01:05:42,890 --> 01:05:46,640 is the difference between an American and a European option. 1251 01:05:46,640 --> 01:05:50,990 An American option is one where you can exercise it early. 1252 01:05:50,990 --> 01:05:54,890 And a European option is one where you can only exercise it 1253 01:05:54,890 --> 01:06:00,440 on a specific date, the maturity date or the expiration date. 1254 01:06:00,440 --> 01:06:03,740 And puts are the opposite of calls. 1255 01:06:03,740 --> 01:06:05,930 Instead of giving you the right to buy, 1256 01:06:05,930 --> 01:06:08,510 it gives you the right to sell or to put 1257 01:06:08,510 --> 01:06:11,780 the stock to somebody else. 1258 01:06:11,780 --> 01:06:14,150 And the prices at which you get to either 1259 01:06:14,150 --> 01:06:18,140 buy in the case of calls, or sell in the case of puts, 1260 01:06:18,140 --> 01:06:22,400 is called the strike price or the exercise price. 1261 01:06:22,400 --> 01:06:23,200 All right. 1262 01:06:23,200 --> 01:06:25,820 So I'm going to define a little bit of notation. 1263 01:06:25,820 --> 01:06:27,890 Stock prices is S sub t. 1264 01:06:27,890 --> 01:06:31,880 Strike price is K. Notice that K does not have a time subscript, 1265 01:06:31,880 --> 01:06:34,880 because it's fixed at the time the options are issued 1266 01:06:34,880 --> 01:06:37,580 and it doesn't change throughout the life of that option, 1267 01:06:37,580 --> 01:06:40,580 it's part of the contract terms. 1268 01:06:40,580 --> 01:06:42,440 And then the call price is C,t. 1269 01:06:42,440 --> 01:06:44,360 Put price is P,t. 1270 01:06:44,360 --> 01:06:47,240 And the value of these contracts at maturity 1271 01:06:47,240 --> 01:06:49,350 is actually pretty simple. 1272 01:06:49,350 --> 01:06:58,140 If today a particular stock is trading at $60 a share, 1273 01:06:58,140 --> 01:07:02,610 and you purchase an option to buy that stock at $70 a share 1274 01:07:02,610 --> 01:07:06,470 in three months, does that piece of paper have any value? 1275 01:07:09,320 --> 01:07:12,110 The current price is $60, this piece of paper 1276 01:07:12,110 --> 01:07:17,594 gives you the right to buy it at $70 in three months. 1277 01:07:17,594 --> 01:07:21,140 Is that worthless? 1278 01:07:21,140 --> 01:07:22,490 Why not? 1279 01:07:22,490 --> 01:07:25,760 The price is at $60, you can get it at $60 today. 1280 01:07:25,760 --> 01:07:28,510 So why would you want it at $70 three months from now? 1281 01:07:31,020 --> 01:07:32,760 Exactly the price may go up. 1282 01:07:32,760 --> 01:07:34,800 The reason the piece of paper is not worth 1283 01:07:34,800 --> 01:07:38,040 zero today is that there is a chance, 1284 01:07:38,040 --> 01:07:40,980 no matter how small you might think it is, 1285 01:07:40,980 --> 01:07:44,250 there is still a chance that something wonderful might 1286 01:07:44,250 --> 01:07:46,860 happen in the next three months, and then 1287 01:07:46,860 --> 01:07:48,510 the price will go up to $80. 1288 01:07:48,510 --> 01:07:51,300 And if it goes up to $80, you'll be very happy 1289 01:07:51,300 --> 01:07:53,370 that you have the right to buy it at $70. 1290 01:07:53,370 --> 01:07:54,930 How happy will you be? 1291 01:07:54,930 --> 01:07:57,180 You'll be $10 per share happy. 1292 01:07:57,180 --> 01:08:00,800 [LAUGHTER] That's what that expression says. 1293 01:08:00,800 --> 01:08:07,020 On the expiration date, you get to buy the shares-- 1294 01:08:07,020 --> 01:08:10,220 if you're holding a call option, you get to buy it for K 1295 01:08:10,220 --> 01:08:14,760 dollars, but in fact the market has determined that the price 1296 01:08:14,760 --> 01:08:19,010 at that time is really S,T dollars. 1297 01:08:19,010 --> 01:08:22,870 So if you're holding this piece of paper, this is your profit-- 1298 01:08:22,870 --> 01:08:25,560 S,T minus K per share. 1299 01:08:25,560 --> 01:08:29,960 Now if it turns out that you get to buy it for $60, 1300 01:08:29,960 --> 01:08:34,250 and it ends up trading at $40, well then 1301 01:08:34,250 --> 01:08:36,649 you're not going to exercise that right. 1302 01:08:36,649 --> 01:08:39,500 You're going to let the option expire, 1303 01:08:39,500 --> 01:08:42,020 and when it expires it'll be worthless 1304 01:08:42,020 --> 01:08:44,210 if this number is negative. 1305 01:08:44,210 --> 01:08:46,520 It can be negative of course, but you're not 1306 01:08:46,520 --> 01:08:49,130 obligated to buy it. 1307 01:08:49,130 --> 01:08:52,100 On the other hand, if this were a futures contract, 1308 01:08:52,100 --> 01:08:55,580 you certainly are obligated to buy it 1309 01:08:55,580 --> 01:08:58,520 and then you'd get a negative return. 1310 01:08:58,520 --> 01:09:03,410 But an option is a wonderful thing, in that 1311 01:09:03,410 --> 01:09:07,069 the payoff is never negative. 1312 01:09:07,069 --> 01:09:14,000 It's either zero or it's S,T minus K. That's for a call. 1313 01:09:14,000 --> 01:09:16,340 Now a put option, it's exactly the reverse. 1314 01:09:16,340 --> 01:09:21,140 If you get to sell the stock, then your profit 1315 01:09:21,140 --> 01:09:23,840 is what you get to sell it at versus 1316 01:09:23,840 --> 01:09:25,819 what it's really trading at. 1317 01:09:25,819 --> 01:09:28,160 And so you actually hope that it's really 1318 01:09:28,160 --> 01:09:30,380 trading at a very low price. 1319 01:09:30,380 --> 01:09:32,420 Because if you get to sell it at a high price, 1320 01:09:32,420 --> 01:09:36,920 but it's trading at a low price, you profit the difference. 1321 01:09:36,920 --> 01:09:38,960 So the payoff for a put option is exactly 1322 01:09:38,960 --> 01:09:45,120 the reverse, maximum of zero and K minus S. 1323 01:09:45,120 --> 01:09:48,895 Now, it's very important that you understand this asymmetry, 1324 01:09:48,895 --> 01:09:50,520 because that asymmetry is going to lead 1325 01:09:50,520 --> 01:09:54,060 to all sorts of interesting things about these instruments. 1326 01:09:54,060 --> 01:09:58,900 And before we go and talk about that kind of asymmetry, 1327 01:09:58,900 --> 01:10:02,050 I want to give you another way of looking at options. 1328 01:10:02,050 --> 01:10:07,110 Which is to look at options as a kind of insurance contract, 1329 01:10:07,110 --> 01:10:11,130 because actually all insurance contracts are 1330 01:10:11,130 --> 01:10:14,280 a form of an option. 1331 01:10:14,280 --> 01:10:16,660 So let me give you an example. 1332 01:10:16,660 --> 01:10:21,150 Suppose that you want to insure the value of a particular stock 1333 01:10:21,150 --> 01:10:22,020 that you're holding. 1334 01:10:22,020 --> 01:10:24,210 You're holding General Electric and it's 1335 01:10:24,210 --> 01:10:26,910 trading at $20 a share, and you'd 1336 01:10:26,910 --> 01:10:34,760 like to make sure that it never goes below $18 a share. 1337 01:10:34,760 --> 01:10:39,720 You want to buy insurance that if it goes below $18 a share, 1338 01:10:39,720 --> 01:10:44,210 you will get paid $18 a share. 1339 01:10:44,210 --> 01:10:49,520 Well, the way you do that is you buy a put option. 1340 01:10:49,520 --> 01:10:52,880 A put option on General Electric where the strike 1341 01:10:52,880 --> 01:10:57,070 price is $18 a share. 1342 01:10:57,070 --> 01:11:00,310 Because if it goes below $18 a share, 1343 01:11:00,310 --> 01:11:03,370 you get to sell General Electric for that $18. 1344 01:11:03,370 --> 01:11:05,650 So you'll get the $18, regardless 1345 01:11:05,650 --> 01:11:10,330 of whether it goes to $10, or $5, or who knows what. 1346 01:11:10,330 --> 01:11:13,700 It turns out that the put option is exactly like insurance, 1347 01:11:13,700 --> 01:11:16,450 and let's take a look and see why. 1348 01:11:16,450 --> 01:11:19,757 These are the typical terms of an insurance contract. 1349 01:11:19,757 --> 01:11:21,340 What's the asset that you're insuring? 1350 01:11:21,340 --> 01:11:23,170 General Electric. 1351 01:11:23,170 --> 01:11:25,120 What's the current asset value? 1352 01:11:25,120 --> 01:11:27,400 $20 a share. 1353 01:11:27,400 --> 01:11:28,970 What's the term of the policy? 1354 01:11:28,970 --> 01:11:30,880 How long do you have the policy for? 1355 01:11:30,880 --> 01:11:33,490 It's the time to maturity. 1356 01:11:33,490 --> 01:11:35,440 What's the maximum coverage? 1357 01:11:35,440 --> 01:11:38,150 What are you covered for? 1358 01:11:38,150 --> 01:11:39,274 $18 a share, that's right. 1359 01:11:39,274 --> 01:11:40,940 That's what you bought the coverage for, 1360 01:11:40,940 --> 01:11:43,330 that's what you're going to get if it goes below. 1361 01:11:43,330 --> 01:11:45,290 What's the deductible? 1362 01:11:45,290 --> 01:11:49,760 How much could you lose before the insurance kicks in? 1363 01:11:49,760 --> 01:11:50,990 $2 a share, exactly. 1364 01:11:50,990 --> 01:11:52,040 That's the deductible. 1365 01:11:52,040 --> 01:11:55,450 And finally, what does it cost you 1366 01:11:55,450 --> 01:11:57,850 to buy this insurance, what's the insurance premium? 1367 01:12:00,590 --> 01:12:02,270 Exactly, the price of the put. 1368 01:12:02,270 --> 01:12:03,800 That's it. 1369 01:12:03,800 --> 01:12:05,270 Beautiful thing. 1370 01:12:05,270 --> 01:12:08,510 A put option is nothing more than an insurance contract 1371 01:12:08,510 --> 01:12:10,850 on the value of a stock. 1372 01:12:10,850 --> 01:12:13,310 And it's going to turn out that a call 1373 01:12:13,310 --> 01:12:18,740 option will be intimately tied to what a put option is. 1374 01:12:18,740 --> 01:12:23,630 So every call option can be converted into a portfolio that 1375 01:12:23,630 --> 01:12:25,340 includes a put. 1376 01:12:25,340 --> 01:12:30,590 So all options you can think of as insurance contracts, 1377 01:12:30,590 --> 01:12:33,860 but there are a few differences. 1378 01:12:33,860 --> 01:12:35,450 The difference between an option is 1379 01:12:35,450 --> 01:12:38,530 that you can exercise it early. 1380 01:12:38,530 --> 01:12:41,720 So for example, for whatever reason, 1381 01:12:41,720 --> 01:12:44,350 if you decide that you want to buy General Electric at $18 1382 01:12:44,350 --> 01:12:48,230 a share, when it's trading at $17.50, 1383 01:12:48,230 --> 01:12:49,960 and you still have one month to go. 1384 01:12:49,960 --> 01:12:54,160 But you want to get paid that $18 now, you can do that. 1385 01:12:54,160 --> 01:12:56,530 You can't do that with your car insurance, right? 1386 01:12:56,530 --> 01:12:59,770 I guess you could, you could ram it into a post, 1387 01:12:59,770 --> 01:13:01,480 and I want to get paid now, so let's-- 1388 01:13:01,480 --> 01:13:04,600 [LAUGHTER] But that's not really considered a proper thing 1389 01:13:04,600 --> 01:13:06,100 to do. 1390 01:13:06,100 --> 01:13:07,600 So early exercise is one difference. 1391 01:13:07,600 --> 01:13:10,300 Second difference is marketability. 1392 01:13:10,300 --> 01:13:14,360 If at some point you don't want the insurance anymore, 1393 01:13:14,360 --> 01:13:17,060 you can't get rid of it and give it to somebody else. 1394 01:13:17,060 --> 01:13:21,350 You can't transfer your auto insurance to your friend, 1395 01:13:21,350 --> 01:13:24,020 if you decide you don't need it anymore. 1396 01:13:24,020 --> 01:13:27,650 But you can transfer the insurance policy here. 1397 01:13:27,650 --> 01:13:31,650 You can sell the option, you can sell it. 1398 01:13:31,650 --> 01:13:33,420 And also there are dividends that 1399 01:13:33,420 --> 01:13:36,090 are being paid on the stock that you have to worry about 1400 01:13:36,090 --> 01:13:39,840 with options, whereas with a typical insurance contract 1401 01:13:39,840 --> 01:13:42,060 a car doesn't necessarily pay dividends. 1402 01:13:42,060 --> 01:13:45,000 And the reason that's important is when it pays dividends, 1403 01:13:45,000 --> 01:13:48,240 the value goes down, and so you have to make adjustments 1404 01:13:48,240 --> 01:13:49,800 for that with an option. 1405 01:13:49,800 --> 01:13:52,904 You have to protect an option for dividend payments. 1406 01:13:52,904 --> 01:13:54,570 You don't need to do that for insurance, 1407 01:13:54,570 --> 01:13:57,120 because typically you don't assume that the insurance 1408 01:13:57,120 --> 01:14:03,311 value, the value of the asset goes down that much over time. 1409 01:14:03,311 --> 01:14:03,810 Yep? 1410 01:14:03,810 --> 01:14:05,460 AUDIENCE: When they buy the put option, 1411 01:14:05,460 --> 01:14:10,530 they also eliminated the chance to enjoy it, 1412 01:14:10,530 --> 01:14:14,960 from the prices are going to go up, 1413 01:14:14,960 --> 01:14:18,410 with the futures we'd have a higher value. 1414 01:14:18,410 --> 01:14:21,390 ANDREW LO: Well, no that's actually not true. 1415 01:14:21,390 --> 01:14:23,070 With the put option, it gives you 1416 01:14:23,070 --> 01:14:25,890 the right to sell the stock. 1417 01:14:25,890 --> 01:14:28,680 If you buy the stock and you hold onto it, 1418 01:14:28,680 --> 01:14:33,400 and you also buy a put, that protects the downside. 1419 01:14:33,400 --> 01:14:35,610 But the upside, that's all yours. 1420 01:14:38,600 --> 01:14:41,360 Because as the stock goes up, what 1421 01:14:41,360 --> 01:14:43,010 happens to the value of the put? 1422 01:14:43,010 --> 01:14:44,690 AUDIENCE: It's going to zero. 1423 01:14:44,690 --> 01:14:46,610 ANDREW LO: Exactly, it stops at zero. 1424 01:14:46,610 --> 01:14:52,430 So as the stock goes up, the put doesn't have any value anymore. 1425 01:14:52,430 --> 01:14:54,560 It becomes worthless, worth less and less. 1426 01:14:54,560 --> 01:14:57,170 And on the date of expiration, if the stock 1427 01:14:57,170 --> 01:15:01,010 is way above the value of the strike, 1428 01:15:01,010 --> 01:15:03,380 then it expires worthless. 1429 01:15:03,380 --> 01:15:05,100 It doesn't go negative. 1430 01:15:05,100 --> 01:15:08,210 If it went negative, if you had a futures position, 1431 01:15:08,210 --> 01:15:12,070 then you'd be right, you've actually capped your gains. 1432 01:15:12,070 --> 01:15:13,400 But this doesn't. 1433 01:15:13,400 --> 01:15:17,920 See with this you get the best of both, or so it seems. 1434 01:15:17,920 --> 01:15:22,360 You get the upside, but it protects the downside. 1435 01:15:22,360 --> 01:15:27,050 And as you all probably know, insurance is not cheap. 1436 01:15:27,050 --> 01:15:30,830 So it sounds good, but you've got to pay for this. 1437 01:15:30,830 --> 01:15:36,910 And so you bet that the price of a call option or put option 1438 01:15:36,910 --> 01:15:40,240 is not zero when you strike it. 1439 01:15:40,240 --> 01:15:43,610 Unlike a futures contract that's worthless, 1440 01:15:43,610 --> 01:15:46,970 an option is not worthless on day zero. 1441 01:15:46,970 --> 01:15:48,200 It's worth a lot. 1442 01:15:48,200 --> 01:15:52,550 For example, right now what's really expensive-- 1443 01:15:52,550 --> 01:15:56,100 and if you want to check this, you could take a look for fun. 1444 01:15:56,100 --> 01:15:59,130 If you want to buy insurance on the S&P 500-- 1445 01:15:59,130 --> 01:16:01,230 now we've had a great rally on Monday, 1446 01:16:01,230 --> 01:16:04,500 the S&P was up 1,000 points. 1447 01:16:04,500 --> 01:16:08,010 If you want to buy insurance on the S&P 500 index, 1448 01:16:08,010 --> 01:16:08,980 you can do that. 1449 01:16:08,980 --> 01:16:12,010 There are options on the index. 1450 01:16:12,010 --> 01:16:14,040 So you might say, OK let's say that the S&P is 1451 01:16:14,040 --> 01:16:18,150 at 1,000 today, I would like to buy protection 1452 01:16:18,150 --> 01:16:22,620 that over the next month it doesn't go down 1453 01:16:22,620 --> 01:16:27,160 by more than 100 points, 10%. 1454 01:16:27,160 --> 01:16:28,000 So what do you do? 1455 01:16:28,000 --> 01:16:33,510 You buy a put option on the S&P with the strike price of what? 1456 01:16:33,510 --> 01:16:34,920 900, right. 1457 01:16:34,920 --> 01:16:37,954 OK, for a month. 1458 01:16:37,954 --> 01:16:39,120 That's what you want to buy. 1459 01:16:41,660 --> 01:16:43,640 Go out and calculate that price. 1460 01:16:43,640 --> 01:16:46,460 You're going to be shocked at how expensive it is, 1461 01:16:46,460 --> 01:16:48,860 to get that insurance for four weeks. 1462 01:16:48,860 --> 01:16:50,570 Four weeks, that's all. 1463 01:16:50,570 --> 01:16:55,220 It's really expensive today. 1464 01:16:55,220 --> 01:16:58,400 I think it's approximately 10 times more expensive today, 1465 01:16:58,400 --> 01:17:00,440 than it was a year ago. 1466 01:17:00,440 --> 01:17:05,740 The implied volatility is up by at least an order of magnitude. 1467 01:17:05,740 --> 01:17:10,710 So if you want that insurance, it's available, 1468 01:17:10,710 --> 01:17:11,990 but you have to pay for it. 1469 01:17:11,990 --> 01:17:15,800 So the question in all of these things is is it worth it? 1470 01:17:15,800 --> 01:17:17,644 In order to decide whether it's worth it, 1471 01:17:17,644 --> 01:17:18,810 you've got to do two things. 1472 01:17:18,810 --> 01:17:22,100 First look into the inner most workings of your own soul 1473 01:17:22,100 --> 01:17:25,335 and ask how frightened you truly are. 1474 01:17:25,335 --> 01:17:27,710 And the second thing you got to do is look at the market. 1475 01:17:27,710 --> 01:17:30,500 And is the market functioning reasonably well, 1476 01:17:30,500 --> 01:17:36,634 or is the market reflecting all of these kinds of crazy fears. 1477 01:17:36,634 --> 01:17:39,050 In order for us to be able to talk about it intelligently, 1478 01:17:39,050 --> 01:17:41,510 we need a way to price it. 1479 01:17:41,510 --> 01:17:43,702 We need the kind of logic that I showed you 1480 01:17:43,702 --> 01:17:44,660 with futures contracts. 1481 01:17:44,660 --> 01:17:45,990 And we're going to get that logic. 1482 01:17:45,990 --> 01:17:48,198 I'm going to show you how to price these things using 1483 01:17:48,198 --> 01:17:51,340 a very, very simple model that is incredibly powerful, 1484 01:17:51,340 --> 01:17:52,340 but we're not there yet. 1485 01:17:52,340 --> 01:17:53,310 Before we do that, I want to make sure 1486 01:17:53,310 --> 01:17:54,768 you understand what these contracts 1487 01:17:54,768 --> 01:17:58,220 can do for you in terms of changing your payoff 1488 01:17:58,220 --> 01:17:59,911 profiles of your portfolio. 1489 01:17:59,911 --> 01:18:00,411 Yeah? 1490 01:18:00,411 --> 01:18:02,135 AUDIENCE: So wouldn't European option 1491 01:18:02,135 --> 01:18:04,520 be similar to a futures, since you have 1492 01:18:04,520 --> 01:18:06,650 that you can only exercise on maturity date? 1493 01:18:06,650 --> 01:18:08,830 ANDREW LO: Well, no, that's not what 1494 01:18:08,830 --> 01:18:10,240 makes it similar to a futures. 1495 01:18:10,240 --> 01:18:13,360 Because while you cannot exercise it early, 1496 01:18:13,360 --> 01:18:16,470 you never have to exercise it at all. 1497 01:18:16,470 --> 01:18:21,380 So a European option gives you only one date 1498 01:18:21,380 --> 01:18:24,920 where you are able to exercise, but even on that date 1499 01:18:24,920 --> 01:18:27,220 you never have to exercise it. 1500 01:18:27,220 --> 01:18:29,150 With the futures contract, you have 1501 01:18:29,150 --> 01:18:31,010 to exercise it on that day. 1502 01:18:31,010 --> 01:18:32,442 You've made a commitment. 1503 01:18:32,442 --> 01:18:35,160 AUDIENCE: But it would have a net present value of zero. 1504 01:18:35,160 --> 01:18:38,950 ANDREW LO: No, no, it won't, because still on that date 1505 01:18:38,950 --> 01:18:41,830 you have a positive amount of protection. 1506 01:18:41,830 --> 01:18:43,480 Like the example I gave you. 1507 01:18:43,480 --> 01:18:47,020 Let's suppose that I bought a European S&P 1508 01:18:47,020 --> 01:18:51,830 option for the day after election day, Wednesday, 1509 01:18:51,830 --> 01:18:53,860 November 3rd is it. 1510 01:18:53,860 --> 01:18:56,150 That will have positive value today. 1511 01:18:56,150 --> 01:18:57,640 In other words, I'm going to have 1512 01:18:57,640 --> 01:18:59,560 to pay money in order for you guys 1513 01:18:59,560 --> 01:19:02,320 to sell it to me, because you're going to be providing me 1514 01:19:02,320 --> 01:19:05,800 with some protection that if the wrong thing happens on Tuesday, 1515 01:19:05,800 --> 01:19:08,154 the world is not going to blow up on Wednesday. 1516 01:19:08,154 --> 01:19:09,820 I'm not telling you what the wrong thing 1517 01:19:09,820 --> 01:19:12,100 is, I'm neutral in all of this. 1518 01:19:12,100 --> 01:19:16,340 But that's an example where that insurance really has value. 1519 01:19:16,340 --> 01:19:18,330 So you're not going to give it to me for free, 1520 01:19:18,330 --> 01:19:19,579 and I'm willing to pay for it. 1521 01:19:22,190 --> 01:19:23,780 All right, since we're out of time, 1522 01:19:23,780 --> 01:19:26,570 I'm going to just leave you with this diagram that 1523 01:19:26,570 --> 01:19:30,170 shows you the difference between a call option and a futures 1524 01:19:30,170 --> 01:19:31,100 contract. 1525 01:19:31,100 --> 01:19:33,380 Remember the futures contract what that looked like-- 1526 01:19:33,380 --> 01:19:34,580 that was a straight line. 1527 01:19:34,580 --> 01:19:35,750 Right Exactly. 1528 01:19:35,750 --> 01:19:38,540 This is not a straight line, this is kinked-- 1529 01:19:38,540 --> 01:19:40,610 very kinky security. 1530 01:19:40,610 --> 01:19:42,770 And so we're going to talk next time 1531 01:19:42,770 --> 01:19:45,290 about how to price kinky securities, 1532 01:19:45,290 --> 01:19:47,570 and how to combine them, and engage in even more 1533 01:19:47,570 --> 01:19:48,770 kinky kinds of payoffs. 1534 01:19:48,770 --> 01:19:50,620 [LAUGHTER]