WEBVTT 00:01.530 --> 00:05.000 So, so far where have we gotten to? 00:05.000 --> 00:09.920 We started summarizing what general equilibrium was. 00:09.920 --> 00:13.540 We saw that Irving Fisher of Yale reinvented general 00:13.539 --> 00:16.449 equilibrium in order to study finance, 00:16.450 --> 00:19.110 and we saw just by reinterpreting the variables of 00:19.105 --> 00:22.135 general equilibrium we could start to say a lot of things 00:22.140 --> 00:25.430 about finance, and in particular we had the 00:25.426 --> 00:28.936 idea of free markets, an argument in favor of free 00:28.944 --> 00:29.484 markets. 00:29.480 --> 00:33.340 We had the idea of arbitrage and no arbitrage so you could 00:33.339 --> 00:36.789 deduce a lot of prices without solving for the whole 00:36.793 --> 00:40.453 equilibrium just by knowing what other prices are. 00:40.450 --> 00:43.910 And we also learned that the price of many things is going to 00:43.914 --> 00:47.614 have to do with the utility and marginal utilities of people, 00:47.610 --> 00:50.750 and that's going to have a lot to do with what their impatience 00:50.746 --> 00:52.816 is, and whether they're rich people 00:52.819 --> 00:55.399 or poor people, redistributions of wealth, 00:55.402 --> 00:58.882 who's got the money and how impatient the people who have 00:58.875 --> 00:59.925 the money are. 00:59.930 --> 01:03.210 So those are the basic lessons that we're going to now carry 01:03.209 --> 01:04.209 into the course. 01:04.209 --> 01:08.279 And so for several lectures now I'm going to leave the abstract 01:08.281 --> 01:12.161 theory of general equilibrium and start teaching you some of 01:12.155 --> 01:16.155 the basic vocabulary of finance that you have to know and that 01:16.161 --> 01:19.971 everybody in finance knows like what is a mortgage, 01:19.970 --> 01:22.080 what's an annuity and stuff like that. 01:22.080 --> 01:27.360 So before I go there, though, I want to remind you of 01:27.364 --> 01:33.364 what Shakespeare had done 300 years before Irving Fisher. 01:33.360 --> 01:36.300 So Irving Fisher, remember, he cleared up the 01:36.302 --> 01:38.512 confusion of what interest was. 01:38.510 --> 01:42.070 He said interest is crystallized impatience. 01:42.069 --> 01:44.419 It's not some horribly unjust thing. 01:44.420 --> 01:47.580 It's not, as Marx thought, exploitation, 01:47.578 --> 01:52.358 but Shakespeare had discovered all this 300 years before. 01:52.360 --> 01:55.480 Now, when I was your age or a little bit younger than you in 01:55.476 --> 01:58.906 high school we all had to read the Merchant of Venice. 01:58.910 --> 02:04.140 I have two Indian coauthors who are vaguely my age, 02:04.140 --> 02:07.090 maybe a little older, but anyway they sort of grew up 02:07.091 --> 02:10.841 in India and they had to learn the Merchant of Venice, 02:10.840 --> 02:12.550 and actually they learned it a lot better than I did. 02:12.550 --> 02:15.440 They both have memorized the Merchant of Venice. 02:15.438 --> 02:18.098 They can recite almost the entire thing by heart. 02:18.098 --> 02:20.958 But anyway, when I was in high school it was completely typical 02:20.956 --> 02:22.936 to study the Merchant of Venice. 02:22.938 --> 02:25.008 I wonder how many of you have actually read it. 02:25.008 --> 02:27.038 Who's read the Merchant of Venice? 02:27.039 --> 02:30.429 Whoa this is Yale, I'm shocked. 02:30.430 --> 02:32.770 So a quarter of you have read it. 02:32.770 --> 02:35.510 Well, I recommend to the other three-quarters that you do read 02:35.514 --> 02:35.744 it. 02:35.740 --> 02:39.230 Now, when it's taught nowadays, especially at Yale, 02:39.226 --> 02:43.686 it's taught as a love story and a commentary on anti-Semitism. 02:43.690 --> 02:46.100 Now, of course, it's both. 02:46.098 --> 02:48.588 It is a love story and commentary on anti-Semitism. 02:48.590 --> 02:50.670 Shylock the lender is Jewish. 02:50.669 --> 02:54.319 And remember what we heard about the great religions? 02:54.318 --> 02:58.658 They were all forbidding lending at interest except for 02:58.663 --> 03:03.413 Judaism which let you loan money at interest to non-Jews. 03:03.408 --> 03:04.508 So Shakespeare [correction: Shylock], 03:04.508 --> 03:07.658 who's the money lender, is Jewish and lending it to 03:07.656 --> 03:11.176 Christians and that plays a big role in the play and what 03:11.181 --> 03:14.271 happens to him, and what people say about 03:14.268 --> 03:17.118 Judaism is a big element of the story. 03:17.120 --> 03:19.650 But the way the play is read now that's the whole story, 03:19.645 --> 03:21.525 and I don't think it's the whole story. 03:21.530 --> 03:24.070 In fact, I think it's quite an unimportant part of the story. 03:24.068 --> 03:28.618 I think the heart of the story is Shakespeare's commentary on 03:28.620 --> 03:29.530 economics. 03:29.530 --> 03:32.470 And so I'm going to try and argue in the next ten minutes 03:32.470 --> 03:34.780 that Shakespeare was not only a great writer, 03:34.780 --> 03:37.300 a great psychologist, but a great economist. 03:37.300 --> 03:40.470 And you're going to see that almost all the elements of the 03:40.466 --> 03:43.456 course are in this play, and that if you read it the way 03:43.464 --> 03:47.014 I think you should read it, it should be obvious that it's 03:47.006 --> 03:50.036 really about economics and not about love. 03:50.039 --> 03:52.289 So how do you know that? 03:52.288 --> 03:55.588 Well, the very first line of the play, Antonio walks in and 03:55.592 --> 03:58.212 he says, "In sooth, I know not why I am so 03:58.211 --> 03:59.011 sad." 03:59.008 --> 04:02.168 And there's an interlocutor, a minor character, 04:02.174 --> 04:05.414 whose name I've forgotten, Salario or something, 04:05.407 --> 04:08.707 says well it must be that you're so nervous. 04:08.710 --> 04:14.960 All your riches are on these boats and they're at risk, 04:14.960 --> 04:18.250 and so anyone who had so much money at risk on boats would 04:18.245 --> 04:21.295 naturally be nervous and therefore maybe depressed. 04:21.300 --> 04:23.120 And Antonio says, no, no, no, no, 04:23.120 --> 04:26.360 I'm not worried about the boats because every boat is on a 04:26.363 --> 04:28.813 different ocean and so I'm not worried. 04:28.810 --> 04:31.350 They are on a different ocean and they're sailing at different 04:31.346 --> 04:31.676 times. 04:31.680 --> 04:33.720 I'm not worried about my boats. 04:33.720 --> 04:36.920 And so then the interlocutor says, well then you must be 04:36.918 --> 04:38.138 worried about love. 04:38.139 --> 04:40.389 And he says, no, no, that's not it at all. 04:40.389 --> 04:43.349 So what do we see at the very beginning of the play? 04:43.350 --> 04:47.890 It's business first, love second; 04:47.889 --> 04:54.569 and secondly, he understands diversification. 04:54.569 --> 04:57.489 Now, what is the plot of play? 04:57.490 --> 05:01.510 Bassanio, who Harold Bloom--so it happens that went to talk to 05:01.505 --> 05:03.475 Harold Bloom-- I saw him in the Whitney 05:03.480 --> 05:07.100 Humanities Center-- one of Yale's greatest scholars. 05:07.100 --> 05:09.800 He's a polymath, he knows about everything, 05:09.803 --> 05:13.603 but including about Shakespeare and he has a much advertised 05:13.603 --> 05:15.153 photographic memory. 05:15.149 --> 05:19.829 So I happened to run into him at the Whitney Humanities 05:19.829 --> 05:24.599 Center, actually in the men's room of Whitney Humanities 05:24.596 --> 05:25.546 Center. 05:25.550 --> 05:29.140 While we were there I asked him about the Merchant of 05:29.136 --> 05:32.846 Venice and whether he happened to remember the rate of 05:32.850 --> 05:36.180 interest that Shylock ends of charging Antonio, 05:36.180 --> 05:41.580 and he said, "Dear boy, I remember almost everything, 05:41.579 --> 05:42.979 but that I've forgotten." 05:42.980 --> 05:46.480 It was so unimportant to him that he didn't even remember the 05:46.480 --> 05:47.590 rate of interest. 05:47.589 --> 05:49.289 But he said, "I happen to be lecturing 05:49.288 --> 05:51.428 about the Merchant of Venice in my class this 05:51.430 --> 05:53.330 afternoon," so I went and heard his lecture 05:53.331 --> 05:54.991 on the Merchant of Venice. 05:54.990 --> 05:58.130 So Bassanio, who's one of the heroes of the 05:58.125 --> 06:02.155 play, according to Harold Bloom is a complete loser. 06:02.160 --> 06:05.850 He's the one who needs the money to woo Portia, 06:05.848 --> 06:10.178 who's this beautiful woman living outside of Venice. 06:10.180 --> 06:12.370 And so he's got to borrow a huge amount of money. 06:12.370 --> 06:14.980 So when he enters he's described as a Venetian, 06:14.983 --> 06:16.463 a scholar and a soldier. 06:16.459 --> 06:19.819 Now, whenever Shakespeare says a scholar and a soldier, 06:19.815 --> 06:23.355 sometimes it's not a Venetian, when he says that the guy's 06:23.360 --> 06:24.790 always a great guy. 06:24.790 --> 06:26.890 So this occurs repeatedly. 06:26.889 --> 06:28.689 So anyway, Bassanio comes in as a star. 06:28.689 --> 06:30.329 He's a Venetian, a scholar, a soldier. 06:30.329 --> 06:32.259 What more can you want to be? 06:32.259 --> 06:35.449 And so he needs the money to woo Portia and he's got a 06:35.446 --> 06:36.946 business plan to do it. 06:36.949 --> 06:39.889 He's tried wooing her before and it's come to nothing and 06:39.886 --> 06:41.036 he's lost his money. 06:41.040 --> 06:43.600 But he says, "If you shoot an arrow and 06:43.596 --> 06:45.836 you lose it, shoot an arrow again the same 06:45.836 --> 06:48.576 way and then follow the second arrow more closely and you'll 06:48.577 --> 06:50.757 figure out where the first arrow goes." 06:50.759 --> 06:54.229 So he's a man on a business venture with a business plan. 06:54.230 --> 06:59.310 So here's Bassanio, and here's Shylock and Antonio. 06:59.310 --> 07:04.050 Now, he needs 3,000 ducats and he doesn't have any collateral 07:04.045 --> 07:05.145 or anything. 07:05.149 --> 07:09.499 And so he goes to Antonio, who's an older man, 07:09.500 --> 07:12.880 and according to Harold Bloom there's some potential gay 07:12.875 --> 07:16.425 relationship and maybe they're lovers and maybe they're not 07:16.434 --> 07:17.114 lovers. 07:17.110 --> 07:19.340 That's half the lecture. 07:19.339 --> 07:24.639 Anyway, so Shylock lends the money, 07:24.639 --> 07:27.189 3,000 ducats, and it's so much money he has 07:27.192 --> 07:30.842 to borrow it from another money lender named Tubal who's even 07:30.841 --> 07:32.181 richer than he is. 07:32.180 --> 07:35.780 So they argue over what the interest rate has got to be. 07:35.779 --> 07:40.869 And so Antonio says--oh dear I've forgotten to change this, 07:40.870 --> 07:44.240 so this is out of order--so they argue over what the 07:44.235 --> 07:47.925 interest rate should be and Antonio and Shylock make this 07:47.932 --> 07:48.792 argument. 07:48.790 --> 07:51.870 Antonio says, it's disgusting that you want 07:51.870 --> 07:53.630 to charge me interest. 07:53.629 --> 07:55.459 I mean, good Christians never charge interest. 07:55.459 --> 07:56.449 I'm appalled at you. 07:56.449 --> 07:58.619 It's because you're Jewish you're charging me interest. 07:58.620 --> 08:01.430 So he's throwing up epithets and insults at Shylock, 08:01.425 --> 08:04.005 but really he just wants a low interest rate. 08:04.009 --> 08:06.879 And so he says, Antonio says, 08:06.884 --> 08:10.984 "Shylock, I would neither borrow nor lend 08:10.975 --> 08:15.055 by taking or giving interest, but to supply the ripe wants of 08:15.055 --> 08:17.125 my friend I'll break a custom." 08:17.129 --> 08:19.739 So "ripe wants of my friend" that's saying 08:19.737 --> 08:22.397 because Bassanio was so impatient to get his hands on 08:22.396 --> 08:24.956 the money to find Portia, she's going to get married if 08:24.961 --> 08:26.491 he doesn't hurry up and marry her himself. 08:26.490 --> 08:29.800 Because of his impatience he's willing to pay a high rate of 08:29.802 --> 08:30.422 interest. 08:30.420 --> 08:34.920 And Shylock says you're always complaining about me that I 08:34.923 --> 08:39.743 charge interest--I've left out a whole bunch of stuff--but I'm 08:39.740 --> 08:40.690 patient. 08:40.690 --> 08:41.880 All of us are patient. 08:41.879 --> 08:43.429 That's the badge of our tribe. 08:43.428 --> 08:46.688 We're patient and so that's why I'm willing to lend you the 08:46.690 --> 08:47.140 money. 08:47.139 --> 08:51.069 So here Shakespeare has laid out, and it goes over five pages 08:51.073 --> 08:52.783 patience and impatience. 08:52.779 --> 09:03.229 So then they get an argument, again, about interest. 09:03.230 --> 09:04.060 So I forgot a slide. 09:04.058 --> 09:07.758 So the argument is Shylock tells a story. 09:07.759 --> 09:11.449 He says even in the Bible, you say that it's un-Christian 09:11.452 --> 09:15.062 to lend at interest, but don't you know the story in 09:15.057 --> 09:17.747 the Bible where Jacob was asked to do, 09:17.750 --> 09:20.960 perform a service in the field, using his fields. 09:20.960 --> 09:23.610 Somebody wanted to use his fields for a while, 09:23.610 --> 09:27.040 and so Jacob said okay you can use my fields but I have to 09:27.038 --> 09:30.588 charge you a fee and the fee's going to be that however many 09:30.590 --> 09:34.020 spotted lambs are born those are the ones that I get. 09:34.019 --> 09:37.049 And so it turned out that there was a huge number of spotted 09:37.048 --> 09:39.588 lambs, and so although Jacob had lent 09:39.586 --> 09:44.016 some of his sheep and his fields to the person who wanted them he 09:44.019 --> 09:47.759 got back vastly more than he lent at the beginning. 09:47.759 --> 09:52.509 And so Antonio answers, well, this isn't interest this 09:52.513 --> 09:53.593 is a risk. 09:53.590 --> 09:55.760 Jacob got so much more because he took a risk. 09:55.759 --> 09:58.889 Who would have known how many lambs were going to be born. 09:58.889 --> 10:03.209 And so you don't really charge interest, you're an investor. 10:03.210 --> 10:06.780 So they haggle over this for a while and they come to the 10:06.782 --> 10:09.782 conclusion that he's going to lend the money. 10:09.778 --> 10:12.278 And so what is the interest that they actually end up 10:12.279 --> 10:15.069 charging, the thing that Harold Bloom couldn't remember? 10:15.070 --> 10:17.440 Well, 0. 10:17.440 --> 10:20.610 "I'll lend you the money and take no doit of usance for 10:20.609 --> 10:22.969 my monies," not a single interest for my 10:22.971 --> 10:23.511 money. 10:23.509 --> 10:26.269 But they have to negotiate something else, 10:26.274 --> 10:29.044 something besides the rate of interest. 10:29.038 --> 10:31.188 They have to negotiate the collateral. 10:31.190 --> 10:34.320 And so they say, "Go with me (blah, 10:34.320 --> 10:37.610 blah, blah, blah), and then if you don't pay let 10:37.606 --> 10:41.866 the forfeit be an equal pound of your fair flesh to be cut off 10:41.873 --> 10:45.933 and taken in what part of your body pleaseth me." 10:45.928 --> 10:48.998 The other half of the--there were two lectures by Harold 10:48.996 --> 10:51.196 Bloom, the second half of the first 10:51.197 --> 10:55.017 lecture was what part of the body is he really talking about, 10:55.019 --> 10:59.889 and there seemed to be only two possibilities, 10:59.889 --> 11:02.609 the heart and another possibility, and Harold Bloom 11:02.605 --> 11:04.395 favored the second possibility. 11:04.399 --> 11:07.479 But anyway, it's collateral that they're putting up for the 11:07.477 --> 11:07.847 loan. 11:07.850 --> 11:11.550 So there's collateral. 11:11.548 --> 11:14.898 So now what we found is that Shakespeare has understood the 11:14.900 --> 11:16.750 impatience theory of interest. 11:16.750 --> 11:19.800 You've got an impatient borrower and a patient lender, 11:19.798 --> 11:23.258 and it's the tradeoff between patience and impatience which is 11:23.261 --> 11:25.931 going to decide what the rate of interest is. 11:25.928 --> 11:28.198 So that's already Irving Fisher's biggest message. 11:28.200 --> 11:29.860 And then the second thing he's noticed, 11:29.860 --> 11:31.590 which Irving Fisher didn't notice at all, 11:31.590 --> 11:34.710 and this is going to be a large part of the rest of the course, 11:34.710 --> 11:37.190 how do we know these people are going to keep their promises. 11:37.190 --> 11:39.010 Why is Antonio going to keep his promises? 11:39.009 --> 11:41.059 Well, it's because he's putting up collateral. 11:41.058 --> 11:44.908 And Antonio is stepping in for Bassanio because his collateral 11:44.909 --> 11:46.929 is worth more than Bassanio's. 11:46.928 --> 11:49.948 Shylock wants his pound of flesh, not Bassanio's pound of 11:49.947 --> 11:50.377 flesh. 11:50.379 --> 11:53.009 So all right, so that's the beginning by the 11:53.011 --> 11:53.381 way. 11:53.379 --> 11:54.879 Just how does the play unfold? 11:54.879 --> 11:55.769 It gets more interesting. 11:55.769 --> 11:59.899 So what happens is after getting his money Bassanio then 11:59.904 --> 12:01.864 goes to woo fair Portia. 12:01.860 --> 12:02.920 And how does he woo her? 12:02.918 --> 12:06.418 Well, it turns out the way that her fabulously wealthy father 12:06.418 --> 12:09.388 has set up the marriage is, there are three caskets, 12:09.394 --> 12:12.404 a gold one, a silver one and a lead one, 12:12.404 --> 12:16.024 and he has to pick one, and one of them contains her 12:16.024 --> 12:17.994 picture, and if you get the one with her 12:17.991 --> 12:19.371 picture you get to marry her. 12:19.370 --> 12:22.350 If you pick the wrong one, and here's the shocking thing, 12:22.350 --> 12:25.480 if you get the wrong one you swear before you choose if you 12:25.476 --> 12:28.386 choose wrong never to speak to lady afterward in way of 12:28.389 --> 12:29.089 marriage. 12:29.090 --> 12:32.160 So not only don't you get Portia, you don't get anybody. 12:32.158 --> 12:37.768 So what is the purpose of this absurd contract? 12:37.769 --> 12:40.609 Well, the purpose is maybe to make sure that people really 12:40.605 --> 12:41.595 want to marry her. 12:41.600 --> 12:44.280 Maybe the father set it up so that only someone who really 12:44.283 --> 12:46.973 wanted to marry her would bother to enter this competition 12:46.966 --> 12:50.426 because the risk is so high, but another way of saying it is 12:50.431 --> 12:53.581 it gives an excuse to Shakespeare to talk about risk 12:53.575 --> 12:57.265 and return and how people who have a higher risk are going to 12:57.273 --> 12:59.003 expect a higher return. 12:59.000 --> 13:01.130 So they talk about risk and return. 13:01.129 --> 13:04.959 And Aragon basically says she's really not that good looking to 13:04.961 --> 13:06.631 justify such a high risk. 13:06.629 --> 13:10.639 But anyway, all those other guys picked the wrong casket and 13:10.638 --> 13:14.918 Bassanio picks the lead one and gets her, and so she becomes the 13:14.918 --> 13:15.528 wife. 13:15.528 --> 13:16.828 Now, of course, she's delighted by this. 13:16.830 --> 13:20.870 He's the one she wanted all along, and so she says, 13:20.868 --> 13:24.098 "Let me give you this ring." 13:24.100 --> 13:27.160 This is yet a third contract. 13:27.158 --> 13:29.398 The first contract is the loan of Shylock. 13:29.399 --> 13:33.019 The second contract is the choosing the caskets and a 13:33.024 --> 13:37.074 contract that you won't marry again if you choose wrong. 13:37.070 --> 13:40.150 And now we have a third contract, which is Portia 13:40.150 --> 13:43.940 deciding that she gives a ring to Bassanio and she says, 13:43.940 --> 13:45.390 "Let this ring represent your love." 13:45.389 --> 13:47.329 And he says, "When this ring parts from 13:47.328 --> 13:49.448 this finger then parts life from hence." 13:49.450 --> 13:50.330 I'll never lose this ring. 13:50.330 --> 13:51.520 I'll never give it up. 13:51.519 --> 13:53.119 I love you so much. 13:53.120 --> 13:55.960 So, of course, the boats appear to sink. 13:55.960 --> 13:57.680 Calamity appears. 13:57.678 --> 14:00.688 "My ships have all mis-credited [correction: 14:00.693 --> 14:01.953 miscarried]." 14:01.950 --> 14:04.580 Shylock wants his collateral. 14:04.580 --> 14:07.710 So Portia now, who turns out to be incredibly 14:07.711 --> 14:11.271 wealthy--so we realize, again, the play's not about 14:11.269 --> 14:11.909 love. 14:11.908 --> 14:14.638 She's beautiful, but she's fabulously rich, 14:14.639 --> 14:18.409 much richer than Shylock is, much richer than Tubal was. 14:18.408 --> 14:21.068 They had to scrounge around to get the 3,000 ducats. 14:21.070 --> 14:25.260 She hands 6,000 ducats, and then 12,000 ducats, 14:25.258 --> 14:27.168 then 36,000 ducats. 14:27.168 --> 14:29.808 Says, look, offer Shylock all this money. 14:29.808 --> 14:31.478 Tell him, here, I've got the money. 14:31.480 --> 14:33.680 Tell him not to take his pound of flesh. 14:33.678 --> 14:36.908 So they hold the trial to decide whether Shylock should 14:36.913 --> 14:38.833 get his pound of flesh or not. 14:38.830 --> 14:41.210 And so Shylock, by this time, 14:41.206 --> 14:44.766 is incredibly pissed off, to say the least, 14:44.772 --> 14:47.152 at Antonio and Bassanio. 14:47.149 --> 14:48.559 And why is he so angry? 14:48.558 --> 14:52.218 Because among other things his daughter Jessica has run off 14:52.216 --> 14:55.616 with a Christian named Lorenzo and stolen his money. 14:55.620 --> 14:57.120 And so he yells, "My daughter, 14:57.116 --> 14:57.906 my ducats." 14:57.908 --> 15:03.088 And so she sold his wife's ring for a monkey, 15:03.090 --> 15:09.330 or his ring that was given to him by his wife Leah. 15:09.330 --> 15:11.300 And he says, "I had it of Leah when I 15:11.302 --> 15:12.122 was a bachelor. 15:12.120 --> 15:14.800 I would not have given it for a wilderness of monkeys." 15:14.798 --> 15:17.718 So Shylock believes in keeping his promise. 15:17.720 --> 15:19.930 He would never have broken a promise. 15:19.928 --> 15:22.648 He never would have given away the ring that was given to him 15:22.653 --> 15:23.293 by his wife. 15:23.289 --> 15:24.649 He absolutely wouldn't do it. 15:24.649 --> 15:29.409 He believes in keeping promises unlike everybody else in the 15:29.408 --> 15:33.038 play, his daughter, everybody as we'll see. 15:33.038 --> 15:37.588 So Lancelot says, "This making of Christians 15:37.591 --> 15:41.101 will raise the price of hogs." 15:41.100 --> 15:44.450 This Jewish girl Jessica has become a Christian so now she's 15:44.446 --> 15:47.676 going to be able to eat pork so it's going to increase the 15:47.678 --> 15:50.968 demand for pork and therefore raise the price of hogs. 15:50.970 --> 15:54.010 So Shakespeare--the play is full of economics. 15:54.009 --> 15:55.649 It's all about teaching economics. 15:55.649 --> 16:03.379 So anyway, they go to the trial and Shylock thinks the guy is a 16:03.384 --> 16:05.384 complete fool. 16:05.379 --> 16:06.959 He doesn't understand interest. 16:06.960 --> 16:10.400 He doesn't understand the whole point of a lending contract and 16:10.404 --> 16:13.074 getting interest, and basically he says--I've got 16:13.072 --> 16:15.242 to skip over this a little quickly. 16:15.240 --> 16:18.960 He says, we've got a contract. 16:18.960 --> 16:22.680 Your city, the greatest commercial city in the world at 16:22.681 --> 16:26.261 that time, can't possibly survive if you don't uphold 16:26.264 --> 16:27.234 contracts. 16:27.230 --> 16:30.260 So, "If you deny me, fie upon your law. 16:30.259 --> 16:32.179 There's no force in the decrees of Venice. 16:32.179 --> 16:33.389 I stand for judgment." 16:33.389 --> 16:36.769 I stand for keeping promises and the law is supposed to 16:36.769 --> 16:37.959 enforce promises. 16:37.960 --> 16:40.350 I stand for law is what Shylock says. 16:40.350 --> 16:43.080 Now, at the trial, who turns out to be the judge? 16:43.080 --> 16:46.460 Well Portia has disguised herself as the judge and she's 16:46.458 --> 16:47.748 actually the judge. 16:47.750 --> 16:50.050 And so she comes in and she has this famous line, 16:50.047 --> 16:52.917 "Who is the Merchant here and which is the Jew?" 16:52.918 --> 16:54.928 So, again, this confirms to me it's about economics. 16:54.928 --> 16:57.878 If it was about Judaism it would be, who's the Christian 16:57.878 --> 16:58.948 and who's the Jew? 16:58.950 --> 17:00.500 She's saying, who's the borrower, 17:00.496 --> 17:01.606 and who's the lender. 17:01.610 --> 17:02.790 That's how she comes in. 17:02.788 --> 17:04.698 And so then she says, "You've got to show 17:04.703 --> 17:05.303 mercy." 17:05.298 --> 17:06.808 And this is the most famous line in the play, 17:06.813 --> 17:08.123 "The quality of mercy," blah, 17:08.119 --> 17:08.429 blah. 17:08.430 --> 17:10.010 You all remember it who've seen it. 17:10.009 --> 17:13.249 And he says, and then Bassanio says look, 17:13.247 --> 17:15.187 I've got 6,000 ducats. 17:15.190 --> 17:16.730 I've got more than that, take that. 17:16.730 --> 17:19.650 And he says a contract is a contract. 17:19.650 --> 17:22.200 You've humiliated me, all kinds of humiliations have 17:22.200 --> 17:23.050 happened to me. 17:23.049 --> 17:23.969 I've got feelings too. 17:23.970 --> 17:24.920 I've been humiliated. 17:24.920 --> 17:27.970 I want the contract and the contract says that I should get 17:27.965 --> 17:29.065 the pound of flesh. 17:29.068 --> 17:32.948 And so Bassanio says, "To do a great right do a 17:32.951 --> 17:34.551 little wrong." 17:34.549 --> 17:37.289 So let him default. 17:37.289 --> 17:41.119 So what does Portia say? 17:41.119 --> 17:42.019 What is the judgment? 17:42.019 --> 17:44.199 She has to play the judge. 17:44.200 --> 17:47.450 It seems like the whole city depends on enforcing contracts 17:47.454 --> 17:50.154 and here it seems like a horrible thing to do. 17:50.150 --> 17:51.870 You're going to have to kill somebody. 17:51.868 --> 17:55.168 So what judgment can she possibly make? 17:55.170 --> 17:57.410 She says, well, the state has to enforce 17:57.414 --> 17:58.744 contracts, of course. 17:58.740 --> 18:02.620 Contracts have to be enforced, but only good contracts should 18:02.615 --> 18:03.515 be enforced. 18:03.519 --> 18:05.519 And so what's wrong with the contract? 18:05.519 --> 18:10.689 Does she say we're going to reduce what you owe from 3,000 18:10.691 --> 18:11.691 to 1,500? 18:11.690 --> 18:13.810 That's principal forgiveness. 18:13.808 --> 18:18.708 Does she say you don't have to--what does she say? 18:18.710 --> 18:22.510 What she says is that what was wrong is, the contract wasn't 18:22.505 --> 18:23.015 right. 18:23.019 --> 18:25.759 It wasn't the interest rate that was wrong. 18:25.759 --> 18:27.509 It wasn't the amount you owe that was wrong. 18:27.509 --> 18:29.289 It was the collateral that was wrong. 18:29.288 --> 18:32.928 So she says the right collateral was a pound of flesh, 18:32.930 --> 18:35.710 but not a drop of blood, and so the state intervenes not 18:35.711 --> 18:38.921 to change the interest rate, not to change the principal, 18:38.915 --> 18:40.665 but to change the collateral. 18:40.670 --> 18:44.600 So all right, that's going to turn out to be, 18:44.604 --> 18:46.844 the leverage was wrong. 18:46.838 --> 18:50.098 So then the play ends with Bassanio asking the judge, 18:50.096 --> 18:53.166 he's so pleased that things have turned out right, 18:53.166 --> 18:55.106 if he can reward the judge. 18:55.108 --> 18:56.348 He doesn't know who the judge is. 18:56.348 --> 18:58.628 And he says, I've got all these ducats that 18:58.631 --> 19:01.081 I've just gotten, why don't I give you some of 19:01.075 --> 19:01.885 the ducats? 19:01.890 --> 19:04.070 And the judge says, well no, I don't want the 19:04.066 --> 19:06.836 ducats, but I notice you've got this ring on your finger, 19:06.836 --> 19:08.366 why don't you give me that? 19:08.368 --> 19:11.148 And he says, well I can't do that, 19:11.153 --> 19:13.433 my Portia, I've promised. 19:13.430 --> 19:17.430 And the judge says, well, give it to me anyway and 19:17.430 --> 19:19.390 he gives her the ring. 19:19.390 --> 19:22.700 And so the play finally ends with her revealing herself and 19:22.701 --> 19:26.071 he's incredibly embarrassed that he's given her the ring. 19:26.068 --> 19:28.908 So this is another contract broken, another default. 19:28.910 --> 19:31.510 And then he says, but I'm never going to default 19:31.507 --> 19:31.947 again. 19:31.950 --> 19:35.230 And Antonio steps in and says I'll guarantee again that he'll 19:35.230 --> 19:37.090 never default again, and of course, 19:37.088 --> 19:39.438 we all know that he's going to default. 19:39.440 --> 19:43.950 So the whole play is just about contracts and breaking 19:43.949 --> 19:44.969 contracts. 19:44.970 --> 19:47.600 And so at first it's about what the rate of interest should be, 19:47.598 --> 19:50.438 then it switches to, should contracts always be 19:50.439 --> 19:52.319 enforced, and yes they should be 19:52.317 --> 19:55.007 enforced, but the enforcement should be the taking of 19:55.009 --> 19:58.009 collateral and sometimes the amount of collateral put up is 19:58.009 --> 19:58.579 wrong. 19:58.578 --> 20:02.048 So that's going to be the conclusion of this course that 20:02.045 --> 20:05.635 what went wrong in the last two years or three years was a 20:05.635 --> 20:09.475 horrible mistake about how much collateral to be put up, 20:09.480 --> 20:12.280 and the Fed instead of just monitoring the interest rate, 20:12.278 --> 20:14.458 which is what you're taught in macroeconomics it's supposed to 20:14.464 --> 20:17.714 do, should be monitoring collateral 20:17.705 --> 20:21.705 as well and maybe even most importantly. 20:21.710 --> 20:27.150 So with that introduction to the rest of the course-- 20:27.150 --> 20:29.400 I don't know how convinced you are about Shakespeare the 20:29.397 --> 20:33.687 economist, but anyway, let's now switch to 20:33.685 --> 20:39.135 learning some of the basic words of finance. 20:39.140 --> 20:47.660 So I'm going to now follow pretty closely what the notes 20:47.660 --> 20:48.590 are. 20:48.588 --> 20:51.988 All right, so let's imagine a world where we've solved for the 20:51.989 --> 20:52.769 equilibrium. 20:52.769 --> 20:55.559 This could be the real world or one of our models, 20:55.563 --> 20:58.363 and there are many time periods, not just two time 20:58.355 --> 20:59.035 periods. 20:59.038 --> 21:02.178 So let's suppose that there, as there are as we're going to 21:02.180 --> 21:05.600 see in great detail later, suppose it's possible to pay 21:05.604 --> 21:08.854 money today in order to get a dollar next year, 21:08.848 --> 21:11.628 or pay some amount of money today in order to get a dollar 21:11.628 --> 21:13.608 in two years, or pay a different amount of 21:13.606 --> 21:15.486 money today to get a dollar in three years. 21:15.490 --> 21:19.100 So pi_t is the amount of money you pay today to get a 21:19.102 --> 21:20.212 dollar at time t. 21:20.210 --> 21:24.230 That's called a zero because there's no coupon. 21:24.230 --> 21:25.990 You just get something at the end. 21:25.990 --> 21:29.580 And so we'll see next class we're going to start talking 21:29.576 --> 21:33.746 about real markets and what the prices of all those zeros are. 21:33.750 --> 21:36.550 So anyway, that pi_t is something that is traded in 21:36.553 --> 21:39.263 the market and everybody at every hedge fund and every Wall 21:39.261 --> 21:41.411 Street bank knows what pi_t is at the 21:41.411 --> 21:42.721 beginning of each day. 21:42.720 --> 21:45.150 Now, Fisher said, well don't get too lost 21:45.153 --> 21:47.103 thinking about pi_t. 21:47.099 --> 21:48.589 Think about p_t. 21:48.589 --> 21:50.519 Take out inflation. 21:50.519 --> 21:52.989 You have to make an expectation about what inflation is, 21:52.990 --> 21:55.420 but assuming you're right you can figure out from these 21:55.420 --> 21:57.310 pi_t's what p_t is, 21:57.308 --> 22:01.098 the present value price: how much would you pay today in 22:01.097 --> 22:03.437 goods to get an apple at time t? 22:03.440 --> 22:05.670 Not a dollar at time t, but an apple at time t, 22:05.672 --> 22:08.492 so it involves knowing what inflation is and what the price 22:08.487 --> 22:10.377 of apples is going to be at time t. 22:10.380 --> 22:12.570 So Fisher said, there's a lot of stuff you can 22:12.570 --> 22:14.520 do, but the pi_ts--there's also 22:14.518 --> 22:17.438 more important stuff you can do with the p_ts. 22:17.440 --> 22:20.130 You should always keep those in mind. 22:20.130 --> 22:25.930 So let's take the simplest case where pi_t is a 22:25.930 --> 22:28.520 constant interest rate. 22:28.519 --> 22:30.549 There's a constant interest rate i. 22:30.548 --> 22:34.938 So if you ask what's a dollar worth today in terms of how many 22:34.939 --> 22:37.889 dollars you can get next year it's 1 i. 22:37.890 --> 22:41.410 What's a dollar worth today in two years is (1 i) squared. 22:41.410 --> 22:44.490 So putting it backwards, a dollar in two years--the 22:44.490 --> 22:47.510 price of it today must be 1 over (1 i) squared. 22:47.509 --> 22:49.389 So a dollar in t years, the value today is 1 i over t 22:49.388 --> 22:50.978 [correction: 1 over (1 i) to the power t]. 22:50.980 --> 22:52.360 So this is just a simplification. 22:52.358 --> 22:56.968 So we'll see that lots of the jargon of economics assumes that 22:56.972 --> 23:01.282 there's this constant interest rate that's determining all 23:01.284 --> 23:02.574 these prices. 23:02.568 --> 23:08.888 So the first thing to realize is what Fisher calls the present 23:08.888 --> 23:10.338 value price. 23:10.338 --> 23:14.208 If there were some asset that paid off money in the future, 23:14.210 --> 23:15.970 m_1 through m_T, 23:15.970 --> 23:19.190 you don't have to solve the whole equilibrium to figure out 23:19.194 --> 23:22.814 what its price would be if you knew the prices of these zeros, 23:22.808 --> 23:24.378 pi_1 through pi_T. 23:24.380 --> 23:27.300 Because to get m_2 dollars at time 2 just cost you 23:27.297 --> 23:29.817 pi_2 times m_2 dollars today. 23:29.818 --> 23:32.678 So you add up the cost of buying all the cash flows or the 23:32.678 --> 23:33.078 asset. 23:33.078 --> 23:35.818 That has to be the price of the asset today. 23:35.818 --> 23:39.818 And if the prices of the zeros are given just by the interest 23:39.818 --> 23:44.018 rate discounting it then it's just m_1 over (1 i), 23:44.019 --> 23:47.489 m_2 over (1 i) squared, and m_T over 23:47.494 --> 23:48.574 (1 i) to the T. 23:48.568 --> 23:53.858 I see there's a typo here--oh no, no there's no typo--it's (1 23:53.855 --> 23:55.085 i) to the T. 23:55.088 --> 23:57.848 They're all these (1 i) to the T. 23:57.848 --> 24:03.058 So and now if the price weren't that, if the price of this bond 24:03.061 --> 24:05.921 were, let's say, smaller than this, 24:05.920 --> 24:07.770 what would you do? 24:07.769 --> 24:10.769 You would buy the bond and at the same time you'd sell 24:10.768 --> 24:12.628 promises to deliver m_1, 24:12.634 --> 24:14.784 m_2, and m_T in the 24:14.784 --> 24:15.524 future. 24:15.519 --> 24:18.319 If you sold those promises and nobody doubted that you would 24:18.321 --> 24:20.991 keep your promise-- so this is something 24:20.988 --> 24:24.658 Shakespeare would have been suspicious of-- 24:24.660 --> 24:28.160 but if you made those promises and no one doubted you'd keep 24:28.162 --> 24:31.372 them you could raise this much money by selling all the 24:31.367 --> 24:32.137 promises. 24:32.140 --> 24:35.490 So you'd get this much money and if the bond cost less than 24:35.489 --> 24:37.799 that you could make all the promises, 24:37.798 --> 24:39.468 get all the money, buy the bond, 24:39.472 --> 24:42.442 have money left over, and then you'd have to keep all 24:42.438 --> 24:44.718 your promises, but the bond itself would be 24:44.718 --> 24:47.758 paying you money in the future that you could use to keep all 24:47.758 --> 24:48.618 your promises. 24:48.618 --> 24:51.958 So it has to be that this is the price of the bond provided 24:51.960 --> 24:55.530 that everybody will allow you to borrow and lend at those rates 24:55.529 --> 24:57.919 of interest, because if it weren't you would 24:57.922 --> 25:00.112 either buy the bond and sell all the promises, 25:00.108 --> 25:03.098 or in the other case were the prices higher you'd sell the 25:03.099 --> 25:07.279 bond, get all this money and then use 25:07.279 --> 25:11.889 that money to buy all those promises. 25:11.890 --> 25:15.660 Then you could make the payments of the bond because the 25:15.657 --> 25:17.917 promises would come due to you. 25:17.920 --> 25:21.430 So in that case you'd have to believe people who made promises 25:21.431 --> 25:21.951 to you. 25:21.950 --> 25:25.190 So as long as nobody's doubting the other people keeping their 25:25.188 --> 25:27.628 promises it has to be that by no arbitrage, 25:27.630 --> 25:30.590 the price of a bond is just the discounted cash flow. 25:30.588 --> 25:33.458 That was Fisher's main principle. 25:33.460 --> 25:34.770 So we saw that last time. 25:34.769 --> 25:36.829 We're just going to do it. 25:36.828 --> 25:40.408 So we're now going to introduce a few vocabularies. 25:40.410 --> 25:42.830 So the first thing is the doubling rule. 25:42.828 --> 25:45.718 So I think at least half of you probably know this, 25:45.722 --> 25:49.082 but it's much better if you can do things in your head than 25:49.079 --> 25:50.989 having to calculate them all. 25:50.990 --> 25:54.620 So the doubling rule says how many years at i percent interest 25:54.624 --> 25:56.774 does it take to double your money. 25:56.769 --> 26:01.329 So you can just solve this. 26:01.328 --> 26:06.078 So (1 i) to the n means that if you take the logs of both sides 26:06.083 --> 26:08.923 and you know that log of 2 is .69, 26:08.920 --> 26:13.480 then you take the log of both sides, 26:13.480 --> 26:20.530 n log (1 i) has to be log of 2, so n = .69 over log of (1 i). 26:20.528 --> 26:26.508 So now log of (1 i) is approximately i. 26:26.509 --> 26:27.249 Why is that? 26:27.250 --> 26:28.340 So this is Taylor's rule. 26:28.338 --> 26:31.538 You don't actually have to know this if you've never seen 26:31.544 --> 26:32.864 Taylor's rule before. 26:32.858 --> 26:37.248 But an approximation of log of (1 i)-- 26:37.250 --> 26:40.940 for any function F of X, it's F of A F prime of A times 26:40.942 --> 26:44.982 (X - A) 1 half F double prime of A times (X - A) squared. 26:44.980 --> 26:46.740 That's the standard Taylor's rule thing. 26:46.740 --> 26:51.360 So therefore log of (1 i) is, you know log of 1 is 0, 26:51.358 --> 26:56.048 so it's going to be 0 i because the derivative of the log is 1 26:56.048 --> 26:58.968 over X and if X = 1 that's 1 over 1. 26:58.970 --> 27:02.270 So it's 0 i, and then the second derivative 27:02.273 --> 27:06.763 is minus 1 over X squared, and if X = 1 that's minus 1. 27:06.759 --> 27:12.819 So with the half here log (1 i) is approximately 0 i - i squared 27:12.815 --> 27:13.675 over 2. 27:13.680 --> 27:19.690 So you can replace log of 1 i with, 27:19.690 --> 27:25.280 I mean .69 over log of 1 i with .69 over i - i squared over 2, 27:25.278 --> 27:30.338 so for very small interest rates i squared is practically 27:30.336 --> 27:31.236 nothing. 27:31.240 --> 27:41.980 So .69 over i if the interest rate is .023 percent and .69 27:41.978 --> 27:46.498 divided by .023 is 30. 27:46.500 --> 27:51.110 So it says that at 2.3 percent interest you double your money 27:51.113 --> 27:52.193 in 30 years. 27:52.190 --> 27:57.360 Well, if i is 7 percent, say, then i squared is starting 27:57.362 --> 28:00.092 to get a little bit bigger. 28:00.089 --> 28:03.599 So i - i squared over 2 is .07. 28:03.598 --> 28:08.478 i squared .0049 over 2 that's .0675. 28:08.480 --> 28:14.670 So if I put in i = .07 it's .69 over .0675. 28:14.670 --> 28:18.050 That's around 69 over 67. 28:18.048 --> 28:21.038 There's a decimal thing, so it's a little over 10, 28:21.038 --> 28:21.708 say 10.2. 28:21.710 --> 28:27.890 That's like .72 over .07, so .72 is the doubling rule. 28:27.890 --> 28:30.960 To get for interest rates around 7 percent, 28:30.961 --> 28:32.861 or 6 percent, or 4 percent, 28:32.863 --> 28:36.593 something like that, you're going to divide not into 28:36.594 --> 28:38.134 69 but into 72. 28:38.130 --> 28:39.950 The interest rate is .07, right? 28:39.950 --> 28:43.040 The interest rate is a percent, so it's a decimal thing. 28:43.039 --> 28:47.359 So .06 is like 72 over 6. 28:47.358 --> 28:51.208 So at 6 percent it takes 12 years to double your money. 28:51.210 --> 28:53.030 So the rule, the basic rule is, 28:53.031 --> 28:56.741 if you want to know how long it takes at 6 percent interest to 28:56.737 --> 29:00.257 double your money you just take 72 divided by 6 and it's 12 29:00.260 --> 29:00.990 years. 29:00.990 --> 29:04.600 If it's 8 percent interest 72 over 8 is about 9 years. 29:04.598 --> 29:08.808 If it's 10 percent interest it's a little over 7 years to 29:08.807 --> 29:10.307 double your money. 29:10.308 --> 29:14.338 And so that rule is incredibly useful to keep in your head 29:14.340 --> 29:18.370 because you can shock and amaze people by how fast you can 29:18.373 --> 29:21.913 compute things if you just remember that rule. 29:21.910 --> 29:27.180 So let's just check the rule, by the way. 29:27.180 --> 29:32.400 So suppose that you have 24 dollars in the bank, 29:32.402 --> 29:36.182 and you have 6 percent interest. 29:36.180 --> 29:38.460 So here I took the 24 dollars. 29:38.460 --> 29:41.580 You look at the top you see that's the B1 number, 29:41.580 --> 29:44.700 and I've just multiplied it by the interest rate, 29:44.702 --> 29:46.982 1.06, and so I keep doing that. 29:46.980 --> 29:50.290 Here I've multiplied the thing above it by 1.06 again. 29:50.288 --> 29:53.138 So I keep investing the money at 6 percent interest, 29:53.142 --> 29:56.612 and over here I've invested the money at 7 percent interest. 29:56.608 --> 30:02.028 So anyway, after 12 years you see that 24 dollars, 30:02.027 --> 30:06.777 this is year 1, so at year 12,24 dollars has 30:06.781 --> 30:08.331 become 48. 30:08.328 --> 30:10.418 So it's a very good approximation. 30:10.420 --> 30:14.250 And so 7 percent it's supposed to take a little over 10 years. 30:14.250 --> 30:17.700 So at 10 years you're not quite there, but 11 years you're past 30:17.701 --> 30:17.981 it. 30:17.980 --> 30:21.080 So you can see how we're starting with 24, 30:21.080 --> 30:24.410 you can see how good the doubling rule is. 30:24.410 --> 30:27.600 So that's just something to keep--so we can now do in class 30:27.598 --> 30:30.628 lots of concrete examples without having to take out our 30:30.625 --> 30:33.915 calculators and stuff because we can do them in class in your 30:33.923 --> 30:34.533 head. 30:34.529 --> 30:45.629 All right, so let's just do that now. 30:45.630 --> 30:49.270 Okay, so in fact why did I pick 24 dollars? 30:49.269 --> 30:52.129 Well, this is a famous story you hear in second grade. 30:52.130 --> 30:56.980 The Indians sold Manhattan for 24 dollars in 1646, 30:56.977 --> 31:01.427 so how bad a deal was that for the Indians? 31:01.430 --> 31:05.060 It looks incredibly stupid, but actually interest 31:05.061 --> 31:07.031 accumulates pretty fast. 31:07.028 --> 31:12.798 So if you look at 6 percent interest, so 360 years gets you 31:12.795 --> 31:13.785 to 2006. 31:13.788 --> 31:16.968 That's a sort of round number at 6 percent. 31:16.970 --> 31:19.180 So at 6 percent how long does it take to double? 31:19.180 --> 31:20.890 It takes 12 years to double. 31:20.890 --> 31:23.980 So that means at 6 percent interest you're doubling every 31:23.981 --> 31:24.591 12 years. 31:24.588 --> 31:29.178 So in 360 years you're going to double 30 times. 31:29.180 --> 31:33.360 So in your head you can figure out that doubling 30 times is 2 31:33.356 --> 31:36.636 to the thirtieth, and of course 2 to the tenth is 31:36.644 --> 31:38.704 something you should know. 31:38.700 --> 31:40.170 It's 1,024. 31:40.170 --> 31:43.560 So I'm sure you know that number, right, 31:43.558 --> 31:46.288 2 to the--anyway, that's a good one to remember 2 31:46.294 --> 31:50.124 to the tenth is about 1,000, so 1,000 cubed is about a 31:50.116 --> 31:53.816 billion, so basically 24 becomes 24 billion. 31:53.818 --> 31:57.268 So at 6 percent interest they sold Manhattan for 24 billion in 31:57.270 --> 31:58.290 today's dollars. 31:58.288 --> 32:02.208 So that's pitifully low, but if you look at 7 percent 32:02.213 --> 32:05.463 interest you can do the same calculation. 32:05.460 --> 32:07.960 So at 7 percent interest you should do this in your head now. 32:07.960 --> 32:11.950 So it's going to double every 72 over 7 years. 32:11.950 --> 32:16.800 So there are 360 years, about, 360 is a very round 32:16.801 --> 32:21.951 number, so 360 divided by 72 over 7 that's 5 times 7, 32:21.951 --> 32:23.141 it's 35. 32:23.140 --> 32:27.730 So 2 to the thirty-fifth, well it's like a billion times 32:27.729 --> 32:30.149 2 to the fifth which is 32. 32:30.150 --> 32:35.630 So 1 dollar becomes 32 billion, but we started with 24 dollars 32:35.625 --> 32:37.595 so it's 768 billion. 32:37.598 --> 32:41.608 So now you're starting to get a little bit closer to what the 32:41.606 --> 32:43.206 value of Manhattan is. 32:43.210 --> 32:46.260 I mean, the value of all the real estate in the country, 32:46.255 --> 32:49.295 all the houses in the country used to be 20 trillion. 32:49.298 --> 32:50.928 I'm not sure how far they've gone down now. 32:50.930 --> 32:52.720 Let's say they're 15 trillion. 32:52.720 --> 32:56.280 So 15 trillion you add commercial real estate, 32:56.279 --> 33:00.319 maybe in the whole country that's worth 25 trillion, 33:00.315 --> 33:04.425 but that went down too so let's say 20 trillion. 33:04.430 --> 33:07.050 Now how much of the 20 trillion could possibly be in New York 33:07.053 --> 33:07.363 City? 33:07.358 --> 33:10.048 I've actually got no idea, but it can't be that much 33:10.048 --> 33:12.208 more--the whole country is 20 trillion. 33:12.210 --> 33:15.780 New York can't be worth more than 1 or 2 trillion of the 20 33:15.778 --> 33:18.178 trillion, so you're not that far off. 33:18.180 --> 33:20.410 So the deal's not that spectacularly bad although it 33:20.413 --> 33:21.293 sounds ridiculous. 33:21.288 --> 33:23.348 Anyway, the point is you can do this in your head. 33:23.348 --> 33:28.828 So now the next thing that you realize in this example is how 33:28.830 --> 33:32.120 huge a difference a percent makes. 33:32.119 --> 33:34.919 So why is that so important? 33:34.920 --> 33:36.970 Well, managers, hedge funds, 33:36.974 --> 33:39.644 we all charge a percent interest. 33:39.640 --> 33:42.220 So look at what's happening. 33:42.220 --> 33:46.050 I mean, if you look at our Indian investment of 24 and you 33:46.047 --> 33:49.737 look--I don't know how many years you want to look over, 33:49.740 --> 33:52.090 but you can look over 36 years. 33:52.088 --> 33:54.088 That's a sort of typical--you're young and making 33:54.085 --> 33:54.745 an investment. 33:54.750 --> 34:02.510 When you get old what's the difference? 34:02.509 --> 34:06.329 This was the 6 percent growth and this was the 7 percent 34:06.325 --> 34:06.945 growth. 34:06.950 --> 34:09.890 This is the difference and this is the, I guess, 34:09.889 --> 34:11.639 the percentage difference. 34:11.639 --> 34:15.499 So it's 28 percent. 34:15.500 --> 34:23.030 Of course I didn't label these, but yeah so this is the 34:23.032 --> 34:29.732 difference and this is the percent difference. 34:29.730 --> 34:33.510 So the percent difference I just showed it to you. 34:33.510 --> 34:38.560 Over 36 years it's a 28.6 percent difference. 34:38.559 --> 34:41.389 So a typical--you're putting money away right now. 34:41.389 --> 34:42.899 You might be giving it to some fund. 34:42.900 --> 34:46.080 You might be investing it--whatever fund you're 34:46.079 --> 34:48.639 investing in, they could be charging 1 34:48.637 --> 34:50.087 percent interest. 34:50.090 --> 34:51.860 And it seems, what's 1 percent, 34:51.862 --> 34:54.642 it's a tiny amount, 1 percent, but over 30 years 34:54.639 --> 34:57.829 they're taking 28 percent of your money, 36 years. 34:57.829 --> 35:00.899 With the Indians over 360 years we saw that it was an 35:00.896 --> 35:03.076 astronomical amount that they took. 35:03.079 --> 35:05.259 They took almost all your money, right? 35:05.260 --> 35:15.000 So look at the percentage that got taken, so 768 billion versus 35:15.000 --> 35:20.970 24 billion, I mean, it's astounding. 35:20.969 --> 35:23.969 So giving 1 percent away to a money manager is giving away a 35:23.967 --> 35:26.807 fortune if you think you're going to stick with the money 35:26.813 --> 35:29.053 manager for a reasonable amount of time. 35:29.050 --> 35:31.310 So if you want the secret to how hedge funds make money 35:31.311 --> 35:33.951 that's the first way they make it and the most important way. 35:33.949 --> 35:37.079 They charge a fee that sounds small, but it adds up over a few 35:37.083 --> 35:39.603 years and it amounts to a huge amount of money. 35:39.599 --> 35:41.849 Now, you can make it much smaller. 35:41.849 --> 35:43.509 Why does it amount to so much money? 35:43.510 --> 35:46.100 Because the money that you put in the fund you're keeping in 35:46.103 --> 35:48.393 the fund, so it's growing and growing and growing. 35:48.389 --> 35:51.319 So they're taking 1 percent of your 24 dollars today. 35:51.320 --> 35:53.870 That sounds like nothing, but the money is still there 35:53.873 --> 35:56.573 and now 40 years later they're taking 1 percent of a much 35:56.572 --> 35:57.442 bigger number. 35:57.440 --> 36:01.120 That's why that number gets to be so large. 36:01.119 --> 36:04.109 So that's the second thing. 36:04.110 --> 36:05.710 So now, let's keep going. 36:05.710 --> 36:07.650 So that's the basic thing. 36:07.650 --> 36:10.590 So now let's go to define a few terms that everybody should 36:10.594 --> 36:10.954 know. 36:10.949 --> 36:12.939 What's a coupon bond? 36:12.940 --> 36:16.030 A coupon bond is the simplest kind of bond, 36:16.027 --> 36:20.287 the first one that was created, and it pays a fixed coupon, 36:20.289 --> 36:23.229 dollars, every period for T periods. 36:23.230 --> 36:24.760 The T's called the maturity. 36:24.760 --> 36:27.920 So it's defined by the coupon which is the fixed payment it 36:27.923 --> 36:31.143 makes every year until period T which is the maturity of the 36:31.143 --> 36:32.883 bond, and then it also, 36:32.880 --> 36:37.250 at the end of period T, pays a principal which is 36:37.248 --> 36:41.228 usually how the bond is denominated-- 36:41.230 --> 36:44.570 the face value of the bond--it pays the principal or face 36:44.572 --> 36:45.052 value. 36:45.050 --> 36:47.640 That's usually 100 or 1,000. 36:47.639 --> 36:53.489 So a coupon might be 6,6, 6,6, 106. 36:53.489 --> 36:56.369 That would be a 6 percent coupon bond. 36:56.369 --> 37:00.009 You can also define the coupon by the percentage of the face 37:00.005 --> 37:02.405 that it pays every year as a coupon, 37:02.409 --> 37:07.609 so little c is the percentage, so .06 times 100 is 6, 37:07.610 --> 37:08.740 6,6, 6,6, 6. 37:08.739 --> 37:11.839 I could use big C as 6 dollars. 37:11.840 --> 37:15.880 So it's defined by its percentage, by the face and by 37:15.882 --> 37:17.052 the maturity. 37:17.050 --> 37:22.000 So the first obvious thing to say is if the interest rate is 6 37:22.003 --> 37:27.123 percent and the bond is paying a 6 percent coupon then it has to 37:27.121 --> 37:30.361 be worth its face-- so let's always assume the face 37:30.364 --> 37:30.724 is 100. 37:30.719 --> 37:35.159 So why is that? 37:35.159 --> 37:39.299 It doesn't seem totally obvious because the formula is you take 37:39.295 --> 37:43.095 100 times c (that's the first payment) divided by 1 i, 37:43.099 --> 37:47.049 then 100 times c divided by (1 i) squared etcetera. 37:47.050 --> 37:49.720 It's not so obvious that's going to turn out to be equal to 37:49.722 --> 37:50.002 100. 37:50.000 --> 37:52.790 But so you just have to think for a second why that should be. 37:52.789 --> 37:56.379 And the way to think of this is if you had 100 dollars in the 37:56.375 --> 38:00.135 bank at 6 percent interest you get 106 dollars the next year. 38:00.139 --> 38:03.459 Take the 6 and spend it, you'd still have 100 dollars in 38:03.456 --> 38:04.116 the bank. 38:04.119 --> 38:06.129 That would give you 6 dollars again the next year. 38:06.130 --> 38:07.590 You could take that 6 dollars and spend it, 38:07.586 --> 38:09.076 you'd still have 100 dollars in the bank. 38:09.079 --> 38:12.589 You keep doing that until the last year when you've got 106 38:12.585 --> 38:13.185 dollars. 38:13.190 --> 38:16.380 So at 6 percent interest putting the money in the bank 38:16.384 --> 38:20.004 and spending the coupons would give you exactly the same cash 38:20.000 --> 38:22.050 flow as the bond's giving you. 38:22.050 --> 38:25.100 So therefore whether you put the money at the bank at 6 38:25.097 --> 38:28.487 percent interest or buy the bond you're getting the same cash 38:28.485 --> 38:30.545 flow, so it has to be by no arbitrage 38:30.550 --> 38:32.440 that the initial outlay was the same, 38:32.440 --> 38:33.820 so it has to be 100 dollars. 38:33.820 --> 38:38.250 Well, that's obvious. 38:38.250 --> 38:40.360 Now you can prove it many different ways. 38:40.360 --> 38:44.450 Now you can also imagine keeping a bond forever paying 6 38:44.454 --> 38:45.874 percent interest. 38:45.869 --> 38:49.419 Then you get--a 100 dollars at 6 percent interest would give 38:49.423 --> 38:50.873 you 6 dollars forever. 38:50.869 --> 38:54.059 So if there was 6 percent interest and you were getting 12 38:54.056 --> 38:57.466 dollars forever, how much would that be worth at 38:57.467 --> 39:00.787 6 percent interest, 12 dollars forever, 39:00.793 --> 39:04.093 6 percent interest, you get 12 dollars every year 39:04.085 --> 39:06.675 forever, what's that? 39:06.679 --> 39:10.579 How many dollars is that worth originally? 39:10.579 --> 39:12.929 If the interest rate that all banks are giving, 39:12.929 --> 39:15.529 and the whole world's agreeing 6 percent is the rate of 39:15.527 --> 39:18.407 interest and someone is offering to give you 12 dollars every 39:18.414 --> 39:21.494 year forever, how much money in present value 39:21.489 --> 39:23.199 terms is he giving you? 39:23.199 --> 39:24.539 Student: 200. 39:24.539 --> 39:25.679 Prof: 200, right? 39:25.679 --> 39:30.129 Because 200 at 6 percent would give you 12 dollars every year, 39:30.134 --> 39:34.154 so these are the most basic formulas to keep in mind. 39:34.150 --> 39:38.420 So those you may be hearing these things for the first time 39:38.416 --> 39:41.356 so it takes a second to adjust to it, 39:41.360 --> 39:44.530 but there's no cleverness involved in figuring these out. 39:44.530 --> 39:50.840 Now, so we've got the doubling rule, we've got coupon bonds, 39:50.838 --> 39:52.868 so that's simple. 39:52.869 --> 39:55.619 Now, somewhat subtler thing is an annuity. 39:55.619 --> 40:02.029 So an annuity pays you a fixed amount for a fixed number of 40:02.034 --> 40:02.924 years. 40:02.920 --> 40:06.260 So it doesn't pay the principal at the end, so it pays that C. 40:06.260 --> 40:07.340 That's supposed to be a capital C. 40:07.340 --> 40:11.620 It pays C, C, C, C for a fixed number of 40:11.621 --> 40:12.501 years. 40:12.500 --> 40:14.790 So it's a T period annuity. 40:14.789 --> 40:19.329 Now annuities also can be changed in two important ways. 40:19.329 --> 40:22.479 They can be indexed to inflation. 40:22.480 --> 40:26.850 That's a much better annuity because now you're protected 40:26.849 --> 40:28.409 against inflation. 40:28.409 --> 40:31.529 It also could be timed to last the rest of your life. 40:31.530 --> 40:33.720 So we're going to come to this when we talk about Social 40:33.721 --> 40:34.161 Security. 40:34.159 --> 40:37.699 The most important annuity by far in the whole economy is the 40:37.697 --> 40:39.227 Social Security annuity. 40:39.230 --> 40:43.650 Once you retire and you're in Social Security they figure out 40:43.652 --> 40:46.972 what your coupon is going to be every year. 40:46.969 --> 40:49.729 I'll tell you the formula in a couple of classes. 40:49.730 --> 40:52.580 So depending on how much you've contributed they calculate what 40:52.581 --> 40:53.871 your coupon is every year. 40:53.869 --> 40:58.289 So from the day you turn 65 for the rest of your life you get 40:58.289 --> 41:00.719 the same C inflation corrected. 41:00.719 --> 41:03.079 So we're going to have to talk about why they decided on that 41:03.077 --> 41:03.507 contract. 41:03.510 --> 41:04.930 But anyway, that's an annuity. 41:04.929 --> 41:07.849 So it depends on the length of life. 41:07.849 --> 41:11.549 So these annuities are famous in history. 41:11.550 --> 41:14.710 Jane Austen in Sense and Sensibility said it was a 41:14.713 --> 41:17.823 disaster because whenever you give someone an annuity they 41:17.822 --> 41:18.752 live forever. 41:18.750 --> 41:22.790 And she said that, some character says her mother 41:22.791 --> 41:27.931 gave the servants in the houses annuities after their husbands 41:27.927 --> 41:31.967 died and she figured that they were so old-- 41:31.969 --> 41:32.939 she gave the annuities. 41:32.940 --> 41:35.850 They were the servants of her mother's and she gave them the 41:35.853 --> 41:37.683 annuity after their husbands died, 41:37.679 --> 41:40.269 and since they were so old she figured she'd pay them a few 41:40.273 --> 41:41.933 years and that'd be the end of it, 41:41.929 --> 41:43.509 and they just went on and on and on, 41:43.510 --> 41:46.630 and she got tired of giving them all the money. 41:46.630 --> 41:49.690 But anyway, so obviously when you're giving a life annuity you 41:49.690 --> 41:52.550 have to calculate how long the person's going to live, 41:52.550 --> 41:54.310 and so we're going to come back to that, 41:54.309 --> 41:56.589 the selection of who takes annuities. 41:56.590 --> 41:58.350 Do they know that they're going to live longer or not? 41:58.349 --> 42:00.549 Anyway, that market's all screwed up and we're going to 42:00.550 --> 42:02.340 come to that later, but it's a famous market, 42:02.342 --> 42:03.282 the annuity market. 42:03.280 --> 42:07.910 Now, how can you figure out the value of an annuity? 42:07.909 --> 42:14.669 So this is a very simple thing to do once you've come this far. 42:14.670 --> 42:16.540 So this is the next thing to remember. 42:16.539 --> 42:20.469 So remember, an annuity's paying C, 42:20.469 --> 42:23.359 C, C, C up to period T. 42:23.360 --> 42:25.990 Here are the periods T. 42:25.989 --> 42:30.239 So how much should this be worth, the present value, 42:30.240 --> 42:33.910 what is the present value today at time 0? 42:33.909 --> 42:38.929 Well, we know that if it actually went forever, 42:38.931 --> 42:44.831 C, C like that it would be--forever, it would go C over 42:44.829 --> 42:47.449 the interest rate i. 42:47.449 --> 42:50.529 Annuities are often inflation corrected so I wrote r for the 42:50.527 --> 42:51.777 real rate of interest. 42:51.780 --> 42:53.840 So you could call it C over r for the real rate of interest, 42:53.835 --> 42:54.215 whatever. 42:54.219 --> 42:55.619 Let's say it's nominal. 42:55.619 --> 42:59.239 Let's keep to i even though I haven't used that notation 42:59.244 --> 43:00.634 there, so C over i. 43:00.630 --> 43:05.770 If you get C dollars forever it's called a perpetuity. 43:05.768 --> 43:09.008 So a perpetuity we already know how to value. 43:09.010 --> 43:10.890 We said C over i, right? 43:10.889 --> 43:13.429 At 6 percent if you're getting 12 dollars every year, 43:13.434 --> 43:14.664 it's worth 200 dollars. 43:14.659 --> 43:16.929 Now, what if it gets cutoff at T? 43:16.929 --> 43:20.349 It sounds like there's going to be a very complicated formula to 43:20.346 --> 43:23.216 calculate, but actually it's a very simple formula. 43:23.219 --> 43:24.469 Why is that? 43:24.469 --> 43:34.679 Because the T period--so here's the perpetuity and the T period 43:34.679 --> 43:44.389 annuity equals the perpetuity minus a perpetuity starting at 43:44.393 --> 43:56.093 time T-- minus perpetuity contracted at 43:56.092 --> 44:00.462 time T-- right? 44:00.460 --> 44:02.460 So why is that? 44:02.460 --> 44:03.810 Here we have a perpetuity. 44:03.809 --> 44:07.989 At time 0 you say to someone, the state, the government says, 44:07.989 --> 44:11.819 we'll pay you and your descendants C dollars forever. 44:11.820 --> 44:14.630 So we know what that's worth, C over i. 44:14.630 --> 44:18.450 Now we say suppose the state tells you we're going to pay you 44:18.447 --> 44:19.527 C until time T? 44:19.530 --> 44:20.510 What's that worth? 44:20.510 --> 44:23.310 Well, it's worth this, the whole thing, 44:23.309 --> 44:27.149 minus this part of it, but looked at from this point 44:27.148 --> 44:31.888 of view here the whole part of it is just a perpetuity again. 44:31.889 --> 44:39.629 So it's just the perpetuity which is C over i - C over i, 44:39.630 --> 44:43.350 another perpetuity here, but as of time T because that's 44:43.353 --> 44:45.343 like the 0 time-- the money's coming, 44:45.338 --> 44:46.818 the next period, forever. 44:46.820 --> 44:49.270 Just like at time 0 the money came starting at period 1 44:49.269 --> 44:52.179 forever, so at time T starting 1 period 44:52.175 --> 44:57.505 later forever, so therefore it's this divided 44:57.505 --> 45:00.065 by (1 i) to the T. 45:00.070 --> 45:07.280 So it's just C over i times (1 - (1 over (1 i) to the T)). 45:07.280 --> 45:09.600 So this is the next thing you have to memorize, 45:09.599 --> 45:11.869 unfortunately, but there are only a few things 45:11.869 --> 45:13.129 you have to memorize. 45:13.130 --> 45:16.950 So this is a very famous formula for the value of an 45:16.949 --> 45:17.699 annuity. 45:17.699 --> 45:24.069 So let's just do an example. 45:24.070 --> 45:27.720 Suppose somebody--maybe I can just do the same examples, 45:27.719 --> 45:30.439 so you've got the proof of that, right? 45:30.440 --> 45:36.970 This is no surprise? 45:36.969 --> 45:39.439 Remember the whole perpetuity is obviously, 45:39.440 --> 45:40.440 it's 6 percent. 45:40.440 --> 45:43.410 Let's just think of something at 6 percent. 45:43.409 --> 45:45.739 So let's do the 6 percent annuity. 45:45.739 --> 46:10.939 At 6 percent interest a 12 dollar perpetuity is worth 200 46:10.940 --> 46:15.440 dollars. 46:15.440 --> 46:17.980 That's what we said before. 46:17.980 --> 46:24.640 So what is a 36 year? 46:24.639 --> 46:29.009 So at 6 percent interest a 12 dollar perpetuity is worth 200 46:29.009 --> 46:29.749 dollars. 46:29.750 --> 46:40.320 So at 6 percent interest what is a 12 dollar 30 year annuity 46:40.317 --> 46:41.747 worth? 46:41.750 --> 46:47.920 It's worth what? 46:47.920 --> 46:52.600 How much is that worth? 46:52.599 --> 46:56.409 So if it went on forever it would be worth $200 dollars. 46:56.409 --> 47:07.209 If we cut it off after 30 years--30 years is a bad time to 47:07.206 --> 47:09.666 cut it off. 47:09.670 --> 47:21.530 Let's cut if off after 24 years. 47:21.530 --> 47:23.890 So you have 6 percent interest. 47:23.889 --> 47:26.679 You get 12 dollars, not for every year in the 47:26.681 --> 47:29.791 future, but for 24 years, how much is it worth? 47:29.789 --> 47:32.199 Well, it can't be worth 200 dollars because it would be 47:32.199 --> 47:33.939 worth 200 dollars if it went forever. 47:33.940 --> 47:37.510 So it's worth less than 200 dollars, but how much less? 47:37.510 --> 47:40.490 So my uncle died, left my sister an annuity. 47:40.489 --> 47:45.699 She just had no idea what the annuity was worth. 47:45.699 --> 47:49.839 So do you have any idea what it's worth? 47:49.840 --> 47:51.030 Yep? 47:51.030 --> 47:52.530 Student: 150 bucks. 47:52.530 --> 47:55.030 Prof: It is, and how did you get that? 47:55.030 --> 47:58.700 Student: The doubling rule at 6 percent interest it 47:58.704 --> 48:02.324 takes 12 years to double your money so in 24 years you're 48:02.317 --> 48:04.507 going to quadruple your money. 48:04.510 --> 48:07.360 So then you just put that 4 into the equation. 48:07.360 --> 48:11.930 Prof: So it's 1 - 1 quarter, so that's 3 quarters, 48:11.925 --> 48:15.915 and 3 quarters times the 200 we got before is 150, 48:15.920 --> 48:16.900 exactly. 48:16.900 --> 48:18.020 Exactly right what he said. 48:18.019 --> 48:22.489 So does everybody get that? 48:22.489 --> 48:24.429 Let's try another one. 48:24.429 --> 48:40.429 So let's suppose I pay 8 dollars. 48:40.429 --> 48:49.199 Let's see, how long is this going to be? 48:49.199 --> 48:52.739 Let me say that again just in case you didn't follow that 48:52.742 --> 48:56.542 because I'm going to give a slightly harder one this time. 48:56.539 --> 48:58.669 So he's saying how do you figure out the value of an 48:58.670 --> 48:59.090 annuity? 48:59.090 --> 49:02.260 Something by next class you'll be able to do in your head. 49:02.260 --> 49:04.950 It's going to be, take the cash flow that you get 49:04.947 --> 49:05.617 over here. 49:05.619 --> 49:08.199 If it went forever it'd be so easy to figure out what the 49:08.204 --> 49:08.764 value was. 49:08.760 --> 49:11.760 If it's 12 dollars at 6 percent interest that's like having 200 49:11.757 --> 49:14.657 dollars in the bank because then at 6 percent interest you're 49:14.657 --> 49:16.927 going to get 12 dollars every year forever. 49:16.929 --> 49:20.579 So we know that 12 dollars a year forever is clearly 200 49:20.576 --> 49:21.236 dollars. 49:21.239 --> 49:24.869 That's C over i, 12 over .06 is 200 dollars, 49:24.869 --> 49:28.499 but it's going to get cut off in year 24. 49:28.500 --> 49:30.870 So we're going to lose all this future stuff, 49:30.869 --> 49:32.969 but the future's not worth very much. 49:32.969 --> 49:34.669 Why isn't it worth very much? 49:34.670 --> 49:37.820 Because by the time we get here we've already discounted by a 49:37.824 --> 49:38.144 lot. 49:38.139 --> 49:41.589 So a dollar starting here is actually only 1 quarter of a 49:41.592 --> 49:44.602 dollar starting back here, because in 24 years at 6 49:44.597 --> 49:46.627 percent interest you've doubled twice, 49:46.630 --> 49:48.020 so it's worth 1 quarter. 49:48.018 --> 49:50.678 So you just take 1 quarter of the same annuity. 49:50.679 --> 49:56.649 So it's 1 - 1 quarter of the same annuity. 49:56.650 --> 50:00.110 So the one that ends in 24 years is like 3 quarters of the 50:00.112 --> 50:03.092 value of the perpetuity, 3 quarters of 200 is 150, 50:03.090 --> 50:04.610 that's how we did it. 50:04.610 --> 50:07.830 So let's reverse the thing. 50:07.829 --> 50:13.929 Suppose we know the present value's 100. 50:13.929 --> 50:16.799 You're now the company, and you're trying to figure out 50:16.802 --> 50:17.762 how much to pay. 50:17.760 --> 50:20.150 So what is the C going to be? 50:20.150 --> 50:25.930 Let's say it's 8 percent interest, and I'll just do the 50:25.925 --> 50:28.915 same example in the notes. 50:28.920 --> 50:35.290 In 30 years a typical thing, so it's not going to work out 50:35.288 --> 50:40.088 exactly evenly, so 8 percent interest for 30 50:40.092 --> 50:41.212 years. 50:41.210 --> 50:47.110 So we know it's worth 100. 50:47.110 --> 50:50.050 So let's get rid of all the irrelevant stuff so you don't 50:50.050 --> 50:51.470 have the board cluttered. 50:51.469 --> 50:56.729 We've got something that's worth 100. 50:56.730 --> 50:59.440 There's the formula down here. 50:59.440 --> 51:02.680 So the thing is worth 100. 51:02.679 --> 51:06.969 You know the interest rate is 8 percent now, and it's a 30 year 51:06.967 --> 51:07.657 annuity. 51:07.659 --> 51:09.949 So if somebody tells you the interest rate's 8 percent these 51:09.947 --> 51:11.607 days, you're going to get a 30 year annuity, 51:11.614 --> 51:13.054 you've got 100 dollars to invest. 51:13.050 --> 51:15.380 You go to the annuities company, the insurance company, 51:15.380 --> 51:17.690 you tell them, "I want an annuity," 51:17.690 --> 51:19.740 how much do they give you every year? 51:19.739 --> 51:21.929 Well, you just have to figure out what C is. 51:21.929 --> 51:29.439 So you put C over .08, so what does that tell you? 51:29.440 --> 51:33.840 What would that be? 51:33.840 --> 51:45.180 What would they be paying you if it was a perpetuity? 51:45.179 --> 51:47.749 If it was a perpetuity what would they be paying you? 51:47.750 --> 51:49.650 They'd be paying 8 dollars a year, right? 51:49.650 --> 51:52.780 So but they're only going to pay you for 30 years, 51:52.775 --> 51:56.345 so how much are they going to pay you, (1 I) to the T. 51:56.349 --> 52:03.119 So this is 1.08 to the thirtieth, and what's 1.08 to 52:03.117 --> 52:05.237 the thirtieth? 52:05.239 --> 52:08.769 Well, 1.08 to the thirtieth by our rule is what? 52:08.768 --> 52:12.688 It's equal to 1.08 to the twenty-seventh-- 52:12.690 --> 52:15.470 in 9 years at 8 percent interest it'll double, 52:15.469 --> 52:19.979 so after 27 years it's going to double 3 times, 52:19.980 --> 52:24.550 1.08 to the third power. 52:24.550 --> 52:28.070 So after 27 years it's going to double 3 times, 52:28.070 --> 52:32.380 so that's eight, right, 2 to the third power is 52:32.380 --> 52:37.820 8 and then at 8 percent over 3 years it's 108 goes to about 52:37.815 --> 52:40.015 116, goes to about 124, 52:40.021 --> 52:44.491 but you know it's going to grow a little faster because 1.08 52:44.487 --> 52:49.177 times 1.08 is a little bit more than 1.16 so it's going to grow 52:49.179 --> 52:55.129 to like 1.25 instead of 1.24, so that's 10. 52:55.130 --> 52:58.040 So this is just 1 over 10. 52:58.039 --> 53:00.039 So the whole thing is 9 tenths. 53:00.039 --> 53:03.939 So basically you get almost all the value. 53:03.940 --> 53:06.950 After 30 years at 8 percent interest it's such a high 53:06.949 --> 53:10.359 interest rate that after 30 years you're getting 9 tenths of 53:10.364 --> 53:13.494 the value of the annuity [correction: perpetuity]. 53:13.489 --> 53:17.769 So you're going to have to get paid 10 ninths, 53:17.768 --> 53:19.668 the 8,000 dollars. 53:19.670 --> 53:21.360 It would have been 8,000 dollars if it were a 53:21.364 --> 53:23.524 perpetuity--you have to pay the guy a little bit more. 53:23.518 --> 53:25.898 You have to get a little bit more because you're only getting 53:25.903 --> 53:26.623 it for 30 years. 53:26.619 --> 53:29.679 But because the interest rate's so high the stuff after 30 years 53:29.681 --> 53:30.801 isn't very important. 53:30.800 --> 53:34.140 You have to be given an extra tenth. 53:34.139 --> 53:39.329 So it's 10 ninths times 8,000 so it's 8,888 is what your 53:39.327 --> 53:42.627 annuity's going to be every year. 53:42.630 --> 53:46.890 So just to summarize it, to say it all again, 53:46.889 --> 53:49.949 we know how to compute perpetuities with ease, 53:49.949 --> 53:51.889 and so if you want 100 [thousand] 53:51.885 --> 53:54.845 dollars and a coupon forever, and the interest rate's 8 53:54.851 --> 53:56.131 percent this is 8,000 forever. 53:56.130 --> 53:58.100 If you only get it for a shorter amount of time, 53:58.097 --> 53:59.477 obviously you have to get more. 53:59.480 --> 54:00.730 How much more? 54:00.730 --> 54:01.820 Well, it depends. 54:01.820 --> 54:04.330 Each year for only 30 years it depends on how much you're 54:04.326 --> 54:05.396 giving up at that end. 54:05.400 --> 54:09.850 And at 8 percent you're only giving up a tenth of the whole 54:09.846 --> 54:10.456 value. 54:10.460 --> 54:16.480 So you have to be compensated for that each year by getting 10 54:16.478 --> 54:20.718 ninths of what you would have gotten before, 54:20.722 --> 54:23.192 so we're up to 8,888. 54:23.190 --> 54:27.610 So those are the words that everybody has to know. 54:27.610 --> 54:32.060 So now let's just do a couple more simple computations here 54:32.061 --> 54:36.131 just to give you an idea of how Fisher helped here. 54:36.130 --> 54:38.480 So I'm going to do a few mortgage things. 54:38.480 --> 54:40.720 I haven't defined mortgage yet. 54:40.719 --> 54:44.959 Why didn't I do that? 54:44.960 --> 54:51.510 So a mortgage is just a 30 year annuity. 54:51.510 --> 54:53.610 So one more thing--a mortgage is an annuity. 54:53.610 --> 55:08.870 A fixed mortgage, a fixed rate mortgage is 55:08.873 --> 55:18.183 defined by a principal. 55:18.179 --> 55:21.549 So when we talk about the crisis this word principal will 55:21.547 --> 55:22.927 come up all the time. 55:22.929 --> 55:33.449 So that's the face value, a principal, 55:33.445 --> 55:45.095 a mortgage coupon rate, and a maturity. 55:45.099 --> 55:45.979 This is a fixed rate mortgage. 55:45.980 --> 55:50.110 So the most common kind of maturity is 30 years, 55:50.110 --> 55:54.450 30 years is the most common and then sometimes there are 15 year 55:54.445 --> 55:56.375 mortgages, and then there's a whole host 55:56.375 --> 55:58.515 of other mortgages we're going to come to later where there's 55:58.516 --> 55:59.476 floating interest rates. 55:59.480 --> 56:02.130 So the 30 year mortgage, how much do you have to pay? 56:02.130 --> 56:07.950 Well, if it were on an annual payment and it were an 8 percent 56:07.949 --> 56:12.339 mortgage for 30 years on a 100,000 dollars, 56:12.340 --> 56:19.410 so if it was a 100,000 dollar principle at 8 percent coupon 56:19.405 --> 56:26.955 for 30 years we just calculated that you would have to pay, 56:26.960 --> 56:32.370 the payment would be 8,888 dollars a year, 56:32.369 --> 56:38.419 because 8,888 dollars a year discounted at 8 percent is going 56:38.420 --> 56:40.640 to give you 100,000. 56:40.639 --> 56:42.059 So that's how the mortgage works. 56:42.059 --> 56:45.329 So whenever you hear about a mortgage you always hear the 56:45.326 --> 56:47.656 mortgage rate, that's the coupon rate. 56:47.659 --> 56:50.509 The maturity is usually 30 years. 56:50.510 --> 56:53.470 Then you'd have to be told how much the mortgage is for. 56:53.469 --> 56:56.879 Then you can figure out what does the guy have to pay every 56:56.878 --> 56:57.288 year. 56:57.289 --> 57:00.719 You just figure out the annuity payment that at this interest 57:00.722 --> 57:04.042 rate makes his payments have present value at this interest 57:04.039 --> 57:05.869 rate equal to the principal. 57:05.869 --> 57:08.949 So we just saw it was 8,888 a year. 57:08.949 --> 57:12.379 And there's one more little twist with mortgages. 57:12.380 --> 57:14.450 So that's not literally true what I said. 57:14.449 --> 57:21.489 Mortgages have monthly payments. 57:21.489 --> 57:32.799 There are monthly payments and so the monthly rate--at monthly 57:32.795 --> 57:39.835 rate equal the coupon divided by 12. 57:39.840 --> 57:43.240 So if it's an 8 percent mortgage then it means that 57:43.242 --> 57:47.472 they're taking 2 thirds-- so in this case we'd have 8 57:47.467 --> 57:52.067 percent over 12 which equals 2 thirds of a percent. 57:52.070 --> 57:58.090 So the mortgage would be .67 percent, and so then you do the 57:58.092 --> 58:00.342 monthly calculation. 58:00.340 --> 58:02.450 So you have to figure out the C. 58:02.449 --> 58:10.419 So it's the summation over 1 2 thirds percent so that's 1.067 58:10.423 --> 58:14.413 in other words, 1.067 to the t, 58:14.411 --> 58:18.931 t = 1 to 360 has to = 100,000. 58:18.929 --> 58:21.769 That's how much you'd have to pay every month. 58:21.768 --> 58:31.298 And so it wouldn't be 8,888 a year it'd be slightly more than 58:31.298 --> 58:36.698 8,888 divided by 12 every month. 58:36.699 --> 58:39.529 This is the last of these definitions for today's class. 58:39.530 --> 58:43.140 So everybody who's on Wall Street knows what a perpetuity 58:43.137 --> 58:47.067 is, and they know how to compute its value at a given interest 58:47.070 --> 58:47.650 rate. 58:47.650 --> 58:50.520 They know what an annuity is and how to compute its present 58:50.523 --> 58:50.923 value. 58:50.920 --> 58:54.340 A mortgage is almost the same thing as an annuity, 58:54.340 --> 58:59.400 the only twist is that the mortgage is computed monthly 58:59.396 --> 59:03.176 instead of annually, using a monthly interest rate, 59:03.175 --> 59:05.665 but when they say the monthly interest rate, 59:05.670 --> 59:08.400 instead of telling you the monthly interest rate they tell 59:08.402 --> 59:10.372 you the monthly interest rate times 12. 59:10.369 --> 59:12.729 It's just a convention. 59:12.730 --> 59:16.130 All right, so those are all the things you have to memorize. 59:16.130 --> 59:21.640 Now, let's try to use the way we can think and do some 59:21.643 --> 59:24.353 practical problems here. 59:24.349 --> 59:29.029 So here's one of the simplest and most important ones is let's 59:29.034 --> 59:31.344 say you're a Yale professor. 59:31.340 --> 59:33.310 I gave this example on the very first day of class. 59:33.309 --> 59:34.909 You're a Yale professor. 59:34.909 --> 59:38.969 When I first gave the example a few years ago when I wrote the 59:38.972 --> 59:41.372 notes the average Yale professor, 59:41.369 --> 59:43.739 so this was quite a few years ago, eight or nine years ago, 59:43.739 --> 59:45.969 was making 115,000 a year. 59:45.969 --> 59:50.159 And as it happens the average Yale salary now is 150,000 a 59:50.164 --> 59:50.684 year. 59:50.679 --> 59:53.939 But anyway, when I wrote it, it was 115,000 a year. 59:53.940 --> 1:00:05.600 So let's suppose this year's professors are making 115,000 1:00:05.596 --> 1:00:17.456 and let's say your salary will go up at 3 percent inflation 1:00:17.456 --> 1:00:22.256 every year, and that's inflation that's 1:00:22.262 --> 1:00:24.082 equal to the general inflation. 1:00:24.079 --> 1:00:27.139 So your salary is keeping pace with general inflation and no 1:00:27.137 --> 1:00:27.497 more. 1:00:27.500 --> 1:00:30.890 So professors, we're not doing that well. 1:00:30.889 --> 1:00:33.109 So the salary is 115,000. 1:00:33.110 --> 1:00:35.700 Now it would be 150,000, but anyway it was 115,000 on 1:00:35.701 --> 1:00:38.541 average and let's say you're just going to be kept up with 1:00:38.541 --> 1:00:39.241 inflation. 1:00:39.239 --> 1:00:41.939 You're going to be told every year you have a 3 percent raise, 1:00:41.938 --> 1:00:44.328 but that's just going to keep you up with inflation. 1:00:44.329 --> 1:00:50.329 Now you know you're going to work for 30 years, 1:00:50.326 --> 1:00:55.146 let's say, and retire for 30 years. 1:00:55.150 --> 1:00:57.100 That's a little ambitious about how long you're going to live, 1:00:57.097 --> 1:00:58.597 but let's just suppose that's what you think. 1:00:58.599 --> 1:01:00.339 You're going to live for 30 years after that. 1:01:00.340 --> 1:01:03.420 So how much should you spend every year? 1:01:03.420 --> 1:01:10.520 Well, you can't answer that--and let's say you want 1:01:10.518 --> 1:01:14.068 level real consumption. 1:01:14.070 --> 1:01:17.120 So you want to consume the same amount every year for the rest 1:01:17.123 --> 1:01:19.133 of your life, which is going to 60 years, 1:01:19.126 --> 1:01:20.476 30 at Yale, 30 retired. 1:01:20.480 --> 1:01:23.780 So how much do you spend every year in consumption? 1:01:23.780 --> 1:01:26.180 Well, you can't answer that until you know the interest 1:01:26.179 --> 1:01:26.489 rate. 1:01:26.489 --> 1:01:34.179 So let's say the interest rate, the nominal interest rate 1:01:34.175 --> 1:01:39.115 equals, let's say, 5.3 percent about, 1:01:39.117 --> 1:01:44.467 a little bit more than 5.3 percent. 1:01:44.469 --> 1:01:47.259 So if the nominal interest rate is 5.3 percent, 1:01:47.260 --> 1:01:50.800 inflation you know is going to be 3 percent and you've got 1:01:50.798 --> 1:01:54.088 115,000 coming going up with inflation every year, 1:01:54.090 --> 1:01:56.880 how are you ever going to figure out how much to spend 1:01:56.878 --> 1:01:59.088 starting next year when your job starts? 1:01:59.090 --> 1:02:00.790 It looks like a hopeless thing. 1:02:00.789 --> 1:02:03.529 You'd have to say, well, if I get 115,000 next 1:02:03.532 --> 1:02:05.102 year, I consume some of it, 1:02:05.099 --> 1:02:08.339 I put the rest in the bank, it makes interest, 1:02:08.335 --> 1:02:11.755 it grows at 5.3 percent, but then inflation is 3 1:02:11.755 --> 1:02:13.935 percent, so I take that into account and I figure out how 1:02:13.938 --> 1:02:15.418 much to spend the year after that, 1:02:15.420 --> 1:02:17.970 but then I'm going to get 115,000 more of that so I'll 1:02:17.972 --> 1:02:20.682 save something, maybe more from my next thing 1:02:20.682 --> 1:02:23.992 and then I'll deposit that at another 5.3 percent, 1:02:23.989 --> 1:02:26.169 and I have to take into account inflation at 3 percent. 1:02:26.170 --> 1:02:28.110 It sounds like it's going to get very complicated. 1:02:28.110 --> 1:02:29.910 How are you going to figure this out? 1:02:29.909 --> 1:02:33.359 But in fact it's very simple, and Irving Fisher pointed the 1:02:33.356 --> 1:02:36.266 way to do it and we can now do it in our heads. 1:02:36.268 --> 1:02:38.718 So Fisher said, don't figure out all this year 1:02:38.722 --> 1:02:41.562 by year stuff and don't get mixed up with the rate of 1:02:41.556 --> 1:02:42.316 inflation. 1:02:42.320 --> 1:02:45.240 You don't care about inflation. 1:02:45.239 --> 1:02:47.789 You're going to look through the inflation and only care 1:02:47.786 --> 1:02:49.126 about the real consumption. 1:02:49.130 --> 1:02:52.520 So the fact is you care about the real rate of interest. 1:02:52.518 --> 1:02:59.648 So the real rate of interest 1 r = 1 i over the rate of 1:02:59.648 --> 1:03:07.438 inflation which equals 1.053 over 1.03 which is about 1.023, 1:03:07.438 --> 1:03:08.758 right? 1:03:08.760 --> 1:03:12.390 We're doing things in our head now so we have to be a little 1:03:12.391 --> 1:03:14.301 bit approximating, so, right? 1:03:14.300 --> 1:03:17.570 If I divide this by this these numbers are so close to 1 that 1:03:17.568 --> 1:03:20.508 I'm basically just subtracting the bottom from the--the 1:03:20.512 --> 1:03:22.422 denominator from the numerator. 1:03:22.420 --> 1:03:29.460 If I multiply 1 g times 1 i, all right, 1:03:29.460 --> 1:03:36.930 1 g times 1 r that's going to equal 1 g r rg and if this is 1:03:36.927 --> 1:03:44.527 .02 and this is .03 then the multiplication is .0006 so this 1:03:44.525 --> 1:03:48.385 is practically irrelevant. 1:03:48.389 --> 1:03:50.969 So multiplying numbers like this, or dividing them, 1:03:50.972 --> 1:03:52.782 is just like adding these things. 1:03:52.780 --> 1:03:56.620 So it's just like taking this term and subtracting that. 1:03:56.619 --> 1:03:59.789 So when you get a number near 1 divided by another number near 1 1:03:59.791 --> 1:04:02.661 you just take the difference from 1 in the numerator minus 1:04:02.663 --> 1:04:04.933 the difference from 1 in the denominator. 1:04:04.929 --> 1:04:07.389 It's pretty close to doing actually the division. 1:04:07.389 --> 1:04:11.379 So this is about 2.3 percent interest. 1:04:11.380 --> 1:04:14.750 So the real interest rate is about 2.3 percent. 1:04:14.750 --> 1:04:17.840 So Fisher would say, ah ha, use the real rate of 1:04:17.836 --> 1:04:18.556 interest. 1:04:18.559 --> 1:04:22.989 You're getting 115,000 real payments every year for 30 years 1:04:22.985 --> 1:04:27.485 at a real interest rate of 2.3 percent, but we know what that 1:04:27.485 --> 1:04:28.005 is. 1:04:28.010 --> 1:04:33.910 So what is 115,000 of real dollars every year at a real 1:04:33.914 --> 1:04:36.434 rate of .023 percent? 1:04:36.429 --> 1:04:37.969 Well, remember what our formula was. 1:04:37.969 --> 1:04:39.979 It's the cash you're getting every year-- 1:04:39.980 --> 1:04:43.770 if it were a perpetuity, you got it every year forever, 1:04:43.768 --> 1:04:47.478 it would just be the cash you're getting divided by the 1:04:47.483 --> 1:04:48.243 interest. 1:04:48.239 --> 1:04:52.109 So 115,000, that's over a tenth of a million every year forever 1:04:52.106 --> 1:04:55.036 at 2.3 percent interest that would be worth-- 1:04:55.039 --> 1:04:59.209 that's 5 million so far, but you're not getting it every 1:04:59.208 --> 1:04:59.738 year. 1:04:59.739 --> 1:05:02.219 You're getting it for 30 years. 1:05:02.219 --> 1:05:10.639 So 1 - [1 over] 1.023 to the thirtieth, 1:05:10.639 --> 1:05:16.399 so what's that equal to? 1:05:16.400 --> 1:05:22.470 It's no longer 5 million because that would be getting 1:05:22.467 --> 1:05:28.417 the money forever, 1.023 to the thirtieth is what? 1:05:28.420 --> 1:05:29.930 Student: It's like > 1:05:29.929 --> 1:05:34.689 Prof: So we said that 2.3 percent interest, 1:05:34.693 --> 1:05:38.293 2.3 into 72 is--2.3 times 30 is 69. 1:05:38.289 --> 1:05:42.569 So because it's close to 0 the 69 rule almost works. 1:05:42.570 --> 1:05:46.240 So anyway, an approximation would say 2.3 into 72 is just a 1:05:46.237 --> 1:05:49.757 little bit over 30, so it doubles every 30 years 1:05:49.759 --> 1:05:55.729 and you've got it for 30 years, so it's just going to be 2. 1:05:55.730 --> 1:06:00.040 This number's about 2, right, 2.3 percent into 72 is 1:06:00.039 --> 1:06:03.589 approximately 30, so every 30 years at this 1:06:03.588 --> 1:06:06.038 interest rate it doubles. 1:06:06.039 --> 1:06:13.519 So therefore you've got 115,000 over .023 times 1 - 1 half. 1:06:13.518 --> 1:06:17.178 You've lost half the value by not getting it forever. 1:06:17.179 --> 1:06:19.549 So that's 2.5 million. 1:06:19.550 --> 1:06:22.180 So Fisher says, look, remember the budget set. 1:06:22.179 --> 1:06:24.089 In GE we studied budget sets. 1:06:24.090 --> 1:06:28.420 We put P_1 X_1 P_2 1:06:28.420 --> 1:06:32.750 X_2 P_60 X_60, 1:06:32.750 --> 1:06:36.610 that's on the left hand side, is less than or equal to 1:06:36.614 --> 1:06:40.264 P_1 endowment 1 P_2 endowment 2 1:06:40.259 --> 1:06:43.029 P_30 times endowment 30. 1:06:43.030 --> 1:06:47.910 You're getting 115,000 of real goods every year for 30 years. 1:06:47.909 --> 1:06:50.639 P_1 is 1 over 1.023. 1:06:50.639 --> 1:06:54.179 P_2 is 1 over 1.023 squared etcetera. 1:06:54.179 --> 1:06:59.599 So this revenue on the right is just the annuity of 30 years of 1:06:59.601 --> 1:07:01.701 115,000 of real goods. 1:07:01.699 --> 1:07:06.489 So it's worth 5 million reduced because it's not a perpetuity, 1:07:06.492 --> 1:07:10.742 it's only an annuity for 30 years and so it's worth 2.5 1:07:10.737 --> 1:07:11.677 million. 1:07:11.679 --> 1:07:13.549 So we've got the right hand side. 1:07:13.550 --> 1:07:17.840 That's this, 2.5 million. 1:07:17.840 --> 1:07:19.210 That's how much the present value is. 1:07:19.210 --> 1:07:23.320 So that's what a professor at Yale can look forward to his 1:07:23.318 --> 1:07:25.598 entire, her entire career if she 1:07:25.603 --> 1:07:28.083 started 10 or 20 years ago would be, 1:07:28.079 --> 1:07:30.759 she'll make 2 and 1 half million in present value terms. 1:07:30.760 --> 1:07:33.840 If she'd gone to Wall Street, in five years, 1:07:33.840 --> 1:07:36.440 if she were a Yale undergraduate and went to Wall 1:07:36.438 --> 1:07:38.218 Street, in five or ten years she'd be 1:07:38.217 --> 1:07:39.667 making more than that every year. 1:07:39.670 --> 1:07:44.160 So well, not everybody, but anyway. 1:07:44.159 --> 1:07:50.559 So how much should she spend every single year of her 60, 1:07:50.556 --> 1:07:51.696 or life? 1:07:51.699 --> 1:07:55.969 Well, so we have to figure out this number C, 1:07:55.969 --> 1:07:57.909 the coupon, right? 1:07:57.909 --> 1:08:04.949 We have to figure out how much can she spend every year of her 1:08:04.947 --> 1:08:11.987 life, what C can she spend at 2.3 percent interest where now I 1:08:11.987 --> 1:08:14.177 have a 60 here? 1:08:14.179 --> 1:08:19.379 So it's an annuity of 60 years of constant consumption at this 1:08:19.376 --> 1:08:22.866 interest rate, so how much is it worth? 1:08:22.868 --> 1:08:29.188 Well, I have to just figure out 1.023 to the sixtieth, 1:08:29.189 --> 1:08:35.749 1.023 to the thirtieth was 2,1.023 to the sixtieth is 4, 1:08:35.747 --> 1:08:38.607 so this is 1 fourth. 1:08:38.609 --> 1:08:41.869 So we have 3 quarters here. 1:08:41.868 --> 1:08:47.658 So this is C over .023 times 3 quarters. 1:08:47.659 --> 1:08:48.699 That's what we have. 1:08:48.698 --> 1:08:52.198 So we multiply 4 thirds by 2.5 million. 1:08:52.198 --> 1:09:09.858 You get 10 million--this is .023 divided by 3 times 10 1:09:09.863 --> 1:09:14.533 million = C. 1:09:14.529 --> 1:09:20.599 So that's like 76,000 something, 3 into .023 is 76 and 1:09:20.604 --> 1:09:27.834 then you have to figure out what decimal place you're at and you 1:09:27.826 --> 1:09:32.866 know it's going to be less than 115,000. 1:09:32.868 --> 1:09:37.168 So it's got to be some number, some reasonable percentage of 1:09:37.167 --> 1:09:39.787 115,000 so it works out to 76,000. 1:09:39.789 --> 1:09:40.349 So that's it. 1:09:40.350 --> 1:09:41.460 You can do that in your head. 1:09:41.460 --> 1:09:44.390 I mean, not today but after looking at it by next time 1:09:44.390 --> 1:09:46.660 you'll be able to do that in your head. 1:09:46.658 --> 1:09:49.788 So this professor can figure out what you should do. 1:09:49.789 --> 1:09:50.899 It seems like a hard problem. 1:09:50.899 --> 1:09:51.809 It's life. 1:09:51.810 --> 1:09:55.680 You've got to figure out what to do every year and now you 1:09:55.679 --> 1:09:59.819 know how to do it very easily, so any questions about this? 1:09:59.819 --> 1:10:03.979 I want to do one more little example. 1:10:03.979 --> 1:10:08.749 All right, so let's do a harder example. 1:10:08.750 --> 1:10:11.400 It's easier computationally, but harder conceptually. 1:10:11.399 --> 1:10:16.419 When I just got tenure at Yale, actually I had tenure for a few 1:10:16.421 --> 1:10:18.861 years; you'll see why this is relevant. 1:10:18.859 --> 1:10:21.139 The President, Benno Schmidt, 1:10:21.135 --> 1:10:24.295 of Yale said, "A horrible thing has 1:10:24.302 --> 1:10:25.362 happened. 1:10:25.359 --> 1:10:29.799 Generations of Yale presidents before me have not realized that 1:10:29.800 --> 1:10:33.310 the buildings were not getting the proper care. 1:10:33.310 --> 1:10:35.020 There's deferred maintenance. 1:10:35.020 --> 1:10:38.280 Generation after generation did no fixing up of the buildings. 1:10:38.279 --> 1:10:41.529 I'm the first president who's going to act responsibly and fix 1:10:41.534 --> 1:10:42.874 up the buildings." 1:10:42.868 --> 1:10:50.338 And he said, "I'm going to fix up the 1:10:50.341 --> 1:10:54.491 buildings, and I can tell you that I've 1:10:54.493 --> 1:10:58.553 hired these planners, and they've come and done an 1:10:58.551 --> 1:11:04.291 exhaustive study and we have to spend 100 million a year for 10 1:11:04.292 --> 1:11:08.412 years, each year for 10 years, 1:11:08.409 --> 1:11:13.959 to fix up the buildings properly." 1:11:13.960 --> 1:11:16.220 So that plan, by the way, is the thing that 1:11:16.220 --> 1:11:18.590 got turned into fixing one college a year. 1:11:18.590 --> 1:11:22.010 "So 100 million for 10 years that's what we need. 1:11:22.010 --> 1:11:24.590 These presidents before me have overlooked it. 1:11:24.590 --> 1:11:26.900 They've spent as if we don't have to keep up the buildings. 1:11:26.899 --> 1:11:28.399 I've recognized the problem. 1:11:28.399 --> 1:11:29.739 I'm going to correct it. 1:11:29.738 --> 1:11:32.098 This is a huge expense they didn't take into account. 1:11:32.100 --> 1:11:33.810 We have to reduce the budget." 1:11:33.810 --> 1:11:35.840 So how much do you reduce the budget by? 1:11:35.840 --> 1:11:40.750 How many cuts should he have made in that first year? 1:11:40.750 --> 1:11:42.930 How would you have figured out what to do? 1:11:42.930 --> 1:11:46.110 So what he did is he recommended firing 15 percent of 1:11:46.113 --> 1:11:48.873 the faculty which didn't go over very well. 1:11:48.868 --> 1:11:52.048 And the faculty, it was an amazing thing, 1:11:52.052 --> 1:11:54.522 there's no structure at Yale. 1:11:54.520 --> 1:11:55.990 The president runs Yale. 1:11:55.989 --> 1:11:57.459 There's no senate. 1:11:57.460 --> 1:11:58.530 There's no labor union. 1:11:58.529 --> 1:11:59.659 There's no nothing. 1:11:59.659 --> 1:12:00.759 It's just the president. 1:12:00.760 --> 1:12:02.740 Suppose the president announces, "I'm going to 1:12:02.735 --> 1:12:04.235 get rid of 15 percent of faculty," 1:12:04.238 --> 1:12:05.778 what is the faculty supposed to do? 1:12:05.779 --> 1:12:07.909 There's no mechanism. 1:12:07.908 --> 1:12:10.378 So what happened is, the old deans who are no longer 1:12:10.376 --> 1:12:12.986 deans, they were just old, almost all of them were men, 1:12:12.987 --> 1:12:14.387 again, I guess, old guys. 1:12:14.390 --> 1:12:16.480 They got together and said, "Well, we have no power. 1:12:16.479 --> 1:12:19.109 We have no position, but we used to be deans at 1:12:19.109 --> 1:12:19.509 Yale. 1:12:19.510 --> 1:12:21.320 It's up to us to do something. 1:12:21.319 --> 1:12:24.099 We're going to appoint the committee who's going to examine 1:12:24.100 --> 1:12:26.020 the logic of the president's decision. 1:12:26.020 --> 1:12:28.970 So we're going to appoint six people that we're going to pick 1:12:28.972 --> 1:12:31.582 out of the blue and they're going make a report to the 1:12:31.581 --> 1:12:33.601 faculty and tell us what to do." 1:12:33.600 --> 1:12:39.890 So I was one of the six and the other five guys were pretty 1:12:39.894 --> 1:12:40.984 nervous. 1:12:40.979 --> 1:12:43.929 Well, we all were nervous about actually getting up in front of 1:12:43.934 --> 1:12:46.794 the president and the provost and the dean and saying that it 1:12:46.792 --> 1:12:48.892 was all wrong and he shouldn't do this, 1:12:48.890 --> 1:12:54.000 but we had tenure so we could get up and say whatever the hell 1:12:54.002 --> 1:12:55.262 we wanted to. 1:12:55.260 --> 1:12:56.430 So what did I say? 1:12:56.430 --> 1:12:58.480 What would you have said if you were me? 1:12:58.479 --> 1:13:06.679 Now the whole budget of Yale was--1 billion equals annual 1:13:06.677 --> 1:13:13.117 budget, and a lot of things you can't cut. 1:13:13.118 --> 1:13:18.258 So notice 1 hundred million a year is 10 percent of the annual 1:13:18.261 --> 1:13:19.021 budget. 1:13:19.020 --> 1:13:21.870 So he basically said, "Well, we've got 100 1:13:21.867 --> 1:13:22.917 million a year. 1:13:22.920 --> 1:13:25.810 We ought to cut out 10 percent of the budget, 1:13:25.810 --> 1:13:27.840 and since there are some things we can't get rid of, 1:13:27.840 --> 1:13:30.650 we've got to keep making fixed payments and the faculty is 1:13:30.649 --> 1:13:32.459 something-- of course I'm not going to fire 1:13:32.458 --> 1:13:34.668 the tenured faculty, I'm going to fire people who 1:13:34.666 --> 1:13:37.716 aren't tenured and when faculty retire I just won't hire anyone 1:13:37.715 --> 1:13:38.645 to replace them. 1:13:38.649 --> 1:13:40.119 That's how I'm going to get rid of the faculty." 1:13:40.119 --> 1:13:41.659 That's how he got to 15 percent. 1:13:41.659 --> 1:13:44.349 So what would you have done? 1:13:44.350 --> 1:13:45.810 What would you have said if you were me? 1:13:45.810 --> 1:13:47.990 "Don't do it," but what else would you have 1:13:47.985 --> 1:13:48.275 said. 1:13:48.279 --> 1:13:51.349 What calculation could you do? 1:13:51.350 --> 1:13:55.540 So you know now what to say yet you can't think of what to say. 1:13:55.539 --> 1:13:57.249 So what would you say? 1:13:57.250 --> 1:14:03.070 I'll come to you in a second. 1:14:03.069 --> 1:14:04.089 What's a reasonable number? 1:14:04.090 --> 1:14:10.360 How would you think of a reasonable number? 1:14:10.359 --> 1:14:12.229 Let's take his facts as correct. 1:14:12.229 --> 1:14:14.529 In fact they didn't turn out to be that far off. 1:14:14.529 --> 1:14:21.259 The people he hired were pretty good at assessing how much stuff 1:14:21.255 --> 1:14:23.385 needed to be done. 1:14:23.390 --> 1:14:24.070 Yes? 1:14:24.069 --> 1:14:26.869 Student: Well, I guess the first thing you do 1:14:26.869 --> 1:14:30.329 is figure out what a 10 year 100 million dollar annuity would be 1:14:30.329 --> 1:14:30.879 worth. 1:14:30.880 --> 1:14:32.670 Prof: Yeah, and then what? 1:14:32.670 --> 1:14:36.220 Student: I don't know. 1:14:36.220 --> 1:14:38.080 Prof: So that's a good start. 1:14:38.078 --> 1:14:42.068 He says the first thing he'd do is he'd think about what a 10 1:14:42.069 --> 1:14:45.659 year annuity at 100 million dollars a year is worth. 1:14:45.659 --> 1:14:46.909 So why would he want to do that? 1:14:46.909 --> 1:14:47.709 So that's good. 1:14:47.710 --> 1:14:49.380 That's what he should do. 1:14:49.380 --> 1:14:53.110 That's how I started, but what's the relevance of 1:14:53.114 --> 1:14:53.664 that? 1:14:53.659 --> 1:14:54.569 Yep? 1:14:54.569 --> 1:14:58.559 Student: Then if he got that lump sum now he could 1:14:58.560 --> 1:15:01.840 afford it without needing to fire everybody. 1:15:01.840 --> 1:15:03.770 Prof: So he could say alumni, 1:15:03.770 --> 1:15:06.110 please do something about, you know, 1:15:06.109 --> 1:15:08.609 it's 1 billion dollars, not quite, something less than 1:15:08.606 --> 1:15:09.546 1 billion dollars. 1:15:09.550 --> 1:15:10.770 We'll figure it out in a minute. 1:15:10.770 --> 1:15:14.750 So alumni please hand over 3 quarters of 1 billion dollars 1:15:14.747 --> 1:15:17.397 and I won't have to fire my faculty. 1:15:17.399 --> 1:15:19.529 He could try that. 1:15:19.529 --> 1:15:22.309 What if the alumni didn't come through? 1:15:22.310 --> 1:15:24.190 I know you're going to say something, but I want to give a 1:15:24.188 --> 1:15:25.538 couple more people a chance back there. 1:15:25.539 --> 1:15:26.489 Yep? 1:15:26.488 --> 1:15:30.968 Student: It might be cheaper to short an annuity, 1:15:30.971 --> 1:15:35.051 and that way it definitely turns out to be less and 1:15:35.046 --> 1:15:37.406 > 1:15:37.408 --> 1:15:39.658 Prof: So you'd short a 10 year annuity. 1:15:39.659 --> 1:15:41.009 Student: Yes. 1:15:41.010 --> 1:15:42.810 Prof: What were you going to say? 1:15:42.810 --> 1:15:45.440 Student: We're going to have to pay for the colleges for 1:15:45.439 --> 1:15:47.639 like 10 years or 12 years, however many years you're 1:15:47.635 --> 1:15:49.825 renovating them, but the faculty are like 1:15:49.826 --> 1:15:50.696 perpetuities. 1:15:50.698 --> 1:15:52.408 You have to pay for them the entire time. 1:15:52.408 --> 1:15:57.148 So if you calculate the C over i for a professor it's probably 1:15:57.153 --> 1:16:00.033 a lot more than he was estimating, 1:16:00.029 --> 1:16:04.359 and see how many of those it would take to compensate for the 1:16:04.358 --> 1:16:05.078 annuity. 1:16:05.078 --> 1:16:08.318 Prof: Now we're on the right track, exactly. 1:16:08.319 --> 1:16:09.809 So I'm going to go a step further. 1:16:09.810 --> 1:16:10.790 I went a step further. 1:16:10.788 --> 1:16:13.998 I said, "Yale is forever." 1:16:14.000 --> 1:16:19.280 So what he's telling us is that we need to catch up to where we 1:16:19.278 --> 1:16:23.788 should be to make up for all that lost maintenance. 1:16:23.788 --> 1:16:26.258 He's not saying, by the way, that the presidents 1:16:26.262 --> 1:16:29.372 who built the colleges in the 1920s and stuff weren't paying 1:16:29.368 --> 1:16:31.208 attention to the physical plan. 1:16:31.210 --> 1:16:33.880 He was talking about the few generations before him. 1:16:33.880 --> 1:16:37.860 So once we make up for those losses and then return to a 1:16:37.863 --> 1:16:42.353 steady state after spending the 100 million a year for 10 years 1:16:42.353 --> 1:16:45.543 we'll be back to Yale in a steady state. 1:16:45.539 --> 1:16:47.579 Yale's going to go on forever. 1:16:47.578 --> 1:16:51.128 So the point is, why should the next 10 1:16:51.127 --> 1:16:56.167 years-generation pay for something that's going to make 1:16:56.167 --> 1:17:01.207 Yale better for the whole infinite future of Yale. 1:17:01.210 --> 1:17:04.740 So I said, "How much would every generation, 1:17:04.738 --> 1:17:07.358 not just today, but forever in the future have 1:17:07.362 --> 1:17:11.152 to consume less in order to make up for this one shot problem, 1:17:11.149 --> 1:17:14.549 this deferred maintenance that a couple generations of Yale 1:17:14.546 --> 1:17:16.476 presidents didn't put in?" 1:17:16.479 --> 1:17:23.049 So in other words, I would figure out the present 1:17:23.047 --> 1:17:28.657 value of the 10 year $100 mil annuity, 1:17:28.658 --> 1:17:37.188 and then I would set that equal to what coupon perpetuity gives 1:17:37.189 --> 1:17:41.179 you the same present value. 1:17:41.180 --> 1:17:43.820 So how can you figure that out? 1:17:43.819 --> 1:17:47.379 So in other words, if you lose 100 million for ten 1:17:47.377 --> 1:17:51.657 years that's equivalent to how much less for every year, 1:17:51.658 --> 1:17:55.068 so it turns out to be quite a big difference. 1:17:55.069 --> 1:17:57.159 So it depends on what the interest rate is. 1:17:57.158 --> 1:18:01.308 Now, it happens that Yale has an interest rate. 1:18:01.310 --> 1:18:03.720 Yale always uses this 5 percent rule. 1:18:03.720 --> 1:18:08.260 So if you take R = 5 percent that's supposedly the money 1:18:08.255 --> 1:18:12.625 Yale, after inflation, is confident that it can get on 1:18:12.625 --> 1:18:14.105 its endowment. 1:18:14.109 --> 1:18:15.509 Usually it thinks it can get more. 1:18:15.510 --> 1:18:19.470 You'd figure out what the annuity value is of 100 million. 1:18:19.470 --> 1:18:20.340 So I'm overtime. 1:18:20.340 --> 1:18:23.170 So anyway, we're going to have to--so the punch line is it 1:18:23.173 --> 1:18:25.763 comes to 32 million a year not 100 million a year. 1:18:25.760 --> 1:18:27.700 We'll do this calculation next time. 1:18:27.698 --> 1:18:31.378 And you don't need to fire 15 percent of the faculty to get 32 1:18:31.382 --> 1:18:32.412 million a year. 1:18:32.409 --> 1:18:33.799 So we'll start next time. 1:18:33.800 --> 1:18:39.000