econ-251: Financial Theory
Lecture 1 - Why Finance? [September 3, 2009]
Chapter 1. Course Introduction [00:00:00]
Professor John Geanakoplos: So anyway, the course I'm going to teach is called Financial Theory. I'm going to teach an actual class. I'm going to spend the first half of the class talking about the course and why you might be interested in it, and then I'm going to start with the course. There are not that many lectures available in the semester so I'm not going to waste this one. So the first half of the class is going to be about why to study it and the mechanics of the course, and the second half of the lecture is going to be actually the first part of the course. It'll give you maybe an idea of whether you'll find the course interesting too.
So I think I'll turn this--I won't have too much PowerPoint here. So you should know that finance was not taught until ten years ago at Yale. It was regarded by the deans and the classically minded faculty of the arts and sciences as a vocational subject not worthy of being taught to Yale undergraduates.
It was growing more and more famous, however, in the world and there was a band of business school professors, Fischer Black, Robert Merton, William Sharpe, Steve Ross, Myron Scholes, Merton Miller, who had a huge following in business schools teaching the subject, and whose students went off to Wall Street, and more or less dominated the investment banking parts of Wall Street, and became extremely successful. Finance became the most highly paid profession. It became the most highly paid faculty in the university, although they were all in business schools. There are more physics PhDs working in finance now than there are working in physics.
So this merry band of financial theory professors didn't really believe in regulation. They believed markets left unfettered worked best of all. They believed in what they called efficient markets and the idea that asset prices reflect all the available possible information. So an implication of that is that if you want to find out whether a company's doing well or not you don't have to take the trouble to read all their financial reports, just look at their stock price. If you wanted to know whether a country's doing well or not you don't have to study its entire political system and current events, just look at the general stock market of the country and that'll tell you.
They believed that you could make as good returns in the market as a lay person as you could as an expert because all the experts were competing to try and get the best possible price, and so the price itself reflected all their knowledge and wisdom and opinions and so the lay person could take advantage of that by buying stocks. Everybody should be an investor, they felt. A monkey throwing darts at a dart board would do as well as any of the greatest experts.
Now, their own theory was basically contradicted by their own experience because all of them seemed to go out into the world and invest, and almost all of them made extraordinary returns and made a huge amount of money all of which made them even less popular in the faculty of arts and sciences.
So, a critical part of their theory was that the markets were so efficient, driven by people like them who are competing to exploit every advantage, and therefore compete away every advantage, and by doing that put all the information they have into the prices. The implication of that theory is that there's an extraordinarily clever way of computing the value of most investment assets, and about deciding when a financial decision's a good thing to do or not, and that was the heart of what they taught in these business schools, these algorithms for valuing assets and making optimal financial decisions. One striking thing is that the people they studied, the business people and the investment bankers they studied adopted their language. So this had never happened in academia before. I mean, anthropologists study primitive tribes and different kinds of people all the time and not one of them, I venture to say, has ever taken over all the language invented by anthropologists to behave themselves in their own societies, but the business people that these professors were studying ended up using exactly the language created in academia.
Now, Yale was very different. There was no divide between economists and finance people, the business school finance people. At Yale the greatest economists in Yale's history were actually very interested in finance. Maybe they were financial economists to begin with. So the greatest Yale economist of the first half of the twentieth century was Irving Fisher who you hear a lot about. He wrote, possibly, the first economics PhD at Yale. There was no economist to teach him so he had to write his PhD with Gibbs, maybe the greatest American physicist of the time. There's a building, as you know, on Science Hill named after Gibbs, and you'll hear more about his dissertation in the 1890s, but he was a mathematical economist, an econometrician but he invented almost all of this economics in order to study finance.
The most famous Yale economist of the second half of the twentieth century was James Tobin, a famous macroeconomist, the most famous macroeconomist, possibly, of the second half of the twentieth century after Keynes, a great Keynesian. But he got the Nobel Prize for work he did on finance in economics. Finance was incredibly interesting to him. So Bob Shiller and I went to Yale and we basically said to the deans, "There's a long tradition of finance and economics hand-in-hand at Yale, and so it's not a vocational subject. It's actually central to economics, and central to understanding the economy, and central to understanding the global economy. So we'd like to teach it to Yale undergraduates, and we believe a few of them will actually take the course," and so they agreed to let us do it, and so we've been teaching it now for the last ten years.
So as you know Shiller has been very critical of the business efficient markets tradition. He feels that these finance professors left something essential out of the whole story. What they left out was psychology. They left out the idea of fads, and rumors, and narratives, which he thinks has as big an effect on prices as the hard information about profits that the business school professors imagined drove profits.
I myself have been quite critical of the financial theory. I started off as a straight pure mathematical economist. To me economics was almost a branch of logic and philosophy that happened to tell you something about the world. So I got my PhD with Ken Arrow, who you'll hear a lot about very shortly. And I came to Yale, I'd been a Yale undergraduate, I came back to Yale and I joined the Cowles Foundation. And the Cowles Foundation's motto was basically, "Can we make economics more mathematical? Economics, a social science, ought to be amenable to mathematical analysis just like physics or chemistry is," and people didn't believe this at first. And the Cowles Foundation, which you'll hear a lot about in these lectures, led the revolution in economics transforming it from a verbal subject, political economy, into a mathematical subject.
Well, I decided around 1989 that since I did mathematical economics, and there were all these finance people doing all kinds of mathematical things on Wall Street and doing it very successfully, I thought I might just check out what they were doing. So it might be fun to see what they were up to. So I went to Wall Street and I joined--most people I knew, in fact, professors I knew went to Goldman Sachs. There was a famous finance professor, who I had mentioned before, named Fischer Black who was there at the time and he attracted a lot of people. And so that was the traditional thing to do, but I decided to go to a littler firm called Kidder Peabody, and it was the seventh biggest investment bank at the time. And one thing led to another, and they decided that they wanted to reorganize their research department in fixed income. And since I was a professor there, and I did mathematical economics, and I was there for the whole year somebody said, the director of the Fixed Income Department said, "Why don't you take charge of it and hire a new Fixed Income Research Department for me. So I did, and ultimately there were seventy-five people in the department.
All the time I was a professor at Yale. And after five years Kidder Peabody, even though it was a hundred thirty-five years old, formed by a famous family, the name should sound--Peabody--familiar to you, it closed down after a hundred thirty-five years, five years after I got there. I had to invite the seventy-five people I'd hired into my office and say, "You're fired." And then I went next door to the office next to mine and the guy there said, "You're fired." And so that was my first taste of Wall Street. And after that six of us founded a hedge fund called Ellington Capital Management, which was a mortgage hedge fund, and we had--I'll tell you a lot about it. It started after the Kidder closing as a rather small hedge fund, but it grew into a very big mortgage hedge fund, in fact the biggest mortgage hedge fund in the country. (Although recently we found out that practically everybody who trades mortgages is basically a hedge fund. Fannie Mae, Freddie Mac, they'll all basically hedge funds, so it doesn't mean anything anymore to say that you're a big mortgage hedge fund.) But anyway, we almost went out of business in '98 a subject, a story I'll tell you at great length, and then we just suffered through this disastrous last year or two, but we're still here. So these experiences, of course, have colored my understanding of Wall Street and my approach to the subject.
Chapter 2. Collateral in the Standard Theory [00:10:16]
So I took on, in my theoretical work, finance and economic theory on its own terms. I didn't think like Shiller to introduce psychology into economics I just take it on in its own terms, in its own mathematical terms. And what I found was that there are two things missing in the Standard Theory. One is that it implicitly assumes you can buy insurance for everything. It's the assumption that's called complete markets. And secondly it leaves out collateral entirely so you'll never see, almost in any single economics textbook, the idea of collateral or leverage. And those, I think, the idea that you can't get insurance for everything and that you need collateral, you know, you have to be able to convince someone you're going to pay them back if you borrow money and collateral is the most convincing way of persuading him he's going to be paid back, the lender. Those two things were missing from the Standard Theory, so I built a theory around incomplete markets and leverage, which is a critique of the Standard Theory. So in a way Shiller and I have been vindicated by the crash. I mean, so let me just show you a picture here. Well, maybe I will, you know, how bad the crash was. So let's look at the Dow Jones.
The Dow Jones is an average of thirty stocks and what their value is. We'll talk more about it later. But here it is back to 1913 moving along breezily going up and up and up, you know, there are a few blips which we'll come to later like this one in 1929, and then--but look what happened lately. Look at that. The Dow Jones was up at 14,000 and it dropped to 6,500, something like that, more than a fifty percent drop and now it's gone fifty percent up again. So if you believe these finance professors you'd have to say that everybody realized that future profits in America were going to be less than half what they thought they were going to be before and that's why the stock market dropped. And then miraculously when it hit a bottom everybody figured, "Oh, my gosh, we misunderstood things. Actually it's not nearly that bad and things are fifty percent higher because now people think that profits really weren't going to go, you know, didn't drop in half, didn't drop by fifty percent, they only dropped by twenty-five percent. And that was the only way, according to the old theory, to explain what happened.
Now Shiller would just say, "Well, everybody's--they're crazy. They got this into their head that the world was just going to be great and then some rumor started, and things were so high, and the narrative changed and they thought things were terrible," and this his story. And I'm not sure how he gets it to go up again. They changed their mind again.
By the way it's a little bit better to look at the Dow correcting for inflation and then you see that the 1929 crash looks--and this is on a log scale, remember before the Depression the stock market was so low. It's grown so much over a hundred years that it hardly seemed like anything was happening. Well, now in log scale--going up two of these is multiplying by ten--you see that in the Depression in 1929 through the early '30s the stock market fell. I don't remember what it is. It looks like it's almost two things. It looks like it's eighty or ninety percent, and the fall this time has been much smaller, fifty percent, not ninety percent. So it's a whole thing down but not two things down. It's not a whole thing down. It's less than that. A whole thing down would be the square root of ten or a third. It didn't go down two thirds. It went down less than two thirds. It went down fifty percent, so the actual percentage drop was much worse in the Depression than it is now. We're going to come back to all these things.
What else can we get out of these numbers? I just want you to notice a couple other things. So these numbers are all very interesting. If you're mathematical these are the sorts of things you pay attention to. So these efficient markets guys, they looked at the change in price every month. So there's a lot to say for their theory. They said, "Look, it goes up and down randomly." In fact we'll see that there are all kinds of tests about whether you can predict it's going to go up tomorrow on the basis of how it did yesterday, and the answer's no. It's very difficult to predict whether the stock market is going up or down. It seems to be random. Well, it's random and they used to think it was normally distributed. A lot of people argued it was normally distributed, but it's hard.
You never get these gigantic outliers if things are normally distributed. They're just way too unlikely to happen. So Mandelbrot, who was a Yale professor who retired a couple years ago, although he wasn't when he formed his theories, the inventor of fractals, he said this couldn't possibly be a random walk in the traditional Brownian motion sense of the word because you'd never get these big outliers, but he offered no explanation for why they might be there, and I don't know if Shiller has an explanation either. I mean, is it that people suddenly get shocked one day and then the next week they change their mind and things aren't so bad after all? But you'll see that the theory of collateral and margins does explain these kinds of things.
Let's just look at the Dow. We just looked at the Dow. Let's look at another, the S&P 500. Where's the S&P 500? Here's the S&P 500 data. Here's the history of the S&P 500. It looks very similar to the Dow, except we have longer history back to 1871, so I just want to point out one more thing in the S&P 500. So this is an average of five-hundred stocks, not just thirty, but it's more or less the same. But let's look at the same thing taking the logarithm and check for inflation. So you see here that there are these four cycles. Things seemed low in 1871. They go up and they go down. Then you've got another up and a down. Then you've got another up and a down. Then you've another up and a down. Four times the same thing has happened.
Now this could be just meaningless accidents, but it will turn out that the demography of the country, the baby boom cycle, we haven't had just one baby boom we've had four of them, so this cycle of stock prices, which they're each time a generation long, happens to correspond exactly to the rise, the different age distribution in the population. So another theory of the stock market, which wouldn't have been entertained by these original financial theorists, is that demography has something to do with the stock market, not information about profits and returns but the distribution of ages in the population. So I'm not saying this theory is correct, although I was one of the proponents of it, but it shows that there's room, I think, in finance for economic things, for demography to matter, for leverage to matter and not just for expectations about future profits.
Chapter 3. Leverage in Housing Prices [00:17:54]
So let me show you another picture. So this is a second way in which Shiller became famous. He said, "Well, look at housing prices," the Case Shiller Housing Index. So he's also famous because he had the idea of collecting housing prices. So it's quite amazing, every town has to record, by law you have to record in the town directory, and they're often on the internet, what the price is of every sale of every house. So everybody has it and it's all publicly available on the internet, or most of it is publicly available on the internet. And nobody thought to gather all this information together and take the average and write down an index until Shiller did it. So here's the Shiller Index. All right, so you can see that housing prices were pretty stable throughout the '80s and then in and around 2000 they started taking off, so this is when the stock market was taking off too.
So Shiller says this is irrational exuberance. People just went crazy. They somehow think things can never go down, and they're just going to keep going up, and they keep buying because they think things are going to go up, and it's crazy. Psychology--eventually a new narrative is going to start. Somebody's going to say, "Oh, they've been going up so long they can't continue to go up. Things have to go down," and things went down.
I think there's something to psychology so there was something missing in the original finance story. The finance guys, by the way, they would say, "Well, the rise is not so surprising. Look at the mortgage rates. (This is the interest rate you have to pay if you get a mortgage.) There's been an incredible decline in mortgage rates over the years, so it's less costly to buy housing. If you take the present value of your expenditures you just have to pay less. You pay over a long period of time, and so the interest rate is less, so the value of the houses is worth more because you're discounting the future benefits at a lower rate. (You'll hear all about discounting later.) So there's no mystery." On the other hand nothing happened to interest rates. They kept getting lower so there's no reason why the market should have crashed.
So, again, this seems like a vindication for Shiller. Now, it also, in a way, is a vindication for my theory which is non-psychological. So I'm distrustful a little bit of psychology because it can be anything, although I agree it's important. So my theory is when you take a loan you have to negotiate two things, the interest rate and how much collateral you put up. Who's going to trust you to pay back? When you buy a house they say, "You can't just borrow the whole value of the house." They say, "Well, make a down payment of twenty percent. Borrow eighty percent of the value of a house." And so what I say is that instead of paying all your attention to the interest rate think about the collateral rate. Why is it twenty percent that you have to put down? Maybe it should be ten percent or forty percent.
Well, in fact, that number changes all the time. So here what I've done is--the pink line from 2000 to the future, that pink line is Shiller's Housing Index inverted. So you notice the scale on the right is the housing prices, but I've inverted it, and on the left I have the down payment percentage. These are non-agency loans. We'll come back to the graph later--I don't have time to explain exactly how I got it--but what you see is that from 2000 onwards the down payment people were asked to make to buy their house got lower, and lower, and lower, and lower and it got down to three percent.
You could put down three percent of the value of the house and borrow the other ninety-seven percent of the value of the house to buy it. So amazingly the prices go up and down just with what's called the leverage. So why is it called leverage? Because the cash you put down payment, say ten percent, you can lever it up and own an asset that's worth a hundred even though you put down ten dollars. So you're leveraged 10:1. If you put down three dollars and you get a hundred dollar house you've leveraged it 30:1 or 33:1. So that's why it's called leverage.
So anyway, the point is that leverage went way up. The margins kept going down and down and down and just at the peak of the housing cycle, which is the bottom of that curve, that's when collateral started getting tougher and people started asking for more money down again, and sure enough the prices turned around. So if you look at the prices of mortgages, again, the inverse on the right, and you look at the margins on the left, not for buying houses but for buying securities--I don't have time to explain this whole graph, but the blue line is the buying securities. So '98 is a big crisis, the margins spike up, I don't have pricing data back until then. That's the blue line. And now from 2007 to 2009 you see the margins spiking up. So to buy a toxic mortgage security investors don't pay cash, they borrow part of the money to buy it. They used to put down only five percent to buy it. Now they have to put down seventy percent to buy it on average.
Well, what happened to prices? Prices--this is the inverse of prices--in 2007 they started to collapse. So this going up means prices are collapsing. So once again, the margins--tougher margins means lower prices and as the margins came down recently the prices have gone up recently. So it's an alternative theory.
So what else do I want to show you? So it doesn't mean that the standard financial theory is wrong. After all, I helped run a hedge fund. Six of us founded it and we've been in business for fifteen years. We must believe in standard financial theory because that's how we've been making a lot of our money. We exploit all those algorithms and those are the things I'm going to teach you, so I certainly believe it and it's very important to teach you that again this semester, but there's more to the theory than just that.
I want to show you one more thing in the Dow Jones or the S&P which I forgot to mention. And where is this? Oh, I can't get it out of that. Let's try Dow. Okay, so Dow. Where was the peak of the Dow? It was right over here. Now what was the date? The date's supposed to flash here. So it's October 1st 2007. So that's when people started to realize something was wrong with the world and things headed down. Until then nothing bad seemed to be happening in the world, but suppose that you look not at the Dow, suppose you looked--sorry. Here's a graph, suppose you looked at the sub-prime mortgage index.
So you see it's a hundred. You'll understand what these things are. So a hundred means nobody thinks there's going to be a default. Over here January 2007, that's ten months before the stock market starts to go down--before it hits its peak. The stock market is still going up here. A month later, this is April 2007, a month later the sub-prime index starts to collapse. You see it goes from a hundred to sixty. We're already--In February or March 2007. So that means the people, those experts trading mortgages, already realized there was a calamity about to happen. This was long before anyone else perceived anything happening, long before the stock market moved, long before the government did anything to correct the problem. So just as financial theory says if you pay attention to the prices you can learn a lot about the world. The people trading those things--their life depends on fixing the right prices. Probably they know stuff that you don't know. The prices are going to reflect their opinion. If the price collapsed part of the reason it collapsed, maybe margins and something had something to do with it, but part of the reason it collapsed was because they knew something bad was happening. So for two and half years we've known there's going to be a major catastrophe in the mortgage market.
To go from a hundred to sixty and since to twenty is a total calamity. So you know that there are one point seven million people who have already been thrown out of their houses. Another three and a half million aren't paying their debts and are seriously delinquent. Probably all of them will be thrown out of their houses, and another four or five million after them might default and have to be thrown out of their houses. So it's a major catastrophe and the market told us and warned us about it two and a half years ago and nobody's done anything about it, basically, until now as we'll find out. So it's not that I think financial theory, the standard financial theory is wrong I think it's incredibly useful. I just think it has to be supplemented by a more general and richer theory.
Maybe I should show you how my hedge fund has done just so that you don't think that it was a total failure. Oh dear, where is my returns? Here we go, EMG returns, it's sort of interesting. So Kidder Peabody went out of business in 1994. There was a tremendous crash in the market, a low of the leverage cycle. The purple is Ellington, that's the hedge fund. You'll see that these are other investment opportunities. The S&P 500 is the green thing which looked like it was doing great for a while. Emerging markets is the blue one, and high yield is the green one, and then there are bunch of other things like treasuries, and this is Libor which is what banks lend to each other at. So this says if you put your money into any of those strategies, in Libor, keep lending your money each month to a bank and seeing what interest you get and seeing how much money you accumulate, or putting your money in Ellington and looking at the purple, or putting your dollar into the stock market and see what happens, the S&P 500, this is what happens.
So you see there was a crash here. You're fired, you're fired. So we start Ellington and Ellington does great, and so we have all these years we're doing great. Then '98 there's another crash. Look what happened. Overnight, practically, we lost a huge amount of money. We almost went out of business. Long Term Capital, which, by the way, was run partly by two Nobel Prize winners, Merton Miller, not Merton Miller, Myron Scholes and Robert Merton, two of the guys I mentioned who were the leaders of the financial crisis [correction: leading finance academics], they bankrupted their company and they went out of business. And why did they go out of business? Because they weren't aware of the leverage cycle, in my view.
Anyway, so the prices collapsed. Then look it, all these returns shoot up again and the world seems to be doing great, the stock market, everybody's doing great. Then there's another crisis in 2007. Everything plummets all together this time and then everything is going up again. So it's hard to see this and to live through that.
So I remember in '98, for example, when there was a margin call. Our lenders called and said, "We want more money. We don't believe that the assets are worth as much as they were and so the collateral is not covering the loan anymore." And we said, "You can't make a margin call. It's not legal. You promised not to change the margins on us for six months. You can't make a margin call." And they said, "Well, blah, blah, blah, we don't really know about that. We're making a margin call." So we called up Warren Buffett and we said, "This is terrible. They're making a margin call. They can't do this. We have great bonds. There's nothing wrong with the bonds. They're going to force us to sell all the bonds to pay them the money, and how can they force us to do that? They shouldn't force us to do that. We've got great bonds, it's a great business, it's a great company and they're going to run us out of business. You can't let this happen. Warren Buffett why don't you buy part of the company and save us and you'll get rich and it'll be great." He said, "Say that again." And we said, "Well, they're going to force us to sell all the bonds on Tuesday to meet their margin call and we'll get terrible prices for the bonds and we'll be driven out of business, even though they're great bonds, just because they're making a margin call. You can’t let this happen to us. Buy part of the business and save us and you'll get rich. You'll own part of a great company." And he said, "Hell, it sounds like I should just show up on Tuesday and buy the bonds."
So we survived. I'll tell you more about what we did. We survived that, no thanks to Warren Buffett, although he had a pretty good idea, and then we survived the last crash. So we survived all these crashes, but the fact is things go up, they crash, they go up, they crash, they go up.
Could it all be my fault? I decided it can't be all my fault. It's got to be there's something more basic at work and that's why I'm going to tell you about the leverage cycle. Now, of course, I realize that my pet theories may not turn out to be right, although I think more and more people are starting to think there's something to it. So I'm not going to spend a huge portion of the course just talking about my pet theories. I mean, I recognize that I have to teach partly what's standard.
So the course is going to be divided in the following way. I'm going to talk about the standard no-arbitrage Financial Theory, and I'm going to talk about it theoretically and mathematically and from a practical point of view, because helping to run the hedge fund--lots of the things that I'll be teaching are things that we actually confronted in the hedge fund. And so you'll get the standard financial theory course taught from a hedge fund perspective both theoretically and from a practical point of view.
On the other hand, I've lived now through three mortgage crises and so it seems silly for me not to describe how the mortgage market works, even through you'll find almost none of that in any standard finance textbooks, how the mortgage market works, and what's going on, and what happened in the crises, and how we survived and how other people didn't. And I'll talk about the leverage cycle. I'll also spend some time--I think it's quite important--on the mathematical logic of the invisible hand argument.
That's the most important argument in economics that the free market does good for the economy and a huge number of people believe it. And part of that argument and part of the sort of hazy knowledge of that argument is what drives resistance to a lot of government programs. I mean, the government can only screw things up is what people generally believe. Is it a prejudice or is there some actual argument behind that?. Well, I want to go over that argument and show you precisely how it works and how it doesn't work in the financial sphere.
And then, I want to talk about Social Security. That's one more program. That's the biggest program in the budget. It's as big as defense and the two of those are much bigger than everything else, vastly bigger than every other thing in the budget. So I want to talk about Social Security and should it be privatized and should it be reformed and why did it go bankrupt.
It's also an interesting mathematical problem because Social Security critically involves the belief that things will go on forever, so there's an infinity in it. Each generation the young are paying for the old. Nobody would do that if they thought they were going to be the last generation paying to the old, and when they got old nobody would help them. So Social Security rests on this world going on forever which makes it mathematically interesting.
Anyway, so I got interested in it from a theoretical point of view and then I got put on all these National Academy panels on Social Security and privatizing. And so I know quite a bit about it so I might as well talk about something I know about, so that's why I'm going to talk about that.
Chapter 4. Examples of Finance [00:33:47]
All right, so this is too hard for you to read so let's do this. So let me just give you a few examples. Uh-oh, I hope I didn't do a terrible thing. No. So let me just give you a few examples here of the kinds, just so you realize there's something to the Standard Theory. There's a lot to it. So I'm going to give you ten examples very quickly, of the Standard Theory. So these are things that I'm guessing you'll have, at least some of them, trouble figuring out how to answer now, but by the end of the course this should be totally obvious to you. So suppose you win the lottery, forty million dollars, it's a hundred million dollars, the lottery. Now they always give you the choice. Do you want to take five million a year over twenty years or just get forty million dollars right now? Which would you do and how do you think about what to do?
So now you get tenure at Yale at the age of 50, say. You're making a hundred fifty thousand dollars a year and you think professors--it's going to go up with the rate of inflation, and that's about it for the next twenty years until you retire. So that's twenty years of that and then you're going to live another twenty years when you're going to be making nothing. So how much of the hundred-fifty-thousand, and let's say inflation is three percent, and what you'd like to do is consume inflation corrected the same amount every year after you retire and before you retire, and so how much of the hundred-fifty-thousand should you spend this year and how much should you save? You'll learn very quickly how to do a problem like that.
Now, President Levin wrote a few months ago, the end of last year if you remember, he said that, "Well, the crisis was bad. Yale was going to weather it, but Yale had lost twenty-five percent, probably, of its endowment. That's five-billion dollars almost of the twenty-three-billion dollar endowment. So how much should he choose to cut? It's his decision. How much should Yale reduce spending every year? The total spending at Yale is a little over two-billion. So the endowment goes down by five-billion what cuts should you take to the budget. Should faculty salaries be cut, be frozen, should you get three TAs instead of four TAs? What should you do? How big a cut should you take?
Now, the same question faced Yale in 1996 or so. I've forgotten exactly the year. Ten or twelve years ago the previous president, Benno Schmidt, he suddenly noticed that there was deferred maintenance, as he called it, a billion dollars to fix the Yale buildings. That's why, incidentally, every year another college gets fixed. They decided there was deferred maintenance of a billion dollars. A hundred million dollars every year for ten years had to be spent. The whole endowment then was three billion, and now we had a one billion dollar deferred maintenance problem. The budget was about one billion then. So how much should you cut the Yale budget at that time? So Benno Schmidt said, "I'm firing fifteen percent of the faculty." He announced he was firing fifteen percent of the faculty. That was on the front page of theNew York Times, "Yale to fire faculty."
Well, did he make the right decision? Rick Levin took over as president three months later, so probably not. What mistake did he make in his calculations? What should he have done? What was the right response? We're going to talk about it. It's not that hard a problem.
Now, let's take a slightly more complicated one. You're a bookie. The World Series is coming up. The Yankees are playing the Dodgers, let's say, and you know that the teams are evenly matched and you've got a bunch of friends who you know every game will be willing to bet at even odds on either side because they think it's a tossup. Well, one of your customers comes to you and says, he's a Yankee fan, he's sure the Yankees are going to win the series. He's willing to put up three hundred thousand dollars to bet on the Yankees. So if the Yankees win he gets two hundred thousand, but if the Yankees lose he loses three hundred thousand. So 3:2 odds he's willing to bet on the Yankees winning the series. Well, you say, "This guy's sort of a sucker here. I can take big advantage of him. On the other hand it's a lot of money, two hundred thousand I might lose if I have to pay off and the Yankees win. So even though I think that my expected profit is positive, because he's putting up three hundred thousand to make only two hundred when they're even odds, in fact--the fact is it's such a big number I'm a little worried about that." So what do you do? So what can you do? You've got these friends who are willing to bet at even odds each game by game, so how much money--Presumably the first night you're going to bet with one of your friends. You take the guy’s bet, the customer, you take his three hundred thousand. You promise to deliver him five hundred back if the Yankees win and to keep it if the Yankees lose.
What should you do with your friends? Should you bet on the Yankees with your friends? Should you bet on the Dodgers with your friends and how much should you bet at even odds the first night? So the answer is, well, I don't want to give all the answer now, but so there's a way of skillfully betting with your friends and not betting two hundred or three hundred thousand the first night with your friends at even odds. You bet some different number than that, which you'll figure out how much to bet so that if you keep betting through the course of the World Series you can never lose a penny. How do you know how much that is? Well, that's the kind of clever thing that these finance guys developed and you're going to know how to do.
So let's do another example like that. I'm running out of time a little bit, but an example. Suppose there's a deck of cards, twenty-six red and twenty-six black cards. Somebody offers to play a game with you. They say, "If you want to pick a card and it's black I'll give you a dollar. If it's red you give me a dollar." So if I'm picking, I'm in the black, I get a dollar, it's in the red I lose a dollar, I have to throw away the card after I pick it. The guy says, "By the way, you can quit whenever you want." So should you pick the first card? It looks like an even chance of winning or losing. Let's say you pick the first card, it's black, you win a dollar. Now the guy says, "Do you want to do it again?" You picked a black one so there's twenty-six red left and twenty-five black. So now the deck is stacked against you. Should you pick another card? Well, it doesn't sound like you should pick another card. But you should pick another card and I can even tell you how many cards to pick. Even if you keep getting blacks you should keep picking and picking. So how could that be? It sounds kind of shocking. Well, it's going to turn out to be very simple for you to solve half way through the course.
So, a more basic question. There are thirty year mortgages now you can get for five and three-quarter percent interest. There are fifteen-year mortgages you can get for less, like five point three percent interest. One’s lower than the other. Should you take the fifteen-year mortgage or the thirty year mortgage? How do you even think about that? Why do they offer one at a lower price than the other?
One more example, suppose you're a bank and you hold a bunch of mortgages. That means the people in the houses, you've lent them the money, they're promising to pay you back. And you value all those mortgages at a hundred million dollars. The interest rates go down. The government lowers the interest rates. Half of them take advantage to refinance. They pay you back what they owe and they refinance into a new mortgage. So now you've only got half the people left. Let's say all the people had the same size mortgage and everything. Half the people are left. That shrunken pool, half as big as the original pool, is that worth fifty-million, half of what it was before, or more than fifty-million, or less than fifty-million?
How would you decide that? Again, this is a question which might be a little puzzling now, but actually you should be able to get the sign of that today even, and we'll start to analyze it. So that's what mortgage traders have to do. They see interest rates went down. A bunch of people acted. The people who are left in the pool are different from the people who started in the pool. Now we've got to revalue everything and rethink it all, so how should we do that?
Let's say you run a hedge fund and some investor comes to you and says, "Oh, things are terrible. Look at all the money you lost for me last year. I know you're doing great this year and you've made it all back that you lost last year, but I don't want to run that risk. So I want to give you my money, a billion dollars, I want to get these superior returns you seem to earn, but you have to guarantee that you don't lose me a penny. I don't want to run any risk. I want a principal guarantee (it's called) that when I give you a hundred dollars you'll always return my hundred dollars, and hopefully much more, but never less than a hundred dollars." So is there any way to do that? You know that you've got a great strategy, but of course it's risky. You could lose money. You've lost money a bunch of times before. So how can you guarantee the guy that he'll get all his money back and still have room to run your strategy? Well, it sounds like you can't do it, but of course a lot of people want to invest that way, so there must be a way to do. So you'll figure out--we'll learn how to do that.
So, three more short ones. A scientist discovers a potential cure for AIDS. If it works he's going to make a fortune. He started a company. He's a Yale scientist, he's--medical school, started this startup company. Yale, of course, is going to take all his profits, but anyway it’s his startup company and if his thing really works he's going to make a fortune. If it doesn't work it's going to be totally zero. You calculate, and let's say you believe your calculation, that the expected profits that he'll make if it works, the probability of it working times the profit, that expected profit is equal to the profits of all of General Electric. Should his company be worth more than General Electric, the same as General Electric, or less than General Electric since it's got the same expected profits? Well, I can tell you the answer to this one because I think most of you would think, first you'd think, "Well, maybe the same." Then you'd say, "Well, this AIDS thing it's so risky. It's either going to be way up here or nothing, and that's so risky, and General Electric is so solid, probably General Electric is worth more." But the answer is the AIDS Company is worth more. So how could that be?
So another question, suppose you believed in this efficient market stuff and you rank all the stocks at the end of this year from top to bottom of which stock had the highest return over the year. It's 2010, let's say 2010, this year's a weird year. So let's say you do it in 2010. All the stocks the highest return to the lowest return. Now, suppose you did the same thing in 2011 with the same stocks? Would you expect to get the same order, or the reverse order, or random order? Now again, if you believe in efficient markets and the market's really functioning, the prices are fair and all, I'll bet most of you will say, you won't know, but you might say it should be random the next time, because firms only did better or worse by luck, but that's not right either. So you're going to know how to answer that question by the end of the class.
One last one, the Yale endowment over the last fifteen years has gotten something like a fifteen percent annualized return. A hedge fund, that I won't name, has gotten eleven percent over the last fifteen years counting all its losses and stuff like that. So is it obvious that the Yale endowment has done better than the hedge fund? Would you say that the Yale manager is better than the hedge fund manager? Its return was fifteen percent. The hedge fund only got eleven percent. So I'm asking the question, and I would say that David Swensen would think about it the same way I think about it. So suppose I even told you that the Yale hedge fund had lower volatility--the Yale hedge fund?--the Yale endowment had lower volatility than the hedge fund, which it surely does, would that convince you now that the Yale endowment had been managed better than the hedge fund? Well, we're going to answer this question again, and you're going to see that the answer's a little surprising. It won't be so surprising--I wouldn't have brought it up otherwise. But anyway, that's the kind of thing that in finance you're taught to think about.
Chapter 5. Why Study Finance? [00:46:13]
So the crisis of 2007, which we're going to spend a long time talking about, I just want to get back to that subject. So that list of questions were the kinds of things that I used to teach for years before I was confident about my theory of crises, and this is the kind of questions you have to face all the time in hedge funds, and decisions you have to make, and things you have to tell investors, and so that's the basic part of the course, but I want to say more. So I want to talk about the crisis of 2007-2009. It started as a mortgage crisis. Now, how could it be that everything goes wrong in mortgages? I mean, they're four thousand years old. The Babylonians invented mortgages. What is a mortgage? You lend somebody money. They put up collateral. They don't pay you take the house or you take the guys life, he's a slave or something, but it's the same thing. You borrow money and the guy promises you can confiscate something if he doesn't pay. Four thousand years and we screwed it up. How could that be?
And why should a screw up in the mortgage market have such a big effect on the rest of the economy? Were sub-prime mortgages a terrible idea? Was there some logic to it? And how did we get out of the crisis? How is it, that everybody was saying this is the worst crisis since the Depression, may be another Depression and things seem to have turned around. What is it that we did to get things to turn around? I don't think we're out of it yet, but things are a lot better than they were a year ago. So what is it that the government did to turn things around? It didn't do nearly enough, I think, but it did something. What exactly did it do? Now, Shiller would talk about the whole thing was irrational exuberance. I'm going to say it's all the leverage cycle, but anyway so that's the mortgage crisis.
Now, are free markets good? I want to talk about the argument. The argument was first made by Adam Smith about the invisible hand. The modern mathematical argument is Ken Arrow’s, my thesis advisor. And of course everybody knows that monopoly and pollution and things like that interfere with the free market and they have to be regulated. But the financial markets, there's no monopoly. As long as there's no monopoly and there's no pollution shouldn't the free market function there? So I want to go over that argument and show you what was missing in it, as I said before, and then lastly we're going to talk about Social Security and how could that system be going bankrupt. I mean, it just seems shocking. There's a two-trillion dollar trust fund that's going to run out in 2024 or something and after that the system will be broke.
So how did it happen? Why is it broke? What can we do to fix it? So George Bush said, "Well, it's terrible. Even if we manage to sort of get the trust fund rehabilitated young people like you are going to get a two percent rate of return. If you put your money in the stock market, even allowing for the last crash, over the long haul, the returns have been six percent. So it's terrible, Social Security. Something's wrong with the system. We should privatize it and let young people like you put your money in stocks instead." Well, Gore, in the debate in 2000 said, "You can't do that because then the old people who are expecting their money can't get paid." And both of them agreed that it was all the baby-boomers’ fault. People like me we're getting old, we're going to retire. That's why the system's going to get broke. So that's the conventional wisdom. All three of those things are wrong, so we're going to find out why.
So in summary, why study finance? It's to understand the financial system, which is really part of the economic system. It's to make informed choices. Is privatizing Social Security a good or bad thing? Is regulation of financial markets a good thing? The language that you learn is the language that's spoken on Wall Street, and was created by professors and yet practitioners use it. For me it's incredibly fun, all these little puzzles. As J.P. Morgan said, "Money's just a way of keeping score." You have to figure out what something's worth in the end and if you get it right you've solved the puzzle right and it'll help you make good financial decisions in a pensioned career. That's the standard reason to take Finance.
Chapter 6. Logistics [00:50:13]
Now, the prerequisites of the course, so I want to make this clear, you don't really need ECON 115. It would be helpful because this logic of the free market being good or bad, that was already started in ECON 115. That's what they call it now, right? It's still called 115. I used to teach it but I haven't done it for years. So anyway, what you really need is mathematical self-confidence. It's not going to be high math. It's going to be simple math, but it's relentless over and over again. And I can tell you that every year there's the five percent of you, let's five or ten out of the hundred-twenty are going to just get bored doing problem after problem and you're probably not that, you know, those ten maybe haven't that much experience doing it, don't feel very confident doing it, stop coming to the class and then really have no idea what's going on. My sister is probably much smarter than I am, but she doesn't like math. She wouldn't take this course. So if you're not confident doing little mathematical problems just don't take the course. You'll save yourself a lot of trouble.
I don't know how to say this any better. I want to warn you not to do it. It's easy math, but it never stops. Every week there's going to be a problem set. The exam--there are problem sets. The exam is doing problems just like the problem sets, but if you don't like that, you know, to me finance is a quantitative subject. What's so beautiful about it in one aspect I really like is that you have these complicated different things you have to weigh, but at the end you have to come up with one number. What is the price you're willing to pay for something? It's very concrete. I'm going to take advantage of the concreteness by turning every question into a number. I hate it when you get on the one hand and on the other hand. It's a number. So if you don't like numbers it's not a good course to take.
So what are the kinds of things you have to know? You have to understand the distributive law of arithmetic (which, I have little kids and I see that's not so easy to understand). Anyway, and then you have to understand the idea of a function which is a contingent plan. Simultaneous equations; that's what we do for equilibrium in arbitrage. Taking a derivative, that's marginal utility. The idea of diminishing marginal utility, a concave function looks like that. That's risk aversion. Bankers invented the logarithm, compound interest, so you have to know what taking a logarithm and exponential means, and you have to understand how to take probability weighted averages of things. And we're going to use Excel for a lot of the problems which we'll teach you. By the end of a day you'll be better at it than I am.
So my office hours are four to six. My secretary assistant is Rendé, there's an accent missing as she always tells me, Wilson. She just started three days ago but I'm sure she'll be great. There are going to be two lectures a week and a TA section. So every Tuesday there'll be a problem set starting this Tuesday due the next Tuesday. There will be two midterms. There's a lot of stuff to learn and so I found, everybody I think agrees who's taken the course, if you take the midterm it'll focus your mind and make it a lot easier, so I give two of them so you only have half the course to study. It makes the final much easier to study for.
I recognize that some of you will have problems on one of them, like especially the first mid-term, and if you do vastly worse on one exam than the rest I'll tend to ignore that, but most people don't, by the way, do vastly worse on one exam than the rest. So the final's forty, the problem set's twenty, and the two midterms are twenty percent. Tuesday to Thursday, and so all the TA sessions are Thursday to Monday so they're going to start next Thursday. So you see the classes are Tuesday-Thursday then the next Tuesday. There's a long time in-between here so all the TA sessions will meet there. So they're at the same moment in the class.
There are all these textbooks, all by the Nobel Prize winners, all by those financial greats. You can buy any one of them, but I have my own lecture notes because as I say I teach a slightly unconventional course and there's a huge list of books on the crisis. Some of them are incredibly interesting and fun, and so they're all on the reading list you can take a look at. I mean, there's never been a more fun time to read this stuff now. So course improvements, anyway. So that's it.
Are there any questions about how the course runs, or how I will run it, or whether you think you should take the course, or whether your preparations--So if you haven't taken ECON 15 it's okay, 115, but you've got to be confident that you can solve problems, otherwise don't do it. Any questions? Yes?
Student: So the first problem set will be assigned next Tuesday?
Professor John Geanakoplos: Yeah, so next Tuesday it's going to be due the Tuesday after. So I know that's early, but you probably already know whether you're going to take the course or not. Yes?
Student: Will you teach this next year?
Professor John Geanakoplos: Will I teach it next year? Actually I probably won't because I'm going to go on leave, but I might, but probably not. Someone else will teach it. Yep?
Student: Which of the books do you suggest we buy?
Professor John Geanakoplos: They're all good. They're all famous people who've written. They're trying to sell copies so they're pitched at a quite low level, but they're very good. Anyone of them is good. Merton's book is good. Steve Ross is a friend of mine. He used to teach at Yale, so his book is good. So any one of those is very good, but they're not quite at the same mathematical level because they're trying to sell thousands of books, and they stick pretty closely to this financial view of the world that everything is efficient. Yes?
Student: Will the taped lectures be available online?
Professor John Geanakoplos: That's a good question. I don't think so. No, they're shaking their head. So it won't be in time for you, but it will be if you want to look back in your old age, "I was there. I saw the leverage cycle." Sorry. Yes?
Student: Are the lecture slides posted before or after the lecture?
Professor John Geanakoplos: Oh, the lecture notes are all posted already before the class. So the first twelve of them are there, and I'm changing them each year so there'll be some changes. So last year's first twelve are there and they might change a little bit, but you can already get an idea of what they're about. This first lecture is not on, but the rest of them are. Any other questions? Yes?
Student: When do we sign up for the TA sections?
Professor John Geanakoplos: Oh, you should be signing up now. I don't know how to do this. It's online or something, right? You sign up online. Yeah, so you should pick your sections. We might add another section if all of you stay, but probably you won't, but if we do we'll add another TA section. Yes?
Student: What's the grade distribution?
Professor John Geanakoplos: The grade distribution? I don't know. The standard Yale junior level course grade distribution which is when I was at Yale things were much tougher, so it's the standard distribution. I don't remember it offhand. But I'll tell you all about the distribution at the midterm. So there will be a midterm before--you'll have chance to drop the course after the midterm and then there will be another midterm right at the end of the course. Yes?
Student: What level of math and type of math should we be comfortable with to take the course?
Professor John Geanakoplos: I was trying to say that. I'm glad you asked me again. So I went over the things that you have to know. If you have 3x-4x2 you have to be able to take the derivative of that which is 3-8x. If you've got the log natural of x you have to take the derivative. It's one over x. If you've got 3x+5=10 and 2x-7=12 you have to be able to solve that simultaneous equation. So that's the kind of thing you have to do, and you have to be able to do it quickly and with total confidence that you're doing it right. And for many of you that's no problem, but for some of you who are maybe even smarter than everybody else that's a problem, and so you'll have to judge yourself whether you can do that comfortably so you don't have to worry about the mechanics of doing that. You can think conceptually about what the question is asking.
Chapter 7. An Experiment of the Financial Market [00:58:22]
When does this end, ten of or quarter of?
Student: Ten of.
Professor John Geanakoplos: Ten of, so we have 13 minutes. I want to end with one experiment. So (Teaching Assistant), can you help me with this? So this is something we're not going to have time to figure out the answer to. So I need sixteen volunteers. How about the first two rows? Why don't you just volunteer. You'll survive, and I know it's a drag but you'll do it. What I'm going to do now is I'm going to run an auction. So please stand up and eight of you go this side and eight come over here. That's okay, you'll be okay. I know everyone's reluctant to do this. So I only need sixteen. (TA), help me count them. Two, four, six, eight, you guys have to come the other way. The TAs aren't going to participate. You're not in this, right? No. Two, four, six, eight so we only need eight, you both sat down. So would you like to participate? Come on. We could use another woman here. Two, four, six, eight, there are eight of them? So can you mix these up? There are going to be eight sellers and eight, we say seller, right? Buyer, so shuffle them up and hand one to each. So we've got eight, and these are the football, they're selling. So we've got eight sellers and eight buyers, and I don't know whether you've ever seen this experiment before, but shuffle them, right?
Student: They're all sellers though.
Professor John Geanakoplos: They're all sellers, but you've got to shuffle them. On the other side there's a number. So we've got eight sellers here and eight buyers. So each seller knows what his football ticket is worth, or hers, so please take one.
Student: I have a seller one.
Professor John Geanakoplos: Oh, you have a seller one? That's bad.
Professor John Geanakoplos: I'm blind.
Student: Thank you.
Professor John Geanakoplos: Buyer, thank you. Does this say buyer and buyer? You should be one short. Here's an extra. So there are eight sellers and eight buyers. They've got the football tickets. Each of them knows what the football ticket is worth to her. There are three women here and only two, so these are the "hers". She knows exactly what it's worth to her. So say it's fifteen. The football ticket's worth fifteen. Now if she can sell it for more than fifteen she's going to do it. She's going to make a profit. If she sells it for less than fifteen she's not a very good trader. She's not going to do that. She's going to say, "If I can get more than the football ticket is worth I'm going to sell it. If I can't get more than it's worth I won't sell it." So everybody knows what the football ticket is worth to herself.
All these guys, they know what the ticket is worth to them. So say someone thinks it's worth thirty that guy's going to say, "If I can get it for less than thirty, like for fifteen, I'm going to get it. That'll give me a profit of fifteen. If I can only get it for forty I'm sure not going to do that because I'm paying more than I think it's worth. So you all got that? You have a reservation value yourself. You don't want to pay more than it's worth because then you're losing money, and they want to sell it for more than they think it's worth because then they're making money. So nobody knows anybody else's valuation. The information is distributed completely randomly across the class.
Now this is a famous experiment. I'm not the first one to run it, although I've done it for ten years. I do it in my graduate class, in my undergraduate class, the undergraduates, by the way, always do better than the graduate students. So this knowledge is distributed in the whole environment, and we're going to see what happens when I start a chaotic interaction between all of these sixteen people. What's going to happen? And you would think it'd be total chaos and nothing sensible is going to happen. And if that does happen it'll be very embarrassing for me. But what the efficient markets guys would say is, "Something amazing is going to happen. The market is going to discover what everybody thinks it's worth and figure out exactly the best and right thing to do and that's what's going to happen."
Now, it's hard to believe that with this little preparation that you've had, zero, zero training, zero experience, and you're only going to have two minutes to do this. So see the class has got eight minutes to go. You're going to miss the grand finale. Anyway, so you've only got eight minutes to go. So with only two minutes of training they're going to get to a result, which if I had to do it myself and read all the numbers and sort them out and sort through them would take me much more than two minutes, and all this is going to happen in two minutes. It's hard to believe. It probably won't happen this time.
So here are the rules. I'm going to put you all together. Start inching your way towards each other, and try not--now, when I say go, which won't be for two minutes you're going to start yelling out an offer. So if you think it's worth fifteen and you're a seller you're not going to sell it for fifteen. You're going to say give me twenty, or give me thirty, or give me twenty-five. You're going to try and get as much as you can. You have to yell it out. The buyers are going to be making their offers. When two of you see that there's a deal you have to shake hands, exchange the football, and leave, and tell your numbers to (TA). Where's (TA)? (TA), you're going to stand outside the group that way. So once you make a deal you just leave and tell what's happened to (TA) who's now standing back here, back there. So it has to be public outcry. It's very important that you're yelling these things publically and all the other people can hear you, and you've only got two minutes.
Now two minutes sounds like an incredibly short period of time, which it is, but it's much longer than you think, wait, quiet here. You shouldn't trade--I'm giving you valuable advice--you should not trade in the first ten or fifteen seconds because you have to hear what everybody else is offering. If you trade right away you're probably doing something really stupid. Two minutes, though, it sounds short, is actually a very long period of time. So be patient. Try to get the best possible price and we'll see what happens. Any questions about what you're doing? And now, in the heat of the moment you might be so frustrated that you can't sell when you think it's worth fifteen that you sell it for ten. I'm going to expose you in front of all these people if you do that, so keep track of what you think the thing is worth. All right, any questions anybody about what is going on? So you have two minutes. Is there a second hand there? I can't see it. No?
Student: It's on the ten, or coming to.
Professor John Geanakoplos: Where is it?
Student: Now it's on the three.
Student: It's moving.
Professor John Geanakoplos: It's on the three. I think I see something. When it gets to the four we're going to start. So start, go.
<<students calling out prices>>
Professor John Geanakoplos: Oh, no collusion. No collusion.
<<students calling out prices>>
Professor John Geanakoplos: Come out and tell (TA). If you made a deal tell (TA).
<<students calling out prices>>
Professor John Geanakoplos: How much time is left? One minute left, plenty of time, one minute. Any other deal made? Write down the price and the two, what price they agreed. How much time? Twenty-five seconds, stay cool. How much time? How much time? I can't see. Fifteen. Stay cool. Don't make any mistakes, ten, five, four, three, two, one, stop. Did you get all the numbers?
<<students discussing sales>>
Professor John Geanakoplos: Give me back the tickets.
Student: Was this designed to make us look bad on camera?
Professor John Geanakoplos: Give me back the tickets.
Student: You designed this to make us look bad on camera.
Professor John Geanakoplos: No, you're going to look great on camera, you are. Give me all the tickets back. (TA), you getting done there?
Teaching Assistant: Yeah.
Professor John Geanakoplos: All the tickets. I need them all back, all the stuff. God, you're big folders here. These tickets have lasted ten years until you guys took over. They're all crumpled up. All the tickets, I need them all back. You can sit down now. Everybody's reported in? Now let's see what happened. You've got them all? Five traded.
Teaching Assistant: Five traded.
Professor John Geanakoplos: Five bought and sold. So here's what happened. Here were the numbers. So we have five minutes just to look at this. So all the buyer prices are in blue, forty-four, forty, thirty-six, you should recognize these you buyers, and the red ones were the sellers. So you notice that every seller, for everybody there's a seller who's underneath. So it could have happened that thirty-eight sold to forty-four, and thirty-four sold to forty at thirty-seven, and twenty-eight sold to thirty-six at thirty-two. You could have had eight trades. So what did happen? Nothing like that happened. You had five trades, five pairs of people traded, and there are those three poor schlumps, pairs of people at the end looking despondent, hopeless, unable to trade, worried that they were on camera. Now, let's see, who are the people who traded? So, (TA), name the buyers who bought.
Teaching Assistant: I don't know the names.
Professor John Geanakoplos: The prices.
Teaching Assistant: The seller got it for nine and managed to sell it for twenty dollars. It was all quick so I don't have everybody's name, because they were all rushing.
Professor John Geanakoplos: You got them.
Teaching Assistant: I got them.
Professor John Geanakoplos: That's everything, great.
Teaching Assistant: I just don't have their names.
Professor John Geanakoplos: Here's what happened. Mister seller ten sold to thirty-six at a price of twenty. Mister seller nine sold to buyer twenty, so nine, there is no nine.
Teaching Assistant: Six.
Professor John Geanakoplos: Nine sold to twenty at a price of what? Six.
Teaching Assistant: Sorry.
Professor John Geanakoplos: That's okay. So seller six sold to twenty at a price of twenty.
Student: Yeah, even though it's cheaper <<inaudible>>.
Professor John Geanakoplos: No, no, buyer twenty paid twenty, so seller six did well. We won't ask who buyer twenty is. Buyer twenty is going to screw everything up. So Buyer fourteen through--I can't read this either.
Teaching Assistant: Forty-four.
Professor John Geanakoplos: Buyer fourteen sold to buyer forty-four for twenty, and buyer twenty sold to buyer forty for twenty-two, and seller twenty-four sold to buyer thirty for twenty-five. So five people traded, now which five were they? The sellers were ten, six, fourteen and twenty-four, one, two, three, four, five, the bottom five. The five buyers were thirty-six, twenty, forty-four, forty and thirty. So basically forty-four, forty, thirty-six, thirty, twenty-six didn't buy, twenty bought instead. So if you look at it, so it's not quite the way theory would have predicted, but almost. If you look at it, if you just shuffle the order and you put the sellers, instead of from top to bottom you put them from bottom to top, you get what looks like a demand curve and a supply curve. And so what happened?
All these five people ended up selling, one, two, three, four, five, those are exactly the sellers. The price they sold for was all between twenty and twenty-five, and the five buyers were forty-four, forty, thirty-six, thirty. Twenty-six didn't manage to buy, but twenty bought. So what is the theory of the free market? The theory of the free market says, "This chaotic situation where they had less than two minutes to decide what to do could be analyzed as if you put a demand curve together with a supply curve and there was one price that they miraculously knew. Here it should have been twenty-five. It turned out to be twenty or twenty-two that all the trade took place at. At that one price you get all the trades happening. The people have the highest valuation buyers they're the ones who get the tickets. The people with the lowest valuation sellers sell it. So the people who end up with the tickets are these red guys at the top and the blue guys at the top. All the tickets go from the people who value the stuff least to the people who value it more. So the market has done an extraordinary thing in two minutes.
So there was one mistake. Mister or miss twenty, whose identity we are protecting, although I'm searching the faces, mister or miss twenty got a very bad deal. She or he, let's say he, bought at twenty when the value was twenty. That was a horrible deal. He didn't get any extra out of it. So he should probably have only bought if the price were lower, and then twenty-six would have bought instead of twenty. So twenty sort of squeezed his way into the market, so twenty-six and twenty between them somehow there was a slight inefficiency. But basically with no training, no background, no practice, these sixteen undergraduates managed to reproduce--they gathered all the information in the whole economy, and they discovered who were the eight people who valued the tickets the most and they ended up with all the tickets. For me to do it and sort it out would have taken longer. The market solves a complicated problem, and gets information incredibly quickly, and puts things into the hands of the people who value it the most. And the marginal buyer thought it was worth about twenty-five or twenty and that's what the price turned out to be. So anyway, we're going to come back to this parable at the beginning of the next class.
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