Financial Theory

ECON 251 - Lecture 26 - The Leverage Cycle and Crashes

Chapter 1. Introduction [00:00:00]

Professor John Geanakoplos: What I'm planning to do today is to spend a half an hour or less just telling you a little bit about what a new theory might be, what I call the Leverage Cycle, and then spend the rest of the time maybe answering questions about the course that you might have. I could, if you wanted to, devote the whole time to what the new theory is, but why don't I at least pause after a half an hour and see if you have questions?

So what is the thing that's been missing from the entire course and has been missing from economic theory, I think, almost entirely for all these years, and certainly missing from all the textbooks that you might have looked at during the course of the semester, and you remember there was a list of 20 books or something you could have read, and that's the idea of collateral.

It's the idea that in order to guarantee that you're going to keep your promise you have to put up collateral, and people just don't trust in everyone else keeping their promise, they want collateral. So if you put that into the model what sorts of things might be different? So I want to just work out an example so you can see how they might change.

I want to talk about an example that's going to illustrate what happened in our crisis. And I guess that it's a little interesting that I wrote this and I presented this in 2000 at the World Congress, and it got published in 2003, so this was long before the crisis. Now, as I said, there had been other smaller crises before in 1998, maybe '94, maybe '87, certainly '98, and of course I was thinking about these previous crises when I built this model, but not many other people thought much of those other crises.

And as it happens, this last one that we're still at the bottom of, or a little past the bottom of, I think is very similar to the ones we had before, but just much bigger. So here's my simple version of it.

I'm going to give two models, a very simple one with two periods and a slightly more complicated one with three periods, and of course all the interesting things happen in the three-period case, but just to make it simple to understand I'm starting with the simpler one.

Chapter 2. Understanding Leverage [00:02:15]

So suppose that there's a security which I'm going to call Y that everybody holds. Why is there no chalk? Gosh, I taught the class in here, I just finished lecturing in here with a whole box, oh here it is, a whole box of chalk. So suppose that there's a security Y that I'm going to think of as a mortgage security, or you could think of it as a house, or you could think of it as an oil well that has uncertain output in the next period. And then there's going to be something like gold that I'll call X.

So this might be like gold, and this might be like a mortgage security, or like an oil well, or you might think of it as a house, but I'll think of a mortgage security, an oil well. It's something that pays an uncertain outcome in the future, and this is something that's very stable and you know exactly you've got gold this period, if you just save it you'll have the same gold next period. So now people are going to differ according to how optimistic or pessimistic they are.

That's my idea of, not everybody's the same. So I imagine that there are two possibilities next period. Either the Y, the oil well, could produce--it's a gold-well really. It could produce 2 pieces of gold, I mean, 1 piece of gold, or it could produce .2, 20 percent of a piece of gold. So everybody begins with 1 oil well, 1 mortgage security and 1 piece of gold, so they can consume the gold or they can make it a filling for their teeth, or they can wait next period and then they'd have it in either state next period because it's perfectly durable, or they could use the gold to buy more oil wells, each of which might pay off 1 or .2. So that's it.

Now people care about the consumption of gold. The only reason to get the oil well, as Fisher, as we've assumed all through the class, the only reason to get the oil well is that it might produce gold for you next period, gushing oil, money, gold.

It might gush some gold for you next period. So people care about consumption, how much gold they eat here, times the probability that they're going to be up here, times how much they eat here, plus the probability that they're going to come down here, times how much they eat here. In other words they are risk neutral with no discounting and they just multiply consumption here and here by the probabilities and add the consumptions, and then add it to the consumption here.

Everybody's got the same utility, but with one difference. H is the probability agent H attaches to going up. So I think of these people as a continuum of buyers now. Instead of 2 buyers like we've always had, or 3 buyers, or even 1 buyer , I've got a continuum and they're different because some are more optimistic than others.

Now, this is stuff that we haven't really paid much attention to before. So these optimists are the people who have H very close to 1, and lots of other people have Hs in the middle, and there are some people who think H is 0. That's the way they differ.

So of course the very most optimistic person thinks the oil well is worth 1 piece of gold. He doesn't discount, and he thinks he's going to get 1 for sure, so he'd be willing to pay 1 for it here. The most pessimistic person thinks the oil well is only worth .2. And let's say she'd only be willing to pay .2 for it here. So what's the price of oil wells going to be?

Well, if we just had our usual model, a one period model, we would see that the people with the high H would sell their gold to buy more oil wells because they thought it would be valuable, and the people with the low Hs, thinking the oil wells weren't worth much, would sell them to the high H people to get more gold in the present. That's basically what would happen. And you'd get some dividing line where the people above A would be buying oil wells, spending all their money.

And the people below A would be selling oil wells and getting more money. So, for example, if A was .69, which is what it's going to turn out to be, Mr. A, what does he think the value of an oil well is? He thinks it's .69 times 1 + .31 times .2 which is .06, so .69 + .06 is .75. So Mr. 69 thinks the oil well's worth about 75.

Everyone above him thinks it's worth more than 75, so if the price were .75 everyone above would want to buy and everyone below would say it's not worth .75 so I'll sell it, and since they're risk neutral their valuation is independent of how much of it they have. So these people below would want to sell everything, and these people above would want to buy everything.

So that's nothing different from what we've done from the very beginning except that maybe the one difference is people would go to the extreme. These guys would spend all their money buying oil wells because every time they bought an oil well at a price of .75 this guy, for example, was sure it's worth 1. The more he buys the better he is. So he'd spend all his money in oil wells and these guys would sell all their oil wells, but other than that it's very similar to what we've done. So what's the difference going to be?

The difference is just one thing. Where do I divide this dividing line A? Well, can these guys up here afford to buy all these oil wells? Well, the answer is, so far, it doesn't look like that's possible, because if the dividing line is way up here these guys up here don't have enough money to buy all the oil wells down here. After all, they only have 1 piece of gold apiece and if the oil well costs 75 they can each buy 1 and 1 third.

If you multiply that by 1 and 1 third you're never going to buy all these oil wells down here. So this seems like it's too high for A to be. So the new twist is, maybe the guys up here who want the oil wells, who are so sure they're going to do well, maybe they can borrow money to buy the oil wells. So they can make a promise to pay money in the future, maybe .5 and .5 in the future, say, and then sell those promises, borrow money in other words, promising in the future, and then use that money to buy more oil wells. So that's what people do in the market.

Any hedge fund, the three definitions of a hedge fund, the three defining characteristics of a hedge fund, I think I might have said once, are, a) that they hedge, so unlike other money managers they're always trying to hedge. And we talked about what hedging is. And many, many more managers are doing that than ever before. It's different from 50 percent of the people, but not from, you know, the hedge funds are 5 percent and the other 45 percent are also hedging, so that's not so different.

The second thing they do is they borrow money to make their investments. A lot of these other managers aren't allowed to borrow. They may not be allowed to hedge either. Those are called long only managers. They can't hedge. Some of them can't borrow. Hedge funds hedge and borrow, and then hedge funds charge high fees. That's the third defining characteristic. But anyway, so they borrow.

And in the economy, I told you last time, a huge number of people borrowed a huge amount of money. So borrowing is obviously very important. So how much are they going to be able to borrow? I mean, this guy, number one, he'd like to borrow as much as he could. Every time he borrows money he's sure that he's going to be up here, so every time he borrows 1 dollar he gets to make an investment that he's sure is going to be a great investment, and he's planning on paying everything back because he's sure he's going to go here, so he's going to be incredibly rich. So he's going to pay back what he borrows, but he's going to get such a profit he's going to make a fortune.

So if people could borrow however much they wanted to, and promise to payback, this guy would borrow everything, Mr. 1, I mean, would borrow everything and imagine he was going to get up here for sure, and imagine he was going to keep his promise for sure, and he bid the price up almost to 1. But now, who's going to lend to him and how much will they actually lend to him?

Well, in our old world we didn't worry about who was going to lend. Everybody assumed they were going to get paid back, but in reality people don't assume they're going to get paid back.

The lenders are going to say to themselves, "Wait a minute, if this guy promises us to pay us, say, .5 and .5 maybe he'll be very rich over here and he'll be able to pay us back, but I'm not sure he's going to be so rich here. I don't even know what he has. How do I know what the borrower is going to actually have in these states?” I don't want to look into his personal bank account and find out everything about him. That's the way, banks who lend sometimes do that and they go to a lot of effort to check how reliable a borrower you are, but people in general, most of the lenders, you don't want to do that.

That was the idea of securitization. We don't have to have so much careful looking into the personal finances of everybody. Much simpler is to use the asset Y as collateral. So if Y is collateral, what does that mean? When you lend 1 dollar to a borrower the borrower just doesn't borrow the dollar promising to pay something back in the future. The borrower says, "if I don't pay you back you can take the asset."

So the question is, for each unit of the asset Y, how much can you borrow when you have the asset as collateral? That's the question of leverage. So if you take the value of Y divided by the cash down--so let's do two numbers. So the borrowed, dollars borrowed using Y as collateral, that divided by the value of Y, that's what we call the loan to value, LTV, loan to value.

Another way of saying that is the borrowed, if you take Y, dollar Y minus dollars borrowed, that--let's write it in the denominator. Dollar Y minus dollars borrowed, and here you put value of Y, so just dollar Y, in other words. The dollar of Y minus the dollar borrowed, that's the cash you had to put down. So that's the dollar of Y divided by the cash down. That's what's called leverage.

Chapter 3. Supply and Demand Effects on Interest Rates and Leverage [00:13:45]

So, and it's obviously the same thing as loan to value because you just sort of invert the number and do a subtraction, you get leverage. So if you knew the loan to value you'd know the leverage and vice versa. They're the same thing. So what should the loan to value be?

And so as I said, historically what's happened over the last ten years for housing is you had to put 14 percent down. The leverage was 7 for buying houses, non-agency houses, non-prime houses, starting in 2000, and then it went to 33 or 35 to 1 because you put down less than 3 percent in 2006. So this leverage shot up and then it suddenly collapsed. You had to put 25 percent down, so leverage fell to 4. So that, I'm going to explain, has a big effect on the price of housing and the price of mortgage securities.

So what should leverage be? How can supply and demand determine what leverage is? So it seems like you've got to clear all these markets. You've got to figure out how does the Y market clear, how does the gold market clear, and then on top of that you have to figure out leverage. It seems like it's a lot of complicated things to figure out.

And I think economists just thought, "Oh, there's so much going on, and people are really generally keeping their promises anyway, let's ignore the fact that you have to have all this collateral." Well, I think that collateral is the heart of the problem in finance. So how would it work in this model? So are you with me about where we're going? So you have to conceptually figure out how to think about the problem.

In other words, conceptually, the question is, how can supply equals demand, which sounds like one equation, how can that determine the interest rate, supply equals demand for loan, how can that determine the interest rate and the leverage? It seems like you have one equation and how can you determine two things with one equation?

Well, the answer is that you can do it, but first we need a conceptual framework to think about it. So it seems like a contradiction almost, a mathematical contradiction, so it must be that the problem is ill posed, and so I claim it is.

So what you really should be thinking is that there's not just one interest rate, and one leverage, you should be thinking that there's the promise and then there's the collateral and those things taken together define the contract. So let's say the promise is .2, .2, and the collateral is 1 unit of Y, .2 of X, .2 of X.

So you're promising 2 units [correction: 0.2 units] of gold in the future and you've got 1 unit of Y as your collateral. So that implies a delivery of .2 and .2. Why is that? Because in the good state at the top the collateral is worth 1, so if you've made the promise and the lender can seize your collateral if you don't pay, you're going to either pay .2 or he's going to seize the collateral, and so you're going to pay .2. Maybe you'll sell some of the collateral to pay .2. And if the promise is .2 down here, the same thing, either he's going to seize the collateral, the lender will seize the collateral or you'll sell it and keep your promise.

In either case it'll deliver .2 and .2, and it's going to sell for some price. And the price is actually going to be 1, so the interest rate effectively is 0. Now, why is that? Well, because at time 0 over here no one discounts the future. Gold at the beginning is worth exact--to everybody--a unit of gold at the beginning is the same as a unit of gold at the end in both states because everyone's probabilities add up to 1. H + (1 - H) is 1.

So you might as well consume at the beginning or for sure at the end. So since there's a lot of gold sloshing around here there are always lenders willing to lend at a 0 percent interest and they're getting their money back for sure. So it'll turn out that the interest rate on this kind of loan, which is riskless, is going to be 0, because no one's discounting and they're getting their money for sure.

But what if you promised .3 and .3 with 1 unit of Y as collateral? Then what would the delivery be in that case? Well, the delivery wouldn't be (.3, .3) because the only thing protecting the promise is the collateral.

The delivery would be .3 and .2, right? Because in the up state your collateral is worth 1, and so you would be forced to pay the .3, in the down state you would do what a lot of homeowners are doing now and say, "Okay, I owe you so much money. My loan to value is 150 percent. The value of my house has gone down to 2 thirds. The loan is 150 percent of the value of my house. I'd be crazy to pay you 150 percent. Effectively I don't own my house. I owe so much more on my house than the house is worth. I can't give it to my children. I can't do anything with the house anyway. Why should I just pay such a huge amount of money? I might as well just give up the house."

They walk away from the house and the lender gets .2. So (.3, .2) would be the delivery, and of course if it was .4 and .4 it would also be .4 and .2.

Now, if you made this promise of .3 and .3 you'd be delivering something more than .2 at the top. So the price, of course, would be more than .3 [correction: more than 0.2]. So the price might be--price of the .3 promise will turn out to be something like .261, say. It might be .261.

Let's just say .261. So effectively you're borrowing .261, you're delivering .3. This is the .3. This is up here, pi.3 = .261, the sub .3. So effectively your interest rate is, in the state when you can pay back at the top, your interest rate is .3 over .261. It's like 14 percent or 15 percent actually. It's 15 percent, so .3 over .261 is 1.15, so this over here means 15 percent interest.

So you've effectively, because they know you're going to default in one of the states you have to pay much more than you borrowed in the good state. So effectively you're promising a 15 percent interest. You're promising it in all the states. You're only delivering a portion of what you promise in the bad state.

All right, so what's my point? My point is that the apparent contradiction, supply equals demand determining both interest and leverage, is no contradiction at all because actually we've got many supply equals demand equations.

There are many different loans depending on the ratio of the collateral to the promise. There are many different loans and each of them sells for a different price. So we've got many different things we're determining, many interest rates, but one supply equals demand equation for each one. So every supply equals demand equation produces one price. There's no contradiction.

Chapter 4. Impatience and Volatility on Setting Leverage [00:21:52]

However, that still leaves us with the question, which of these many contracts are going to be traded? Can we say that the economy as a whole has a single leverage? And there the surprise is, and this is the end of the first part of the model, the surprise is, yes we can. Only this one is going to get traded.

So everybody in the economy, no matter how optimistic you are or how pessimistic you are, even though you have the available chance to make a bigger promise, and of course having to promise a bigger interest rate, sorry, there's the interest rate. Even though everyone has available that opportunity, they won't avail themselves of that. Everybody will trade on this promise. So how could that be?

And by the way, before we answer that question let's just see that if everyone used this promise that in fact the price we talked about before would prevail. So why is this .69--that A should be a little lower, it doesn't look like .69. It looks a little too high, but anyway it's supposed to be 69 percent of the way up.

Why is that the right price? Well, how much could these guys buy? Well, the top 31 percent, what can they do? They've got .31 cigarettes. So I'll write it over here. They've got .31 cigarettes between them. The top 31 percent are the buyers, right? So we've got 31 percent here and 69 percent of the people down here, and here's A = .69. So these guys have .31 cigarettes between them.

Now, if they promise, every time they buy an oil well they promise .2 units, every one of them, they're going to buy all the oil wells in the whole economy. So however many people there are here, let's call it mass of 1, maybe it's a million people, mass of 1, they're going to borrow .2. So this is their own gold and this is borrowed gold.

Student: When you say cigarettes you're talking about gold?

Professor John Geanakoplos: Did I say cigarettes? Yes, I meant, yeah. It's another example of gold. I meant gold. So you could think of gold, consume it now or consume it later. Cigarettes you can consume now or consume later. I have all these things in my head of what I could have interpreted, so yeah, I mean gold.

So you can consume the gold, thank you, the gold now or the gold later, so each of these guys owns 1 unit of gold. So 31 percent of the population has 1 unit of gold. So you've got .31 total units of gold.

They end up buying all the oil wells, and so how much can they borrow on all the oil wells using as collateral? So the oil wells they started with, they borrow using those as collateral, and the oil wells that they buy they also use as collateral. So they've got all the oil wells. They're making the (.2, .2) promise but it has a price of 1. There's no interest. The interest rate is 0, so they're borrowing .2. So the total amount of gold that they have at their disposal is .31 + .2, and how many oil wells do they have to buy, 69 percent of the oil wells, .69.

And if you take 31 and 20 that's 51 over 69, which is about .75, which is exactly what I said the price is that's going to make this guy, Mr. 69, exactly indifferent to buying or selling. So all the people up here are going to say, "At the price of .75 it really is a good deal, I want to buy and borrow as much as I can."

People down here are all going to want to sell. The people up here with the money they started with plus what they can borrow are going to be able to indeed buy all these oil wells at a price of .75. That's what we just found and that's why that's the equilibrium. Did that go too fast, or almost too fast? Yeah, question?

Student: I was just wondering, for the price of the .2 pounds, why is that 1?

Professor John Geanakoplos: Because you're going to get the money for sure. So how much money is being lent, basically .2. So there are a huge number of guys down here. Their total amount of gold is .69, right? There's one unit of gold in the whole economy.

They own 69 percent of the gold and they're only lending in total .2. So there's lots of extra gold that they have that they're not lending. They don't care whether they get gold now or gold later because there's no discounting and they're getting the money back for sure. So competition between these lenders is going to drive the interest rate all the way to 0.

If the interest rate were positive they'd all want to rush in and lend because then they're going to get more gold out at the end than they had at the beginning and there's not discounting. So the competition among lenders will drive the interest rate down to 0, and they're guaranteed to get paid back because the collateral's big enough. You had a question?

Student: I'm still confused. For the first state if you only promise to pay .2 in the future, so shouldn't the price be .2 right now?

Professor John Geanakoplos: Oh, and I said the price is 1. Yes. The price per unit is .2. Yeah, that's horrible. Thank you. The price is .2, exactly. The price is .2 for the promise of (.2, .2). It's price of 1 per unit promise. The price is .2, exactly. Gosh, what a terrible mistake.

Thank you very much. It's .2, exactly, and that's why these guys they're able to--they're promising .2 and the price per unit promise, so this price was, yeah, its price is .2. So per unit promise their price is 1, in other words. So they're promising .2 and per unit promise the price is 1, so the price of the whole promise is .2, exactly, so it's just that, so that was--so the price is .2.

Using the whole of the economy's worth of oil wells as collateral you can promise 20 percent of all the gold and then you're going to get--you'll be able to borrow doing that the same amount, 20 percent of all the gold, because the interest rate's 0. Yes?

So that's why this total amount of gold that they can get their hands on, some people call it liquidity, all the stuff they can get their hands on, capital, they take all that and they buy all the oil wells they can. This is how many are being sold, and that's therefore what the price is. The ratio of 51 to 69 is almost exactly .75, so I'm rounding off a little bit.

And that's why Mr. A of .69 is indifferent at this price to buying or selling. The guys above him all want to buy. This is how much money they can get their hands on and therefore what they can spend. All these guys want to sell. That's what they're selling.

That's why this justifies the price, and these guys are the ones lending to these guys. The pessimists have nothing to do but lend because they don't want to buy the asset. Does this make sense? I'm just going to repeat the same thing with a three period model where it gets more exciting, but the logic of this is critical. So is everyone with me?

Now, there's one thing I left out in this one period model, two period model, which is what about the (.3, .3) promise? The optimist, H equals 1. Take that guy. He says to himself, "I can't lose. Why should I be satisfied with only promising (.2, .2)? Why don't I make a bigger promise like (.3, .3). With my bigger promise I get more money today, and with that extra money today I can use it and buy an oil well, and I'm going to make a profit of 33 percent. My .75 is going to turn into 1 for sure, so why isn't that just a brilliant thing for me to do? Why should I be satisfied? The more oil wells I get my hands on the better I seem to do."

So why is he not making the (.3, .3) promise? So it sounds like he ought to, but if you think about it one more minute you'll realize that he shouldn't. And why is that, because he could promise (.2, .2). So if he makes the (.3, .3) promise of course he has to give up the (.2, .2) promise because the oil well he used as collateral for the (.3, .3) promise he no longer has available for the (.2, .2) promise.

So the question isn't, should he do a (.3, .3) promise. Well, if that was the only thing he could do of course he would do that, so of course it looks profitable, but he's already got a great profit opportunity. The question is, is it a better profit opportunity and the answer is no.

Why is that? Because he is still delivering .2 down here when he makes the (.3, .3) promise, but when he makes the (.3, .3) promise he delivers more at the top, namely .3, but that's the state he's sure is going to happen. So compared to the (.2, .2) promise he's giving away more money just in the state that he thinks is going to occur.

That's very expensive for him. That's a horrible thing for him to have to do. And who's lending him the money? It's the guy down here, and the guy down here, that's the pessimist. He doesn't think that top state's going to occur so he's only willing to pay extra money at the beginning--he's not willing to pay very much extra money at the beginning because he's going to get stuff in a state he doesn't think is going to happen.

So anyway, I don't have time work it all out, but if you think it through you'll realize that nobody wants to do this trade, because the guys at the top who seem to have the greatest advantage in borrowing more, when they borrow more in this way where they're defaulting, they're actually paying more only in the state that they think is going to occur and the people doing the lending are getting money only in the state they think won't occur. So both of them think it's a worse arrangement than the original (.2, .2) arrangement, and so even though there's a price and it's available to be traded nobody will want to trade it.

So the market does indeed pick out a single leverage, and what is the leverage? The leverage as we calculated from this number is the price of the asset, which is .75 divided by the cash down which is .55, because you can borrow .2, and that's 1.4 or something. I don't know exactly, but let's say 1.38 leverage, 1.35 is the leverage. So it's not that high, the leverage.

And the principle is, that we just discovered when you have this kind of heterogeneity, different kinds of heterogeneity produce different amount of leverage, and I'm not going to be able to talk about that, but with this kind of leverage the promise will always be the maximum for which there is no default. That's how much borrowing is going to happen, and the market's going to allow.

So in what market do we always see that happening? In the Repo market, it's a one day market overnight. You put up a security as collateral, and you can borrow money on it, and there's almost never any default on those markets.

Even in the tremendous crisis we just had almost zero defaults in the Repo markets. Mortgage markets there were defaults, but there the heterogeneity isn't just how optimistic you are, it's whether you like to live in the house or not, so it's a different case which I won't have time to cover. So this is part one. We're just going to say the same thing in part two. I'm going slower than I thought, but anyway, the last model is going to be part two. So are there any questions about that? Did this first part... Yeah?

Student: Maybe this is sort of a silly question, but...

Professor John Geanakoplos: I'm sure it's not.

Student: Are there some lenders sort of in the middle like more optimistic pessimists who think the upstate is more likely to occur so maybe they're willing to lend more money?

Professor John Geanakoplos: There are. There are a whole continuum of people between 0 and 1, so the guys in the middle they really don't have any choice here. You see in the next model there's going to be a difference, but now you really don't have any choice. If you're above A you should buy to the maximum. If you're below A you should sell everything, and you don't care if you lend or not because you're definitely going to get paid back. So they're all willing to lend.

Chapter 5. Bad News, Pessimism, Price Drops, and Leverage Cycle Crashes [00:34:48]

So let's now go to the next model. So that was a great question. So far we only get two categories of people, buyers-borrowers, sellers-lenders, so we're going to move beyond that in the next example. Any questions about this one? So we get equilibrium leverage and leverage has a tremendous effect on the price.

Why does it affect the price, because the fact that these guys were able to borrow so much money is what made the price so high. If they couldn't borrow that would wipe out this .2. They couldn't have borrowed that, so they would have only had this much to spend, so the price would have had to be much lower.

And of course these guys wouldn't have been able to afford all of this. So as the price gets much lower more people would want to buy and you would have the marginal buyer down here, and there'd be a much lower price. So this borrowing is what jacked up the price.

Leverage means high prices. It seems like the most obvious thing in the world and commonsensical thing in the world, but remember it never got mentioned in this course, right? It never gets mentioned in any textbook. The price is supposed to be the fundamental value, the present value of all the dividends, or the expected present value of all the dividends, meaning minus the covariance or something.

Where was leverage in that formula? It didn't happen because we didn't have the idea. We assumed that everyone could borrow as much as they wanted to, but here we see that they can't borrow as much as they want to. They're limited in how much they can borrow, and because they're limited it's going to turn out, if you make the limit less severe they're going to borrow more and the price is going to be higher.

So you ignore leverage by saying people can always borrow whatever they want to, then it never gets mentioned, but it's the heart of the matter, I think, at least in a crisis. So let's just do one more version of the model, which is this same thing, but now with 1 extra period. So what's the extra period going to do?

The extra period is, we've got instead of two periods we have three periods. So what's going to happen is the .2 only happens with two pieces of bad news. You have to go down twice to get .2. Otherwise Y pays off 1. And everyone's going to begin at the beginning there with 1 unit of Y and 1 unit of gold just as before, and they could consume in the middle, or they could consume in the end, but they have no more endowments.

All their endowments are right at the beginning, 1 unit of Y and 1 unit of gold. There's no discounting. They just care about the expected consumption. The difference is now it takes two periods to see the realization, so two pieces of bad news. Now, why is that interesting, two pieces of bad news?

Well, when I was in the crisis both in '98 when I thought about this model, created this model, but also recently, is people start to realize things are going wrong. So if something goes wrong and now everyone says, "Well, things are still okay now, but I realize we're closer." It takes a lot of things to go wrong for things to collapse, but each time one of them goes wrong you're a little closer to the collapse.

So I make the assumption that agents are all identical except agent H--high H means you think you're going to get up moves, but there are two moves, at the beginning and also in the second period. So if you're an optimist about the first up move you're also going to be an optimist about the second up move. Now, let's suppose your H equals .87, say, just to pick a number, which it's going to turn out to be a pivotal guy.

Mr. 87 at the beginning, the chances of going down are 13 percent for him, then 13 percent more, so the chance of getting a disaster, he thinks, is 13 percent squared, 1.69 percent, under 2 percent. So he thinks the value of the asset is over 98, under 2 percent here the rest of the 98 must be over there somewhere, so obviously his valuation is over 98.

Now, once he gets down to here he realizes the chances have gone from 1.69 percent to 13 percent. So his valuation is going to be a little bit more than 87, because it's going to be 87 percent of that and 13 percent of that, so it's 87 plus a little bit. So he's going to go down from 98 something, to 87 something.

So of course when the first down state happens everybody gets more pessimistic including Mr. 87. He now thinks that the asset value maybe went from 98 to 87, which is an 11 point drop, and everybody's going to have a drop. He went from 98 plus to 87 plus a little bit. So it's an 11 point drop is what he thinks happened. So you can see this is bad news.

When it takes two things to go wrong the first piece of bad news people are going to take it as bad news, but the interesting thing that happens is that actually they get more uncertain. Things go up you get 1 for sure. Now you've learned something. There's no uncertainty. Here the move down created more uncertainty than you had before, and not only that, more disagreement. I mean, Mr. .9 and Mr. .8, neither of them thought there was much chance of getting down to here. .9 thought 1 percent squared, that's negligible. .8 thought 2 percent squared; that’s .004.

The difference between negligible an .004 is still negligible, practically, so they hardly disagree here, but once you get down to here they're both starting to get more worried and they're actually differing a little bit more than they did before. So that's what I think happens in these crises. You go from everyone knowing if 25 things in a row go wrong we're in trouble, but nobody's really thinking, except the guys at the very bottom, that all of this stuff can go wrong.

But once each thing goes wrong now everyone gets more and more worried and there's more separation between what people think. So that's just description of the model. So what's going to happen is the question. So we're almost at the end here because we don't have to do much more calculations. So what will the prices be at the beginning and down here, and what will the leverage be at the beginning and down here?

Well, remember our principle that the leverage will always be worked out in this case of heterogeneous beliefs so that people can promise--so there will be no default. The maximum promise is the most you can make without any chance of default. So you can see that--I'll tell you what the prices are.

They're going to be that. So if you made a two period loan, a long loan, a lot can go wrong over a long loan. You can get all the way down to .2, so you're not going to be able to borrow very much if you make a two period loan. If you make a one period loan, in a day not much can go wrong.

That's why these Repo markets are so short. In one day practically nothing can go wrong, well here something does go wrong, but you can fall to .69. It's a lot better than .2. So you could borrow at the beginning .69. That'll be the equilibrium promise at the beginning, will be .69 with no interest. The equilibrium promise here will be .2 with no interest. The equilibrium promise there will be 1 with no interest.

So this turns out to be the equilibrium. Why? Notice how shocking it is. Nobody thinks the price drop from 95 to 69 is justified. That's a huge 26 percent drop. Mr. 87, he thought the price should go from 98 to 87. That's an 11 point drop. Mr. 1 thought it was worth 1 at the beginning. He still thinks it's worth 1. That's no drop. Mr. H equals 0 thought it was worth .2 at the beginning and still thinks it's worth .2. That's no drop.

No matter who you pick, I think the worst one is .5, .5 thought it was worth--we have to figure it out, 25 percent chance of going down here, 75 up there. So .75 + .5 is .8, right? 25 percent of .2 is .05. So Mr. H equals .5, thinks the expected payoff is .8, 75 percent of one of those 1s, and 25 percent of .2 is another .05. So .75 and .05 is .8. So he thinks down here where he's a .5 it's now worth .5 and .5 of this. It's .6. So he thought the drop would be from 80 to 60, a 20 point drop.

That's the biggest drop anybody could imagine, 20 points. Most people are at 11 points or 0 points or something like that. Nobody's at a 26 point drop. That's way bigger than anybody could imagine is justified by the bad news in the economy, yet that's what the equilibrium becomes, from 95 percent to 69 percent. So why is that?

And that's the end of the story. What happened in the drop? Well, three things went wrong. The first thing is that 87 is the marginal buyer, so everyone above him bought. All these optimists were buying. Everyone else sold and lent money.

Student: You just assume that, right.

Professor John Geanakoplos: What?

Student: You just said let's assume 87 is the marginal buyer?

Professor John Geanakoplos: I'm assuming that and it's going to turn out to be the correct answer. Now, how did I know 87? Well, you'll see at the end. Yeah, question? No. Just fixing your hair, that's okay. So Mr. 87 is the marginal buyer. So those guys at the top bought.

Now, how could they afford to buy so much? Well, they're borrowing so much. They're borrowing .69 plus they already had their .31 [correction: their .13], so together they can spend .69 + .13.

That's .82 that they're spending and they're only buying 87, and so 82 over 87 is about 95. So there's a little rounding going on. So that's why the price is .95. Now, why did it crash to .69?

It crashed because look what happened. These total optimists at the beginning, the top 13 percent, they spent all the money that they had, their 13 percent gold, they spent the 13 percent. They borrowed everything they could to the hilt so they owed .69 in both states. So what happens to them here? They spent all their gold and they owe the total value of their collateral. They're wiped out here. They've got nothing left. So the most optimistic people in the economy, they're just out of the economy. They've all gone bankrupt.

So now we've got a smaller population with less optimistic people, and so these new optimists are going to do the buying now. Well, first of all they don't think the asset's worth as much for a bunch of reasons. One is they got bad news, so the people who are left don't think it's worth as much as they did from the beginning.

Plus the most optimistic people at the beginning aren't there either, and then lastly and most importantly the people who are left can't borrow very much money because the leverage at the beginning was .95 over .26, you could borrow 69, so you had to pay down .26. That's 3.6 leverage. Here the price is .69. You can only borrow .2, so you have to put .49 down. The leverage is 1.4.

So you went from 3 and 1 half leverage to 1 and 1 half leverage. The leverage collapsed, and so these guys who are left they are not as optimistic themselves because they've got bad news, the most optimistic people are gone, and the people who want to do the buying can't borrow as much. So there are three reasons that drives the price down. The marginal buyer becomes a much lower guy than before, and so that's why the price is lower.

It's not just the bad news because Mr. 87 would never have justified that drop. It's because the thing has fallen into more pessimistic hands. So all those bankers and hedge funds who bought all those mortgage securities at the beginning, they've been wiped out by now. They're way up here. They can't buy. They're much more sober people who are left who also know we've had bad news. They're willing to pay less to begin with, and they are more pessimistic, and they can't borrow very much, so the price drops for all those reasons.

I think that's the essence of the crash. Three reasons, the people going bankrupt who are the most optimistic buyers, the second reason because the news was bad. That's the first reason. The news was bad, optimistic buyers going out and the leverage collapsing, so the price drops a long way.

Chapter 6. Can Leverage Be Monitored? [00:48:01]

So I'll end with one more slide and then sum up.

The last slide is his question about the classes of people. It's a little different now than it was before. There are different classes of people. So let's just think about this. Why was the marginal buyer Mr. 87? I mean, after all we just computed, Mr. 87 thinks the value of the asset's 98, not 95. Mr. 86 also thinks the value of the asset is 98 about, so why didn't 86 buy? He was getting a good deal at the beginning. Why wasn't 86 buying when he thinks it's worth 98 here?

Mr. .86, remember, is not supposed to buy. He's going to buy the next time. See Mr. 86 there, he's the cautious optimist. Mr. 86 there, just below 87, he's going to buy after the crash, but he's not buying now. So why is it that he's not buying at the beginning?

Well, so this is the only subtlety, but it's the answer to your question. Mr. 86 says to himself, "I can make a profit. I think it's worth 98 and I only have to pay 95. That's like a 3 percent expected return and I'm risk neutral so that's great. If I'm right it goes from 95 to 100. I can get 5 percent. On the other hand, maybe I should wait for the crash. If the crash comes I only have to pay 69. I can get 40 percent return, 31 over 69, whatever that is. I can get a 40 percent return if there's a crash. That's much better than my 5 percent if I'm right." So that guy is waiting to make money in the cash.

So of course by waiting and buying in the crash he's helping to reduce the terrible calamity, because he's a buyer. If we just had more people like that--I think of that as Warren Buffett, I called him the cautious optimist, all the way down to Mr. .74. Mr. .75, for example, also thinks the asset is worth more than .95 at the beginning, but he doesn't buy either, so all these people, the cautious optimists, they're holding out for the crash and the crash would be much worse without them, but they don't eliminate the crash because there are not enough of them.

So here are the three classes of people you were thinking about. They're not quite as optimistic. They still think it's a good buy, but they decide not to buy waiting for the crash. Now, how did I know that it would stop at 87 and 74? How did I get all those numbers? Well, I don't have time to derive them, those are the equations, but I can explain it very simply.

You see, thinking you're going to take advantage of the crash means you must have a high H. You think if things go here they're still going to end up okay. That's why you think there's a big profit opportunity.

But if your H is too high you don't think you're ever going to get to the crash. So you've only got this small intermediate group of people, the Warren Buffett like people, who are optimistic enough to think that we're going to pull out of our depression, pull out of the crash and still there's a profit opportunity, and yet think that the crash is likely enough so that they'll wait for it.

People who think they'll make a bigger profit, higher H once the crash starts, well, they don't even think the crash is going to happen. So I've made a big assumption that the people with high Hs always have high Hs, but I think that's life. I think that's not a bad assumption. Every hedge fund guy I've ever talked to who thought that this was a low probability event also thought we were going to come out of it and things wouldn't be that bad.

So I'm not saying that these people don't learn. Everybody learns. When they see the first piece of bad news they're more pessimistic. You go from 1.69 percent to 13 percent. So it's not like people aren't learning. They are learning, but relative to the rest of the population if you started optimistic you stay optimistic, and that's why there's only a small group of Warren Buffetts who can save the situation.

So that's my model of the leverage cycle, of what happens. Three bad things happen, bad news, can't do anything about that, the leveraged buyers get crushed, go out of business and leverage collapses. And when the prices are really low the whole economy is suffering tremendously and innocent people who had nothing to do with all these markets, the price of everything, every asset is low so they can't borrow. They can't get loans. Margins are so tough. They're small businesses. They can't borrow.

They're totally crushed down here, so how would we save the economy? We'd undo the three things that happened. We can't undo the bad news, but the three things that happened were uncertainty went up. It wasn't just bad news, it was scary bad news. So this gap between 1 and .2 is much bigger than that gap.

That's why the leverage went down. Volatility went up. So you have to contain the bad news. That would help. You have to contain the bad news, that's A. So you can't eliminate the bad news, but you can contain the volatility of the bad news.

Secondly you have to increase the leverage, and thirdly you have to make up for the people who've gotten destroyed. The buying power is gone. Somehow the government has to replace that temporarily. So those are the three things we should be doing now, and in the long run we should never have let leverage get so high up here. That's what made the price so high up here, and that's why everyone got wiped out down here because they were borrowing so much.

We should never have let that happen. So if we regulate the economy not to let leverage get so high we won't have such a crash, but if we do have a crash the way to deal with it is to undo the three things that went wrong. That's the sort of story that I've been telling. Yes?

Student: Do you have a theory for what the right amount of leverage is?

Professor John Geanakoplos: That's a wonderful question, and of course I've been asked that before. So let me put it in several different ways. Let's take the most hypercritical way.

I presented this theory, remember, starting in 2000, so way before the crash. And so people would say then, "Oh, very nice, very cute, but first all there's not going to be a crash and secondly how could we ever know what the right amount of leverage is. It's an impossible pie in the sky goal to regulate leverage.

Well, you see, that's why--I say it's difficult, I agree, but we've already faced this problem. We regulate the interest rate. How does the Fed know that the interest rate's too low or too high? What the Fed does is it monitors a bunch of stuff and realizes the economy is overheated. Things are changing. Suddenly output is going way up and inflation is starting to go up. Then the Fed raises the interest rate, or maybe people are being thrown out of work then the Fed lowers the interest rate.

So something changes in the economy. They don't know so precisely what to do, but something's changed that gives them a clue about which way to move interest rates, and over the course of 80 years, I guess since the Depression, since it was created, over 70 or 80 years since then they've gotten better and better at regulating the interest. So I put this picture up for a reason last class.

You remember the picture, which I'm going to get to now, of the history of leverage. So here's the history of leverage, the purple, in the housing market. And then the blue is the history of leverage, it's the loan to value, basically. I put money down starting from the top and going down. So from the bottom it's loan to value. So I've got the history of loan to value in the securities market and in the mortgage market.

Now, I think that the Fed should be monitoring this, and not only should be monitoring it, should be making it as public as the interest rates are. So how come I had to present Ellington's data on observations it made in the market, because Ellington seems to have been the only company in the county that kept this data. Nobody else seemed to recognize how important it was, and we kept it.

So the Fed doesn't have these numbers going back. If it did it would have seen that leverage had suddenly jumped up here and that leverage was much higher than it was before, and it would see if it monitored leverage in the housing market that leverage was skyrocketing.

Of course everybody knew this, they just didn't think it was an important thing to pay attention to, but if they were paying attention to it and keeping these numbers, we had to do this at Ellington by going house by house through every house looking at what the leverage was and taking the average, if they had done that, I mean they could have done that easily, and if they did do that, and if they were publishing it, and every economist was aware of it I think things would have been very different. They would have said we ought to tighten leverage.

Exactly how much should we tighten it? Well, they would have said, "I don't know exactly, but we would have forced banks not to allow loans with 3 percent down." Should it be 10 percent, or 15 percent, or 8 percent? It's a little hard to say what exactly the right number is, but we would have picked a number higher than 3 percent and we would have avoided a huge problem, and in later years we'll get better and better at picking that number. So I'm trying to answer your question.

So in the securities market another thing you could do, another trick you could do is you could say we'll pass a rule that says you can't--here leverage is going down, right? They're asking for more and more margins. You could pass a rule that says you can't double your margins from 10 percent to 20 percent or 20 to 40. You can't double them in under four months, say, on average across some security class. You can't double them in less than four months or less than six months.

So that would have kept leverage from collapsing so fast, and then lenders knowing that when the crisis was starting, you know, they're making one day loans. See, they always think. "Well, it's a one day loan and things start to look dicey I'll just demand a huge amount of leverage the next day. I'll get my money back tomorrow and then the day after tomorrow I'm not going to make the same loan. I'll ask for a lot more margin." So I'm saying, suppose you tell them in advance you have to keep making the same loan and you can't double the margin? You can increase it but you have to take at least six months to double it.

Well, they'll know in advance that they're not going to be able to react very quickly to problems, and so in advance they'll ask for more margin down so they won't have to double to get to a safe level when something starts happening because they'll already be safer.

So that's a way of not having to actually know what the right number is by just slowing down their response and relying on them to anticipate how bad things might be and they're already starting to respond at the beginning. So I'm not saying I've got exactly the right formula, but you see I think if you think about it and start to work on this, and most importantly you make these numbers public, you're going to change the way everybody, you know, rules will develop. Yeah?

Student: To sort of connect to that, so are they going to set like one leverage rate or is it going to be like for each class?

Professor John Geanakoplos: Yes, each class of security will have a different leverage.

Student: When you say class of security like do you mean like different...

Professor John Geanakoplos: Well, the government already makes a lot of loans through Fannie Mae and Freddie Mac, but Fannie Mae and Freddie Mac will have to ask for at least 20 percent down. Prime securities, prime mortgages will have to have at least this much amount of money down. So, on the housing market you'll have to have a certain amount of money down.

On Treasuries you can have a very high leverage. On mortgages, plain simple mortgages, you can have not quite as high a leverage, but a pretty high leverage. On mortgage derivatives, which are much more complicated, the leverage has to be much less. So you might say there'll be some rule that says--so anyway those are the kinds of classes that I have in mind, and we have to work out exactly how they're going to be regulated.

So it's a little bit complicated. So let me answer your question in two parts. Yes, it has to depend on the kind of security, and b) even trying to answer your question I'm revealing that it's not so obvious exactly what the formula is and how to do it, but this has to be worked out. Yep?

Student: Is this some kind of like Phillips curve relationship here that you could make between the amount of leverage and unemployment that kind of it's all the same like Phillips curve like other occasions that end up being awful also or is it...

Professor John Geanakoplos: Yes, yes. I think that's the whole point of the crisis that the things feedback on each other.

The feedback is the most important thing. So in the crisis let's take any one of these. When leverage starts to go down that makes the prices start to go down, but when the prices start to go down people get more worried that things are going to go down further, I mean, they have good reason to worry, and so the leverage goes down more which makes the prices go down more, and so they feed back on each other. So definitely it's a spiral of one thing affecting the other.

And of course, the more the prices are going down the more the optimists are losing money and your best buyers are getting wiped out, and that's a third thing. Those three things are always feeding back on each other.

Student: Is there a Lucas like critique, though, of saying that people should be able to expect this coming forward and they should account for that?

Professor John Geanakoplos: No, because the model was totally rational. Every person did expect all this. Everyone anticipated perfectly what would happen.

So Lucas critique is people should realize the environment they're in, but here in this environment everybody up here understood from the very beginning that the prices were going to go down to .69.

They realized that there was going to be this acceleration of problems, and so they all anticipated it, but still they wanted to buy because they didn't think they were going to get down there. They thought they were going to go up here. So remember, I don't know if I have it in this slide, but one of my most amazing pictures was this one of what happened to the market. Open. So what happened to the market here, which I think I showed you last time, I mean, I know I did, but I'll just show it to you again.

Now with this new perspective you can look at it. Presents, so this is Jerusalem, I gave this talk in Jerusalem. Second talk, so you remember this picture? I hope it was in this slide. Yes, it was here. Here.

Remember what happened in the world? It was shocking how bad and how fast it was. So in 2007, beginning of 2007, right, we're not far from the beginning of 2007. That's three years ago people were expecting 40 percent losses for these lower tranches. So how could you get such an astronomical loss?

What was happening? They were already anticipating this spiral. If you looked at just what housing prices were there, and you say 30 percent guys being thrown out, and housing prices are down 4 percent, that's hardly any loss at all, because if you get 96 percent back on the house and you have a few expenses and only 30 percent are defaulting, there was hardly anybody defaulting.

Remember that curve we showed where there weren’t almost any losses and no one going delinquent yet? They already anticipated that there were going to be lots of people thrown out of their houses and when they got thrown out of their houses the housing prices were going to collapse. So this market was collapsing already because people were anticipating a lot of the feedbacks and stuff that were going to happen later.

They didn't just extrapolate the number of defaults, they also had to extrapolate the housing prices and stuff going down. And so in this model everybody is doing that complicated extrapolation and they're figuring it all out, but even so they still want to put themselves in the cycle because they still think they have a profit opportunity. They can't stop themselves from investing.

That's why you need regulation. It's like a prisoner's dilemma. Everybody knows what the danger is, they still want to do it and the only way to stop them from doing it, you can't lecture them about irrational exuberance, they know what's going to happen and they still want to do it. They don't think that's going to happen. They know what could happen and they still want to do it.

Now, I think in reality Shiller is partly right. I think that people didn't really realize how bad it could have gotten. My own hedge fund lost money. We didn't anticipate how bad it was because so many things went wrong. We just underestimated all the feedbacks. So there is the spiral and there were just more things going wrong than we anticipated. So I wouldn't stick 100 percent to my story. I think there's something to what Shiller says, but I wouldn't definitely stick to 100 percent of his story of it being all irrational exuberance.

Any other questions? Now that we have five minutes left for--so I'm willing to keep going. So let's just pause. Any more questions on this story of the crisis or anything else about the crisis you want to ask, or...? Yeah?

Student: How receptive are the regulators to this idea?

Professor John Geanakoplos: Well, that's a good question. I talk to them now all the time whereas I never did before. So I'm meeting Dudley tomorrow. He's the head of the New York Fed. So I go there quite frequently like once a month now. I'm on some panels.

There are other academics going too. So I didn't do that before, so clearly they are paying attention to it. I think there are other people saying that leverage is important, Soros, being a famous hedge fund person who says it.

There are other people saying that you should reduce principal. Remember, I said that the way to solve the housing foreclosure problem is reducing principal. They're now holding hearings in Congress. I could have gone Tuesday to testify, but I have already testified, but they're having other hearings now. I didn't go because I was teaching, but there were a lot of people who went, and a lot of people said we should reduce principal. And a year ago when I was saying that hardly anyone else was saying it, although there were others, but very few.

The people at my hedge fund, we all pretty much see eye to eye on this and some other hedge funds were saying that. But now, I think, there's a growing consensus that we have to reduce principal. What does that do? It makes the loan smaller relative to the value of the house. In other words, it reduces the leverage of homeowners. So we have to get back to a credible level of leverage.

So the bad news is that although they're very receptive and although they're listening carefully and they keep inviting me to speak I don't see much signs that they're doing anything. And the one thing that they should have done by now is collected all this data. So they should have gone to all the big lenders and said, the Fed should have, and said, "This is the margins we're charging on all our different securities, here they are," and then the Fed would be able to monitor how much they were going up and down.

Now, a bunch of these lenders themselves have also become excited about what I'm doing, and they're starting to publish reports about it. So one, Credit Suisse, for example, their research department now thinks that a better measure of money is not just M1 and M2 and all that stuff, but how many leveraged loans are made in the Repo market, and they add that to the money supply, and they think that gives them a much better picture of the economy. So it's all sort of based on these ideas and I think I got them interested in it, or was one of the people that got them interested in it.

But they aren't going to publish their leverage numbers unless everybody else does because why should they give away private information? Why should they say, "We're lending to Ellington on slightly less generous or more generous terms than we're lending to some other guy." One of the two of us is going to feel bad about it, and so they're not going to do that. And so the government is the only one that can get the information out of them.

And the government shouldn't say who are they lending to person by person, they should give the average number. This is the average margin they're charging people, the average number the banks in general are charging people then you won't be revealing any private information, giving away any secrets. So that's the worst news that they're not collecting the data yet, and it's shocking to me. So I'm going to yell at Dudley about that again Friday, but I've done it before, so hopefully they're going to do that. They say they're going to do that, so I believe they'll do that.

And I believe that once they have all these numbers they're going to start to think differently. So there are all these initiatives in Congress, and in the Fed, and in the Treasury to try and monitor leverage and try to regulate it, but every time they get down to actually doing something they ask questions like you did, what exactly should the rule be, and they seem paralyzed by not being able to figure out the exact rule.

But I think that's an unnecessary paralysis because we don't have to have to the final rule to start doing stuff. Yes?

Student: I've got one more question. How and who do you think should be doing this?

Professor John Geanakoplos: The Fed. The Fed has the power to do it. The Fed already regulates margins on stocks, right? They set the margin at 50 percent or something, and so they could change that and they have changed that in the past. So the Fed has the authority to do that.

The Fed did that after 9/11. They called everybody up and said, right after 9/11, and said, "You cannot change your margins," and nobody changed their margins. I mean if ever there was a day when people were nervous and wanted to have a higher margin it was on 9/12. Nobody changed their margins. So they've done it before, but that's a pretty extreme day.

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