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The Leverage Cycle

2010; University of Chicago Press; Volume: 24; Issue: 1 Linguagem: Inglês

10.1086/648285

1537-2642

John Geanakoplos,

Economic Theory and Policy

Previous articleNext article FreeThe Leverage CycleJohn GeanakoplosJohn GeanakoplosYale University Search for more articles by this author Yale UniversityPDFPDF PLUSFull Text Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinked InRedditEmailQR Code SectionsMoreI. Introduction to the Leverage CycleAt least since the time of Irving Fisher, economists, as well as the general public, have regarded the interest rate as the most important variable in the economy. But in times of crisis, collateral rates (equivalently margins or leverage) are far more important. Despite the cries of newspapers to lower the interest rates, the Federal Reserve (Fed) would sometimes do much better to attend to the economy-wide leverage and leave the interest rate alone.When a homeowner (or hedge fund or a big investment bank) takes out a loan using, say, a house as collateral, he must negotiate not just the interest rate but how much he can borrow. If the house costs $100, and he borrows $80 and pays $20 in cash, we say that the margin or haircut is 20%, the loan to value (LTV) is $$\$ 80/ \$ 100=80\% $$, and the collateral rate is $$\$ 100/ \$ 80=125\% $$. The leverage is the reciprocal of the margin, namely, the ratio of the asset value to the cash needed to purchase it, or $$\$ 100/ \$ 20=5$$. These ratios are all synonymous.In standard economic theory, the equilibrium of supply and demand determines the interest rate on loans. It would seem impossible that one equation could determine two variables, the interest rate and the margin. But in my theory, supply and demand do determine both the equilibrium leverage (or margin) and the interest rate.It is apparent from everyday life that the laws of supply and demand can determine both the interest rate and leverage of a loan: the more impatient borrowers are, the higher the interest rate; the more nervous the lenders become, or the higher volatility becomes, the higher the collateral they demand. But standard economic theory fails to properly capture these effects, struggling to see how a single supply-equals-demand equation for a loan could determine two variables: the interest rate and the leverage. The theory typically ignores the possibility of default (and thus the need for collateral) or else fixes the leverage as a constant, allowing the equation to predict the interest rate.Yet, variation in leverage has a huge impact on the price of assets, contributing to economic bubbles and busts. This is because, for many assets, there is a class of buyer for whom the asset is more valuable than it is for the rest of the public (standard economic theory, in contrast, assumes that asset prices reflect some fundamental value). These buyers are willing to pay more, perhaps because they are more optimistic, or they are more risk tolerant, or they simply like the assets more. If they can get their hands on more money through more highly leveraged borrowing (that is, getting a loan with less collateral), they will spend it on the assets and drive those prices up. If they lose wealth, or lose the ability to borrow, they will buy less, so the asset will fall into more pessimistic hands and be valued less.In the absence of intervention, leverage becomes too high in boom times and too low in bad times. As a result, in boom times asset prices are too high, and in crisis times they are too low. This is the leverage cycle.Leverage dramatically increased in the United States and globally from 1999 to 2006. A bank that in 2006 wanted to buy a AAA-rated mortgage security could borrow 98.4% of the purchase price, using the security as collateral, and pay only 1.6% in cash. The leverage was thus 100 to 1.6, or about 60 to 1. The average leverage in 2006 across all of the US$2.5 trillion of so-called toxic mortgage securities was about 16 to 1, meaning that the buyers paid down only $150 billion and borrowed the other $2.35 trillion. Home buyers could get a mortgage leveraged 35 to 1, with less than a 3% down payment. Security and house prices soared.Today leverage has been drastically curtailed by nervous lenders wanting more collateral for every dollar loaned. Those toxic mortgage securities are now (in 2009:Q2) leveraged on average only about 1.2 to 1. A homeowner who bought his house in 2006 by taking out a subprime mortgage with only 3% down cannot take out a similar loan today without putting down 30% (unless he qualifies for one of the government rescue programs). The odds are great that he would not have the cash to do it, and reducing the interest rate by 1% or 2% would not change his ability to act. Deleveraging is the main reason the prices of both securities and homes are still falling.The leverage cycle is a recurring phenomenon. The financial derivatives crisis in 1994 that bankrupted Orange County in California was the tail end of a leverage cycle. So was the emerging markets mortgage crisis of 1998, which brought the Connecticut-based hedge fund Long-Term Capital Management to its knees, prompting an emergency rescue by other financial institutions. The crash of 1987 also seems to be at the tail end of a leverage cycle. In figure 1, the average margin offered by dealers for all securities purchased at the hedge fund Ellington Capital is plotted against time. (The leverage Ellington actually used was generally far less than what was offered.) One sees that the margin was around 20%, then spiked dramatically in 1998 to 40% for a few months, and then fell back to 20% again. In late 2005 through 2007, the margins fell to around 10%, but then in the crisis of late 2007 they jumped to over 40% again and kept rising for over a year. In 2009:Q2, they reached 70% or more.Fig. 1. View Large ImageDownload PowerPointThe theory of equilibrium leverage and asset pricing developed here implies that a central bank can smooth economic activity by curtailing leverage in normal or ebullient times and propping up leverage in anxious times. It challenges the “fundamental value” theory of asset pricing and the efficient markets hypothesis. It suggests that central banks might consider monitoring and regulating leverage as well as interest rates.If agents extrapolate blindly, assuming from past rising prices that they can safely set very small margin requirements, or that falling prices means that it is necessary to demand absurd collateral levels, then the cycle will get much worse. But a crucial part of my leverage cycle story is that every agent is acting perfectly rationally from his own individual point of view. People are not deceived into following illusory trends. They do not ignore danger signs. They do not panic. They look forward, not backward. But under certain circumstances, the cycle spirals into a crash anyway. The lesson is that even if people remember this leverage cycle, there will be more leverage cycles in the future, unless the Fed acts to stop them.The crash always involves the same three elements. First is scary bad news that increases uncertainty and so volatility of asset returns. This leads to tighter margins as lenders get more nervous. This, in turn, leads to falling prices and huge losses by the most optimistic, leveraged buyers. All three elements feed back on each other; the redistribution of wealth from optimists to pessimists further erodes prices, causing more losses for optimists, and steeper price declines, which rational lenders anticipate, leading then to demand more collateral, and so on.The best way to stop a crash is to act long before it occurs. Restricting leverage in ebullient times is one policy that can achieve this end.To reverse the crash once it has happened requires reversing the three causes. In today’s environment, reducing uncertainty means, first of all, stopping foreclosures and the free-fall of housing prices. The only reliable way to do that is to write down principal. Second, leverage must be restored to reasonable levels. One way to accomplish this is for the central bank to lend directly to investors at more generous collateral levels than the private markets are willing to provide. Third, the lost buying power of the bankrupt leveraged optimists must be replaced. This might entail bailing out crucial players or injecting optimistic capital into the financial system.My theory is not, of course, completely original. Over 400 years ago, in The Merchant of Venice, Shakespeare explained that to take out a loan one had to negotiate both the interest rate and the collateral level. It is clear which of the two Shakespeare thought was the more important. Who can remember the interest rate Shylock charged Antonio? (It was 0%.) But everybody remembers the pound of flesh that Shylock and Antonio agreed on as collateral. The upshot of the play, moreover, is that the regulatory authority (the court) decides that the collateral Shylock and Antonio freely agreed upon was socially suboptimal, and the court decrees a different collateral: a pound of flesh but not a drop of blood. In some cases, the optimal policy for the central bank involves decreeing different collateral rates.In more recent times there has been pioneering work on collateral by Shleifer and Vishny (1992), Bernanke, Gertler, and Gilchrist (1996, 1999), and Holmstrom and Tirole (1997). This work emphasized the asymmetric information between borrower and lender, leading to a principal agent problem. For example, in Shleifer and Vishny (1992), the debt structure of short versus long loans must be arranged to discourage the firm management from undertaking negative present value investments with personal perks in the good state. But in the bad state this forces the firm to liquidate, just when other similar firms are liquidating, causing a price crash. In Holmstrom and Tirole (1997) the managers of a firm are not able to borrow all the inputs necessary to build a project, because lenders would like to see them bear risk, by putting down their own money, to guarantee that they exert maximal effort. The Bernanke et al. (1999) model, adapted from their earlier work, is cast in an environment with costly state verification. It is closely related to the second example I give below, with utility from housing and foreclosure costs, taken from Geanakoplos (1997). But an important difference is that I do not invoke any asymmetric information. I believe that it is important to note that endogenous leverage need not be based on asymmetric information. Of course, the asymmetric information revolution in economics was a tremendous advance, and asymmetric information plays a critical role in many lender-borrower relationships; sometimes, however, the profession becomes obsessed with it. In the crisis of 2007–9, it does not appear to me that asymmetric information played a critical role in determining margins. Certainly the buyers of mortgage securities did not control their payoffs. In my model, the only thing backing the loan is the physical collateral. Because the loans are no-recourse loans, there is no need to learn anything about the borrower. All that matters is the collateral. Repo loans, and mortgages in many states, are literally no-recourse loans. In the rest of the states, lenders rarely come after borrowers for more money beyond taking the house. And for subprime borrowers, the hit to the credit rating is becoming less and less tangible. In looking for determinants of (changes in) leverage, one should start with the distribution of collateral payoffs and not the level of asymmetric information.Another important paper on collateral is Kiyotaki and Moore (1997). Like Bernanke et al. (1996), this paper emphasized the feedback from the fall in collateral prices to a fall in borrowing capacity, assuming a constant loan to value ratio. By contrast, my work defining collateral equilibrium focused on what determines the ratios (LTV, margin, or leverage) and why they change. In practice, I believe the change in ratios has been far bigger and more important for borrowing than the change in price levels. The possibility of changing ratios is latent in the Bernanke et al. models but not emphasized by them. In my 1997 paper I showed how one supply-equals-demand equation can determine leverage as well as interest even when the future is uncertain. In my 2003 paper on the anatomy of crashes and margins (it was an invited address at the 2000 World Econometric Society meetings), I argued that in normal times leverage and asset prices get too high, and in bad times, when the future is worse and more uncertain, leverage and asset prices get too low. In the certainty model of Kiyotaki and Moore (1997), to the extent leverage changes at all, it goes in the opposite direction, getting looser after bad news. In Fostel and Geanakoplos (2008b), on leverage cycles and the anxious economy, we noted that margins do not move in lockstep across asset classes and that a leverage cycle in one asset class might spread to other unrelated asset classes. In Geanakoplos and Zame (2009), we describe the general properties of collateral equilibrium. In Geanakoplos and Kubler (2005), we show that managing collateral levels can lead to Pareto improvements.1The recent crisis has stimulated a new generation of important papers on leverage and the economy. Notable among these are Brunnermeier and Pedersen (2009), anticipated partly by Gromb and Vayanos (2002), and Adrian and Shin (2009). Adrian and Shin have developed a remarkable series of empirical studies of leverage.It is very important to note that leverage in my paper is defined by a ratio of collateral values to the down payment that must be made to buy them. Those securities leverage numbers are hard to get historically. I provided an aggregate of them from the database of one hedge fund, but, as far as I know, securities leverage numbers have not been systematically kept. It would be very helpful if the Fed were to gather these numbers and periodically report leverage numbers across different asset classes. It is much easier to get “investor leverage” (debt + equity)/equity values for firms. But these investor leverage numbers can be very misleading. When the economy goes bad and the true securities leverage is sharply declining, many firms will find their equity wiped out, and it will appear as though their leverage has gone up instead of down. This reversal may explain why some macroeconomists have underestimated the role leverage plays in the economy.Perhaps the most important lesson from this work (and the current crisis) is that the macro economy is strongly influenced by financial variables beyond prices. This, of course, was the theme of much of the work of Minsky (1986), who called attention to the dangers of leverage, and of James Tobin (who in Tobin and Golub [1998] explicitly defined leverage and stated that it should be determined in equilibrium, alongside interest rates) and also of Bernanke, Gertler, and Gilchrist.1For Pareto-improving interventions in credit markets, see also Gromb and Vayanos (2002) and Lorenzoni (2008).A. Why Was This Leverage Cycle Worse than Previous Cycles?There are a number of elements that played into the leverage cycle crisis of 2007–9 that had not appeared before, which explains why it has been so bad. I will gradually incorporate them into the model. The first I have already mentioned, namely, that leverage got higher than ever before, and then margins got tighter than ever before.The second element is the invention of the credit default swap. The buyer of “CDS insurance” gets a dollar for every dollar of defaulted principal on some bond. But he is not limited to buying as much insurance as he owns bonds. In fact, he very likely is buying the credit default swaps (CDS) nowadays because he thinks the bonds are bad and does not want to own them at all. These CDS are, despite their names, not insurance but a vehicle for optimists and pessimists to leverage their views. Conventional leverage allows optimists to push the price of assets up; CDS allows pessimists to push asset prices down. The standardization of CDS for mortgages in late 2005 led to their trades in large quantities in 2006 at the very peak of the cycle. This, I believe, was one of the precipitators of the downturn.Third, this leverage cycle was really a combination of two leverage cycles, in mortgage securities and in housing. The two reinforce each other. The tightening margins in securities led to lower security prices, which made it harder to issue new mortgages, which made it harder for homeowners to refinance, which made them more likely to default, which raised required down payments on housing, which made housing prices fall, which made securities riskier, which made their margins get tighter, and so on.Fourth, when promises exceed collateral values, as when housing is “under water” or “upside down,” there are typically large losses in turning over the collateral, partly because of vandalism and so on. Today subprime bondholders expect only 25% of the loan amount back when they foreclose on a home. A huge number of homes are expected to be foreclosed (some say 8 million). In this model we will see that even if borrowers and lenders foresee that the loan amount is so large that there will be circumstances in which the collateral is under water and therefore this will cause deadweight losses, they will not be able to prevent themselves from agreeing on such levels.Fifth, the leverage cycle potentially has a major impact on productive activities for two reasons. First, investors, like homeowners and banks, that find themselves under water, even if they have not defaulted, no longer have the same incentive to invest (or make loans). This is called the debt overhang problem (Myers 1977). Second, high asset prices mean strong incentives for production and a boon to real construction. The fall in asset prices has a blighting effect on new real activity. This is the essence of Tobin’s q. And it is the real reason why the crisis stage of the leverage cycle is so alarming.B. OutlineIn Sections II and III, I present the basic model of the leverage cycle, drawing on my 2003 paper, in which a continuum of investors differ in their optimism. In the two-period model of Section II, I show that the price of an asset rises when it can be leveraged more. The reason is that then fewer optimists are needed to hold all of the asset shares. Hence the marginal buyer, whose opinion determines the asset price, is more optimistic. One consequence is that “efficient markets” pricing fails; even the law of one price fails. If two assets are identical, except that the blue one can be leveraged and the red one cannot, then the blue asset will often sell for a higher price.Next I show that when news in any period is binary, namely good or bad, then the equilibrium of supply and demand will pin down leverage so that the promise made on collateral is the maximum that does not involve any chance of default. This is reminiscent of the repo market, where there is almost never any default. It follows that if lenders and investors imagine a worse downside for the collateral value when the loan comes due, there will be a smaller equilibrium loan and, hence, less leverage.In Section III, I again draw on my 2003 paper to study a three-period, binary tree version of the model presented in Section II. The asset pays out only in the last period, and in the middle period information arrives about the likelihood of the final payoffs. An important consequence of the no-default leverage principle derived in Section II is that loan maturities in the multiperiod model will be very short. So much can go wrong with the collateral price over several periods that only very little leverage can avoid default for sure on a long loan with a fixed promise. Investors who want to leverage a lot will have to borrow short term. This provides one explanation for the famous maturity mismatch, in which long-lived assets are financed with short-term loans. In the model equilibrium, all investors endogenously take out one-period loans. and leverage is reset each period.When news arrives in the middle period, the agents rationally update their beliefs about final payoffs. I distinguish between bad news, which lowers expectations, and “scary” bad news, which lowers expectations and increases volatility (uncertainty). This latter kind depresses asset prices at least twice, by reducing expected payoffs on account of the bad news and by collapsing leverage on account of the increased volatility. After normal bad news, the asset price drop is often cushioned by improvements in leverage.When “scary” bad news hits in the middle period, the asset price falls more than any agent in the whole economy thinks it should. The reason is that three things deteriorate. In addition to the effect of bad news on expected payoffs, leverage collapses. On top of that, the most optimistic buyers (who leveraged their purchases in the first period) go bankrupt. Hence, the marginal buyer in the middle pieriod is a different and much less optimistic agent than in the first period.I conclude Section III by describing five aspects of the leverage cycle that might motivate a regulator to smooth it out. Not all of these are formally in the model, but they could be added with little trouble. First, when leverage is high, the price is determined by very few “outlier” buyers who might, given the differences in beliefs, be wrong! Second, when leverage is high, so are asset prices, and when leverage collapses, prices crumble. The upshot is that when there is high leverage, economic activity is stimulated; when there is low leverage, the economy is stagnant. If the prices are driven by outlier opinions, absurd projects might be undertaken in the boom times that are costly to unwind in the down times. Third, even if the projects are sensible, many people who cannot insure themselves will be subjected to tremendous risk that can be reduced by smoothing the cycle. Fourth, over the cycle inequality can dramatically increase if the leveraged buyers keep getting lucky and dramatically compress if the leveraged buyers lose out. Finally, it may be that the leveraged buyers do not fully internalize the costs of their own bankruptcy, as when a manager does not take into account that his workers will not be able to find comparable jobs or when a defaulter causes further defaults in a chain reaction.In Section IV, I move to a second model, drawn from my 1997 paper, in which probabilities are objectively given, and heterogeneity among investors arises not from differences in beliefs but from differences in the utility of owning the collateral, as with housing. Once again, leverage is endogenously determined, but now default appears in equilibrium. It is very important to observe that the source of the heterogeneity has implications for the amount of equilibrium leverage, default, and loan maturity. In the mortgage market, where differences in utility for the collateral drive the market, there has always been default (and long maturity loans), even in the best of times.As in Sections II and III, bad news causes the asset price to crash much further than it would without leverage. It also crashes much further than it would with complete markets. (With objective probabilities, the lovers of housing would insure themselves completely against the bad news, and so housing prices would not drop at all.) In the real world, when a house falls in value below the loan and the homeowner decides to default, he often does not cooperate in the sale, since there is nothing in it for him. As a result, there can be huge losses in seizing the collateral. (In the United States it takes 18 months on average to evict the owners, the house is often vandalized, and so on.) I show that even if borrowers and lenders recognize that there are foreclosure costs, and even if they recognize that the further under water the house is the more difficult the recovery will be in foreclosure, they will still choose leverage that causes those losses.I conclude Section IV by giving three more reasons, beyond the five from Section III, why we might worry about excessive leverage. Sixth, the market endogenously chooses loans that lead to foreclosure costs. Seventh, in a multiperiod model some agents may be under water, in the sense that the house is worth less than the present value of the loan but not yet in bankruptcy. These agents often will not take efficient actions. A homeowner may not repair his house, even though the cost is much less than the increase in value of the house, because there is a good chance he will have to go into foreclosure. Eighth, agents do not take into account that by overleveraging their own houses or mortgage securities they create pecuniary externalities; for example, by getting into trouble themselves, they may be lowering housing prices after bad news, thereby pushing other people further under water, and thus creating more deadweight losses in the economy.Finally, in Section V, I combine the two previous approaches, imagining a model with two-period mortgage loans using houses as collateral and one-period repo loans using the mortgages as collateral. The resulting double leverage cycle is an essential element of our current crisis. Here, all eight drawbacks to excessive leverage appear at once.C. Leverage and Volatility: Scary Bad NewsCrises always start with bad news; there are no pure coordination failures. But not all bad news leads to crises, even when the news is very bad.Bad news, in my view, must be of a special “scary” kind to cause an adverse move in the leverage cycle. Scary bad news not only lowers expectations (as by definition all bad news does) but it must create more volatility. Often this increased uncertainty also involves more disagreement. On average, news reduces uncertainty, so I have in mind a special, but by no means unusual, kind of news. One kind of “scary” bad news motivates the examples in Sections II and III. The idea is that at the beginning, everyone thinks the chances of ultimate failure require too many things to go wrong to be of any substantial probability. There is little uncertainty and therefore little room for disagreement. Once enough things go wrong to raise the specter of real trouble, the uncertainty goes way up in everyone’s mind, and so does the possibility of disagreement.An example occurs when output is one unless two things go wrong, in which case output becomes .2. If an optimist thinks the chance of each thing going wrong is independent and equal to .1, then it is easy to see that he thinks the chance of ultimate breakdown is $$.01=( .1) ( .1) $$. Expected output for him is .992. In his view ex ante, the variance of final output is $$.99( .01) ( 1-.2) ^{2}=.0063$$. After the first piece of bad new, his expected output drops to .92, but the variance jumps to $$.9( .1) ( 1-.2) ^{2}=.058$$, a 10-fold increase.A less optimistic agent who believes the probability of each piece of bad news is independent and equal to .8 originally thinks the probability of ultimate breakdown is $$.04=( .2) ( .2) $$. Expected output for him is .968. In his view ex ante, the variance of final output is $$.96( .04) ( 1-.2) ^{2}=.025$$. After the first piece of bad news, his expected output drops to .84. But the variance jumps to $$.8( .2) ( 1-.2) ^{2}=.102$$. Note that the expectations differed originally by $$.992-.968=.024$$, but, after the bad news, the disagreement more than triples to $$.92-.84=.08$$.I call the kind of bad news that increases uncertainty and disagreement “scary” news. The news in the last 18 months has indeed been of this kind. When agency mortgage default losses were less than 1/4%, there was not much uncertainty and not much disagreement. Even if they tripled, they would still be small enough not to matter. Similarly, when subprime mortgage losses (i.e., losses incurred after homeowners failed to pay, were thrown out of their homes, and the house was sold for less than the loan amount) were 3%, they were so far under the rated bond cushion of 8% that there was not much uncertainty or disagreement about whether the bonds would suffer losses, especially the higher rated bonds (with cushions of 15% or more). By 2007, however, forecasts on subprime losses ranged from 30% to 80%.D. Anatomy of a CrashI use my theory of the equilibrium leverage to outline the anatomy of market crashes after the kind of scary news I just described:1. Assets go down in value on scary bad news.2. This causes a big drop in the wealth of the natural buyers (optimists) who were leveraged. Leveraged buyers are forced to sell to meet their margin requirements.3. This leads to further loss in asset value and in wealth for the natural buyers.4. Then, just as the crisis seems to be coming under control, margin requirements are tightened because of increased uncertainty and disagreement.5. This causes huge losses in asset values via forced sales.6. Many optimists will lose all their wealth and go out of business.7. There may be spillovers if optimists in one asset hit by bad news are led to sell other assets for which they are also optimists.8. Investors who survive have a great opportunity.E. Heterogeneity and Natural BuyersA crucial part of my story is heterogeneity between investors. The natural buyers want the asset more than the general public. This could be for many reasons. The natural buyers could be less risk averse. Or they could have access to hedging techniques the general public does not have that makes the assets less dangerous for them. Or they could get more utility out of holding the assets. Or they could have access to a production technology that uses the assets more efficiently than the general public. Or they could have special information based on local knowledge. Or they could simply be more op