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ADB's Distinguished Speakers Program Measuring the Connectedness of the Financial System: Implications for Risk Management

2014; The MIT Press; Volume: 31; Issue: 1 Linguagem: Inglês

10.1162/adev_a_00026

1996-7241

Robert C. Merton,

Global Financial Crisis and Policies

Asian Development ReviewVol. 31, No. 1, pp. 186-210 (2014) Open AccessADB's Distinguished Speakers Program Measuring the Connectedness of the Financial System: Implications for Risk ManagementRobert C. MertonRobert C. MertonSchool of Management Distinguished Professor of Finance at the MIT Sloan School of Management.https://doi.org/10.1162/ADEV_a_00026Cited by:3 Previous AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Librarian ShareShare onFacebookTwitterLinked InRedditEmail Well thank you very much. I greatly appreciate the opportunity to speak to you today and for your taking the time to do so.As an introduction, the topic for today is looking at connectedness in the financial system, and I'll talk about a specific way that connectedness is defined in this context, and we'll talk about developing a new and better way to measure the degree of connectedness in the institution in a useful way, with respect to credit risk in particular, and how we might look at all that information and convey it in a fashion that we might be able to monitor, or at least get better information or insights, into potential systemic events.Macro financial risk propagation is a big issue for governments and financial stability, but it also is important in the private sector, particularly for very large asset managers. Managers that have very large asset pools, are too large to actually get out of harm's way, and so like the rest of us, they have to be prepared to deal with large market shocks—instead of simply trying to get away from them.The crisis of 2008 and 2009 was centered on credit risk involving money markets as well, but it was essentially a credit risk issue. The ongoing European debt crisis is, at least in my mind, not yet fully resolved—that also is an issue of credit. So the substantive issue for my remarks is going to be on credit. What I want to deal with is to look at how the propagation of credit risk among financial institutions and sovereigns is related to how connected they are, and in the process develop tools for measuring the connectedness and its dynamic changes. As you'll see from the numbers and the pictures, mostly pictures, the degree of connectedness among institutions and sovereigns is not constant or even approximately so through time. It changes quite substantially and dynamically. A last point, this is work that I've done with five other co-authors; they are not to be held accountable for my bringing it here. The scientific paper is not yet finished. There was an earlier paper describing it but I'm bringing it to you because I, as well as my co-authors, believe the technique, the tool used here, will prove to be well-founded. The numbers may change with the data when we finish refining it, but the principles I don't think will. So I stake my reputation that this approach is worth looking at, even though the scientific paper to support it is not complete.What I'm going to show you mostly are lots of very colorful pictures. So it's going to be a picture show, and in past people have liked it. But as Eugene Fama who just received a Nobel Prize is fond of pointing out, as did the late Paul Samuelson in a similar work, there's no free lunch; and there's no free lunch for you in this talk. So if you want to get to the pretty pictures you're going to have to pay a price (by going back to school). I've already said to you we're going to be looking at the connectedness of credit risk. If we're going to do that you've got to know about credit. So in the next 14 minutes, I'm going to make you credit risk experts. Those of you who want after the talk to be certified as level 1 credit risk experts, see me, and I'll sign your program. So are you ready to go back to school? We're going to learn first how to become credit experts, and then you'll get your reward.Let's get started. Now, as I talk about lending, I'm going to invariably use United States (US) dollars which is provincial but you can make the translation. If I start to try doing it and multiplying by 45 which is current currency rate, I'll surely get it wrong. So, what I'm holding here in my hand is a mortgage on a house or residence, a corporate bond, a bank loan, not a 16 or 22 tranche structured product, a vanilla mortgage bank loan or corporate bond, in dollars. If I now staple to this, a full faith and credit guarantee of the payments on this, whatever it is, loan, mortgage, or so forth, from the US government, what is this combined instrument functionally? It's a risk-free asset in dollars. Why? Because if the issuer of this bond, mortgage, or loan doesn't pay, the US government will. By the way, this isn't hypothetical: the US government has for a long time and in recent times in great quantity issued quite a number of such guarantees so you should be familiar with it. Everybody, just move your head up and down, if you agree this is a risk-free asset. Now watch. I just ripped the guarantee off, we're back to where we started. So if the original was risk-free, what's this? Risk-free minus a guarantee, what I just ripped off, you see the logic of that. This is shown in Figure 1: risky debt is risk-free debt minus the guarantee of debt.Figure 1. Functional Description of Being a Lender or Guarantor of Debt When There Is Risk of DefaultNow, the first lesson to draw from this is the following: every time we issue these kinds of loans, whatever they are, to whomever buys those loans or holds those loans, they will actually be engaging in two very different kinds of investing or risk-taking. They're lending money risk-free, which is very well defined. It's the time value of money—I give money now, and I get money with some interest, not much lately, for sure, we all understand risk-free lending. But they're also doing what else? They're writing a guarantee, that's what a minus guarantee means. It means instead of owning one, they're issuing one. And what is a guarantee? Functionally it's insurance. I guarantee the value, I guarantee an asset, or I guarantee something, that's insurance. So every time the investor pursues debt, he has two activities: risk-free lending and insurance writing. Now insurance writing is an old and honorable activity. So there is nothing wrong with it. But it is very important to know that's what you're in the business of doing. So functionally that's what it is. That's the first lesson. Debt buyers are engaging in two very different financial activities.Let's focus on the guarantee, and try to understand a little bit more about it. And so what I am going to propose for you is a very simple example. From Figure 1, we have a corporation that has assets with value A, it has debt, and it has common stock with value E—the simplest case. Assume all the debt is the same, and let's make it zero-coupon, and what it basically says on the maturity day of the debt, the firm or the corporation promises to pay B dollars, say, or a billion dollars. It's very simple. If you don't want to use a corporation as an example, replace it in the box title with Household, on the left side instead of Operating Assets write House, on the right side instead of Debt write Mortgage and Equity for Common Stock.Now to figure out what the guarantee is, first we know always the left side and right side of the balance sheet are equal to each other as an identity, both in value and risk, and we can ask the question of what the guarantee is worth. I ask you the question: What happens on the day when the debt comes due? There are actually two possibilities: Possibility one is when you get there you bring your bond, and they pay you what they promised you, your billion dollars. You're happy and you go off, end of story. In that case if the corporation pays, what was the guarantee worth after the fact? Nothing, you didn't need it, so the value is zero. That's very common for insurance isn't it? This is typical to buy insurance and in fact, we even hope that it doesn't have value, because the thing we're insuring against we don't want to have happened. So, if we get paid it's worth zero. But what if we're not paid? What happens when we show up and the corporation says, sorry, we can't pay you? Well what happens next in the real world is a pretty complicated process called default, and bankruptcy, and trying to get the money back. I'm not going to take you through all of the nightmares of the legal system.But one thing in common to all debt contracts no matter where they are issued or by whom, is the basic principle that, if the borrower does not pay back what was promised, then the lender gets to seize the assets of the borrower that are behind that. It may be hard to get them, it may be expensive to get them, but at the end of the day, that's what they get. So in the second case, what will the holder of the bond get? They'll get the value of the assets A. We know the assets aren't worth as much as a billion dollars because if they were, they've been better off just to pay us, by either selling the assets or raising new money to do it which they could. So we know A is less than a billion, and A is what we call recovery value. So if there's $700 million, even if we were promised a billion, we get the assets worth $700 million, so that our recovery value is only $700 million. That's basically the outcome.So, therefore, what is the value of the guarantee as a function of the value of the assets of the borrower? It's equal to either zero or the amount that you would receive with the guarantee which is the $1 billion or B dollars minus what you would have gotten in the recovery which is A. So in the example, the guarantee would be worth a billion minus $700 million or, $300 million. So the simple mathematical statement of what that payoff is, the guarantee at the end is worth the maximum of zero or B the promised payment, minus A, the value of the assets of the borrower, or max(0,B–A) = max(0,1000–700 million).Does anyone in the audience recognize that payoff? It looks like Figure 2.Figure 2. Value of Guarantee at MaturityYes, it's a put option, that's exactly a structure of put option. You knew I'd bring options in somehow, those of you who know my background. Put option is insurance, it is value insurance, and the strike price of the put option is the promised payment on the debt, the expiration date of the option is the maturity of the debt, and the option is on the assets of the borrower, but it is an exact analogy with the same payoff. Why do I point that out to you other than curiosity? Because for more than 40 years, we have been trading, valuing, estimating, understanding the risk and valuation of options, particularly puts, and calls, so we have a lot of experience and have made many sophisticated models for valuing them.So, for those of you who never knew anything about credit, but took at least some class sometime in finance, and know what an option is, you now are already well on your way to becoming an expert in credit risk, because everything you know about puts can be used to value the credit, and that's why I show you this. So, for example, you know that the value of put option or call option goes up, when the volatility of the asset increases even if the value doesn't change. The same thing here, if the volatility of the borrower's assets increases, nothing else changes—the asset value doesn't, then the guarantee goes up which means that that value of debt goes down. So you see once you understand put options you have all that knowledge, you can instantly bring all of that empirical and theoretical knowledge to bear in understanding credit. The bottom line is, a bond is nothing more or less than risk-free lending, minus a put option on the borrower's assets, and you're writing a put option, so you're writing value insurance.Now with your newfound knowledge, let's look at what we can use this to figure out about what happens to debt as conditions change. You understand that risky debt is risk-free minus the put option or minus the guarantee, and the topmost chart in Figure 3 gives a representation of that. The horizontal axis shows the assets of the borrower and the vertical axis the value of the loan, the mortgage, or whatever and it is, this value curve is concave. This is no one's particular theory, this concave value curve holds in general. All the action in the debt valuation comes from the put option component. We all know what a risk-free bond is, so let's focus on the guarantee, shown in the lower left chart in Figure 3. The guarantee is a put, and a put option will in general have a shape like this one. So you all see that's generic not model specific and what it says is, at a given point in time the higher the assets, the lower the value of the guarantee. If you're insuring and there are a lot of assets there, such that if value of the assets goes down, the value of the insurance goes up.Figure 3. Non-Linear Macro Risk Build-upLet's now look at this work in the context of banks because we want to talk about the banking system and institutions. Banks issue loans, therefore with bank loans, the banks are writing put options on their customers' assets. Let's look at the bank's liability for the guarantee. If you start in AC, at the time you make the loan and the guarantee is written, there's some value in the guarantee which is GC. What happens if the assets fall to A? Then, if they did it within a short span of time so you don't have to shift curves, you see the guarantee goes up to G. So what's the next observation? If the assets fall, the debt has to fall in value, even though the borrower has not defaulted on any payment; it just becomes less valuable. And in most real-world cases, bank loans are not marked this way. They only get marked down when some event occurs, but economics says it has to fall. By how much? That's an issue of empirics and analytics, but we know it has to fall.What would that mean for a bank? Well, if the bank had these loans, if the assets of the borrowers fell, and nothing else changed, bank assets go down. What happens to their capital? It has to go down. What does that mean about risk? Well, the bank is more leveraged now if it changes nothing and so the risk goes up. Most people understand that, if bank capital goes down, then risk goes up, but the part of risk change that's insidious about credit risk, and I think quite a propos for understanding at least a portion of what happened in the crisis, is you can see from this fact that these curves in the bottom charts in Figure 3 happen to be convex. What I mean is it holds water, using an analogy from high school math class, versus spills it when it is concave. But look here, when you did the original loan and if you use risk analysis, ask the following question: As a result of doing this loan, and as a result of writing this guarantee, how exposed are we to risk of the assets that support it? And for small movements in the asset price, it moves up a dollar, or down a dollar, what is that risk? It's roughly the slope of the curve in the left, bottom chart in Figure 3, or the tangent to point (Ac, Gc).So let's say that the tangent is –0.10, it's minus because the slope is downward sloping. What that means is, for a small movement in asset value when you first did the loan the risk exposure to the bank through the guarantee written, is that for each dollar declines in borrower's assets, the loan would lose, for example, ten cents. So it's pretty easy to quantify how much risk, which in our example, is about $0.10 on this loan for a dollar of asset value movement. Moving to A, we already have an increase in the bank's leverage because of the capital reduction, but what else do you see now? What if I ask the same question for the second round now after value of the asset moves?The slope is steeper at point (A, G) i.e., it is bigger in absolute value. Instead of being –0.10, the slope is now –0.15, and you see it's getting steeper just by the convexity nature of the curve; this is no specialized theory, it is inherent to the structure. What does that mean? It means for the same loan, nothing has changed except for another decline of the same magnitude that just occurred before. When it occurs a second time, the impact is larger, in this example 50% larger, so instead of losing a dime on every dollar, you lose $0.15. Do you see that if you had a third move down, it gets steeper and steeper? So one of the insidious things about credit (which at some level looks simple but isn't), is that as the asset value moves, the risk of the particular loan changes, and its risk is not linearly changing. So what does that mean? It means when you have this decline, the bank becomes much riskier than simply the decline in bank capital, that's just one part of the increase. Because its asset value went down. You have a second impact that each loan itself is now riskier. Thus, even if the bank replaced its lost capital to keep the same leverage, it is still riskier than before and therefore a second shock will have a bigger effect than simply a reduction in capital ratio would predict. If you haven't seen this before, that's what you want to embed it in your head to remember, because that's the real secret to understanding how risk evolves and how bad things can happen in credit if you don't recognize its convexity.Now we're going to use that to examine the crisis. This is not to say this is the complete explanation. So you can see for example if you go back when banks were losing billions every quarter back in 2008, 2009, into 2010, what did you hear? Banks lost $5 billion, they've announced they're going to do no more new loans, they're not going to increase their portfolio, they're not going to do anything, and next quarter, similar declines happen, and they lose more than $5 billion. How can they lose more if they have the same assets? The answer you can see is, although it's the same asset by name, that asset is more risky. There are alternative possible explanations for increased losses for the same loan base. They could have cooked the books or whatever. However, what you see here is structural, and thus applies always as at least a part of the driver of credit risk change.This is no one's particular theory, and if borrower asset declines happen several times, this is how you can get what looks like ever larger losses even though the positions haven't increased. They also give you a hint of how you can get what are called "ten sigma" events. You know these sensational stories we all heard where a journalist would call up someone in Goldman Sachs or Deutsche Bank, and say, "What's the likelihood that a 10-sigma event will occur in a normal distribution," and of course the answer is like once every billion years. "Well, we have seen three of them in the last week." There are other possible explanations for that, no one doubts there can be fat tails in the distributions of events but you can see that it can come from another structural source. Suppose that most of your experience with bank loans in recent times had been when the assets were large, out in the right-most portion of borrower assets in the Banking System Liability chart in Figure 3, then you see the measured sensitivity of the guarantee to asset values, the slope, is very flat. So historical experience when you fit the data of how sensitive bank loans are to the assets, are all measured in a period where it's pretty flat, that is, insensitive. So you fit the data, whether it's a regression, or something more fancy, that guarantee sensitivity is low in what you get for the numbers. If you assume that the elasticity of response is the same going forward, when the value of the assets fall and you move toward the left side portion of the Banking System Liability chart, which of course you can see is an incorrect assumption, then you say, well if the slope is only this, and if the loan value changed by a large amount, that looks like a 10-sigma event for the underlying assets and for loan value change. Actually the slope is now five times larger and what actually happened was a 2-sigma event in the underlying asset, not a 10-sigma one.So, two sigmas with a five times larger slope looks like 10-sigma with a constant slope. That's the concept. So from all your hard work of learning to be credit experts, you can explain phenomenon about the crisis that many people asserted were "outside the box" of past experience did not fit the models or the principles of economics and finance being used, and thus calling for the creation of a new paradigm. With your acquired understanding of the credit risk structure, you can see that there is no need to scrap the current principles to understand the phenomenon. This offers a mainstream explanation.You've been so good let me offer you an extra learning dividend. You now understand what the banks' or other lenders' risk is. But what do we know about sovereigns' role in the risk propagation process? Among many things, they have a habit: namely they almost always guarantee their banks, either explicitly or implicitly. So, what do the sovereigns do, what is their liability? It's a put option again they are providing. Right? That's what we saw was the structure of a guarantee. So when the US government writes that guarantee, they're writing a put option. On what? On the bank assets. What are the bank assets? Bank loans. What are bank loans when you pierce through them? Risk-free lending, and having sold an insurance contract or a put option on the assets of the borrower. So what is that government guarantee? It's a put option on a put option. In other words, if you break through and look at the actual assets that are affecting things, whether it is real estate, or stocks, or corporate assets, or whatever, the government then issues a put option on a put option. That's a convexity on convexity, making government guarantees doubly convex. What does that mean?If we were to plot the government's guarantee value not against bank assets but against the real economic assets that are behind it, we will see that while it has the same shape, it is much flatter and rises much quicker because it's convex on convex, it's like double speed of change. Why is that interesting, just from a qualitative point of view? It shows you, right from the core theory how it's possible for a country, or government, to be in relatively stable environment and guaranteeing loans and other things without a problem, and then seemingly get into a lot of trouble rather quickly when borrower assets decline. And what I'm saying is because of the high convexity or the high rate of change of the risk, that's possible to happen from nothing more than the structure, and as you would predict it happening.Now, I wasn't here in Asia in 1997, but if you look at some of the cases, you know there were countries that had real estate sector problems, and all of a sudden the banks also had problems, and not too long after that, the whole country was finding itself with enormous liabilities from the guarantees by government. Some estimate guarantee liability of as much as 70% of gross domestic product, clearly untenable to deal with, and the currency decline took care of the rest. How could that happen? It is predictable as a structure—not that I could've predicted the crisis itself—I'm saying given the assets fell, say real estate falls, this is how you can get this propagation. You also see that depending on what sector it happens in, this is how you start getting propagations from the real sector, to the financial sector, to the government sector, and so forth. And there are many of these you can map. So this is the lesson we're going to use, and now I think I'm prepared to qualify those who want it, as credit risk experts level 1.Consider guarantors writing guarantees of their own guarantors. What does this mean? Well I've got some examples here. Let's say I am a bank, and the lady seated in front of me represents my sovereign. We know that as sovereign, she's guaranteeing me, but suppose at the moment she's having a little trouble funding herself. So she comes to me and says, "Bank, I think it will be great if you bought some of your own country's bonds," and that seems reasonable. I say fine. Now what? Will she guarantee me? What do we know from our credit-learning work? I've written a guarantee on the sovereign, because I'm holding the sovereign's debt. Now let's talk our way through as what happens next if there is a shock. It's never the fault of the sovereign; I'm a bank, so I made a mistake, I bet too much or just bad luck. My assets, or my borrowers' fall, and I become a worst credit. She's my guarantor, so because I'm a worst credit her guarantee liabilities go up which makes her weaker, but since I've guaranteed her as well and she's become weaker, what does that mean about my guarantees that I've written on my liabilities? They go up again which makes me weaker. Do you see feedback?Well, this is a simplified version. You are likely aware of this in what you've seen in Europe and Figure 4 shows a more colorful and complex version of this feedback. In Europe for example, what was the circumstance? Banks did not only own their own sovereign's debt, but also other sovereign debt, and vice versa. So you now have this feedback between the bank and sovereigns, and since the banks deal with each other, the dynamics of asset values, risk, and cost of guarantees become a lot more complicated because these feedbacks go across geopolitical borders, and one sovereign can affect other sovereigns through this mechanism. So destructive feedback moves are something that are inherently in there, and Figure 4 shows the various channels.Figure 4. Feedback Loops of Risk from Explicit and Implicit GuaranteesSo let me describe what we did with credit risk structure on connectedness. We estimated the cost of the credit guarantee—the put option—for banks, insurance companies, and sovereigns. The higher the premium for the insurance, for every dollar of loan insured, the more risky the credit for the same maturities. If you pay a larger amount for the insurance policies, the higher the premium paid, the higher the put option value, and the less worthy your credit is, just by definition.So you know how we measure creditworthiness. Next I describe a little more detail within the data. We divide the value of the guarantee by the risk-free value of the bond that would be the value of the instrument or the loan or whatever, if it were fully guaranteed by a credible guarantor. This calculation is shown in the first equation in Figure 5.Figure 5. Measuring Connectivity and Influence on Credit Ratings between Sovereigns and Financial InstitutionsThe resulting number is a percentage, say 6% or 7%. One never pays more than 100% for the guarantee because that's just the whole thing if you do. So it's a number like 6%, or 7%, or 12%, or 4%, or 2%. It has an inaccurate name: expected loss rate (ELR). This ratio has nothing to do with expected values in the usual sense, but that's the terminology convention. We then compute that measure of the cost of the creditworthiness such that the higher that number, the less credit worthy to analyze connectedness in credit among institutions and sovereigns.This approach to the credit guarantee valuation for sovereigns is different than for banks and insurance companies, so let me explain why. We measure the credit risk estimate for the sovereigns using the credit default swap (CDS) market. So these are market prices, and not ratings based. These are market prices for what it would cost to guarantee that sovereign's debt. Why did we not use CDS for banks and insurance coverage, even though they were available? The answer is we want the total credit risk of the entity, not just that part of the credit risk being borne by the private sector. CDS prices reflect only the latter. So for example, when Ireland guaranteed all the Irish banks, the CDS of the Irish banks fell dramatically. But did these Irish banks have better coverage ratios, better assets, or better loans? No, they're exactly the same banks they were before that announcement. Why CDS for them fell is essentially the government took on some of the credit risk (or more of the credit risk than the market had thought it was taking on), by making that statement and taking that action.As an extreme case, imagine you have a terrible bank in terms of its financials, and the US government guaranteed 100% of the bank. Its CDS rate would be very close to US Treasury CDS not because there was no credit risk in the sense that the bank was sound, but simply because the credit risk had been transferred out of the private market and this is all that CDS measures. Since we want to understand the connection of actual institutions' real credit exposures, we don't want to use just the private sector's risk, and that's why we use an alternative. What we use is a family of models, connected in some way or another to my name. The Merton (1974) model for pricing corporated debt, published 39 years ago, was derived with the same perspective on credit that I give here and a refined version is used here to estimate the Expected Loss Ratio for institutions. This is a well-known credit model, although a much more sophisticated version than is in my paper, and has been widely used in practice for at least 20 years. It took 25 years for the innovation to be widely adapted—sometimes you have to wait a while for adoption, but it is widely used, and for purposes of measuring credit (we're not trading on it), it's going to be more than accurate enough for estimation of market value for total credit risk. Understand that we're not trading these things; we do not have to get it precisely. We just want a good credit cost indicator. The advantage of that, this allows us to get a va