This module is the first of two modules on Credit Default Swaps. In this module, we are going, we are going to introduce you to the details of what a Credit Default Swap is. Talk about, on an intuitive level, of how Credit Default Swaps give you some information about the default probability. And how these quantities can be used for hedging, can be used for investment, can be used for speculation. And how Credit Default Swaps have played an important role in the financial crisis and also the sovereign debt crisis that is currently going on in Europe. The seller of a Credit Default Swap, CDS, agrees to compensate the buyer in the event of a loan default or some other credit event on a reference entity. The reference entity could be a corporation, it could be a sovereign that's a country, in return for periodic premium payments. So, the dynamics are as follows. This is what happens to the buyer. So, the buyer pays periodic premiums and what is a premium? It's some coupon rate S, which is also called the spread. d is in a year, it's a fraction of a year. So, d times S is the total coupon that has been accumulated over the years. N is a notional principal. So, there's a certain amount of principal that has been protected. In order to protect that principal, you have to pay a spread or a coupon S times N. It has to be paid every d fraction of the year. So, every coupon payment is going to be d times S times N. And this keeps on going until some kind of a credit event happens. Maybe the corporation defaults on the bond, maybe the country is not able to make an interest payment, and so on. It's, we going to talk about credit events later on and talk about the fact that defining whether a credit event has happened or not in itself, a difficult problem. So, once that credit event happens, two things happen. This credit event has happened somewhere in between two coupon payments. There should have been a coupon payment there. There should have been a coupon payment there. So, the credit event happened right in between these two coupon payments. So, at the next coupon payment date, the buyer has to pay the accrued interest over this interval . And I'm showing this with a smaller arrow to suggest that the accrued interest is actually less than the full coupon payment. On the other hand, the seller, the one who decided to sell the protection on this underlying credit event, after the credit event has happened at time, at the next coupon date, the seller has to pay 1 minus R, where R is the recovery rate, times the notional payment, N. Because the buyer pays premiums, this, the premium payments are sometimes called the premium leg of the CDS. And because the seller always pays the amount only on default, this is also called the protection leg. Here's a simple numerical example. So, consider a hypothetical 2-year CDS on a notional principal N equal to $1 million. And the spread S equal to 160 basis points, so just about 1.6%. And lets assume that the payments are quarterly. Suppose a default occurs in month 16 of a 24-month protection period. And the recovery rate at that time is 45%. And now, let's understand what happens to the payments of the buyers and the sellers. The buyer pays premiums, so he pays premiums at month 3, 6, 9, 12, and 15, and this is going to be S, the spread, times the notional principal of $1 million divided by four. Why? Because these are quarterly payments, so it's 1 4th of a year. So, the payments in all of these months is going to be $4000. Now, here's month 15. The next coupon is going to be on 18. But in month 16, the default has happened. So, this is the period over which the interest has accrued. So, the accrued interest that I have, that the buyer has to pay in month 18, is just 1 3rd of 4,000, so it's $1333.33. What about the payments from the protection's seller? Nothing paid up to month 15, because the default has not happened. Default happens in month 16 and month 18, which is the next coupon date. The seller has to pay 1 minus R times N. R was 45%, therefore, 1 minus R is 55% of N, which is $550,000. This is the total protection payment. Some other names for these payments. We've called them premium payments. We have called them, another name for the same payment is fixed leg or the fixed payments. Because the premiums are fixed, except for the accrued interest amount. The name for the protection sellers payment is also sometimes called a contingent leg or the contingent payment because it's contingent on a default happen. So, the basic model for the CDS cash flow that we're going to be using in this module is what we saw in this example. There will be a faction, delta, which is a fraction of a year, times k, would be the times at which the coupon payments are going to happen. Delta typically is 1 quarter, that is quarterly payments. And the dates of the payments are also set. The March 20th, June 20th, September 20th, and December 20th. If the reference entity is not in default at time tk, the buyer pays the premium delta which is the fraction times S, which is the spread times N which is the notional principle. If the reference en, entity defaults at some time tao between tk minus 1 and tk, the contract terminates at time tk. So, in the example, the default time was 116. This was between the two coupon payments at month 15 and month 18. The contract terminates at time 18. The buyer appraised the accrued interest over whatever fraction is left over. So, one month was what we did in the numerical example. And the buyer receives or equally the seller pays, 1 minus R times N where R denotes the recovery rate of the underlying. We are going to be working with this basic model to price and understand what is going to happen to the CDS sensitivities. But the details behind CDSs are enormous. they have been standardized by the International Swaps and Derivative Association, ISDA, in 1999. There were changes made in 2003. Then again, changes were made in 2009. And may yet again, changes be made, once if CDSs become exchange trader. And the reason there are so many different details in a CDS contract is there are many difficult issues. How does one define that a credit event has occurred? was the interest payment just late, did it not occur at all? It's a problem. How does one determine the recovery rate? there's often litigation, there's delays and so on. So, we're not going to be worrying about that in this module. We are going to assume that the recovery rate is somehow known. And we're going to price assuming that this recovery rate is known. But also many, many details. How is the spread set? How is it set for junk bonds versus investment grade bonds? What about countries? How is the spread set for countries? When is the coupon payment done? In advance or in arrears? How is the spread quoted? Is the spread quoted in terms of par spread, meaning the value that makes the net value the CDS equal to 0, or some other standardized spread. All these details are important when you talk about particular CDS contracts. But in order to understand the basic mechanisms of how CDSs work, the basic model that we have introduced is sufficient and it highlights all the main features. So, we're going to focus on the basic model to illustrate the details of pricing and the sensitivity to hazard rates, which are the probabilities of default. Later on, in the next module, I'm going to show you that the CDS spread, S is approximately 1 minus R times h, here R is the recovery rate and h is the hazard rate. So, for a fixed value of R, the CDS spreads are directly proportional to the hazard rate h. And the hazard rate is the conditional probability of default. So, you will end up getting that the conditional probability of default is approximately equal to S divided by 1 minus R. And therefore, CDS spreads end up giving you a very good handle on the probability that a particular company or a particular country, or a sovereign, is going to default on the next period. So, here, just as an illustration, I'm showing you what happens to the fove, what happened to the five year CDS spread for Ford, GM and AIG in the first nine months of 2008. The, this data up here, is all in basis points. So, it started around, a thousand basis points, and it went, oh, it started rising as the dates went by. And it didn't, neither of these companies actually defaulted. But the probabilities of default are going very high because the spreads are going high. AIG went all the way up to 3500 basis points before coming back down because this is where bail out event started to happen. The only idea that I wanted to take away from this picture is the fact that CDS spreads react to news events. AIG was very low. And then, suddenly, it started to shoot up because there was feeling in the market that the default is going to happen. And using the formula that h is approximately equal to S divided by 1 minus R, we can back out what is the probability of default from the spread rates. In this slide, the y axis is in percentages and not in basis points. [SOUND] And it gives you a sense of the credit worthiness of different countries. So, if you look at Greece, Greece, all the way, went up to 25% default on around, 20, 25% spread around January 12th. So, if the recovery rate is, let's say, approximately 50%. Then, h, which is S divided by 1 minus R. Will turn out to be, approximately a 50% default probability. So, the, the market taught that the probability that Greece is going to default is going to be very, very high. The next one over is Portugal, but it's only at around 1.5%, which is the period over here. And Germany which is exactly flat down here is pretty close to zero. And so, in some sense its going to be considered the most safe or risk free of the countries. Just to give you a sense of what the development of the applications of CDS, I'm going to trace some of the history. The development of the modern merger CDS is credited to Blythe Masters of JP Morgan. It was created in 1994 to cover JP Morgan for the $4.8 billion credit line that it had issued to Exxon to cover the possible punitive damages in the Exxon Valdez spill. So, after extending the credit line, JP Morgan protected itself by buying protection from the European Bank for Reconstruction and Development using a CDS. The CDS market, since then, has grown tremendously. By the end of 2007, the CDS market had a notional value for 62 trillion. Since then, things have become better. The DTCC estimates of the gross notional amount, gross years stands for the fact that after netting of, off setting CDS agreements, the notional amount in 2012 was about 25 trillion. So, 2007 was before the financial crisis, 2012 is after the financial crisis and things have started to come down. CDSs is where initially developed for hedging. they allow to hedge concentrations of credit risk privately. So, if, take the example of JP Morgan, Exxon. JP Morgan makes a loan to Exxon. It wants to protect itself. So, there are two possibilities. One, it could write the loan off to somebody else, in this case, the European Bank for Reconstruction and Development. But that would mean that it would have to inform Exxon that the loan has been written, written to another corporation. That might affect the relationship of JP Morgan and Exxon. Instead, you could construct, you could create a CDS contract and effectively still remove that credit off of your balance sheet. you can create, you can hedge credit exposures when no publicly traded debt exists. And this is because CDSs can be written on anything pretty much, and it's a contract, it's not really a bond or a cash bond. And therefore, you can use this construct to hedge against situations where bonds, or publicly traded debt, is not available. Although, CDS can be used to protect against losses, it's very different from an insurance contract. It's a contract that can be returned to cover anything. You can buy protection even when you don't hold the underlying debt. In order to buy insurance, you have to hold the underline quantity. To buy the insurance on a house, you have to be the owner of the house. To buy insurance on a bond, you need to hold the bond. You can buy a CDS on a bond without even holding the bond. CDS is easy to create and until recently completely unregulated. And because of these reasons, investing, and in some cases, speculation, became the main application very soon. CDS has provided an unfunded way to create credit risk. So, in order to take a credit risk on a particular company, you either have to take by the bond or you have to short sell the bond. Now, short selling bonds is very difficult. On the other hand, by writing a CDS from a particular company, you can expose yourself with a credit risk. You can tailor the credit exposure to match the precise requirement. This is because CDS is a contract and you can precisely define the contract that you want. CDS has allowed you to take view on the credit quality of the referenced credit. If you think that the credit quality is going to go down, you're going to buy protection. If you think that the credit quality is going to go up, then you're going to sell the protection. So, in both directions you can take a view, a positive view or a negative view. Buying protection, which means that when you have a negative view in a market, is often easier than shorting the asset. So, CDSs are became the real easy way of taking negative bets on various corporations. Another way CDS has started to be used is to arbitrage between the reference bond and the CDS price. It's not coupon, but a reference bond and the CDS spreads, gave another opportunity to find an investment opportunity to make the difference. CDSs have been blamed for the financial crisis and the debt crisis. And there are many reasons why this happened. CDS positions are not transparent. The riskiness of financial intermediaries, therefore cannot be accurately evaluated, because they don't, these positions don't show up on a balance sheet. And because of that, because of the fact that you could not accurately evaluate the riskiness of financial intermediaries, it threatened the trust in all counter parties. Since no one knew who faced losses when a crisis event happened, all the counter parties were suspect and entire trading came to a halt. CDS were treated on an OTC market and because of that, because impossible for any dealer to know what previous deals a customer had made. Resulting in situations where some dealers could make lots of CDS deals without putting up enough collateral. So, AIG was able to leverage its high credit rating to sell approximately $500 billion worth of CDSs, without putting up the enough collateral. Because it was in the OTC market and because they were, because these trades were opaque, it allowed a small number of CDS traders to take on huge amounts of risk. And it also allowed them to be very severely interconnected in terms of their obligations. And as a result of this interconnectedness, the dealers led to worries about contagion. CDSs also have been blamed during the financial crisis to adversely affect the cost of borrowing of a firm in a country. And recently, more so in the European debt crisis, CDS have been blamed for the fact that the cost of borrowing of countries have gone tremendously high. So, the story here is that speculated purchase CDS, without holding the underlying debt, sometimes called a naked CDS. Once a lot of these speculators actually start buying these naked CDS, this drives the spread higher. And when the spread goes high, because the market perceives the spread as the riskiness of a particular company or a particular country, the firms start appearing risky. And the cost of borrowing of the firm increases. The cost of borrowing of the sovereign increases. And this can lead to collapse. Various policy decisions have been made in the recent past to try to correct all of these problems. Try to get CDS positions and balance sheets. Trying to move the CDS, at least, to a clearing house. And then, to an exchange credit situation. this allow naked CDSs. Many of these are things that are in, in place, some of them completed, some of them are still being discussed. But CDSs have played their role and will, unless something is done, will continue to be a risky part of the economy.
