1. COURS TITLE Derivatives Markets
dr Krzysztof SPIRZEWSKI
Wydział Nauk Ekonomicznych
Uniwersytetu Warszawskiego

2. Lecture 11 Management of credit risk Default probabilities
Management of credit risk
Default probabilities
Credit risk in derivatives transactions
Credit Derivatives (CDS and CDO)

3. Management of credit risk
Introduction
The value-at-risk measure (we covered in Theory of Finance lecture) and the Greek letters are aimed at quantifying market risk. Today we consider another important risk for financial institutions: credit risk.
Most financial institutions devote considerable resources to the measurement and management of credit risk. Regulators have for many years required banks to keep capital to reflect the credit risks they are bearing. This capital is in addition to the capital, that is required for market risk.
Credit risk arises from the possibility that borrowers and counterparties in derivatives transactions may default.
Today we discusses a number of different approaches to estimating the probability that a company will default and explains the key difference between risk-neutral and real-world probabilities of default. It examines the nature of the credit risk in over-the-counter derivatives transactions and discusses the clauses derivatives dealers write into their contracts to reduce credit risk. In addition we will discuss credit derivatives.
An important development in derivatives markets since the late 1990s has been the growth of credit derivatives. In 2000, the total notional principal for outstanding credit derivatives contracts was about $800 billion. By December 2009, this had become $32 trillion. Credit derivatives are contracts where the payoff depends on the credit-worthiness of one or more companies or countries. We will discussed how credit derivatives work and how the CDS is valued.

4. I. Default probabilities
The are several approach to estimating the probability of default when loan is given. We will discuss the three of them.
CREDIT RATINGS
RECOVERY RATES
ESTIMATING DEFAULT PROBABILITIES FROM BOND PRICES
 a. First approach to estimating the probability of default when loan is given
Rating agencies, such as Moody's, S&P, and Fitch, are in the business of providing ratings describing the creditworthiness of corporate bonds.
The best rating assigned by Moody's is Aaa. Bonds with this rating are considered to have almost no chance of defaulting. The next best rating is Aa. Following that comes A, Baa, Ba, B, Caa, Ca, and C. Only bonds with ratings of Baa or above are considered to be investment grade.
The S&P and Fitch ratings corresponding to Moody's Aaa, Aa, A, Baa, Ba, B, Caa, Ca, and C are AAA, AA, A, BBB, BB, B, CCC, CC, and C, respectively. To create finer rating measures, Moody's divides its Aa rating category into Aal, Aa2, and Aa3, its A category into Al, A2, and A3, and so on. Similarly, S&P and Fitch divide their AA rating category into AA+, AA, and AA-, their A rating category into A+, A, and A-, and so on.
Moody's Aaa category and the S&P/Fitch AAA category are not sub­divided, nor usually are the two lowest rating categories.

5. I. Default probabilities
HISTORICAL DEFAULT PROBABILITIES Table 23.1 is typical of the data produced by rating agencies. It shows the default experience during a 20-year period of bonds that had a particular rating at the beginning of the period. For example, a bond with a credit rating of Baa has a 0.176% chance of defaulting by the end of the first year, a 0.494% chance of defaulting by the end of the second year, and so on. The probability of a bond defaulting during a particular year can be calculated from the table. Example: the probability that a bond initially rated Baa will default during the second year is = 0.318%.

6. I. Default probabilities
Hazard Rates
From Table 23.1 we can calculate the probability of a bond rated Caa or below defaulting during the third year as = 9.298%. We will refer to this as the unconditional default probability.
It is the probability of default during the third year as seen at time 0. The probability that the bond will survive until the end of year 2 is = %. The probability that it will, default during the third year conditional on no earlier default is therefore / , or 13.17%.
The 13.17% we have just calculated is for a 1-year time period.
Conditional default probabilities are referred to as hazard rates or default intensities.

7. I. Default probabilities
b. RECOVERY RATES
When a company goes bankrupt, those that are owed money by the company file claims against the assets of the company.1 Sometimes there is a reorganization in which these creditors agree to a partial payment of their claims. In other cases the assets are sold by the liquidator and the proceeds are used to meet the claims as far as possible. Some claims typically have priority over other claims and are met more fully.
The recovery rate for a bond is normally defined as the bond's market value a few days after a default, as a percent of its face value.
Recovery rates are significantly negatively correlated with default rates. This means that a bad year for the default rate is usually doubly bad because it is accompanied by a low recovery rate.
For example, when the default rate for non-investment-grade bonds in a year is only 0.1%, the average recovery rate might be relatively high at 60%. When the default rate is relatively high at 3%, the average recovery rate might be only 35%.
1 In the United States, the claim made by a bond holder is the bond’s face value plus accrued interest.

8. I. Default probabilities
c. ESTIMATING DEFAULT PROBABILITIES FROM BOND PRICES The probability of default for a company can be estimated from the prices of bonds it has issued. The usual assumption is that the only reason a corporate bond sells for less than a similar risk-free bond is the possibility of default. Example: Consider first an approximate calculation. Suppose that a bond yields 200 basis points more than a similar risk-free bond and that the expected recovery rate in the event of a default is 40%. The holder of a corporate bond must be expecting to lose 200 basis points (or 2% per year) from defaults. Given the recovery rate of 40%, this leads to an estimate of the probability of a default per year conditional on no earlier default of 0.02/( ), or 3.33%. In general, (23.2) Where: - is the average hazard rate (default intensity) per year, s - is the spread of the corporate bond yield over the risk-free rate, and R - is the expected recovery rate.

9. I. Default probabilities
The Risk-Free Rate
A key issue when bond prices are used to estimate default probabilities is the meaning of the terms "risk-free rate" and "risk-free bond." In equation (23.2), the spread s is the excess of the corporate bond yield over the yield on a similar risk-free bond.
The benchmark risk-free rate that is usually used in quoting corporate bond yields is the yield on similar Treasury bonds. (For example, a bond trader might quote the yield on a particular corporate bond as being a spread of 250 basis points over Treasuries.)
As discussed traders usually use LIBOR/swap rates as proxies for risk-free rates when valuing derivatives. Traders also often use LIBOR/swap rates as risk-free rates when calculating default probabilities. For example, when they determine default probabilities from bond prices, the spread s in equation (23.2) is the spread of the bond yield over the LIBOR/swap rate.
COMPARISON OF DEFAULT PROBABILITY ESTIMATES
The default probabilities estimated from historical data are usually much less than those derived from bond prices. The difference between the two was particularly large during the credit crisis which started in mid This is because there was what is termed a "flight to quality" during the crisis, where all investors wanted to hold safe securities such as Treasury bonds. The prices of corporate bonds declined, thereby increasing their yields. The credit spread s on these bonds increased and calculations such as the one in equation (23.2) gave very high default probability estimates.

10. I. Default probabilities
Table 23.4 shows that the ratio of the hazard rate backed out from bond prices to the hazard rate calculated from historical data (Dec and June 2007) is very high for investment-grade companies and tends to decline as a company's credit rating declines. The difference between the two hazard rates tends to increase as the credit rating declines.
Real-World vs. Risk-Neutral Probabilities
The default probabilities implied from bond yields are risk-neutral probabilities of default.
To explain why this is so, consider the calculations of default probabilities.
The calculations of default probabilities assume that expected default losses can be discounted at the risk-free rate. The risk-neutral valuation principle shows that this is a valid procedure providing the expected losses are calculated in a risk-neutral world. This means that the default probability must be a risk-neutral probability.

11. I. Default probabilities
By contrast, the default probabilities implied from historical data are real-world default probabilities (sometimes also called physical probabilities). The expected excess return arises directly from the difference between real-world and risk-neutral default probabilities. If there were no expected excess return, then the real-world and risk-neutral default probabilities would be the same, and vice versa.
But there is big differences between real-world and risk-neutral default probabilities. This is the same as with corporate bond traders who earn more than the risk-free rate on average.
One reason often advanced for the results is that corporate bonds are relatively illiquid and the returns on bonds are higher than they would otherwise be to compensate for this. This is true, but research shows that it does not fully explain the results. Another possible reason for the results is that the subjective default probabilities of bond traders may be much higher than the those given in Table Bond traders may be allowing for depression scenarios much worse than anything seen during the period covered by historical data.
Which Default Probability Estimate Should Be Used?
At this stage it is natural to ask whether we should use real-world or risk-neutral default probabilities in the analysis of credit risk. The answer depends on the purpose of the analysis.
When valuing credit derivatives or estimating the impact of default risk on the pricing of instruments, risk-neutral default probabilities should be used. This is because the analysis calculates the present value of expected future cash flows and almost invariably (implicitly or explicitly) involves using risk-neutral valuation.
When carrying out scenario analyses to calculate potential future losses from defaults, real-world default probabilities should be used.

12. II. Credit risk in derivatives transactions
The credit exposure on a derivatives transaction is more complicated than that on a loan. This is because the claim that will be made in the event of a default is more uncertain. Consider a financial institution that has one derivatives contract outstanding with a counterparty. Three possible situations can be distinguished:
Contract is always a liability to the financial institution
Contract is always an asset to the financial institution
Contract can become either an asset or a liability to the financial institution.
An example of a derivatives contract in the first category is a short option position; an example in the second category is a long option position; an example in the third category is a forward contract.
Derivatives in the first category have no credit risk to the financial institution. If the counterparty goes bankrupt, there will be no loss. The derivative is one of the counter­party's assets. It is likely to be retained, closed out, or sold to a third party. The result is no loss (or gain) to the financial institution.
Derivatives in the second category always have credit risk to the financial institution. If the counterparty goes bankrupt, a loss is likely to be experienced. The derivative is one of the counterparty's liabilities. The financial institution has to make a claim against the assets of the counterparty and may receive some percentage of the value of the derivative.
(Typically, a claim arising from a derivatives transaction is unsecured and junior.)
Derivatives in the third category may or may not have credit risk. If the counterparty defaults when the value of the derivative is positive to the financial institution, a claim will be made against the assets of the counterparty and a loss is likely to be experienced. If the counterparty defaults when the value is negative to the financial institution, no loss is made because the derivative is retained, closed out, or sold to a third party.

13. II. Credit risk in derivatives transactions
  CREDIT RISK MITIGATION
In many instances the analysis we just have presented overstates the credit risk in a derivatives transaction. This is because there are a number of clauses that derivatives dealers include in their contracts to mitigate credit risk. We discuss following:
Netting,
Collateralization, and
Downgrade Triggers.
1. Netting
A clause that has become standard in the Master Agreements that govern transactions in the over-the-counter market is known as netting. This states that, if a company defaults on one transaction it has with a counterparty, it must default on all outstanding transactions with the counterparty.
Netting has been successfully tested in the courts in most jurisdictions. It can substantially reduce credit risk for a financial institution.
Example:
Consider a financial institution that has three transactions outstanding with a particular counterparty. The transactions are worth +$10 million, +$30 million, and -$25 million to the financial institution. Suppose the counterparty runs into financial difficulties and defaults on its outstanding obligations. To the counterparty, the three transactions have values of -$10 million, -$30 million, and +$25 million, respectively. Without netting, the counterparty would default on the first two transactions and retain the third for a loss to the financial institution of $40 million. With netting, it is compelled to default on all three transactions for a loss to the financial institution of $15 million.

14. II. Credit risk in derivatives transactions
2. Collateralization Another clause frequently used to mitigate credit risks is known as collateralization. Suppose that a company and a financial institution have entered into a number of derivatives transactions. A typical collateralization agreement specifies that the transac­tions be valued periodically. If the total value of the transactions to the financial institution is above a specified threshold level, the agreement requires the cumulative collateral posted by the company to equal the difference between the value of the transactions to the financial institution and the threshold level. If, after the collateral has been posted, the value of the transactions moves in favor of the company so that the difference between value of the transactions to the financial institution and the threshold level is less than the total margin already posted, the company can reclaim margin. In the event of a default by the company, the financial institution can seize the collateral. If the company does not post collateral as required, the financial institution can close out the transactions. The margin must be deposited by the company with the financial institution in cash or in the form of acceptable securities such as bonds. The securities are subject to a discount known as a haircut applied to their market value for the purposes of margin calculations. Interest is normally paid on cash.
Example:
Suppose, that the threshold level for the company is $10 million and the transactions are marked to market daily for the purposes of collateralization. If on a particular day the value of the transactions to the financial institution rises from $9 million to $10.5 million, it can ask for $0.5 million of collateral. If the next day the value of the transactions rises further to $ 11.4 million, it can ask for a further $0.9 million of collateral. If the value of the transactions falls to $10.9 million on the following day, the company can ask for $0.5 million of the collateral to be returned.
Note that the - threshold ($10 million in this case) can be regarded as a line of credit that the financial institution is prepared to grant to the company.

15. II. Credit risk in derivatives transactions
If the collateralization agreement is a two-way agreement a threshold will also be specified for the financial institution. The company can then ask the financial institu­tion to post collateral when the value of the outstanding contracts to the company exceeds the threshold. Collateralization agreements provide a great deal of protection against the possibility of default (just as the margin accounts provide protection for people who trade futures on an exchange). However, the threshold amount is not subject to protection. Furthermore, even when the threshold is zero, the protection is not total. This is because, when a company gets into financial difficulties, it is likely to stop responding to requests to post collateral. By the time the counterparty exercises its right to close out contracts, their value may have moved further in its favor. As explained, over-the-counter derivatives are increasingly moving to clearing houses where market participants post both an initial margin and maintenance margins. 3. Downgrade Triggers Another credit risk mitigation technique sometimes used by a financial institution is known as a downgrade trigger. This is a clause stating that if the credit rating of the counterparty falls below a certain level, say Baa, the financial institution has the option to close out a derivatives transaction at its market value. Downgrade triggers do not provide protection from a big jump in a company's credit rating (for example, from A to default). Also, downgrade triggers work well only if relatively little use is made of them. If a company has many downgrade triggers outstanding with its counterparties, they are liable to provide little protection to any of the counterparties . The example of Enron’s Bankruptcy, stock price fell sharply in the period leading up to the bankruptcy illustrates that this techniques provide protection only when relatively little use is made of them.

16. III. Credit Derivatives (CDS and CDO)
Introduction
Credit derivatives allow companies to trade credit risks in much the same way that they trade market risks. Banks and other financial institutions used to be in the position where they could do little once they had assumed a credit risk except wait (and hope for the best). Now they can actively manage their portfolios of credit risks, keeping some and entering into credit derivatives contracts to protect themselves from others. As indicated in Business Snapshot 24.1, banks have been the biggest buyers of credit protection and insurance companies have been the biggest sellers.
Credit derivatives can be categorized as "single-name" or "multi-name."
The most popular single-name credit derivative is a credit default swap (CDS). The payoff from this instrument depends on the creditworthiness of one company or country. There are two sides to the contract: the buyer and seller of protection. There is a payoff from the seller of protection to the buyer of protection if the specified entity (company or country) defaults on its obligations.
The most popular multi-name credit derivative is a collateralized debt obligation (CDO). In this, a portfolio of debt instruments is specified and a complex structure is created where the cash flows from the portfolio are channeled to different categories of investors. Before we discussed how multi-name credit derivatives were created from residential mortgages during the period leading up to the credit crisis (securitization and the credit crisis of 2007). This chapter focuses on the situation where the underlying credit risks are those of corporations or countries. Multi-name credit derivatives increased in popularity relative to single-name credit derivatives up to June 2007 but became less popular during the credit crisis.

17. III. Credit Derivatives (CDS and CDO)
Business Snapshot Who Bears the Credit Risk?
Traditionally banks have been in the business of making loans and then bearing the credit risk that the borrower will default. However, banks have for some time been reluctant to keep loans on their balance sheets. This is because, after the capital required by regulators has been accounted for, the average return earned on loans is often less attractive than that on other assets. As discussed, banks created asset-backed securities to pass loans (and their credit risk) on to investors.
In the late 1990s and early 2000s, banks also made extensive use of credit derivatives to shift the credit risk in their loans to other parts of the financial system.
If banks have been net buyers of credit protection, who have been net sellers? The answer is insurance companies. Insurance companies are not regulated in the same way as banks and as a result are sometimes more willing to bear credit risks than banks.
The result of all this is that the financial institution bearing the credit risk of a loan is often different from the financial institution that did the original credit checks. As the credit crisis of 2007 has shown, this is not always good for the overall health of the financial system.

18. III. Credit Derivatives (CDS and CDO)
CREDIT DEFAULT SWAPS (CDS) The most popular credit derivative is a credit default swap (CDS). This is a contract that provides insurance against the risk of a default by particular company. The company is known as the reference entity and a default by the company is known as a credit event. The buyer of the insurance obtains the right to sell bonds issued by the company for their face value when a credit event occurs and the seller of the insurance agrees to buy the bonds for their face value when a credit event occurs. The total face value of the bonds that can be sold is known as the credit default swap's notional principal. The buyer of the CDS makes periodic payments to the seller until the end of the life of the CDS or until a credit event occurs. These payments are typically made in arrears every quarter, but deals where payments are made every month, 6 months, or 12 months also occur and sometimes payments are made in advance. The settlement in the event of a default involves either physical delivery of the bonds or a cash payment. Example An example will help to illustrate how a typical deal is structured. Suppose that two parties enter into a 5-year credit default swap on March 20, Assume that the notional principal is $100 million and the buyer agrees to pay 90 basis points per annum for protection against default by the reference entity, with payments being made quarterly in arrears. The CDS is shown in Figure If the reference entity does not default (i.e., there is no credit event), the buyer receives no payoff and pays 22.5 basis points (a quarter of 90 basis points) on $100 million on June 20, 2012, and every quarter thereafter until March 20, The amount paid each quarter is x 100,000,000, or $225,000.

19. III. Credit Derivatives (CDS and CDO)
If there is a credit event, a substantial payoff is likely. Suppose that the buyer notifies the seller of a credit event on May 20, 2015 (2 months into the fourth year). If the contract specifies physical settlement, the buyer has the right to sell bonds issued by the reference entity with a face value of $100 million for $100 million. If, as is now usual, there is cash settlement, an ISDA-organized auction process is used to determine the mid-market value of the cheapest deliverable bond several days after the credit event. Suppose the auction indicates that the bond is worth $35 per $100 of face value. The cash payoff would be $65 million. The regular quarterly, semiannual, or annual payments from the buyer of protection to the seller of protection cease when there is a credit event. However, because these payments are made in arrears, a final accrual payment by the buyer is usually required. In our example, where there is a default on May 20,2015, the buyer would be required to pay to the seller the amount of the annual payment accrued between March 20, 2015, and May 20, 2015 (approximately $150,000), but no further payments Would be required. The total amount paid per year, as a percent of the notional principal, to buy protection (90 basis points in our example) is known as the CDS spread. Several large banks are market makers in the credit default swap market. When quoting on a new 5-year credit default swap on a company, a market maker might bid 250 basis points and offer 260 basis points. This means that the market maker is prepared to buy protection by paying 250 basis points per year (i.e., 2.5% of the principal per year) and to sell protection for 260 basis points per year (i.e., 2.6% of the principal per year).

20. III. Credit Derivatives (CDS and CDO)
Many different companies and countries are reference entities for the CDS contracts that trade. As mentioned, payments are usually made quarterly in arrears. Contracts with maturities of 5 years are most popular, but other maturities such as 1,2, 3,7, and 10 years are not uncommon. Usually contracts mature on one of the following standard dates: March 20, June 20, September 20, and December 20. The effect of this is that the actual time to maturity of a contract when it is initiated is close to, but not necessarily the same as, the number of years to maturity that is specified. Example Suppose you call a dealer on November 15,2012, to buy 5-year protection on a company. The contract would probably last until December 20, Your first payment would be due on December 20, 2012, and would equal an amount covering the November 15, 2012, to December 20, 2012, period. A key aspect of a CDS contract is the definition of a credit event (i.e., a default). Usually a credit event is defined as a failure to make a payment as it becomes due, a restructuring of debt, or a bankruptcy. Restructuring is sometimes excluded in North American contracts, particularly in situations where the yield on the company's debt is high. More information on the CDS market is given in Business Snapshot 24.2

21. III. Credit Derivatives (CDS and CDO)
Business Snapshot The CDS Market.
In 1998 and 1999, the International Swaps and Derivatives Association (ISDA) developed a standard contract for trading credit default swaps in the over-the-counter market. Since then the market has grown very fast. A CDS contract is like an insurance contract in many ways, but there is one key difference. An insurance contract provides protection against losses on an asset that is owned. In the case of a CDS, the underlying asset does not have to be owned.
During the credit turmoil that started in August 2007, regulators became very concerned about systemic risk. They felt that credit default swaps were a source of vulnerability for financial markets. The danger is that a default by one financial institution might lead to big losses by its counterparties in CDS transactions and further defaults by other financial institutions. Regulatory concerns were fueled by troubles at insurance giant AIG. This was a big seller of protection on the AAA-rated tranches created from mortgages. The protection proved very costly to AIG and the company was bailed out by the U.S. government.
Regulatory concerns have led to the development of clearing houses for CDS trades (and other over-the-counter derivatives) between financial institutions. The clearing house requires market participants to post margin on their CDS trades in much the same way that traders post margin on futures contracts.
During 2007 and 2008, trading ceased in many types of credit derivatives, but CDSs continued to trade actively (although the cost of protection increased dramatically). The advantage of CDSs over some other credit derivatives is that the way they work is straightforward. Other credit derivatives, such as those created from the securitization of household mortgages, lack this transparency.
It is not uncommon for the volume of CDSs on a company to be greater than its debt. Cash settlement of contracts is then clearly necessary. When Lehman defaulted in September 2008, there was about $400 billion of CDS contracts and $155 billion of Lehman debt outstanding. The payout to the buyers of protection (determined by an auction process) was % of principal.

22. III. Credit Derivatives (CDS and CDO)
VALUATION OF CREDIT DEFAULT SWAPS The CDS spread for a particular reference entity can be calculated from default probability estimates. We will illustrate how this is done with a simple example. Example Suppose that the probability of a reference entity defaulting during a year conditional on no earlier default is 2%. Table 24.1 shows survival probabilities and unconditional default probabilities (i.e., default probabilities as seen at time zero) for each of the 5 years. The probability of a default during the first year is 0.02 and the probability the reference entity will survive until the end of the first year is The probability of a default during the second year is 0.02 x 0.98 = and the probability of survival until the end of the second year is 0.98 x 0.98 = The probability of default during the third year is 0.02 x = , and so on.

23. III. Credit Derivatives (CDS and CDO)
We will assume that defaults always happen halfway through a year and that payments on the credit default swap are made once a year, at the end of each year. We also assume that the risk-free (LIBOR) interest rate is 5% per annum with continuous compounding and the recovery rate is 40%. There are three parts to the calculation. These are shown in Tables 24.2, 24.3, and Part I Table 24.2 shows the calculation of the present value of the expected payments made on the CDS assuming that payments are made at the rate of s per year and the notional principal is $1. Example: there is a probability that the third payment of s is made. The expected payment is therefore s and its present value is se-0.05x3 = 0.810s. The total present value of the expected payments is s.

24. III. Credit Derivatives (CDS and CDO)
Part II Table 24.3 shows the calculation of the present value of the expected payoff assum­ing a notional principal of $1. As mentioned earlier, we are assuming that defaults always happen halfway through a year. Example: there is a probability of a payoff halfway through the third year. Given that the recovery rate is 40%, the expected payoff at this time is x 0.6 x 1 = The present value of the expected payoff is e-005x2.5 = The total present value of the expected payoffs is $

25. III. Credit Derivatives (CDS and CDO)
Part III As a final step, Table 24.4 considers the accrual payment made in the event of a default. Example: there is a probability that there will be a final accrual payment halfway through the third year. The accrual payment is 0.5s. The expected accrual payment at this time is therefore x 0.5s = s. Its present value is se-0.05x2.5 = s. The total present value of the expected accrual payments is s.
From Tables 24.2 and 24.4, the present value of the expected payments is
4.0704s s = s 
From Table 24.3, the present value of the expected payoff is Equating the two gives s = or s =
The mid-market CDS spread for the 5-year deal we have considered should be times the principal or 124 basis points per year.

26. III. Credit Derivatives (CDS and CDO)
The Future of the CDS Market The credit default swap market survived the credit crunch of 2007 reasonably well. It is true that it has come under a great deal of regulatory scrutiny and CDSs are being moved to clearing houses. But their importance is unlikely to decline. They are important tools for managing credit risk. A financial institution can reduce its credit exposure to particular companies by buying protection. It can also use CDSs to diversify credit risk. For example, if a financial institution has too much credit exposure to a particular business sector, it can buy protection against defaults by companies in the sector and at the same time sell protection against default by companies in other unrelated sectors. Some market participants think the CDS market will eventually be as big as the interest rate swap market. Others are less, optimistic. There is a potential asymmetric information problem in the CDS market that is not present in other over-the-counter derivatives markets (see Business Snapshot 24.3).

27. III. Credit Derivatives (CDS and CDO)
Business Snapshot Is the CDS Market a Fair Game?
There is one important difference between credit default swaps and the other over-the-counter derivatives that we have considered in this book. The other over-the-counter derivatives depend on interest rates, exchange rates, equity indices, commodity prices, and so on. There is no reason to assume that any one market participant has better information than any other market participant about these variables.
Credit default swaps spreads depend on the probability that a particular company will default during a particular period of time. Arguably some market participants have more information to estimate this probability than others. A financial institution that works closely with a particular company by providing advice, making loans, and handling new issues of securities is likely to have more information about the creditworthiness of the company than another financial institution that has no deal­ings with the company. Economists refer to this as an asymmetric information problem.
Whether asymmetric information will curtail the expansion of the credit default swap market remains to be seen. Financial institutions emphasize that the decision to buy protection against the risk of default by a company is normally made by a risk manager and is not based on any special information that may exist elsewhere in the financial institution about the company.

28. III. Credit Derivatives (CDS and CDO)
COLLATERAL DEBT OBLIGATIONS (CDO) We discussed asset-backed securities (ABSs) in previous lecture. Figure 8.1 shows a simple structure. An ABS where the underlying assets are bonds is known as a collateralized debt obligation, or CDO. A waterfall similar to that indicated in Figure 8.2 is defined for the interest and principal payments on the bonds. The precise rules underlying the waterfall are complicated, but they are designed to ensure that if one tranche is more senior than another it is more likely to receive promised interest payments and repayments of principal.

29. III. Credit Derivatives (CDS and CDO)
Synthetic CDOs
When a CDO is created from a bond portfolio, the resulting structure is known as a cash CDO. In an important market development, it was recognized that a long position in a corporate bond has a similar risk to a short position in a CDS when the reference entity in the CDS is the company issuing the bond. This led an alternative structure known as a synthetic CDO, which has become very popular.
The originator of a synthetic CDO chooses a portfolio of companies and a maturity (e.g., 5 years) for the structure. It sells CDS protection on each company in the portfolio with the CDS maturities equaling the maturity of the structure. The synthetic CDO principal is the total of the notional principals underlying the CDSs. The originator has cash inflows equal to the CDS spreads and cash outflows when companies in the portfolio default. Tranches are formed and the cash inflows and outflows are distributed to tranches. The rules for determining the cash inflows and outflows of tranches are more straightforward for a synthetic CDO than for a cash CDO. Suppose that there are only three tranches: equity, mezzanine, and senior. The rules might be as follows:
The equity tranche is responsible for the payouts on the CDSs until they reach 5% of the synthetic CDO principal. It earns a spread of 1000 basis points per year on the outstanding tranche principal.
The mezzanine tranche is responsible for payouts in excess of 5% up to a maximum of 20% of the synthetic CDO principal. It earns a spread of 100 basis points per year on the outstanding tranche principal.
The senior tranche is responsible for payouts in excess of 20%. It earns a spread of 10 basis points per year on the outstanding tranche principal.

30. III. Credit Derivatives (CDS and CDO)
Example: To understand how the synthetic CDO would work, suppose that its principal is $100 million. The equity, mezzanine, and senior tranche principals are $5 million, $15 million, and $80 million, respectively. The tranches initially earn the specified spreads on these notional principals. Suppose that after 1 year defaults by companies in the portfolio lead to payouts of $2 million on the CDSs. The equity tranche holders are responsible for these payouts. The equity tranche principal reduces to $3 million and its spread (1,000 basis points) is then earned on $3 million instead of $5 million. If, later during the life of the CDO, there are further payouts of $4 million on the CDSs, the cumulative of the payments required by the equity tranche is $5 million, so that its outstanding principal becomes zero. The mezzanine tranche holders have to pay $1 million. This reduces their outstanding principal to $14 million. Cash CDOs require an initial investment by the tranche holders (to finance the underlying bonds). By contrast, the holders of synthetic CDOs do not have to make an initial investment. They just have to agree to the way cash inflows and outflows will be calculated. In practice, they are almost invariably required to post the initial tranche principal as collateral. When the tranche becomes responsible for a payoff on a CDS, the money is taken out of the collateral. The balance in the collateral account earns interest at LIBOR.

31. Management of credit risk
SUMMARY The probability that a company will default during a particular period of time in the future can be estimated from historical data, bond prices, or equity prices. The default probabilities calculated from bond prices are risk-neutral probabilities, whereas those calculated from historical data are real-world probabilities. The expected loss experienced from a counterparty default is reduced by what is known as netting. This is a clause in most contracts written by a financial institution stating that, if a counterparty defaults on one contract it has with the financial institution, it must default on all contracts it has with the financial institution. Losses are also reduced by collateralization and downgrade triggers. Collateralization requires the counterparty to post collateral and a downgrade trigger gives a financial institution the option to close out a contract if the credit rating of a counterparty falls below a specified level. Credit derivatives enable banks and other financial institutions to actively manage their credit risks. They can be used to transfer credit risk from one company to another and to diversify credit risk by swapping one type of exposure for another. The most common credit derivative is a credit default swap (CDS). This is a contract where one company buys insurance from another company against a third company (the reference entity) defaulting on its obligations. The payoff is usually the difference between the face value of a bond issued by the reference entity and its value immediately after a default. Credit default swaps can be analyzed by calculating the present value of the expected payments and the present value of the expected payoff in a risk-neutral world. In a collateralized debt obligation (CDO) a number of different securities are created from a portfolio of corporate bonds or commercial loans. There are rules for determining how credit losses are allocated. The result of the rules is that securities with both very high and very low credit ratings are created from the portfolio. A synthetic collateralized debt obligation creates a similar set of securities from credit default swaps.