fabozzi_BMAS9_IM_32.docx

CHAPTER 32 CREDIT DEFAULT SWAPS CHAPTER SUMMARY In this chapter, we describe the different types of credit default swap (CDSJ), the basics of CDS valuation for a single-name CDS, and how a CDS can be used to control risk. We begin with the critical element in a CDS: the definition of a credit event. CREDIT EVENTS

A credit default swap (CDS) has a payout that is contingent upon a credit event occurring. The ISDA provides definitions of what credit events are. The 1999 ISDA Credit Derivatives Definitions (referred to as the “1999 Definitions”) provides a list of eight credit events: (1) bankruptcy, (2) credit event upon merger, (3) cross acceleration, (4) cross default, (5) downgrade, (6) failure to pay, (7) repudiation/moratorium, and (8) restructuring. These eight events attempt to capture every type of situation that could cause the credit quality of the reference entity to deteriorate, or cause the value of the reference obligation to decline. Bankruptcy is defined as a variety of acts that are associated with bankruptcy or insolvency laws. Failure to pay results when a reference entity fails to make one or more contractual payments when due. When a reference entity breaches a covenant, it has defaulted on its obligation. When a default occurs, the obligation becomes due and payable prior to the scheduled due date had the reference entity not defaulted. This is referred to as an obligation acceleration . A reference entity may disaffirm or challenge the validity of its obligation. This is a credit event that is covered by repudiation/moratorium .

The most controversial credit event that may be included in a credit default product is restructuring of an obligation. A restructuring occurs when the terms of the obligation are altered so as to make the new terms less attractive to the debt holder than the original terms. The terms that can be changed would typically include, but are not limited to, one or more of the following: (1) a reduction in the interest rate, (2) a reduction in the principal, (3) a rescheduling of the principal repayment schedule (e.g., lengthening the maturity of the obligation) or postponement of an interest payment, pa yment, or (4) a change in the level of seniority of the obligation in the reference entity’s debt structure. Credit Events for an Asset-Backed Security CDS are written on asset-backed securities (ABS) and referred to as ABS CDS. There are unique aspects of an ABS that required a modification of the ISDA documentation with respect credit event definitions when the reference entity is an ABS tranche. In June 2005, the ISDA released what it refers to as its pay-as-you-go (PAUG) template for ABS. The focus was on cash flow adequacy of the ABS structure rather than the potential for bankruptcy. Accordingly, the ISDA

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PAUG template provided the following three credit events that focus on cash flow adequacy for ABS transactions: Failure to pay. The underlying reference obligation fails to make a scheduled interest or principal payment. Writedown. The principal component of the underlying reference obligation is written down and deemed irrecoverable. Distressed ratings downgrade. The underlying reference obligation is downgraded to a rating of Caa2 / CCC or lower lower 

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SINGLE-NAME SINGLE-NAME CDS

In a single-name CDS, there is only one reference entity or reference obligation. There are single-name CDSs written on a corporate debt issuer (bonds or leverage loans) sovereign issuer municipal bond issuer tranche of an asset-backed security To explain the mechanics of a single-name CDS we will use an illustration for a CDS written on a corporate bond issuer. The underlying for the CDS is $10 million par value of the XYZ bond issue, and a notional amount of $10 million.    

The swap premium (the payment made by the protection buyer to the protection seller) is 200 basis points. The standard contract for a single-name CDS calls for a quarterly payment of the swap premium. The day count convention used for CDSs is actual / 360. Consequently, the swap premium payment for a quarter is quarterly swap premium payment = notional amount × swap rate (in decimal) ×

actual number of days in quarter 360

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Given 92 actual days in a quarter and the swap premium of 200 basis points (0.02), the quarterly swap premium payment made by the protection buyer would be quarterly swap premium payment = $10,000,000 × 0.02 ×

92 360

= $51,111.11.

If a credit event occurs, two things happen. First, there are no further payments of the swap premium by the protection buyer to the protection seller. Second, a termination value is determined for the swap. With physical settlement the protection buyer delivers a specified amount of the face value of bonds of the reference entity to the protection seller. The protection seller pays the protection buyer the face value of the bonds. Because unlike in our hypothetical illustration for XYZ Corporation where only one issue of the reference entity was assumed to be outstanding, in the real world all reference entities have many issues outstanding and therefore there will be


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a number of alternative issues of the reference entity that the protection buyer can deliver to the protection seller. These issues are known as deliverable obligations . An alternative to the standard CDS contract which specifies physical settlement is a fixed recovery CDS . The type of CDS eliminates the uncertainty on the recovery rate by fixing at the time of the trade a specific recovery value. With a fixed recovery CDS, if a credit event is triggered by the reference entity, the protection seller makes a cash settlement that is equal to 100 minus the specified fixed recovery rate. Approximating the Value of a Single-Name CDS Let’s look at the general principles for pricing or valuing single -name CDS on a corporate bond issuer. We begin with a set of simplifying assumptions. There are eight assumptions needed to value a single-name CDS with a maturity of T years for a reference entity. Given these assumptions, we want to know how the CDS premium, denoted by S , of a single-name CDS with a maturity of T for some reference entity is determined. Consider the following strategy:  

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Buy the floating-rate debt obligation with maturity T issued by the reference entity. Fund the purchase of the floating-rate debt obligation by borrowing for the life of that debt obligation (which is also the term of the CDS), T , in the repo market. To hedge the credit risk associated with the floating-rate debt obligation, purchase protection by buying a CDS with a maturity of T on the reference entity.

This strategy is equivalent to a default-free investment. Let’s look at the payoff for the two possible outcomes: no credit event occurs or a credit event occurs. If no credit event occurs, then the floating-rate debt obligation matures. Over the life of the debt obligation, the interest earned is equal to LIBOR + F each period. The cost of borrowing (i.e., the repo rate) for each period is LIBOR + B. Hence, LIBOR + F is received from ownership of the asset and LIBOR + B is paid out to borrow funds. The net cash flow is therefore what is earned: F – B. That is, under our simplifying assumptions, the strategy will have a payoff of F – B in the no credit event scenario.

Consider next what would happen if there is a credit event. Assuming physical delivery of the floating-rate debt obligation, the floating-rate debt obligation is delivered to the credit protection seller (i.e., the seller of the single-name CDS). Because we assume the credit event occurs right after the floating-rate debt obli gation’s coupon payment is made, there are no further coupon payments and no accrued CDS payment. The proceeds obtained from the CDS protection seller are used to repay the amount borrowed to purchase the floating-rate debt obligation. Hence, the repo loan has been repaid. As a result, we have the same payoff for this strategy as in the scenario where there is no credit event: F – B. Asset Swap When an investor owns an asset and converts its cash flow characteristics, the investor is said to have created an asset swap. Let’s now illustrate a basic asset swap. Suppose that an investor purchases $10 million par value of a 7.85%, 5-year bond of a BBB rated corporation at par value.


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The coupon payments are semiannual. At the same time, the investor enters into a 5-year interest-rate swap with a dealer where the investor is the fixed-rate payer and the payments are made semiannually. Suppose that the swap rate is 7.00% and the investor receives 6-month LIBOR. Let’s look at the cash flow for the investor ev ery six months for the next five years:

Received from bond: 7.85% – Payment to dealer on swap: 7.00% + Payment from dealer on swap: 6-month LIBOR Net received by investor: 0.85% + 6-month LIBOR Thus, regardless of how interest rates change, if the issuer does not default, the investor earns 85 basis points over 6-month LIBOR. Effectively, the investor has converted a fixed-rate BBB 5-year bond into a 5-year floating-rate bond with a spread over 6-month LIBOR. Thus, the investor has created a synthetic floating-rate bond. The purpose of an asset swap is to do precisely that: create a synthetic credit-risky floating-rate security. An asset swap typically combines the sale of a credit-risky bond owned to a counterparty at par and with no interest accrued, with an interest-rate swap. This type of asset swap structure or package is referred to as a par asset swap . The coupon on the bond in the par asset swap is paid in return for LIBOR, plus a spread if necessary. This spread is the asset swap spread and is the price of the asset swap. To illustrate this asset swap structure, suppose that in our previous illustration the swap rate prevailing in the market is 7.30% rather than 7.00%. The investor owns the bonds and sells them to a dealer at par with no accrued interest. The asset swap agreement between the dealer and the investor is as follows:   

The term is five years. The investor agrees to pay the dealer semiannually 7.30%. The dealer agrees to pay the investor every six months 6-month LIBOR plus an asset swap spread of 30 basis points.

Let’s look at the cash flow for the investor every six months for the next five years for this asset swap structure:

Received from bond: 7.85% – Payment to dealer on swap: 7.30% + Payment from dealer on swap: 6-month LIBOR + 30 basis points Net received by investor: 0.85% + 6-month LIBOR In our first illustration of an asset swap, the investor is creating a synthetic floater without a dealer. The investor owns the bonds. The only involvement of the dealer is as a counterparty to the interest-rate swap. In the second structure, the dealer is the counterparty to the asset swap structure and the dealer owns the underlying credit-risky bonds. If there is a default, the dealer returns the bonds to the investor.


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CDS Implied Default Probabilities In the early days of the CDS market, the following naïve relationship was used to back out default probabilities from the observed CDS spread: Observed CDS spread in bps / 10,000 = (1 – Assumed recovery rate) × (Assumed default probability) Note that in this formula, we use default probability. Given an assumed recovery rate, then an implied default probability can be obtained by solving the above equation for the default probability: Implied default probability =

Observed CDSspread in bps / 10,000 1 – Assumed recovery rate

Market players will employ an industry standard fixed recovery rate depending on the underlying to obtain the implied default probability. INDEX CDS

An index CDS is a CDS written on a standardized basket of reference entities and include CDS written on     

Corporate debt issuers Sovereign government issuers Municipal debt issuers Tranches of asset-backed securities Tranches of commercial mortgage-backed securities

The mechanics of an index CDS are slightly different from that of a single-name CDS. As with a single-name CDS, a swap premium is paid. However, if a credit event occurs, once the accrued payment to the credit event date is paid, the swap premium payment ceases in the case of a single-name CDS. In contrast, for an index CDS, the swap payment continues to be made by the protection buyer. Index CDS Written on Corporate, Sovereign, and Municipal Debt Issuers The two most actively traded CDX on corporate bonds for reference entities in North America are the North America Investment Grade Index (denoted by CDX.NA.IG) and the North America High Yield Index (denoted by CDX.NA.HY). In addition to index CDS on corporate bond issuers, there is an index CDS on leveraged loans (denoted LCDX). What differentiates the LCDX from the corporate bond CDX such as the CDX.HY is that the LCDX references a collection of loans (i.e., any / all outstanding senior secured bank debt of the reference issuer).


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There are index CDS written on sovereign governments in regions throughout the world. There is an index CDS written on 50 municipal entities (denoted by MCDX) ranging from general obligation debt to revenue bonds from municipal authorities. Index CDS Written on Tranches of ABS The index CDS written on ABS transactions are called ABX.HE. The index includes 20 home equity loan deals from the “top 20” issuers at the time. The mechanics of an ABX.HE differ from that of the other index CDS beyond that of defining of a credit event. The other index CDS we have described exchange payments quarterly. In the case of the ABX.HE, the protection buyer makes the swap payment monthly based on the notional amount. The notional amount will decline over time due to the amortization of the tranches. Index CDS Written on Tranches of Commercial Mortgage-Backed Securities There are index CDS written on deals of commercial mortgage-backed securities (CMBS). This index CDS, denoted by CMBX, consists of deals from 25 CMBS transactions. As with the ABX.HE, there are sub-indices based on tranche ratings. The PAUG template is used as with the ABX.HE. ECONOMIC INTERPRETATION OF A CDS AND INDEX CDS

To appreciate the potential application of a CDS and index CDS to control a portfolio’s credit risk that will be discussed in the next section, let’s look at the economic interpretation of these deriva tive products from the perspective of the credit protection seller and the credit protection buyer.

Credit Protection Seller Consider first the credit protection seller in a single-name CDS. What is the equivalent position of the credit protection seller in the cash market? For illustration purposes, we will assume that the reference obligation is bond ABC. If an investor buys bond ABC, then the investor will have the following cash flow:  

Cash outlay equal to bond ABC’s price, P 0. Semiannual cash inflows equal to one half of bond ABC’s annual coupon rate

The semiannual coupon payments will be received as long as bond ABC does not default. If the investor sells bond ABC at time T , then there will be a cash inflow equal to bond ABC’s sale price, P T . Suppose that at time T an adverse event occurred causing bond ABC’s price to fall below the purchase price paid by the investor (i.e., P T < P 0). The investor then realizes a loss equal to the P T − P 0. Let’s look at the cash flow for the credit protection seller where the reference obligation is bond ABC. This party to the CDS receives a quarterly payment equal to the CDS spread. That is, there is a cash inflow equal to the quarterly swap payment. However, the swap payments are only made if bond ABC does not trigger a credit event.


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Let’s now suppose that a credit event occurs. The protection seller must make a payment to the protection buyer. This payment represents a cash outlay or loss for the protection seller. But consider that there is a loss that occurs for the investor who buys bond ABC if an adverse event occurs. Once again, this cash flow attribute is similar for both the protection seller and an investor in a bond.

Consequently, the protection seller has an economic position that is analogous to an investor in a cash bond (i.e., an investor who owns a bond). This makes sense because both the protection seller and the investor long a cash bond are buyers of the bond issuer’s credit risk. Credit Protection Buyer It should be no surprise that if the protection seller in a CDS has a position analogous to a long position in the cash bond that the protection buyer in a CDS has a position analogous to a short position in a cash bond. Let’s see why once again using a single-name CDS where the reference obligation is bond ABC. If an investor shorts bond ABC, then the investor will have the following cash flow: Cash inflow equal to bond ABC’s price, P 0. Semiannual cash outflows equal to one half of bond ABC’s annual coupon rate The semiannual coupon payments will be made by the investor because the short is responsible for reimbursing the party that it borrowed the bond from an amount equal to the coupon payment. This payment occurs as long as bond ABC does not default. If the investor buys bond ABC at time T to cover the short position, then there will be a cash outflow equal to bond ABC’s sale price, P T . Suppose that at time T an adverse event occurred causing bond ABC’s price to fall below the price the investor sold the bond short (i.e., P T < P 0). The investor then realizes a gain equal to the P 0 − P T . Let’s look at the cash flow for the credit protection buyer where the reference obligation is bond ABC. This party to the CDS makes a quarterly payment equal to the CDS spread. However, the swap payments are only made if bond ABC does not trigger a credit event. Thus, as with an investor who shorted bond ABC, there are periodic cash outflows as long as there is no adverse credit event that stops the payments (default in the case of shorting the cash bond and credit event in the case of a CDS). This cash flow characteristic of the protection buyer’s position is similar to that of a short seller of a cash bond. Let’s now suppose that a credit event occurs. The protection buyer no longer must make any payment to the protection buyer. Consequently, the protection buyer has an economic position that is analogous to a short position in a cash bond. USING CDS FOR CONTROLLING CREDIT RISK

Consider a single-name credit CDS written on a corporate reference entity. The liquidity of the CDS market compared to the corporate bond market makes it more efficient to obtain exposure


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to a reference entity by taking a position in the CDS market rather than in the cash market. For a portfolio manager seeking a leveraged position in a corporate bond, this can be done with a CDS because the economic position of a protection seller is equivalent to a leveraged position in a corporate bond. A portfolio manager can shed the exposure to a particular corporate issuer held in a portfolio by buying protection via a single-name CDS. A reasonable question is why a portfolio manager may want to do using a CDS rather than merely selling the bond in the cash market. One reason for less liquid corporate bond names is that conditions in the cash market may be such that it is difficult for the portfolio manager to sell the current holding of a corporate bond of an issuer for which the manager has a credit concern. What is important to note is that although CDS do offer leveraging opportunities for a portfolio manager who is permitted to do so, no leveraging need occur if the funds that would have been used to purchase the reference entities are placed in cash rather than used to purchase other reference entities. KEY POINTS 

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Interest-rate derivatives can be used to control interest-rate risk with respect to changes in the level of interest rates. Credit derivatives can be used to control the credit risk of a security. By far, the most dominant type of credit derivative is the credit default swap wherein the protection buyer makes a payment of the swap premium to the protection seller; however, the protection buyer receives a payment from the protection seller only if a credit event occurs. The payments for a CDS depend on the triggering of a credit event. The International Swaps and Derivatives Association documentation for a trade define potential credit events. The most controversial credit event is restructuring. There are special credit event definitions for CDS written on tranches of asset-backed securities (the pay-as-you go definitions). The is only one reference entity or reference obligation in a single-name CDS, and these contracts are written on a corporate debt issuer (bonds or leverage loans), sovereign issuer, tranche of an asset-backed security, and municipal bond issuer. The value of a single-name CDS can be approximated by the difference between the asset swap spread (from the par asset swap market) and the spread over LIBOR in the repo market. An asset swap structured by a dealer firm involves an investor selling a fixed-rate credit risky bond to the dealer firm and receiving floating-rate payments. A CDS valuation model can be used to obtain the implied default probability for a reference entity. However, the probability calculated depends on the validity of the model and the estimated inputs. A CDS written on a standardized basket of reference entities is called an index CDS; this type of CDS is written on corporate debt issuers, sovereign government issuers, municipal debt issuers, tranches of asset-backed securities, and tranches of commercial mortgage-backed securities.


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Unlike a single-name CDS where the contract terminates upon the triggering of a credit event, for an index CDS, the swap payments continue if a credit event for one of the reference entities is triggered. However, the swap payments are reduced because of the lower notional amount resulting from the removal from the index of the reference entity for which a credit event was triggered. The economic interpretation of the credit protection seller is that it is analogous to a leveraged position in the reference entity (in the case of a single-name CDS) or the standardized basket of reference entities (in the case of an index CDS). For the credit protection buyer, the position is analogous to a short position in the reference entity or reference entities. Single-name CDS and be used to alter the credit risk exposure of reference entity. Typically liquidity is greater in the CDS market than in the cash market and it is easier to short in the CDS market. An index CDS can be used to adjust the credit exposure of a portfolio: increasing credit exposure by being the credit protection seller and decreasing credit exposure by being the credit protection buyer.


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ANSWERS TO QUESTIONS FOR CHAPTER 32 (Questions are in bold print followed by answers.) 1. How does the role of a credit derivative differ from that of an interest-rate swap in terms of controlling risk?

Recall that derivatives can be used to control risk (hedging being a special case of risk control where risk is eliminated) and provide a more transactionally efficient vehicle for doing so. Thus, a credit derivative controls for a credit risk in a manner that an interest-rate swap cannot. More details are given below. A credit derivative is a securitized derivative whose value is derived from the credit risk on an underlying bond, loan or any other financial asset. In this way, the credit risk is on an entity other than the counterparties to the transaction itself. This entity is known as the reference entity and may be a corporate, a sovereign or any other form of legal entity which has incurred debt. Credit derivatives are bilateral contracts between a buyer and seller under which the seller sells protection against the credit risk of the reference entity. An interest rate swap is a derivative involving an agreement between two parties (known as counterparties) where one stream of future interest payments is exchanged for another based on a specified principal amount. A company will typically use interest rate swaps to limit or manage exposure to fluctuations in interest rates, or to obtain a marginally lower interest rate than it would have been able to get without the swap. Interest rate swaps expose users to interest rate risk and credit risk. A typical swap consists of two legs, one fixed, the other floating. Some think that the risky component is the floating leg, because the underlying interest rate floats and so is unknown. However, the risky component is in fact the fixed leg because the value of the floating leg changes very little during the life of a swap. On the other hand the fixed leg of a swap is equivalent to a coupon bond and fluctuations of the swap rate may have major effects on the value of the future fixed payments. To hedge the credit risk associated with the floating-rate debt obligation, one can purchase protection by buying a credit derivative swap with a maturity of T on the reference entity. Credit risk on the swap comes into play if the swap is in the money or not. If one of the parties is in the money, then that party faces credit risk of possible default by another party. Risks involving credit derivatives are a concern among regulators of financial markets. One challenge in regulating these and other derivatives is that the people who know most about them typically have a vested incentive in encouraging their growth and lack of regulation. 2. Why is a portfolio manager concerned with more than default risk when assessing a portfolio’s credit exposure?

Credit risk includes three types of risk: (i) the risk that the issuer will default (default risk), (ii) the risk that the credit spread will increase (credit spread risk), and (iii) the risk that an issue will be downgraded (downgrade risk). Thus, when assessing a portfolio’s credit exposure, more than just default risk needs to be considered.


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3. Answer the below questions. (a) What is meant by a reference entity?

The ISDA documentation will identify the reference entity and the reference obligation. The reference entity is the issuer of the debt instrument and hence also referred to as the reference issuer. It could be a corporation or a sovereign government. For example, a reference entity could be Sunset Chevrolet Credit Company. (b) What is meant by a reference obligation?

The reference obligation, also referred to as the reference asset, is the particular debt issue for which the credit protection is being sought. For example, if the reference entity is Sunset Chevrolet Credit Company, then the reference obligation would be a specific Sunset Chevrolet Credit Company bond issue. 4. What authoritative source is used for defining a “credit event”?

The International Swap and Derivatives Association (ISDA) provide definitions of what credit events are. The 1999 ISDA Credit Derivatives Definitions (referred to as the “1999 Definitions”) provides a list of eight credit events: bankruptcy, credit event upon merger, cross acceleration, cross default, downgrade, failure to pay, repudiation/moratorium, and restructuring. These eight events attempt to capture every type of situation that could cause the credit quality of the reference entity to deteriorate, or cause the value of the reference obligation to decline. In January 2003, the ISDA published its revised credit events definitions in the 2003 ISDA Credit Derivative Definitions (referred to as the “2003 Definitions”). The revised definitions reflected amendments to several of the definitions for credit events set forth in the 1999 Definitions. Specifically, there were amendments for bankruptcy, repudiation, and restructuring. The major change was to restructuring, whereby the ISDA allows parties to a given trade to select from among the following four definitions: (i) no restructuring; (ii) “full” or “old” restructuring, which is based on the 1993 Definitions; (iii) “modified restructuring,” which is based on the Supplement Definition; and (iv) “modified modified restructuring.” The last choice is new and was included to address issues that arose in the European market. 5. Why is “restructuring” the most controversial credit event?

The most controversial credit event that may be included in a credit default swap is restructuring of an obligation. A restructuring occurs when the terms of the obligation are altered so as to make the new terms less attractive to the debt holder than the original terms. The terms that can be changed would typically include, but are not limited to, one or more of the following: (i) a reduction in the interest rate, (ii) a reduction in the principal, (iii) a rescheduling of the principal repayment schedule (e.g., lengthening the maturity of the obligation) or postponement of an interest payment, or (iv) a change in the level of seniority of the obligation in the reference entity’s debt structure.


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The reason why restructuring is controversial is that a protection buyer profits from the inclusion of a restructuring as a credit event and feels that eliminating restructuring as a credit event will erode its credit protection. The protection seller, in contrast, would prefer not to include restructuring because even routine modifications of obligations that occur in lending arrangements would trigger a payout to the protection buyer. Moreover, if the reference obligation is a loan and the protection buyer is the lender, there is a dual benefit for the protection buyer to restructure a loan. First, the protection buyer receives a payment from the protection seller. Second, the accommodating restructuring fosters a link between the lender (who is the protection buyer) and its customer (the corporate entity that is the obligor of the reference obligation). 6. Why does a credit default swap have an option-type payoff?

A credit default swap has an option-type payoff because the occurrence of a contingent event triggers the buyer to exercise their right to enhance their value. More details are given below. Credit default swaps are used to shift credit exposure to a credit protection seller. Their primary purpose is to hedge the credit exposure to a particular asset or issuer. In this sense, credit default swaps operate much like a standby letter of credit or insurance policy. In a credit default swap, the protection buyer pays a fee to the protection seller in return for the right to receive a payment conditional upon the occurrence of a credit event by the reference obligation or the reference entity. If a credit event occurs, then the protection seller must make a payment. Because an option by definition involves a right and not an obligation to do something conditional upon an event occurring, the credit default swap involves an option-type payoff. The payoff is made when the credit event occurs in which case the protection buyer settles with the protection seller and receives the designated payment. Credit default swaps can be settled in cash or physically. Physical delivery means that if a credit event as defined by the documentation occurs, the protection buyer delivers the reference obligation to the protection seller in exchange for cash payment. Because physical delivery does not rely upon obtaining market prices for the reference obligation in determining the amount of the payment in a single-name CDS, this method of delivery is more efficient. Finally, the credit default swap can be documented much like a credit put option where the amount to be paid by the protection seller is an established strike price less the current market value of the reference obligation. 7. Comment on the following statement: “Restructuring is included in credit default swaps and therefore the reduction in a reference obligation’s interest rate will result in the triggering of a payout. This exposes the protection seller to substantial risk.”

Reduction in a reference obligation’s interest rate is one term of the contract that can cause a restructuring. This exposes the protection seller to risk because restructuring tends to favor the protection buyer. More details are given below.


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The most controversial credit event that may be included in a credit default swap is restructuring of an obligation. A restructuring occurs when the terms of the obligation are altered so as to make the new terms less attractive to the debt holder than the original terms. The terms that can be changed would typically include, but are not limited to, one or more of the following: (i) a reduction in the interest rate, (ii) a reduction in the principal, (ii) a rescheduling of the principal repayment schedule (e.g., lengthening the maturity of the obligation) or postponement of an interest payment, or (iv) a change in the level of seniority of the obligation in the reference entity’s debt structure. The reason why restructuring is so controversial is a protection buyer benefits from the inclusion of a restructuring as a credit event and feels that eliminating restructuring as a credit event will erode its credit protection. The protection seller, in contrast, would prefer not to include restructuring because even routine modifications of obligations that occur in lending arrangements would trigger a payout to the protection buyer. Moreover, if the reference obligation is a loan and the protection buyer is the lender, there is a dual benefit for the protection buyer to restructure a loan. The first benefit is that the protection buyer receives a payment from the protection seller. Second, the accommodating restructuring fosters a relationship between the lender (who is the protection buyer) and its customer (the corporate entity that is the obligor of the reference obligation). Because of this problem, the Restructuring Supplement to the 1999 ISDA Credit Derivatives Definitions (the Supplement Definition) issued in April 2001 provided a modified definition for restructuring. There is a provision for the limitation on reference obligations in connection with restructuring of loans made by the protection buyer to the borrower that is the obligor of the reference obligation. This provision requires the following in order to qualify for a restructuring: (i) there must be four or more holders of the reference obligation and (ii) there must be consent to the restructuring of the reference obligation by a supermajority (66 2/3%). In addition, the supplement limits the maturity of reference obligations that are physically deliverable when restructuring results in a payout triggered by the protection buyer. 8. All other factors constant, for a given reference obligation and a given scheduled term, explain whether a credit default swap using full or old restructuring or modified restructuring would be more expensive.

A credit default swap using the old restructuring should be more expensive to the protection seller to the extent that it allows for a wider range of acceptable credit events through a more liberal interpretation that has fewer constraints as to what qualifies for a credit event. However, to the extent a modified restructuring reduces the costs associated with a credit event, then the expenses can be reduced. More details are supplied below. Because of costly squabbles over restructuring, the Restructuring Supplement to the 1999 ISDA Credit Derivatives Definitions (the Supplement Definition) issued in April 2001 provided a modified definition for restructuring. There is a provision for the limitation on reference obligations in connection with restructuring of loans made by the protection buyer to the borrower that is the obligor of the reference obligation.


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As the credit derivatives market developed, market participants learned a great deal about how to better define credit events, particularly with the record level of high yield corporate bond default rates in 2002 and the sovereign defaults, particularly the experience with the 2001-2002 Argentina debt crisis. In January 2003, the ISDA published its revised credit events definitions in the 2003 ISDA Credit Derivative Definitions (referred to as the “2003 Definitions”). The revised definitions reflected amendments to several of the definitions for credit events set forth in the 1999 Definitions. Specifically, there were amendments for bankruptcy, repudiation, and restructuring. The major change was to restructuring, whereby the ISDA allows parties to a given trade to select from among the following four definitions: (i) no restructuring; (ii) “full” or “old” restructuring, which is based on the 1993 Definitions; (ii) “modified restructuring,” which is based on the Supplement Definition; and (iv) “modified modified restructuring.” The last choice is new and was included to address issues that arose in the European market. 9. The focus in an asset-backed securities CDS is on the cash-paying ability of the collateral and not on bankruptcy. Why?

CDS are written on asset-backed securities (ABS) and referred to as ABS CDS. As explained in Chapters 13, 14, and 15, ABS includes a wide range of asset types. Recall that the convention in the marketplace prior to 2007 was to classify those residential mortgage-backed securities where the collateral was a pool of subprime mortgage loans as part of the ABS market and not the MBS market. Consequently, much of the CDS written on ABS involved subprime mortgage pools. There are unique aspects of an ABS that required a modification of the ISDA documentation with respect credit event definitions when the reference entity is an ABS tranche. In June 2005, the ISDA released what it refers to as its pay-as-you-go (PAUG) template for ABS. The focus was on cash flow adequacy of the ABS structure rather than the potential for bankruptcy. (Recall from Chapter 15 that the issuer of an ABS is not a corporation but a bankruptcy remote trust.) Accordingly, the ISDA PAUG template provided the following three credit events that focus on cash flow adequacy for ABS transactions: 1) Failure to pay. The underlying reference obligation fails to make a scheduled interest or principal payment. 2) Writedown. The principal component of the underlying reference obligation is written down and deemed irrecoverable. 3) Distressed ratings downgrade. The underlying reference obligation is downgraded to a rating of Caa2/CCC or lower As can be seen, unlike a CDS where the reference entity is a corporation where a credit event is intended to capture an event of default, the PAUG template seeks to capture any non-default events that impact the cash flow of the specific reference ABS tranche. 10. Answer the below questions. (a) For a single-name credit default swap, what is the difference between physical settlement and cash settlement?


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For a single-name credit default swap (CDS), physical delivery for a credit event means that the protection buyer delivers a reference obligation to the protection seller in exchange for a cash payment. For a single-name CDS, physical delivery does not rely on getting market prices for the reference obligation in determining the amount of cash payment. For a single-name CDS, cash settlement is not preferred method of settlement. However, if settled with cash, the termination value is equal to the difference between the nominal amount of the reference obligation for which a credit event has occurred and its market value at the time of the credit event. The termination value is then the amount of the payment made by the protection seller to the protection buyer. No bonds are delivered by the protection buyer to the protection seller. More details are given below. The interdealer market has evolved to where single-name CDSs for corporate and sovereign reference entities are standardized. Although trades between dealers have been standardized, there are occasional trades in the interdealer market where there is a customized agreement. Because physical delivery does not rely upon obtaining market prices for the reference obligation in determining the amount of the payment in a single-name CDS, the method of physical delivery is more efficient. The payment by the credit protection seller if a credit event occurs may be a predetermined fixed amount or it may be determined by the decline in value of the reference obligation. The standard single-name CDS when the reference entity is a corporate bond or a sovereign bond is fixed based on a notional amount. When the cash payment is based on the amount of asset value deterioration, this amount is typically determined by a poll of several dealers. If no credit event has occurred by the maturity of the swap, both sides terminate the swap agreement and no further obligations are incurred. The methods used to determine the amount of the payment obligated of the protection seller under the swap agreement can vary greatly. To illustrate the mechanics of a single-name CDS, assume that the reference entity or reference name is XYX Corporation and the underlying is $10 million par value of XYZ bonds. The $10 million is the notional amount of the contract. The swap premium — the payment made by the protection buyer to the protection seller — is 200 basis points. The standard contract for a single-name CDS calls for a quarterly payment of the swap premium. The quarterly payment is determined using one of the day count conventions in the bond market. The day count convention used for credit default swaps is actual/360, the same convention as used in the interest-rate swap market. A day convention of actual/360 means that to determine the payment in a quarter, the actual number of days in the quarter is used and 360 days are assumed for the year. Thus, the swap premium payment for a quarter is: quarterly swap premium payment = notional amount × swap rate (in decimal) ×



.

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For example, assume a hypothetical credit default swap where the notional amount is $10 million and there are 92 actual days in a quarter. Because the swap premium is 200 basis points (0.02), the quarterly swap premium payment made by the protection buyer is: quarterly swap premium payment = $10,000,000 × 0.02 ×

92 360

= $51,111.11

In the absence of a credit event, the protection buyer will make a quarterly swap premium payment over the life of the swap. If a credit event occurs, two things happen. First, there are no further payments of the swap premium by the protection buyer to the protection seller. Second, a termination value is determined for the swap. The procedure for computing the termination value depends on the settlement terms provided for by the swap. This will be either physical settlement or cash settlement. (b) In physical settlement, why is there a cheapest-to-deliver issue?

There is a cheapest-to-deliver issue because (by convention or design) protection sellers have been granted an embedded option allowing them to deliver that issue which is the least expensive or at least the most convenient. More details are given below. The market practice for settlement for single-name CDSs is physical settlement as opposed to cash settlement. With physical settlement the protection buyer delivers a specified amount of the face value of bonds of the reference entity to the protection seller. The protection seller pays the protection buyer the face value of the bonds. Because all reference entities that are the subject of credit default swaps have many issues outstanding, there will be a number of alternative issues of the reference entity that the protection buyer can deliver to the protection seller. These issues are known as deliverable obligations. The swap documentation will set forth the characteristics necessary for an issue to qualify as a deliverable obligation. Recall that for Treasury bond and note futures contracts the short has the choice of which Treasury issue to deliver that the exchange specifies as acceptable for delivery. The short will select the cheapest-to-deliver issue, and the choice granted to the short is effectively an embedded option. The same is true for physical settlement for a single-name CDS. From the list of deliverable obligations, the protection buyer will select for delivery to the protection seller the cheapest-to-deliver issue. 11. For a CDS with the following terms, indicate the quarterly premium payment by filling in the below exhibit.

Swap Premium (a) 600 bps (b) 450 bps (c) 720 bps

Notional Amount $15,000,000 $ 8,000,000 $15,000,000

Days in Quarterly Quarter Premium Payment 90 91 92

In the absence of a credit event, the protection buyer will make a quarterly swap premium payment given by the below formula: Copyright © 2016 Pearson Education, Inc.

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quarterly swap premium payment = notional amount × swap rate (in decimal) ×


.

For swap premium (a) of 600 bps, we insert the given value into our quarterly swap premium payment formula and get:

quarterly swap premium payment = $15,000,000 × 0.060 ×

90 360

= $225,000.00 .

For swap premium (b) of 450 bps, we insert the given value into our quarterly swap premium payment formula and get:


91 360

= $91,000.00 .

For swap premium (c) of 720 bps, we insert the given value into our quarterly swap premium payment formula and get:


92 360

= $276,000.00 .

Below we fill in the missing values in the above exhibit. We have: Swap Premium (a) 600 bps (b) 450 bps (c) 720 bps

Notional Amount $15,000,000 $ 8,000,000 $15,000,000

Days in Quarterly Quarter Premium Payment 90 $225,000.00 91 $ 91,000.00 92 $276,000.00

12. In the ISDA’s pay-as-you go template, why might there be payments by the credit protection buyer to the credit protection seller beyond that of the swap premium?

Under the ISDA’s pay-as-you go template, a trigger event can occur. If so, this causes the credit protection buyer to make additional payments to the credit protection beyond that of the swap premium. More details are given below.

The mechanics of an ABX.HE differ from that of the other index CDS described above beyond that of defining of a credit event. The other index CDS we have described exchange payments quarterly. In the case of the ABX.HE, the protection buyer makes the swap payment monthly based on the notional amount. The notional amount will decline over time due to the amortization of the tranches. The protection buyer receives payments from the protection seller in the case of a credit event, which as explained earlier results from an interest shortfall, principal shortfall, or writedowns. However, unlike the other index CDS, under the pay-as-you-go (PAUG) template a trigger event such as a writedown and interest shortfall may be reversed in a subsequent period. That is, the protection buyer would have to reimburse the protection seller in such instances. Copyright © 2016 Pearson Education, Inc.

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13. How do the cash flows for a CDS swap differ from that of a single-name CDS?

The cash flows for a CDS swap differ from that of a single-name CDS in that the cash flows cease for the latter when a credit event occurs. More details are provided below. In a CDS swap, the credit risk of a standardized basket of reference entities is transferred between the protection buyer and protection seller. As of year-end 2005, the only standardized indexes are those compiled and managed by Dow Jones. For the corporate bond indexes, there are separate indexes for investment grade and high-grade names. The most actively traded contract as of year-end 2005 is the one based on the North American Investment Grade Index (denoted by DJ.CDX.NA.IG). The mechanics of an index CDS are slightly different from that of a single-name CDS. As with a single-name CDS, a swap premium is paid. However, if a credit event occurs, the swap premium payment ceases in the case of a single-name CDS. In contrast, for an index CDS, the swap payment continues to be made by the protection buyer. However, the amount of the quarterly swap premium payment is reduced. This is because the notional amount is reduced as result of a credit event for a reference entity. For example, suppose that a portfolio manager is the protection buyer for a DJ.CDX.NA.IG and the notional amount is $200 million. Using the formula below for computing the quarterly swap premium payment, the payment before a credit event occurs would be $200,000,000 × swap rate (in decimal) ×


.

After a credit event occurs for one reference entity, the notional amount declines from $200 million to $199,840,000. The reduction is equal to 99.2% of the $200 million because each reference entity for the DJ.CDX.NA.IG is 0.8%. Thus, the revised quarterly swap premium payment until the maturity date or until another credit event occurs for one of the other 124 reference entities is $199,840,000 × swap rate (in decimal) ×


.

As of this writing (2005), the settlement term for an index CDS is physical settlement. However, the market is considering moving to cash settlement. The reason is because of the cost of delivering an odd lot of the bonds of the reference entity in the case of a credit event. For example, in our hypothetical credit default swap index if there is a credit event, the protection buyer would have to deliver to the protection seller bonds of the reference entity with a face value of $160,000. Neither the protection buyer nor the protection seller would like to deal with such a small position. 14. How does one approximate the CDS spread for a single-name CDS on a corporate entity?

For a single-name CDS on a corporate entity, one approximate the credit default swap spread by using the asset swap market for par asset swaps where a proxy for the spread over LIBOR (F)


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can be obtained. The first approximation for a single-name CDS is the difference between the asset swap spread (from the par asset swap market) and the spread over LIBOR in the repo market. 15. Answer the below questions. (a) What is an asset swap?

An asset swap is created by an investor when the investor owns an asset and converts its cash flow characteristics. An asset swap is an interest rate swap or cross currency swap used to convert the cash flows from an underlying security (a bond or floating rate note), from fixed coupon to floating coupon, floating coupon to fixed coupon, or from one currency to another. The underlying security and swap may be transacted together (as a package) with the same counterparty or separately with different counterparts. The asset swap may be transacted at the time of the security purchase or added to a bond or floating rate note already owned by the investor. A fixed rate bond plus an asset swap converting the bond to floating rate is known as a synthetic floating rate note. The security plus asset swap can be sold as a package, or separately. If the issuer of the bond defaults on the issue, the investor must continue to make payments to the counterparty of the interest-rate swap (i.e., the swap dealer) and is therefore still exposed to the credit risk of the issuer. (b) In pricing a single-name CDS, what information does the par asset swap market contain?

There are eight assumptions needed to value a single-name CDS with a maturity of T years for a reference entity. Assumption 1 states that there exists a floating-rate security issued by the reference entity that has a maturity of T that is trading at par value and offers a coupon rate of LIBOR plus a spread denoted by F . (That is, the coupon reset formula for this security is LIBOR + F .) In practice, we know that Assumption 1 may not hold. That is, for corporate issuers that are reference entities for a single-name CDS, there is not likely to be a floating-rate security trading at par. For this reason, market participants look to the asset swap market. Thus, in pricing a singlename CDS, the par asset swap market contains information that would be provided by a floatingrate security trading at par (if that security existed). 16. The following is an excerpt from “MCDX Municipal CDS index on the rise,” Credit Default Swap Market Reporting, July 1, 2010 (http://blog.creditlime.com/2010/07/01/municipal-cds-index-rising/)

The 5-year MCDX increased from 115 bps to 209 bps during the period from April 20 to June 11, 2010 and had nearly doubled 11 days later when it closed at 226.5 bps on June 22. Between September 28, 2009 and April 20, 2010, the index had only increased from 90 bps to 115 bps. The reason for the rise has been obvious, if not evident in CDS market prices, for quite a while now. Ballooning municipal deficits and lower revenues are creating fiscal problems for many states across America. California and Massachusetts have both announced probes (though mostly inconclusive to date) into municipal CDS trading while Illinois has seen its credit default swaps achieve the status as riskiest state in America. (a) What is meant by a 5-year MCDX?


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A 5-year MCDX is a credit default swap (CDS) index of 50 municipal credits ranging from general obligation debt to revenue bonds from municipal authorities (excluding tobacco and healthcare bond issues). By buying (or selling) the index, you are in effect buying (or selling) equal portions of 50 different protection contracts. If one of the credits within the MCDX defaults, the buyer of protection delivers a qualified obligation of the defaulted credit to the seller of protection. In return the seller of protection pays 100% of the face value. The par amount of the bond delivered is equal to 1/50th of the original notional amount. Suppose the current 5-year MCDX spread is 100bps. This means that in order to buy $10 million in default protection against the 50 names in the MCDX, investors make the equivalent of $100,000 in annual payments, assuming a new contract were created today. A weak economy generally, and declining property tax collections specifically, could result in unusual pressure on municipal credits. (b) What is the link between the “ballooning municipal deficits and lower revenues” and the increase in CDS spreads?

With ballooning municipal deficits and lower revenues, the default probability increases. Thus, the link between the “ballooning municipal deficits and lower revenues” and the increase in CDS spreads reflect the market’s view on the default probability associated with the reference entity and the amount that will be recovered should a default occur. More details are given below. In the early days of the CDS market, the following naïve relationship was used to back out default probabilities from the observed CDS spread: Observed CDS spread in bps / 10,000 = (1 – Assumed recovery rate) × (Assumed default probability) Note that in this formula, we use default probability. What this means when using a CDS is not necessarily a bankruptcy but, more broadly, it is the probability of a realizing a credit event. Given an assumed recovery rate, then an implied default probability can be obtained by solving the above equation for the default probability: Implied default probability =


So, for example, if the observed 5-year CDS spread for a corporation is 500 basis points and the assumed recovery rate is 40%, then the implied default probability is 8.33% shown as follows: Implied default probability =

500 / 10,000

1

– 0.40

= 0.0833 = 8.33%

Notice that the higher the recovery rate assumed, the higher the implied default probability for a given CDS spread. So, for example, if a 60% recovery rate is assumed, the implied default probability is 12.5%. Market players will employ an industry standard fixed recovery rate depending on the underlying to obtain the implied default probability. For example, the market practice is to assume a higher


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recovery rate for loans compared to corporate bonds and higher recovery rates for municipal bonds than for corporate debt. As the CDS market has matured, it has become widely recognized that the formula given above for the implied default probability is only a very rough approximation of the default probability. The formula fails to take into account several factors that impact CDS spreads such as bid-ask spread and counterparty risk. Moreover, it assumes that the recovery rate is correct and constant over time. 17. In an April 21, 2011 article in Bloomberg.com by Abigail Moses entitled, “ Greece, Portugal Sovereign Credit-Default Swaps Jump to Records,” (http://www.bloomberg.com/news/2011-0421/greece-portugal-sovereign-credit-default-swaps-jump-to-records.html ), the following statement appears:

“Credit-default swaps on Greece jumped 40 basis points to 1,340 basis points according to CMA, signaling a 68 percent chance of default within five years.” (a) How is the “68 percent chance of default” obtained?

The “68 percent chance of default” can be obtained from relations that back out default probabilities from the observed CDS spread. We begin with the equation:

Observed CDS spread in bps / 10,000 = (1 – Assumed recovery rate) × (Assumed default probability) Note that in this formula, we use default probability. What this means when using a CDS is not necessarily a bankruptcy but, more broadly, it is the probability of a realizing a credit event. Given an assumed recovery rate, then an implied default probability can be obtained by solving the above equation for the default probability: Implied default probability =


So, for example, if the observed 5-year CDS spread for a corporation is 3,400 basis points and the assumed recovery rate is 50%, then the implied default probability is 68% as shown below: Implied default probability =

3,400 / 10,000

1

– 0.50

= 0.6800 = 68.00%

Notice that the higher the recovery rate assumed, the higher the implied default probability for a given CDS spread. So, for example, if a 60% recovery rate is assumed, the implied default probability is 85%. (b) What assumptions must be made to use this estimate of default?

The 68 percent chance of default was determined from a series of formulas that allows a computation of the probability of default given assumption about of several factors that impact CDS spreads. These factors include the bid-ask spread, counterparty risk, and the recovery rate.


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18. Answer the below questions. (a) Explain how a single-name CDS can be used by a portfolio manager who wants to short a reference entity.

If a portfolio manager expects that an issuer will have difficulties in the future and wants to take a position based on that expectation, it will short the bond of that issuer. However, shorting bonds in the corporate bond market is difficult. The equivalent position can be obtained by entering into a swap as the protection buyer. More details are provided below. Credit derivatives (like a single-name CDS) are used by bond portfolio managers in the normal course of activities to more efficiently control the credit risk of a portfolio and to more efficiently transact than by transacting in the cash market. For example, credit derivatives allow a mechanism for portfolio managers to more efficiently short a credit-risky security than by shorting in the cash market, which is oftentimes difficult to do. For traders and hedge fund managers, credit derivatives provide a means for leveraging an exposure in the credit market. For a portfolio manager who engages in a single-name CDS, the manager can note that the market practice for settlement is physical delivery. With physical settlement the protection buyer delivers a specified amount of the face value of bonds of the reference entity to the protection seller. The protection seller pays the protection buyer the face value of the bonds. Because all reference entities that are the subject of credit default swaps have many issues outstanding, there will be a number of alternative issues of the reference entity that the protection buyer can deliver to the protection seller. These issues are known as deliverable obligations. The swap documentation will set forth the characteristics necessary for an issue to qualify as a deliverable obligation. Just like for Treasury bond and note futures contracts, the short (in a single-name CDS) has the choice of which issue to deliver that is specified as acceptable for delivery. The short will select the cheapest-to-deliver issue, and the choice granted to the short is effectively an embedded option. From the list of deliverable obligations, the protection buyer will select for delivery to the protection seller the cheapest-to-deliver issue. (b) Explain how a single-name CDS can be used by a portfolio manager who is having difficulty acquiring the bonds of a particular corporation in the cash market.

If the portfolio manager desires a bond it is likely because of the cash flows (associated with the bond) help the manager match assets and liabilities. Although the “ideal” bond may be hard to find and purchase, a single-name CDS can help realize the same desired cash flows. Thus, a single-name CDS can be used by a portfolio manager who is having difficulty acquiring the bonds of a particular corporation in the cash market. 19. How are index CDS used by portfolio managers?

By using index CDSs, portfolio managers can gain credit exposure for a standard basket of reference entities by selling credit protection; a portfolio manager can reduce exposure for a standard basket of reference entities by buying credit protection. Thus, adjusting index CDS


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positions allows a portfolio manager to alter credit exposure to the bond market. This use of index CDSs is particularly valuable for portfolio managers of small bond portfolios. Managing a bond portfolio relative to a bond index involves considerable idiosyncratic risk because all of the issues in a broad-based bond index cannot be purchased given the large number of issues in a typical index. One way of gaining exposure to a larger number of reference entities in a bond sector that comprises a broad-based bond index is via an index CDS. What is important to note is that although CDSs do offer leveraging opportunities for a portfolio manager who is permitted to do so, no leveraging need occur if the funds that would have been used to purchase the reference entities are placed in cash rather than used to purchase other reference entities. If a portfolio manager uses a derivative for the purpose of leveraging, that can be easily identified by looking at a portfolio’s key risk measures. In the case of interest-rate futures and swaps, this can be seen in the portfolio’s duration. In the case of CDSs, it will show up in the portfolio’s spread duration. 20. How can a client determine if a portfolio manager is using a CDS for leveraging in such a way as to increase the portfolio’s risk relative to a bond index?

A credit default swap is an agreement between two parties, one of whom (the protection seller) will collect periodic payments from the other (the protection buyer). In the event of default in the underlying bond portfolio, the protection seller will owe the protection buyer a lump sum payment equivalent to the loss of principal in the bond portfolio. If the protection buyer owns a portfolio of bonds representing the index, then a credit default swap effectively transfers that bond exposure to the protection seller and so no additional leverage is introduced into the system (though this does leave the protection buyer exposed to the risk of the protection seller's potential to default). If the protection buyer does not own the underlying bond then the CDS serves to effectively create it synthetically; the protection seller receives payments that are roughly equivalent to the coupons and is at risk of losing the principal (in the form of a payout) in the event that the bond issuers default. What is important to note is that although CDS do offer leveraging opportunities for a portfolio manager who is permitted to do so, no leveraging need occur if the funds that would have been used to purchase the reference entities are placed in cash rather than used to purchase other reference entities. The same point was made in discussing interest rate futures and swaps. If a portfolio manager uses a derivative for the purpose of leveraging, that can be easily identified by looking at a portfolio’s key risk measures. In the case of interest rate futures and swaps, this can be seen in the portfolio’s duration. In the case of CDS, it will show up in the portfolio’s spread duration.


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