CHAPTER 24
CREDIT DERIVATIVES IN BOND PORTFOLIO MANAGEMENT368
I . INTRODUCTION
Derivatives are financial instruments designed to efficiently transfer some form of risk between two parties. Derivatives can be classified based on the type of risk that is being transferred. In the fixed-income market, derivatives include interest rate derivatives which transfer interest rate risk and credit derivatives which transfer credit risk. With credit derivatives, a portfolio manager can either acquire or reduce credit risk exposure. Many managers have portfolios that are highly sensitive to changes in the spread between riskless and risky assets and credit derivatives are an efficient way to manage this exposure. Conversely, other managers may use credit derivatives to target specific exposures as a way to enhance portfolio returns. In each case, the ability to transfer credit risk and return provides a tool for portfolio managers to improve performance.
Credit derivatives can be classified as follows:
• total return swaps
• credit default products
• credit spread options
Credit derivative products used in structured credit products include synthetic collateralized debt obligations and credit-linked notes. In this chapter we will review each type of credit derivative describing their structure and how they can be used by portfolio managers. After reviewing credit derivatives, we will explain synthetic credit debt obligations.
We begin this chapter with a short discussion about the participants in the credit derivatives market and why credit risk is important.
II. MARKET PARTICIPANTS
According to the British Bankers Association (BBA), the dominant center for the global credit derivatives market is London, which is well ahead of New York and Asia.369 The credit derivatives market consists of three groups of players:2
• end-buyers of protection
• end-sellers of protection
• intermediaries
End-buyers of protection are entities that seek to hedge credit risk taken in other parts of their business. The predominate entity in this group is commercial banks for their loan portfolio. However, there are also insurance companies, pension funds, and mutual funds who seek protection for credits held in their portfolio. End-sellers of protection are entities that seek to diversify their current portfolio and can do so more efficiently with credit derivatives. An entity that provides protection is seeking exposure to a specific credit or a basket of credits.
Intermediaries include investment banking arms of commercial banks and securities houses. Their key role in the credit derivatives market is to provide liquidity to end-users. They trade for their own account looking for arbitrage opportunities and other profitable opportunities. In addition, some intermediaries will assemble, using credit derivatives, structured products which, in turn, they may or may not manage.
III. WHY CREDIT RISK IS IMPORTANT
A fixed-income instrument represents a basket of risks. There is (1) interest rate risk (as measured by duration and convexity), (2) call risk, and (3) credit risk. Credit risk includes the risk of defaults, downgrades, and widening credit spreads. The total return from a fixed-income instrument is the compensation for assuming all of these risks. Depending upon the rating on the underlying debt instrument, the return from credit risk can be a significant part of a bond’s total return.
A. Types of Credit Risk
Credit risk may affect a portfolio in three ways: default risk, credit spread risk, and downgrade risk. Each can have a detrimental impact on the value of a fixed-income portfolio.
1. Default Risk Default risk is the risk that the issuer will default on its obligations. The default rate on credit risky bonds can be quite high. For example, estimates of the average default rates for high-yield bonds in the United States range from 3.17% to 6.25%.3 However, default rates increase significantly during periods of economic malaise. For example, during the recession of 2001, the default rate for high-yield bonds was 10.2%. All told, there were a total of $106 billion of corporate bond defaults in 2001.370 The greatest default rate in the United States for all corporate bonds (high yield and investment grade) was 9.2% during the Great Depression in the 1930s.371
There is default risk associated with investing in the foreign currency debt of another nation compared to an investor’s home country. Most investors consider the sovereign debt of the G-7 countries (the largest industrialized nations in the world: The United States, the United Kingdom, France German, Italy, Canada, and Japan) to be default free. The reason is that these countries have significant internal resources and borrowing capacity to support the prompt payment of their outstanding debt.
Instead, sovereign debt default risk is associated mainly with emerging economies. An emerging economy relies on two forms of cash flows to finance its government programs and to pay its debt obligations: taxes and revenues from state-owned enterprises. Taxes can come from personal income taxes, corporate taxes, import duties, and other excise taxes. State-owned enterprises can be oil companies, telephone companies, national airlines and railroads, and other manufacturing enterprises. In times of economic turmoil such as a recession, cash flows from state-owned enterprises decline along with the general malaise of the economy. Additionally, tax revenues decline as corporations earn less profits, as unemployment rises, and as personal incomes decline. Lastly, with a declining foreign currency value, imports decline, reducing revenue from import taxes.
The possibility of default is a significant risk for portfolio managers, and one that can be effectively hedged by shifting the credit exposure to another party. Credit derivatives therefore appeal to portfolio managers who invest in corporate bonds—particularly, high-yield corporate bonds—and sovereign bonds.
2. Credit Spread Risk Credit spread risk is the risk that the interest rate spread for a risky bond over a riskless bond will increase after the risky bond has been purchased. For instance, in the United States, U.S Treasury securities are generally considered to be without credit risk (default free). Therefore, corporate bonds, agency debentures, and the debt of foreign governments are typically priced at a spread to comparable U.S. Treasury securities. Should this spread widen after purchase of the credit risky bond, the value of the bond would decline. Credit spreads can widen based on macroeconomic events in the domestic or global financial markets.
As an example, in October of 1997, a rapid decline in Asian stock markets spilled over into the U.S. stock markets, causing a significant decline in financial stocks. The turbulence in the financial markets, both domestically and worldwide, resulted in a flight to safety of investment capital. In other words, investors sought safer havens for their investment capital in order to avoid further losses and volatility. This flight to safety resulted in a significant increase in credit spreads of corporate bonds to U.S. Treasuries. For instance, on June 30, 1997, corporate bonds rated BB by Standard & Poor’s were trading at an average spread over U.S. Treasuries of 215 basis points.372 However, by October 31, 1997, this spread had increased to 319 basis points. For a $1,000 market value BB-rated corporate bond with a duration of 5, this resulted in a loss of value of about $52.50 per bond.
An estimate of this credit spread risk is spread duration, a measure discussed earlier. For credit-risky bonds, spread duration is the approximate percentage change in the bond’s price for a 100 basis point increase in the credit spread (holding the Treasury rate constant). For example, a spread duration of 3 means that for a 100 basis point increase in the credit spread, the bond’s price will decline by approximately 3%. The spread duration for a portfolio is found by computing a market weighted average of the spread duration for each bond. The same is true for a bond market index. Note, however, that the spread duration reported for a bond market index is not the same as the spread duration for estimating the credit spread risk of an index. For example, on April 25, 2003, the spread duration reported for the Lehman Brothers Aggregate Bond Index was 2.99. However, the spread duration for the index is computed by Lehman Brothers based on all non-Treasury securities. Some of these sectors offer a spread to Treasuries that reflects more than just credit risk. For example, the mortgage sector in the index offers a spread due to prepayment risk. The same is true for some sub-sectors within the ABS sector. Lehman Brothers does have a Credit Sector for the index. For that sector, the spread duration reflects the exposure to credit spreads in general. It was 1.49 on April 25, 2003 and is interpreted as follows: If credit spreads increase by 100 basis points, the approximate decline in the value of the index will be 1.49%.
3. Downgrade Risk Downgrade risk occurs when a nationally recognized statistical rating organization such Standard & Poor’s, Moody’s Investors Services, or Fitch Ratings reduces its outstanding credit rating for an issuer based on an evaluation of that issuer’s current earning power versus its capacity to pay its fixed income obligations as they become due.373
The rating agencies construct credit transition matrices. These matrices can be used to forecast the probabilities of credit upgrades or downgrades for a particular class of rated bonds. For example, a transition matrix might forecast the probability (on average) of a company rated “single A” being upgraded to “double A” to be 2%. Conversely, a transition matrix might forecast the probability of a company rated “single A” being downgraded to “triple B” to be 5%.
B. Reasons for Selling Credit Protection
Credit risk is not all one-sided. A market participant may be willing to be a seller of credit protection. This can be done in one of two ways. First, a market participant can sell contingent or insurance-type protection. That is, if the market participant believes that credit performance will be such that it will be unnecessary to make an insurance payment to a counterparty (i.e., the party buying credit protection), then the market participant earns the insurance premium received. Second, a market participant may want to take the opposite view of a credit protection buyer and in fact benefit from an improvement in a credit. This is done by selling protection.
There are at least three reasons why a portfolio manager may be willing to assume the credit risk of an underlying asset or issuer. First, there are credit upgrades as well as downgrades. A factor affecting credit rating upgrades is a strong stock market which encourages public offerings of stock by credit risky companies. Often, a large portion of these equity financings are used to reduce outstanding costly debt, resulting in improved balance sheets and credit ratings for the issuers.
A second reason why a portfolio manager may be willing to sell credit protection is that there is an expectation of other credit events which have a positive effect on credit risky bonds. Mergers and acquisitions, for instance, have been historically a frequent occurrence in the high-yield corporate bond market. Even though a credit risky issuer may have a low debt rating, it may have valuable technology worth acquiring. High-yield corporate bond issuers tend to be small to mid-cap companies with viable products but nascent cash flows. Consequently, they make attractive takeover candidates for financially mature companies.
The third reason is that with a growing economy, banks may be willing to provide term loans to high-yield companies at more attractive rates than the bond market. Consequently, it has been advantageous for credit risky companies to redeem their high-yield bonds and replace an outstanding bond issue with a lower cost term loan. The resulting premium for redemption of high-yield bonds is a positive credit event which enhances portfolio returns.
IV. TOTAL RETURN SWAP
A total return swap in the fixed-income market is a swap in which one party makes periodic floating payments to a counterparty in exchange for the total return realized on an individual reference obligation or a basket of reference obligations. A total return payment includes all cash flows that flow from the reference obligations as well as any capital appreciation or depreciation. The party that agrees to make the floating payments and receive the total return is referred to as the total return receiver; the party that agrees to receive the floating payments and pay the total return is referred to as the total return payer. When the reference obligation is a sector of a bond index, it is called a total return index swap.
Notice that in a total return swap, the total return receiver is exposed to both credit risk and interest rate risk. For example, the credit risk spread can decline (resulting in a favorable price movement for the reference obligation), but this gain can be offset by a rise in the level of interest rates.
A portfolio manager typically uses a total return swap to increase credit exposure. A total return swap transfers all of the economic exposure of a reference obligation or reference obligations to the total return receiver. In return for accepting this exposure, the total return receiver makes a floating payment to the total return payer.
A. Illustration of a Total Return Swap
Consider a portfolio manager who believes that the fortunes of XYZ Mobile Corporation will improve over the next year, and that the company’s credit spread relative to U.S. Treasury securities will decline. The company has issued a 10-year bond at par with a coupon rate of 8.5% and therefore the yield is 8.5%. Suppose at the time of issuance, the 10-year Treasury yield is 5.5%. This means that the credit spread is 300 basis points and the portfolio manager believes it will decrease over the year to less than this amount.
The portfolio manager can express this view by entering into a total return swap that matures in one year as a total return receiver with the reference obligation being the 10-year, 8.5% XYZ Mobile Corporate bond issue. Suppose (1) the swap calls for an exchange of payments semiannually and (2) the terms of the swap are such that the total return receiver pays the 6-month Treasury rate plus 140 basis points in order to receive the total return on the reference obligation. The notional amount for the contract is $10 million.
Assume that over the one year, the following occurs:
• the 6-month Treasury rate is 4.6% initially
• the 6-month Treasury rate for computing the second semiannual payment is 5.6%
• at the end of one year the 9-year Treasury rate is 7%
• at the end of one year the credit spread for the reference obligation is 200 basis points
First let’s look at the payments that must be made by the portfolio manager. The first semi-annual swap payment made by the portfolio manager is 3% (4.6% plus 140 basis points divided by two) multiplied by the $10 million notional amount. The second swap payment made is 3.5% (5.6% plus 140 basis points divided by two) multiplied by the $10 million notional amount. Thus,
| First swap payment paid : $10 million × 3% | = | $300, 000 |
| Second swap payment paid : $10 million × 3.5% | = | $350, 000 |
| Total payments | = | $650, 000 |
The payments that will be received by the portfolio manager are the two coupon payments plus the change in the value of the reference obligation. There will be two coupon payments. Since the coupon rate is 8.5%, the amount received for the coupon payments is $850,000.
Finally, the change in the value of the reference obligation must be determined. At the end of one year, the reference obligation has a maturity of 9 years. Since the 9-year Treasury rate is assumed to be 7% and the credit spread is assumed to decline from 300 basis points to 200 basis points, the reference obligation will sell to yield 9%. The price of an 8.5%, 9-year bond selling to yield 9% is 96.96. Since the par value is $10 million, the price is $9,696,000. The capital loss is therefore $304,000. The payment to the total return receiver is then:
| Coupon payment | = | $850, 000 |
| Capital loss | = | $304, 000 |
| Swap payment | = | $546, 000 |
Netting the swap payment made and the swap payment received, the portfolio manager must make a payment of $104,000.
Notice that even though the portfolio manager’s expectations were realized (i.e., a decline in the credit spread), the portfolio manager had to make a net outlay. This illustration highlights one of the disadvantages of a total return swap: the return to the investor is dependent on both credit risk (declining or increasing credit spreads) and market risk (declining or increasing market rates). Two types of market interest rate risk can affect the price of a fixed-income instrument. Credit independent market risk is the risk that the general level of interest rates will change over the term of the swap. This type of risk has nothing to do with the credit deterioration of a reference obligation. Credit dependent market interest rate risk is the risk that the discount rate applied to the value of an asset will changed based on either perceived or actual default risk.
In the illustration, the reference obligation was adversely affected by credit independent market interest rate risk, but positively rewarded for accepting credit dependent market interest rate risk. To remedy this problem, a total return receiver can customize the total return swap transaction. For example, the portfolio manager could negotiate to receive the coupon income on the reference obligation plus any change in value due to changes in the credit spread. Now the portfolio manager has expressed a view exclusively of credit risk; credit independent market risk does not affect the swap outcome. In this case, in addition to the coupon income, the portfolio manager would receive the difference between the present value of the reference obligation at a current spread of 200 basis points and the present value of the reference obligation at a credit spread of 300 basis points.
B. Benefits of Total Return Swaps
There are several benefits in using a total return swap as opposed to purchasing reference obligations themselves. First, the total return receiver does not have to finance the purchase of the reference obligations. Instead, it pays a fee to the total return payer in return for receiving the total return on the reference obligations.
Second, the total return receiver can achieve the same economic exposure to a diversified basket of assets in one swap transaction that would otherwise take several cash market transactions to achieve. In this way a total return swap is much more efficient means for transacting than the cash market.
Finally, an investor who wants to short the corporate bond of one or more issuers will find it difficult to do so in the corporate bond market. An investor can do so efficiently by using a total return swap. In this case the investor will pay the total return and receive a floating payment.
V. CREDIT DEFAULT PRODUCTS
Credit default products fall into two categories:
• credit default swap
• credit default options on a credit-risky asset
By far, the most popular type of credit derivative is the credit default swap. An annual survey of the BBA finds that credit default swaps account for almost half of the credit derivatives market. Not only is this form of credit derivative the most commonly used stand-alone product, but it is also used extensively in structured credit products.
A. Credit Default Swaps
A credit default swap is probably the simplest form of credit risk transference among all credit derivatives. 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.
While credit default swaps are customized transactions, there has been standardization of contract terms and provisions for certain types of credit default swaps. Swaps are usually documented under a standard set of forms published by the International Swap and Derivatives Association (ISDA).
In a credit default swap, the documentation will identify the reference entity and the reference obligation. The reference entity is the issuer of the debt instrument. It could be a corporation or a sovereign government. The reference obligation is the particular issue for which the credit protection is being sought. For example, one of the most liquid reference entities traded in the credit default swap market is Ford Motor Credit Company. The reference obligation would be a specific Ford Motor Credit Company bond issue.
A credit default swap in which there is only one reference obligation is called a single-name credit default swap. When there is a portfolio of reference obligations (e.g., a high-yield corporate bond portfolio), it is referred to as a basket default swap. For a credit default swap index the underlying is a standardized basket of reference entities. The most actively traded credit default swap index is the North American Investment Grade Index. The index consists of 125 corporate names.
EXHIBIT 1 Credit Default Swap
In a single-name 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. Should a credit event occur, the protection seller must make a payment. The payments made by the protection buyer are called the premium leg; the contingent payment that might have to be made by the protection seller is called the protection leg. Exhibit 1 shows the payments in a credit default swap.
In a basket default swap, a credit event with respect to one reference obligation may or may not trigger a payment from the protection seller. The number of reference obligations for which a credit event must occur to obtain a payment is specified in the contract. In Section VIII, we will explain the different types of basket default swaps and credit protection they provide.
The interdealer market has evolved to where single-name credit default swaps for corporate and sovereign reference entities are standardized. While trades between dealers have been standardized, there are occasional trades in the interdealer market where there is a customized agreement. For portfolio managers seeking credit protection, dealers are willing to create customized products.
In the interdealer market, the tenor, or length of time of a credit default swap, is typically five years. Portfolio managers can have a dealer create a tenor equal to the maturity of the reference obligation or to a shorter time period to match the portfolio manager’s investment horizon.
1. Settlement Methods Credit default swaps can be settled in cash or physically. In the interdealer market, single-name credit default swaps are typically settled physically. Physical delivery means that if a credit event as defined by the documentation occurs, the reference obligation is delivered by the protection buyer to the protection seller in exchange for a 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 credit default swap, this method of delivery is more efficient. When a credit default swaps is cash settled, there is a netting of payment obligations with the same counterparty.
If no credit event has occurred by the maturity of the swap, both sides terminate the swap agreement and no further obligations are incurred.
2. Determination of the Payment Obligation The methods used to determine the amount of the payment obligation of the protection seller under the swap agreement can vary greatly. For instance, a credit default swap can specify at the contract date the exact amount of payment that will be made by the protection seller should a credit event occur. Conversely, the credit default swap can be structured so that the amount of the swap payment by the seller is determined after the credit event. Under these circumstances, the amount payable by the protection seller is determined based upon the observed prices of similar debt obligations of the reference entity in the market. Finally, the swap can be documented much like a credit put option (discussed later) where the amount to be paid by the protection seller is an established strike price less the current market value of the reference obligation.
The cash 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 asset. In the interdealer market, the standard single-name credit default swap when the reference obligation 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.
In a typical credit default swap, the protection buyer pays for the protection premium over several settlement dates rather than upfront. A standard credit default swap in the interdealer market specifies quarterly payments.
3. Credit Event Definitions The most important section of the documentation for a credit default swap is what the parties to the contract agree constitutes a credit event for a credit default payment. Definitions for credit events are provided by the ISDA. First published in 1999, there have been periodic updates and revisions of these definitions.
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
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 required 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. In the U.S. credit default swap market, obligation acceleration and repudiation/moratorium were dropped as standard credit events in November 2002. In April 2003, these two credit events were dropped in the standard credit default swap in the European market.
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, or (4) a change in the level of seniority of the obligation in the reference entity’s debt structure.
Restructuring is the most controversial credit event that may be included in a credit default swap. The reason why it is so controversial is easy to understand. 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 since 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 it 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. The modified definition includes 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.374
Consequently, in the credit default swap market, until 2003, the parties to a trade had the following three choices for restructuring:
1. no restructuring
2. restructured based on the 1999 Definition for restructuring, referred to as “old restructuring” or “full restructuring”
3. restructuring as defined by the Restructuring Supplement Definition, referred to as “modified restructuring.”
Modified restructuring is typically used in North America while old restructuring is used in Europe. When the reference entity is a sovereign, restructuring is often old restructuring.
Whether restructuring is included and, if it is included, whether it is old restructuring or modified restructuring, affects the swap premium. Specifically, all other factors constant, it is more expensive if restructuring is included. Moreover, old restructuring results in a larger swap premium than modified restructuring.
EXHIBIT 2 Credit Event Selection Portion of “Exhibit A to 2003 ISDA Credit Derivatives Definitions”
Source: International Swaps and Derivatives Association, Inc.
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, experienced 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 (the “2003 Definitions”).
The revised definition 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:
1. no restructuring
2. “full” restructuring, with no modification to the deliverable reference obligations aspect
3. “modified restructuring”
4. “modified modified restructuring”
The last choice is a new one and was included to address issues that arose in the European market.
The ISDA’s confirmation form for credit derivative transactions, “Exhibit A to 2003 ISDA Credit Derivatives Definitions,” sets forth the terms and conditions for the transaction. The definitions for a credit event are in “check box” format. Exhibit 2 shows the portion of the confirmation form where the two parties select the credit events that are to be included in the trade.
4. Illustration of a Standard Single-Name Credit Default Swap Let’s illustrate the mechanics of a standard single-name credit default swap where the reference entity is a corporation. We will use an actual trade on November 26, 2002 as reported by creditex, a major broker in the credit default swap market, where the reference obligation is a specific senior bond issue of Ford Motor Credit Company. The scheduled term for the trade is November 26, 2007. That is, it was a 5-year scheduled term—the typical tenor in the interdealer market. The tenor of a swap is referred to as “scheduled” because a credit event will result in a payment by the protection seller, resulting in the credit default swap being terminated. The swap premium—the payment made by the protection buyer to the protection seller—was 410 basis points. If a credit event occurs, the protection seller pays the protection buyer the notional amount of the contract. In our illustration, we will assume that the notional amount is $10 million.
The notional amount is not the par value of the reference obligation. For example, suppose that a bond issue is trading at 80 (par value being 100). If a portfolio manager owns $12.5 million par value of the bond issue and wants to protect the current market value of $10 million (= 80% of $12.5 million), then the portfolio manager will want a $10 million notional amount. If a credit event occurs, the portfolio manager will deliver the $12.5 million par value of the bond and receive a cash payment of $10 million.
The standard contract for a single-name credit default swap in the interdealer market 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. A day count convention indicates the number of days in the month and the number of days in a year that will be used to determine how to prorate the swap premium to a quarter. The possible day count conventions are (1) actual/actual, (2) actual/360, and (3) 30/360. The day count convention used in the U.S. government bond market is actual/actual, while the convention used in the corporate bond market is 30/360. The day count convention used for credit default swaps is actual/360. This is the same convention 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 are used and 360 days are assumed for the year. Consequently, the
For example, if the notional amount is $10 million and there are 92 actual days in a quarter, then if the swap rate is 410 basis points (0.0410), the quarterly swap premium payment made by the protection buyer would be:
In the absence of a credit event occurring in any quarter, the protection buyer will continue to make a quarterly swap premium payment. If a credit event occurs, the protection seller pays the protection buyer the notional amount, $10 million in our illustration, and receives from the protection buyer the Ford Motor Credit Company senior bonds (i.e., the reference obligation).
5. Market Terminology Newcomers to the credit default swap market sometimes get confused regarding market terminology. The first potential source of confusion arises because market participants attempt to relate a position in the derivative market to a position in the cash market. The second potential source has to do with the use of the term “swap” to describe the transaction when the payment is contingent on the a credit event occurring.
a. Cash versus Credit Default Swap Market Terminology Participants in derivatives markets find it helpful to compare their exposure (long or short) in the derivative market to that of an exposure in the cash market. Sometimes the relationship is straightforward. For example, as explained in Chapter 22, a long position in a Treasury bond futures contract is equivalent to a long position in the Treasury bond market; a short position in a Treasury bond futures contract is equivalent to a short position in the Treasury bond market. In other cases, the relationship is not straightforward. For example, in a generic interest rate swap, the fixed-rate payer is said to be “short the bond market” and the fixed-rate receiver is said to be “long the bond market.” This is because for the fixed-rate payer, the value of an interest rate swap increases when interest rates increase. A position in the cash market whereby the value of the position increases when interest rates increase is a short bond position. Similarly, for the fixed-rate receiver, the value of an interest swap increases when interest rates decrease and therefore is equivalent to being long a bond.
The terminology of the position of the parties in a credit default swap can be confusing. To “go long” an instrument generally is to purchase it. In the cash market, going long a bond means one is buying a bond and so receiving the coupon payments; the bond buyer has therefore taken on credit risk exposure to the issuer. In a credit default swap, going long is to buy the swap, but the buyer is purchasing protection and therefore paying the swap premium; the buyer has no credit exposure on the reference entity and has in effect “gone short” on the reference obligation (the equivalent of shorting a bond in the cash market and paying coupons). So buying a credit default swap (buying protection) is frequently referred to in the credit derivatives market as “shorting” the reference obligation.
b. Swap versus Option Nomenclature The protection seller has literally “insured” the protection buyer against any credit losses on the reference obligation. While the term “swap” is used to describe this credit derivative, it should be clear that it has an option-type payoff. That is, it does not have the characteristics of the typical swap found in the derivatives market. For example, in a plain vanilla or generic interest rate swap, two parties swap payments periodically. One of the counterparties pays a fixed rate (called the “swap rate”) and the other party pays a floating rate. The payments are made by both parties over the term of the swap agreement. Moreover, the payments are not contingent on some event and the occurrence of any event does not terminate the swap agreement. This is not a characteristic of a credit default swap.
The question is then: Why is the transaction referred to as a swap? The reason has to due with the way one characterizes an option. There are two attributes for characterizing a derivative as an option. The first attribute is that there is an asymmetric payoff. The second attribute involves the price performance feature. While a credit default swap does have an asymmetric payoff, its price performance is like that of a swap rather than an option. The price performance of an option depends on the price of the underlying. When a credit-risky bond is the underlying, it is the credit spread that affects the price of the bond. So the price performance mechanism for an option is as follows: changes in the credit spread affect the price of the underlying bond which, in turn, changes the price of the option. In the case of a credit default swap, the change in the credit spread directly affects the price of the transaction rather than through its effect on the reference obligation (i.e., underlying bond). This is a characteristic of a swap such as an interest rate swap where the price of a swap depends directly on interest rates. It is for this reason that a credit default swap is referred to as a swap.
B. Default Options on a Credit Risky Asset
A default option on a credit risky asset is another form of credit default product. These options have not been nearly as popular as credit default swaps. Consequently, we will only provide a brief review of them.
In a binary credit option the option seller will pay out a fixed sum if and when a default event occurs with respect to a reference obligation or reference entity. Therefore, a binary option represents two states of the world: default or no default. It is the clearest example of credit protection. At maturity of the option, if the reference obligation or reference entity has defaulted, the option holder receives a predetermined payout. If there is no default at maturity of the option, the option buyer receives nothing.
A binary credit option could also be triggered by a rating downgrade.We’ll illustrate a binary credit option (both a put and a call) based on a credit rating. Consider the situation where a portfolio manager holds an investment-grade bond but is concerned that the credit rating for the issuer will be lowered and that the bond will decline in value. The portfolio manager can purchase a binary credit put option which allows putting the bond back to the option seller at the bond’s par value if the bond issuer is downgraded below investment grade.
As an example, assume that the portfolio manager purchased at par $1 million of Company W bonds, currently rated AA. The portfolio manager purchases a put option where he can sell the bonds at par value to the put option seller should the credit rating for Company W fall below investment grade (below BBB). The payoff to this binary put option can be described as:
Equation (1) is called a binary credit option because of its “either or” payout structure. Either Company W’s credit rating is below investment grade or it is not. Therefore, the portfolio manager receives a payout on the credit put option only in one state of the world: Company W is downgraded to below investment grade; otherwise, the portfolio manager receives nothing.
Let’s now consider a binary credit call option. Suppose that instead of purchasing a binary credit put option on the par value of the bonds to protect her investment, the portfolio manager purchases a series of call options that provide her with additional income should Company W be downgraded. In other words, whenever Company W is downgraded, the portfolio manager gets to call for a payment that will compensate her for the greater credit risk associated with her bond holdings. This is like receiving additional coupon income to reflect the higher credit risk associated with Company W’s bonds.
Consider the example where the portfolio manager gets to call for an additional 25 basis points of income should Company W be downgraded one credit rating, 50 basis points of income should Company W be downgraded two steps, and so forth. The pay out to this credit call option may be described as:
where $2, 500 = 0.25% × $1, 000, 000
and $5,000 = 0.50% × $1, 000, 000
Equation (2) is different from equation 1 in that the payout to the binary credit call option is not a function of the bonds’ market value.
VI. CREDIT SPREAD PRODUCTS
The third category of credit derivatives is credit spread products which include:
• credit spread options
• credit spread forward
We describe each below. However, it should be noted that the market for credit spread options has not developed as rapidly as market participants had anticipated.
A. Credit Spread Options
A credit spread option is an option whose value/payoff depends on the change in credit spreads for a reference obligation. It is critical in discussion of credit spread options to define what the underlying is. The underlying can be:
• a reference obligation with a fixed credit spread
• the level of the credit spread for a reference obligation
1. Underlying is a Reference Obligation with a Fixed Credit Spread When the underlying is a reference obligation with a fixed credit spread, then a credit spread option is defined as follows:
Credit spread put option: An option that grants the option buyer the right, but not the obligation, to sell a reference obligation at a price that is determined by a strike credit spread over a referenced benchmark at the exercise date.
Credit spread call option: An option that grants the option buyer the right, but not the obligation, to buy a reference obligation at a price that is determined by a strike credit spread over a referenced benchmark at the exercise date.
A credit spread option can have any exercise style: only at the exercise date (European), at any time prior to the exercise date (American), or only on specified dates by the exercise date (Bermudean).
The price for the reference obligation (i.e., the credit-risky bond) is determined by specifying a strike credit spread over the referenced benchmark, typically a default-free government security. For example, suppose that the reference obligation is an 8% 10-year credit-risky bond selling to yield 8%. The price of this bond is 100. Suppose further that the referenced benchmark is a same maturity U.S. Treasury bond that is selling to yield 6%. Then the current credit spread is 200 basis points. Assume that a strike credit spread of 300 basis points is specified and that the option expires in six months. At the end of six months, suppose that the 9.5-year Treasury rate is 6.5%. Since the strike credit spread is 300 basis points, then the yield used to compute the strike price for the reference obligation is 9.5% (the Treasury rate of 6.5% plus the strike credit spread of 300 basis points). The price of a 9.5-year 8% coupon bond selling to yield 9.5% is $90.75 per $100 par value.
The payoff at the expiration date would then depend on the market price for the reference obligation. For example, suppose that at the end of six months, the reference obligation is trading at 82.59. This is a yield of 11% and therefore a credit spread of a 450 basis points over the 9.5-year Treasury yield of 6.5%. For a credit spread put option, the buyer can sell the reference obligation (selling at 82.59) for the strike price of 90.75. The payoff from exercising is 8.16. This payoff is reduced by the cost of the option. For a credit spread call option, the buyer will not exercise the option and will allow it to expire worthless. There is a loss equal to the cost of the option.
There is one problem with using a credit spread option in which the underlying is a reference obligation with a fixed credit spread. The payoff is dependent upon the value of the reference obligation’s price, which is affected by both the change in the level of the interest rates (as measured by the referenced benchmark) and the change in the credit spread. For example, suppose in our illustration that the 9.5-year Treasury at the exercise date is 4.5% (instead of 6.5%) and the credit spread increases to 450 basis points. This means that the reference obligation is trading at 9% (4.5% plus 450 basis points). Since it is an 8% coupon bond with 9.5-years to maturity selling at 9%, the price is 93.70. In this case, the credit spread put option would have a payoff of $965 because the price of the reference obligation is 93.70 and the strike price is 103.35. Thus, there was no protection against credit spread risk because interest rates for the referenced benchmark fell enough to offset the increase in the credit spread.
Notice the following payoff from the perspective of the owner of the option before taking into account the option cost when the underlying for the a credit spread option is the reference obligation with a fixed credit spread:
Consequently, to protect against credit spread risk, an investor can buy a credit spread put option where the underlying is a reference obligation with a fixed credit spread.
| Type of option | Positive payoff if at expiration |
|---|---|
| Put | credit spread at expiration > strike credit spread |
| Call | credit spread at expiration < strike credit spread |
2. Underlying is a Credit Spread on a Reference Obligation When the underlying for a credit spread option is the credit spread for a reference obligation over a referenced benchmark, then the payoff of a call and a put option if exercised are as follows:
where the strike credit spread (in decimal form) is fixed at the outset of the option; the credit spread at exercise (in decimal form) is the credit spread over a referenced benchmark at the exercise date; and, the risk factor is based on the interest rate sensitivity of the debt instrument.
Credit spread call option:
payoff = (credit spread at exercise - strike credit spread) × notional amount × risk factor
Credit spread put option:
payoff = (strike credit spread - credit spread at exercise) × notional amount × risk factor
Notice that when the underlying for the credit spread option is the credit spread for a reference obligation over a referenced benchmark, a credit spread call option is used to protect against an increase in the credit spread. In contrast, when the underlying for the credit spread option is the reference obligation, a credit spread put option is used to protect against an increase in the credit spread.
The risk factor is determined by the sensitivity of the reference obligation to changes in the credit spread. The risk factor can be computed in one of several ways. One way is to compute the percentage change in the price of the reference obligation to a 100 basis point change in interest rates. Since the percentage price change will differ depending on whether we are looking at an increase or decrease in the credit spread, the change used will be dictated by the circumstances. For example, if the option involved a credit spread widening, an increase in interest rates is used to determine the price decline. Once the percentage change in price is determined for a 100 basis point change in rates, then it is divided by 100 to get the approximate percentage price change for a 1 basis point change in rates. That is,
To scale the risk factor in terms of how the credit spread at expiration and the strike credit spread are defined, the following calculation is performed:
risk factor = percentage price change for a 1 basis point change in rates × 10, 000
By including the risk factor, this form of credit spread option overcomes the problem we identified with the credit spread option in which the underlying is a reference obligation: the payoff depends on both changes in the level of interest rates (the yield on the referenced benchmark) and the credit spread. Instead, it is only dependent upon the change in the credit spread. Therefore, fluctuations in the level of the referenced benchmark’s interest rate will not affect the value of the options.
To illustrate a credit spread call option, consider the BB rated, 7.75 Niagara Mohawk Power bond due in 2008. In September 1998, this bond was trading at a price of $104.77 with a yield to maturity around 7.08%. The risk factor is determined using the percentage change in price for a 100 basis point increase in interest rates.375 For the Niagara Mohawk bond, there would be a percentage price change of 6.65% for a 100 basis point increase in rates. So, for each 1 basis point increase in the credit spread, there would be approximately a 0.0665% price change. The risk factor is then:
0.000665 × 10, 000 = 6.65
At the time that this bond was offering a yield of 7.08%, the 10-year Treasury note was yielding about 5.3% for a credit spread of 178 basis points. At the time this was a very narrow spread considering Niagara Mohawk Power’s BB credit rating. Perhaps the market was implying that the credit risk of Niagara Mohawk was closer to BBB than BB.
Alternatively, it could be that the market overvalued the bond. If a portfolio manager believed that the bond was overvalued, the portfolio manager could purchase a credit spread option struck at 178 basis points. This is the same as the portfolio manager expressing a view that the price of the reference obligation is inflated at the prevailing credit spread, and expecting the credit spread to widen out to more normal levels.
Suppose that the manager believes that the credit spread for this bond will increase to 250 basis points in one year. The portfolio manager can purchase a $20 million notional at-the-money call option on the credit spread between the debt of Niagara Mohawk Power and U.S. Treasuries. The tenor of the option is one year, the premium costs 125 basis points, and the risk factor is 6.65. 
EXHIBIT 3 Niagara Mohawk Power Option Struck at 178 Basis Points.
At the maturity of the option, if the credit spread is 250 basis points (i.e., the credit spread at expiration) the portfolio manager will receive:
payoff = (0.025 - 0.0178) × $20, 000, 000 × 6.65 = $957, 600
The amount earned by the portfolio manager is the amount received less the cost of the option. Since the option cost is 125 basis points for a notional amount of $20 million, the option cost is $250,000. The portfolio manager’s profit is $707,600 (= $957,600 - $250,000).
This profit/loss profile is demonstrated in Exhibit 3.
B. Credit Spread Forwards
Credit spread forward requires an exchange of payments at the settlement date based on a credit spread. As with a credit spread option, the underlying can be the value of the reference obligation with a fixed credit spread or the credit spread. The payoff depends on the credit spread at the settlement date of the contract. The payoff is positive (i.e., the party receives cash) if the credit spread moves in favor of the party at the settlement date. The party makes a payment if the credit spread moves against the party at the settlement date.
For example, suppose that a manager has a view that the credit spread will increase (i.e., widen) to more than the current 250 basis points in one year for a credit-risky bond. Then the payoff function for this credit spread forward contract would be:
(credit spread at settlement date - 250) × notional amount × risk factor
Assuming that the notional amount is $10 million and the risk factor is 5, then if the credit spread at the settlement date is 325 basis points, then the amount that will be received by the portfolio manager is:
(0.0325 - 0.025) × $10, 000, 000 × 5 = $375, 000
Instead, suppose that the credit spread at the settlement date decreased to 190 basis points, then the portfolio manager would have to payout $300,000 as shown below:
(0.019 - 0.025) × $10, 000, 000 × 5 = -$300, 000
In general, if a portfolio manager takes a position in a credit spread forward to benefit from an increase in the credit spread, then the payoff would be as follows:
(credit spread at settlement date - contracted credit spread) × notional amount × risk factor
For a portfolio manager taking a position that the credit spread will decrease, the payoff is:
(contracted credit spread - credit spread at settlement date) × notional amount × risk factor
VII. SYNTHETIC COLLATERALIZED DEBT OBLIGATIONS
Credit derivatives are used to create debt instruments with structures whose payoffs are linked to, or derived from, the credit characteristics of a reference obligation or entity or a basket of reference obligations or entities. These products are called structured credit products. We will focus on one of these products: synthetic collateralized debt obligations.
Previously, collateralized debt obligations were explained. A collateralized debt obligation (CDO) is backed by a diversified pool of one or more of the following types of debt obligations: investment-grade corporate bonds, high-yield corporate bonds, emerging market bonds, bank loans, asset-backed securities, residential and commercial mortgage-backed securities, and real estate investment trusts. In a CDO structure, there is a collateral manager responsible for managing the collateral assets. The funds to purchase the collateral assets are obtained from the issuance of bonds. Typically, there are senior bonds and mezzanine bonds. There is also a subordinate/equity tranche.
A CDO is classified as either a cash CDO or a synthetic CDO. In a cash CDO the collateral manager purchases the collateral assets. It was the cash CDO that was discussed. Our focus in this section is on synthetic CDOs, the fastest growing sector of the CDO market. A synthetic CDO is so named because the collateral manager does not actually own the pool of assets on which it has the credit risk exposure. Stated differently, a synthetic CDO absorbs the credit risk, but not the legal ownership, of its reference credit exposures. A basket credit default swap is typically employed to allow institutions to transfer the credit risk, but not the legal ownership, of underlying assets.
The basic structure of a synthetic CDO is as follows. As with a cash CDO, there are liabilities issued. The proceeds received from the bonds sold are invested by the collateral manager in assets with low risk. At the same time, the collateral manager enters into a basket credit default swap with a counterparty in which it will provide credit protection (i.e., the collateral manager is a protection seller) for the reference obligations that have credit risk exposure. Because it is selling credit protection, the collateral manager will receive the credit default swap premium.
On the other side of the basket credit default swap is a protection buyer who will be paying the swap premium to the collateral manager. This entity will be a financial institution seeking to shed the credit risk of assets that it owns and are the reference obligations for the credit default swap. If a credit event does not occur, the return realized by the collateral manager that will be available to meet the payment to the CDO bondholders is the return on the collateral consisting of low risk assets plus the credit default swap premium. If a credit event occurs for any of the reference obligations, the collateral manager must make a payment to the counterparty. This reduces the return available to meet the payments to CDO bondholders.
Recently, a new form of synthetic CDO was traded: Standard tranches of credit default swap indices.376
VIII. BASKET DEFAULT SWAPS
Because of the growing importance of the synthetic CDO market and the role of basket default swaps in these structures and other types of credit structured products that may be created in the market, in this section we will take a closer look at the different types of basket default swaps. In a basket default swap, there is more than one reference entity. Typically, in a basket default swap, there are three to five reference entities. There are different types of basket default swaps. They are classified as follows:
• N th-to-default swaps
• Subordinate basket default swaps
• Senior basket default swaps In this section we describe each type.
A. Nth-to-Default Swaps
In an Nth-to-default swap, the protection seller makes a payment to the protection buyer only after there has been a default for the Nth reference entity and no payment for default of the first (N - 1) reference entities. Once there is a payout for the Nth reference entity, the credit default swap terminates. That is, if the other reference entities that have not defaulted subsequently do default, the protection seller does not make any payout.
For example, suppose that there are five reference entities. In a first-to-default basket swap, a payout is triggered after there is a default for only one of the reference entities. There are no other payouts made by the protection seller even if the other four reference entities subsequently have a credit event. If a payout is triggered only after there is a second default from among the reference entities, the swap is referred to as a second-to-default basket swap. So, if there is only one reference entity for which there is a default over the tenor of the swap, the protection seller does not make any payment. If there is a default for a second reference entity while the swap is in effect, there is a payout by the protection seller and the swap terminates. The protection seller does not make any payment for a default that may occur for the three remaining reference entities.
B. Subordinate and Senior Basket Credit Default Swaps
In a subordinate basket default swap there is (1) a maximum payout for each defaulted reference entity and (2) a maximum aggregate payout over the tenor of the swap for the basket of reference entities. For example, assume there are five reference entities and that (1) the maximum payout is $10 million for a reference entity and (2) the maximum aggregate payout is $15 million. Also assume that defaults result in the following losses over the tenor of the swap:
Loss resulting from default of first reference entity = $6 million
Loss result from default of second reference entity = $10 million
Loss result from default of third reference entity = $16 million
Loss result from default of fourth reference entity = $12 million
Loss result from default of fifth reference entity = $15 million
When there is a default for the first reference entity, there is a $6 million payout. The remaining amount that can be paid out on any subsequent defaults for the other four reference entities is $9 million. When there is a default for the second reference entity of $10 million, only $9 million will be paid out. At that point, the swap terminates.
In a senior basket default swap there is a maximum payout for each reference entity, but the payout is not triggered until after a specified dollar loss threshold is reached. To illustrate, again assume there are five reference entities and the maximum payout for an individual reference entity is $10 million. Also assume that there is no payout until the first $40 million of default losses (the threshold). Using the hypothetical losses above, the payout by the protection seller would be as follows. The losses for the first three defaults is $32 million. However, because of the maximum loss for a reference entity, only $10 million of the $16 million loss is applied to the $40 million threshold. Consequently, after the third default, $26 million ($6 million + $10 million + $10 million) is applied toward the threshold. When the fourth reference entity defaults, only $10 million is applied to the $40 million threshold. At this point, $36 million is applied to the $40 million threshold. When the fifth reference entity defaults in our illustration, only $10 million is relevant since the maximum payout for a reference entity is $10 million. The first $4 million of the $10 million is applied to cover the threshold. Thus, there is a $6 million payout by the protection seller.
C. Comparison of Riskiness of Different Default Swaps377
Let’s compare the riskiness of each type of default swap from the perspective of the protection seller. This will also help reinforce an understanding of the different types of swaps. We will assume that for the basket default swaps there are the same five reference entities. Four credit default swaps, ranked by highest to lowest risk for the reasons to be explained, are:
1. Subordinate basket default swap: he maximum for each reference entity is $10 million with a maximum aggregate payout of $10 million.
2. First-to-default swap: he maximum payout is $10 million for the first reference entity to default.
3. Fifth-to-default swap: he maximum payout for the fifth reference entity to default is $10 million.
4. Senior basket default swap: here is a maximum payout for each reference entity of $10 million, but there is no payout until a threshold of $40 million is reached.
All but the senior basket default swap will definitely require the protection seller to make a payout by the time the fifth loss reference entity defaults (subject to the maximum payout on the loss for the individual reference entities). Consequently, the senior basket default swap exposes the protection seller to the least risk.
Now let’s look at the relative risk of the other three default swaps with a $10 million maximum payout: subordinate basket default swap, first-to-default swap, and fifth-to-default swap. Consider first the subordinate basket swap versus first-to-default swap. Suppose that the loss for the first reference entity to default is $8 million. In the first-to-default swap the payout required by the protection seller is $8 million and then the swap terminates (i.e., there are no further payouts that must be made by the protection seller). For the subordinate basket swap, after the payout of $8 million of the first reference entity to default, the swap does not terminate. Instead, the protection seller is still exposed to $2 million for any default loss resulting from the other four reference entities. Consequently, the subordinate basket default swap has greater risk than the first-to-default swap.
Finally, the first-to-default has greater risk for the protection seller than the fifth-to-default swap because the protection seller must make a payout on the first reference entity to default.
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