A Primer on Credit Default Swaps (Cds)

A PRIMER ON CREDIT DEFAULT SWAPS (CDS) Thomas S. Coleman, PhD Close Mountain Advisors LLC [email protected] 21 October 2008, updated 23 March 2009, 29 December 2009 (to include pricing) INTRODUCTION The market for Credit Default Swaps (CDS) has grown from nothing just over ten years ago to a huge market today. But what is a CDS? How does a CDS behave in response to changes in the markets? How does one value a CDS? What is the risk? This primer aims to answer these questions for plain- vanilla single-name CDS. Although CDS are often portrayed as complex, mysterious, even malevolent, they are really no more complex or mysterious than a corporate bond. I show how and why a CDS behaves, in almost all respects, as a leveraged or financed floating-rate corporate bond. The equivalence between a CDS and a floating-rate bond is very useful because it means that anyone acquainted with corporate bonds, anyone who understands how and why they behave in the market as they do, how they are valued, and what their risks are, understands the most important aspects of a CDS. In essence, a CDS is no harder (and no easier) to value or understand than the underlying corporate bond. I also point out the particular ways in which a CDS differs from a corporate bond. To preview the main points: • Selling protection through a CDS is equivalent to buying a floating-rate corporate bond (a floating rate note or FRN) using leverage. − Selling protection for x years is in most respects the same as being long a corporate bond with x years to maturity. − The exposure to credit spreads is the same whether one sells CDS protection or buys an FRN. In other words, when credit spreads move or upon default one can lose as much, but no more, through selling $100 worth of CDS protection as buying $100 worth of a corporate FRN with the same maturity and underlying credit. • Conversely, buying protection through a CDS is the same as shorting a corporate FRN: the exposure to credit spreads is the same and an investor can make or lose just as much from buying CDS protection as they can when shorting a corporate bond – the investor loses if credit spreads tighten and the price of the FRN goes up. • CDS are often spoken of as insurance contracts but a CDS more usefully can be considered a capital markets product: equivalent to a levered FRN. In reality, a CDS is no more (and no less) an insurance contract than is a corporate bond. • A CDS entails no investment up-front (apart from margin or collateral the counterparty to the CDS may demand): It is equivalent to a leveraged position in an FRN. As with any leveraged position a CDS may generate losses greater than the original investment. • Entering into a CDS does involve one additional risk that a corporate bond does not – the counterparty exposure that one party to the CDS may not live up to their side of the bargain. Generally this is not large, but it can be, and will be, important at times. STRUCTURE OF A SINGLE-NAME CREDIT DEFAULT SWAP A Credit Default Swap is an agreement between two parties (say A and B) to make a payment upon the default of a bond issued by a third party (C). Let us take an example of the following five-year CDS: • Five-year CDS on bond issued by company C Coleman December 2009 1 • Coupon 100bp • Party A “buys protection” • Party B “sells protection” This means that: • As long as the bond issued by C does not default (during the next five years) - Party A agrees to make regular payments of 100bp per year - Party B agrees to do nothing • As soon as bond issued by C does default (during the next five years) - Party B agrees to pay $100 to party A - Party A agrees to deliver the bond to party B The following diagram shows the payments, with the dotted line (⋅⋅⋅⋅) representing periodic payments (say once a quarter) that are made as long as the bond issued by C is not in default, and the dot-dash line (– ⋅ – ⋅ –) representing payments made upon default. Figure 1 – CDS between parties A and B, with A paying quarterly premiums and B paying loss upon default The result of this swap of payments is that party A makes periodic payments as long as the bond issued by C does not default, while A is compensated by receiving $100, the par value of the bond, if the bond defaults. In this sense, A is protected against the default of the bond issued by C, while B is at risk to pay $100 upon default. For this reason, one says that party A buys protection and party B sells protection. Note one important point. Party B must pay $100 upon default but receives the defaulted bond in return. Defaulted bonds usually do not go to zero since there is some recovery, although less than $100. The net result is that party B does not lose $100 upon default of the bond issued by C, but rather $100 less the recovery value of the bond. The CDS described above is said to involve physical delivery, since party A actually or physically delivers the bond to party B upon default. Many CDS were in fact structured as physical delivery in the early days of the market, but generally CDS now involve cash delivery where party B pays the net amount of $100 – post-default value of the bond. As long as markets are relatively well-behaved there should be no difference between physical and cash delivery, and I will ignore any differences. EQUIVALENCE OF CDS AND FLOATING RATE NOTE When first introduced to a CDS and after reflecting on figure 1, it is natural to think that the risk or exposure of parties A and B are quite asymmetric: A has what look like fixed payments and thus what Coleman December 2009 2 looks like a known or fixed value, while B has a large contingent liability and thus what looks like a quite uncertain value. In fact, this is far from the truth. In the example above the risk or exposure for party B is the same as the risk of owning a five-year FRN issued by C, while the exposure for A is the same as the risk of shorting a five-year FRN. Just as the FRN may go up or down due to changes in C’s credit status, so the CDS may go up or down and either party A or party B may gain (or lose). To see why a CDS is really the same as a floating rate bond (FRN), first consider figure 2, which shows the CDS cash flows over time for party B, who sells protection, from the example above. Party B receives premiums until the maturity of the CDS or default, whichever occurs first. Since the premiums are paid only if there is no default, they are risky. If there is a default, then party B must pay 100 – Recovery. Figure 2 – Time-line of CDS Payments (Sell Protection) Now we can utilize an elegant trick. With any swap agreement only net cash flows are exchanged. This means we can insert any arbitrary cash flows we wish, so long as the same amount is paid and received and the net is zero. Let us add and subtract libor payments at each premium date, and also 100 at CDS maturity, but only when there is no default. These libor payments are thus risky. But since they net to zero, they have absolutely no impact on the price or risk of the CDS. The top part of figure 3 shows the original CDS plus these net-zero cash flows. The bottom part of figure 3 then re- arranges these cash flows in a convenient manner: • Left panel produces an FRN by combining: - CDS premium and + libor into a risky floating coupon, paid only if there is no default - +100 into a risky principal repayment, paid only if there is no default - Convert the payment of –Recovery into receiving +Recovery, paid only if there is default • Right panel produces a libor floater by combining: - libor into a risky floating coupon, paid until default or maturity, whichever occurs earlier - 100 paid at maturity if there is no default - 100 paid at default if there is default The lower left panel is exactly a floating rate bond (FRN): if no default occurs then party B receives coupon of (libor + spread) and final principal at maturity, while if default occurs then party B receives the coupon up to default and then Recovery. The combination in the lower right panel looks awkward but is actually very simple: it is always worth 100 today. It is a libor floating bond with maturity equal to the date of default or maturity of the CDS: payments are libor + 100 whether there is a default or not, with the date of the 100 payment being determined by date of default (or CDS maturity). The timing of the payments may be uncertain, but that does not affect the price because any bond that pays libor + 100, when discounted at libor (as is done for CDS), is worth 100 irrespective of maturity. Coleman December 2009 3 Figure 3 – CDS Payments plus Offsetting Payments = FRN – libor floater In other words, we have just proven, rather simply and without any complex mathematics, that a CDS(sell protection) is just a combination of long an FRN and short a libor floater (worth $100): CDS(sell protection) ⇔ + FRN – libor floater = + FRN – 100 .

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