Credit Default Swaps
READING 29: CREDIT DEFAULT SWAPS
EXAM FOCUS
A credit default swap (CDS) is a contract between two parties in which one party purchases protection from another party against losses from the default of a borrower. For the exam, you should be able to describe CDS, as well as related securities such as index CDS. You should know what a credit event is and how the different protocols for settlement work. You should be familiar with the principles and factors that drive market pricing of CDS. Be able to describe how CDS are used to manage credit exposure, how they can be used to profit from anticipated changes in the credit curve, and how CDS are used for arbitrage to take advantage of relative mispricings of different risky securities.
MODULE 29.1: CDS FEATURES AND TERMS
CREDIT DEFAULT SWAPS
Video covering this content is available online.
A credit default swap (CDS) is essentially an insurance contract. If a credit event occurs, the credit protection buyer is compensated by the credit protection seller. To obtain this coverage, the protection buyer pays the seller a premium called the CDS spread. The protection seller is assuming (that is, long) credit risk, while the protection buyer is short credit risk. The CDS provides protection only against credit risk, not against market-wide interest rate risk. The contract is written on a face value of protection called the notional principal (or "notional").
PROFESSOR'S NOTE
The terminology related to CDS is counterintuitive: the protection buyer is the short party (short the credit risk of the reference asset and short the CDS), while the protection seller is the long party (long the CDS and long the credit risk of the reference asset).
Even though the CDS spread should be based on the underlying credit risk of the reference obligation, market standardization has led to a fixed coupon on many CDS products: 1% for investment-grade securities and 5% for high-yield securities. Hence, the coupon rate on the CDS and the actual credit spread of the reference obligation may differ. The present value of the difference between the standardized coupon rate and the reference obligation's credit spread is paid upfront by one of the parties to the contract.
Example explanation: a CDS on an investment-grade bond with a credit spread of 75 basis points (bps) would require a premium payment of 100 bps (CDS coupon rate) by the protection buyer. To compensate the protection buyer, the protection seller would pay upfront the present value of 25 bps of the notional principal.
For a protection buyer, a CDS has some characteristics similar to a put option-when the underlying performs poorly (credit event), the protection buyer receives a compensating payment.
The market publishes standardised contract terms and conventions (market documentation) to facilitate the functioning of the CDS market.
LOS 29.a: Describe credit default swaps (CDS), single-name and index CDS, and the parameters that define a given CDS product.
SINGLE-NAME CDS
In a single-name CDS, the reference obligation is the fixed-income security on which the swap is written, usually a senior unsecured obligation for a senior CDS. The issuer of the reference obligation is called the reference entity. The CDS pays off not only when the reference entity defaults on the reference obligation but also when the reference entity defaults on any other issue that is ranked pari passu (that is, the same seniority) or higher. The CDS payoff is based on the market value of the cheapest-to-deliver (CTD) bond that has the same seniority as the reference obligation.
PROFESSOR'S NOTE
The cheapest-to-deliver bond is the debt instrument with the same seniority as the reference obligation that can be purchased and delivered at the lowest cost.
EXAMPLE: Cheapest-to-deliver
Party X is a protection buyer in a $10 million notional principal senior CDS of Alpha, Inc. There is a credit event (Alpha defaults) and the market prices of Alpha's bonds after the credit event are as follows:
- Bond P, a subordinated unsecured debenture, is trading at 15% of par.
- Bond Q, a five-year senior unsecured debenture, is trading at 25% of par.
- Bond R, a three-year senior unsecured debenture, is trading at 30% of par.
What will be the payoff on the CDS?
Answer:
The cheapest-to-deliver senior unsecured debenture (that is, same seniority as the senior CDS) is bond Q.
payoff = $10 million - (0.25)($10 million)
payoff = $10,000,000 - $2,500,000
payoff = $7,500,000.
INDEX CDS
An index CDS covers multiple issuers, allowing market participants to take exposure to the credit risk of several companies simultaneously in the same way that stock indices allow exposure to several equities. In an index CDS, protection for each issuer is equally weighted and the total notional principal is the sum of the protection on all issuers.
EXAMPLE: Index CDS
Party X is a protection buyer in a five-year, $100 million notional principal CDS for CDX-IG, which contains 125 entities. One index constituent, company A, defaults and its bonds trade at 30% of par after default.
- What will be the payoff on the CDS?
- What will be the notional principal of the CDS after default?
Answer:
1.
The notional principal attributable to entity A is $100 million / 125 = $0.8 million.
Party X should receive payment of $0.8 million - (0.3)($0.8 million).
Party X should receive payment of $800,000 - $240,000.
Party X should receive payment of $560,000.
2.
Post the default event, the remainder of the CDS continues with a notional principal of $99.2 million.
The pricing of an index CDS depends on the correlation of default (credit correlation) among index constituents. The higher the correlation of default among index constituents, the higher the spread on the index CDS.
LOS 29.b: Describe credit events and settlement protocols with respect to CDS.
CREDIT EVENTS
A default is defined as the occurrence of a credit event. Common credit events specified in CDS agreements include:
- Bankruptcy. A bankruptcy protection filing allows the defaulting party to work with creditors under court supervision to avoid full liquidation.
- Failure to pay. Occurs when the issuer misses a scheduled coupon or principal payment without filing for formal bankruptcy.
- Restructuring. Occurs when the issuer forces its creditors to accept terms different from those specified in the original issue. Restructuring is less common in the United States, where issuers often prefer bankruptcy protection.
A market body (via a Determinations Committee or similar committee) declares whether a credit event has occurred. A supermajority vote (for example, at least 12 of 15 members) is typically required for a credit event declaration.
SETTLEMENT PROTOCOLS
When a credit event occurs, the swap is settled either by physical delivery or by cash settlement.
With physical delivery, the protection seller receives the reference obligation (the bond or loan) and pays the protection buyer the notional amount. This process is illustrated conceptually in Figure 29.1 (referenced in the original material).
With cash settlement, the payout amount is the payout ratio times the notional principal, where:
payout amount = payout ratio × notional principal
and
payout ratio = 1 - recovery rate (%)
The payout ratio depends on the recovery rate, the proportion of par at which the bond trades after default. Figure 29.2 in the original material illustrates this cash settlement relationship.
MODULE 29.2: FACTORS AFFECTING CDS PRICING
Video covering this content is available online.
LOS 29.c: Principles and factors that influence CDS pricing
The factors that influence the pricing of a CDS (that is, the CDS spread) include:
- Probability of default (POD)
- Loss given default (LGD)
- Coupon rate on the swap
The CDS spread is higher for a higher probability of default and for a higher loss given default. The discussion that follows focuses on single-name CDS; the same principles apply to index CDS.
Earlier study material showed the calculation of credit valuation adjustment (CVA), which is the present value of expected loss. CVA is the best estimate of the value of a hedging instrument to cover the risk of the protection seller.
PROBABILITY OF DEFAULT AND HAZARD RATE
Probability of default (POD) is the likelihood of default by the reference entity in a given year. For multi-year CDS, POD is not constant; it usually increases over time. The POD in any year is the product of the probability of survival at the end of the prior year and the hazard rate (the conditional probability of default given no earlier default) in that year.
PODt = PS(t-1) × hazard ratet
EXAMPLE: Hazard rate
Consider a five-year senior CDS on Xeon Corp. Xeon's hazard rate is 2% and increases by 1% per year.
Compute the survival rate in five years.
Answer:
The hazard rates for the five years are: 2%, 3%, 4%, 5%, and 6%.
survival rate in five years = (1 - 0.02)(1 - 0.03)(1 - 0.04)(1 - 0.05)(1 - 0.06)
survival rate in five years = 0.98 × 0.97 × 0.96 × 0.95 × 0.94
survival rate in five years = 0.815 or 81.5%
SINGLE-PERIOD APPROXIMATION
For a single-period CDS, ignoring the time value of money, the CDS premium can be approximated as:
CDS spread ≈ (1 - RR) × POD
where RR is the recovery rate. For example, if the recovery rate is 50% and POD is 3%, then:
CDS spread = 0.5 × 0.03 = 0.015 or 150 bps.
PREMIUM LEG AND PROTECTION LEG
The cash payments made by the protection buyer on the CDS (the coupon payments) cease on default (when the CDS terminates). Therefore, the expected present value of the coupon payments depends on the hazard rate.
The payments by the protection buyer to the seller constitute the premium leg. The contingent payment the protection seller must make on default constitutes the protection leg. The difference between the present values of these legs determines any upfront payment required at inception:
upfront payment (by protection buyer) = PV(protection leg) - PV(premium leg)
APPROXIMATE UPFRONT PREMIUM
We can approximate the upfront premium as the difference between the CDS spread and the CDS coupon rate, multiplied by the duration of the CDS. Be careful: this uses the duration of the CDS instrument, not the duration of the reference obligation.
upfront premium % ≈ (CDS spread - CDS coupon) × duration
Thus, we can also quote the CDS price (per $100 notional) approximately as:
price of CDS (per $100 notional) ≈ $100 - upfront premium (%)
EXAMPLE: Upfront premium and price of CDS
Aki Mutaro, bond portfolio manager for a regional bank, is considering buying protection on one of the bank's high-yield holdings: Alpha, Inc., bonds. Ten-year CDS on Alpha bonds have a coupon rate of 5% while the 10-year Alpha CDS spread is 3.5%. The duration of the CDS is 7.
Calculate the approximate upfront premium and price of a 10-year Alpha Inc. CDS.
Answer:
upfront premium % ≈ (CDS spread - CDS coupon) × duration
upfront premium % ≈ (0.035 - 0.05) × 7
upfront premium % ≈ (-0.015) × 7
upfront premium % ≈ -0.105 or -10.5%
Hence, the protection seller would pay (approximately) 10.5% of the notional to the protection buyer upfront because the CDS coupon is higher than the credit spread.
CDS price = 100 - (-10.5)
CDS price = 110.50 per $100 notional.
VALUATION AFTER INCEPTION OF CDS
At inception, the CDS spread and any upfront premium are computed based on the credit quality of the reference entity. After inception, credit quality (or the credit risk premium in the market) may change, so the CDS will generally have a nonzero value.
If credit spreads decline after inception, the protection seller who locked in a higher spread at initiation would gain; conversely, if spreads widen, the protection buyer benefits.
The change in value of a CDS after inception can be approximated by the change in spread multiplied by the duration of the CDS:
profit for protection buyer ≈ change in spread × duration × notional principal
or
profit for protection buyer (%) ≈ change in spread (%) × duration
Note that because the protection buyer is short credit risk, this buyer benefits when credit spreads widen (profit is positive when spreads increase).
The protection buyer or seller can unwind an existing CDS exposure before maturity by entering into an offsetting transaction. For example, a protection buyer can remove exposure by selling protection with the same terms and remaining maturity as the existing CDS. The difference between the upfront premiums paid and received approximately equals the profit (or loss) of the original position. Capturing value from an in-the-money CDS exposure in this manner is called monetising the gain.
MODULE 29.3: CDS USAGE
LOS 29.d: Describe the use of CDS to manage credit exposures and to express views regarding changes in the shape and/or level of the credit curve.
Video covering this content is available online.
CREDIT CURVE
The credit curve is the relationship between credit spreads for different bonds issued by an entity and the bonds' maturities. The credit curve is analogous to the term structure of interest rates. If longer maturity bonds have higher credit spreads than shorter maturity bonds, the credit curve is upward sloping. If the hazard rate is constant across maturities, the credit curve will be flat.
CDS can be used to manage credit exposures of a bond portfolio. For example, if a portfolio manager expects credit spreads to decline, they may increase credit exposure by being a protection seller; if they expect credit spreads to widen, they may decrease credit exposure by being a protection buyer.
In a naked CDS, an investor with no underlying bond exposure purchases (or sells) protection in the CDS market.
In a long/short trade, an investor purchases protection on one reference entity while simultaneously selling protection on another (often related) reference entity. The investor is betting that the difference in credit spreads between the two reference entities will change in the investor's favour. This trade is similar to going long (selling protection) on one bond and short (buying protection) on another bond.
A curve trade is a long/short trade where the investor buys and sells protection on the same reference entity but with different maturities. Examples:
- If the investor expects an upward-sloping credit curve to flatten, they may buy protection in a short-maturity CDS and sell protection in a long-maturity CDS.
- If the investor expects the short-term outlook to be better than the long-term outlook (that is, expects the curve to steepen), they may buy protection in a long-term CDS and sell protection in a short-term CDS.
An investor worried about short-term credit deterioration but confident about long-term prospects might buy protection in short-term CDS and offset premium cost by selling protection in long-term CDS. Conversely, an investor bearish on short-term prospects can use curve-flattening trades.
LOS 29.e: Use of CDS for valuation disparities among markets
CDS are used to take advantage of valuation disparities among markets such as bonds, loans, equities, and equity-linked instruments.
USES OF CDS
Earning arbitrage profits is a key motivation for trading in the CDS market. Differences in pricing between asset and derivative markets, or differences in pricing across products, can create arbitrage opportunities.
A basis trade seeks to exploit the difference in credit spreads between the bond market and the CDS market. Basis trades rely on the assumption that such mispricings will be temporary and will converge over time. Example: if a bond trades at a credit spread of 4% over risk-free rates while the CDS spread on the same bond is 3%, a trader can buy the bond and take the protection buyer position in the CDS market; if prices converge, the trader profits.
Another arbitrage involves buying and selling different debt instruments issued by the same entity depending on which instruments the CDS market indicates are undervalued or overvalued.
In a leveraged buyout (LBO), a firm issues considerable debt to repurchase publicly traded equity. The additional debt increases the CDS spread because default becomes more likely. An investor who anticipates an LBO might purchase both the stock and CDS protection because both instruments often increase in value when the LBO occurs.
For an index CDS, the index value should equal the sum of the values of the index components. Arbitrage exists if the credit risk of the index constituents is priced differently from the index CDS spread.
Collateralized debt obligations (CDO) are claims against a portfolio of debt securities. A synthetic CDO can be created using CDS exposures rather than cash debt securities. If a synthetic CDO can be assembled at a lower cost than an equivalent cash CDO, investors can buy the synthetic CDO and sell the cash CDO to obtain arbitrage profit.
MODULE QUIZ 29.1, 29.2, 29.3
Use the following information to answer Questions 1 through 6.
Jamshed Banaji, CFA, manages a $400 million bond portfolio for a large public pension fund. Banaji is concerned about volatility in the credit markets and expects credit spreads to widen in the short term but revert back to current levels over the long term.
Banaji has flagged two of his holdings for further scrutiny: IDG Corp. and Zeta Corp. The portfolio currently has $10 million par value of 6% 10-year senior unsecured IDG Corp. bonds. Because he is concerned about IDG's credit risk, Banaji enters into a credit default swap as a protection buyer. Banaji selects a five-year senior CDS for IDG with a coupon rate of 5% and a duration of 4. IDG bonds have a yield-to-maturity of 6.5%. The MRR yield curve is flat at 2%.
Banaji is also concerned about the Zeta Corp. bonds that he holds. Zeta's management is planning to pursue a recapitalization plan that involves a large stock buyback program financed by new debt.
1.
The most appropriate strategy for Banaji, given his expectation about changing credit spreads, is a:
A.
credit curve trade; selling protection in the short-term and purchasing protection in the long-term.
B.
credit curve trade; buying protection in the short-term and selling protection in the long-term.
C.
CDS trade; buying protection in the short-term only.
2.
At inception of the CDS for IDG bonds, Banaji is most likely to:
A.
receive a premium of $200,000.
B.
pay a premium of $300,000.
C.
receive a premium of $400,000.
3.
For this question only, suppose that six months after the inception of the swap, IDG declares bankruptcy. Figure 1 shows the market prices of IDG bonds after the company files for bankruptcy. If Banaji has a choice of settlement procedure, he is most likely to choose:
A.
physical settlement.
B.
cash settlement and the payoff would be $6 million.
C.
cash settlement and the payoff would be $7 million.
4.
Which of the following statements about hazard rate is most accurate? Hazard rate:
A.
is the probability of default given that default has already occurred in a previous period.
B.
affects both the premium leg as well as the protection leg in a CDS.
C.
is higher for higher loss given default.
5.
The most appropriate strategy for Banaji to follow in regard to Zeta Corp. would be to buy Zeta Corp.:
A.
stock and buy CDS protection on Zeta Corp. bonds.
B.
bonds and sell CDS protection on Zeta Corp. bonds.
C.
stock and sell CDS protection on Zeta Corp. bonds.
6.
The statement "credit spreads are positively related to loss given default and to hazard rate" is:
A.
correct.
B.
correct regarding loss given default but incorrect regarding hazard rate.
C.
correct regarding hazard rate but incorrect regarding loss given default.
KEY CONCEPTS
LOS 29.a
A credit default swap (CDS) is essentially an insurance contract in which, upon occurrence of a credit event, the credit protection buyer is compensated by the credit protection seller. To obtain this coverage, the protection buyer pays the seller a premium called the CDS spread. In a single-name CDS, the reference obligation is the fixed-income security on which the swap is written. An index CDS covers an equally weighted combination of borrowers.
LOS 29.b
A default is the occurrence of a credit event. Common credit events specified in CDS agreements include bankruptcy, failure to pay, and restructuring. When a credit event occurs, the swap is settled either by cash settlement or by physical delivery.
LOS 29.c
The factors that influence the pricing of a CDS (the CDS spread) include probability of default, loss given default, and the coupon rate on the swap. The CDS spread is higher for a higher probability of default and for a higher loss given default. The conditional probability of default (that is, the probability of default given that default has not occurred) is called the hazard rate.
(expected loss)t = (hazard rate)t × (loss given default)t
The upfront premium on a CDS can be computed as:
upfront payment (by protection buyer) = PV(protection leg) - PV(premium leg)
Or approximately:
upfront premium ≈ (CDS spread - CDS coupon) × duration
The change in value for a CDS after inception can be approximated by the change in spread multiplied by the duration of the CDS:
profit for protection buyer ≈ change in spread × duration × notional principal
profit for protection buyer (%) ≈ change in spread (%) × duration
LOS 29.d
In a naked CDS, an investor with no exposure to the underlying purchases protection in the CDS market. In a long/short trade, an investor purchases protection on one reference entity while selling protection on another. A curve trade is a long/short trade in which the investor buys and sells protection on the same reference entity but with different maturities. An investor expecting the short-term outlook to be better than the long-term outlook can use a curve-steepening trade (buy protection in long-term CDS and sell protection in a short-term CDS) to profit if the credit curve steepens. Conversely, an investor bearish about short-term prospects will enter into a curve-flattening trade.
LOS 29.e
A basis trade attempts to exploit differences in credit spreads between bond markets and the CDS market. Basis trades rely on the idea that such mispricings will be temporary and that disparity should eventually disappear. If a synthetic CDO can be created at a cost lower than the equivalent cash CDO, investors can buy the synthetic CDO and sell the cash CDO to obtain a profitable arbitrage.
ANSWER KEY FOR MODULE QUIZZES
Module Quiz 29.1, 29.2, 29.3
1.
B Banaji expects credit spreads to widen in the short term; therefore, the appropriate strategy is to buy short-term CDS protection and sell long-term protection (a credit curve trade: buying protection in the short term and selling protection in the long term). Buying protection only would cost more (the protection buyer premium is not offset by premium income from selling protection) and would not use Banaji's entire information set, so it is not most appropriate. (Module 29.2, LOS 29.c)
2.
Credit spread on IDG bonds = yield - MRR = 6.5% - 2% = 4.5%
upfront premium (paid by protection buyer) ≈ (CDS spread - CDS coupon) × duration × notional principal
= (0.045 - 0.05) × 4 × $10 million
= (-0.005) × 4 × $10,000,000
= (-0.02) × $10,000,000
= -$200,000
Because the computed value is negative, $200,000 would be received by Banaji as the protection buyer. (Module 29.2, LOS 29.c)
3.
B The CDS in the question is a senior CDS; hence the reference obligation is a senior unsecured bond. The payoff on the CDS is based on the CTD with the same seniority as the reference obligation. From the three choices given, the five-year 5% senior unsecured is the cheapest to deliver. Hence, the payoff will be notional principal - market value of the CTD = $10 million - $4 million = $6 million.
Note that physical settlement would not be advantageous to Banaji; Figure 1 indicates that the IDG bonds Banaji is currently holding have a market value of $4.5 million, so the implied payoff of physically delivering these bonds in exchange for $10 million would be $10 million - $4.5 million = $5.5 million, which is less than the $6 million cash settlement payoff. (Module 29.2, LOS 29.c)
4.
B Hazard rate is the conditional probability of default given that default has not occurred in previous periods. The hazard rate affects the protection leg: a higher hazard rate increases the expected value of payoffs made by the protection seller upon default. The hazard rate also affects the premium leg because once default occurs, the CDS ceases to exist and premium income stops. Loss given default depends on the recovery rate and not on hazard rate (probability of default). (Module 29.2, LOS 29.c)
5.
A Due to leveraged recapitalization of Zeta Corp., credit spreads on Zeta bonds are expected to widen, increasing the value of CDS protection for a protection buyer. The stock buyback would be expected to increase the value of Zeta stock. Banaji should purchase both the stock and CDS protection; both will increase in value when the leveraged recapitalization (or LBO) occurs. (Module 29.3, LOS 29.d)
6.
A Credit spreads are positively related to hazard rates and to loss given default, and negatively related to recovery rates. (Module 29.3, LOS 29.d)
Topic Quiz: Fixed Income
You have now finished the Fixed Income topic section. Please log into your online dashboard and take the Topic Quiz on this section. The Topic Quiz provides immediate feedback on how effective your study has been for this material. Questions are more exam-like than typical Module Quiz or QBank questions; a score of less than 70% indicates that your study likely needs improvement. These tests are best taken timed; allow three minutes per question.
