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FI 5 – Credit Default Swaps

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A credit derivative is any derivative whose underlying is a measure of how creditworthy a borrower is. Four instruments fall into that family: total return swaps, credit spread options, credit-linked notes, and credit default swaps. Only the last of these trades in genuine size, so a credit default swap, or CDS, is what this reading examines. In every other derivative the payoff is read off the performance of some observable underlying, a share price, an interest rate, a currency. Here the underlying is something less tangible: the market judgement of whether a particular borrower will pay.

The contract itself is simple to state. Two parties agree. The credit protection buyer commits to a series of periodic payments over the life of the contract, fixed in size at inception. In return the credit protection seller promises to compensate the buyer for credit losses if a credit event strikes a named third party. Should that credit event occur, the periodic payments stop.

Figure 1: Cash flows over the life of a CDS

Premiums run above the line from buyer to seller. The single payment below the line runs the other way and arrives only if a credit event is declared. Once it does, the premium stream ends.

The option analogy, and where it breaks down

A CDS behaves rather like a put option written on the credit of the reference borrower. A put lets its holder sell the underlying to the writer when the underlying performs badly. In the same spirit, when a credit event strikes, the protection buyer collects from the protection seller an amount equal to par, or notional, less what the defaulted debt is expected to be worth. If credit quality simply deteriorates without an outright credit event, the buyer collects nothing unless the position is unwound, in which case the accumulated gain is realised through the price of the contract itself.

That last point deserves emphasis, because it is where most of the analytical content of this reading sits. A CDS does not sit dormant waiting for a default that may never happen. Its value moves continuously with the market view of the reference borrower. Opinions about how likely a default is, and about how much would be lost if one occurred, change every day, and the contract is marked to those opinions. A bond investor who watches the price of a holding fall as fears rise has already taken a loss even though nothing has formally defaulted. The CDS records the mirror image of that loss as a gain for the protection buyer.

A CDS reduces credit risk but does not remove it

Two residual risks survive the hedge. First, the definition of default written into the contract may not line up exactly with what an investor would intuitively call a default, so the change in value of the swap need not match the change in value of the debt it was bought to protect. Second, the protection buyer takes on counterparty risk against the protection seller. There is no guarantee that a seller will be able to pay, as several very large financial institutions demonstrated during the crisis that began in 2007. In practice most sellers of protection are strong credits, because a weak one would find no takers.

Why investors use them

Hedging credit exposure is the obvious motive, but it is not the only one. Market participants also turn to CDS to add leverage to a portfolio, to obtain exposure at maturities where no suitable bond exists, to isolate credit risk from interest rate risk, and to improve portfolio liquidity given how thinly much of the corporate bond market trades. Alongside these private benefits, the market has produced a public one: it has made the cost of credit risk far more visible. Because CDS participants are relatively sophisticated and the instruments relatively liquid, price discovery is sharper, and trading can continue in the swap when the underlying cash bond market has seized up.

Most CDS reference debt issued by corporate borrowers, and that is the focus here. The same machinery is applied to sovereign borrowers, to state and local government issuers, and to portfolios of loans, mortgages or securities.

Three structures exist. Options written on CDS, sometimes called CDS swaptions, fall outside this discussion.

The three CDS structures

Structure	What it covers	Key idea
Single-name CDS	One reference entity, identified through a reference obligation	Payoff is set by the cheapest-to-deliver obligation
Index CDS	A standardised portfolio of single-name exposures	Credit correlation drives the cost of protection
Tranche CDS	A combination of borrowers, but only across a pre-specified band of losses	Loss layers, in the manner of asset-backed securities

Tranche CDS are named for completeness only; their mechanics are outside the scope of this reading.

The single-name contract and the cheapest-to-deliver obligation

A CDS written on one borrower is a single-name CDS. The borrower is the reference entity, and the contract names a specific debt instrument issued by that borrower, the reference obligation. Only a limited group of issuers, those with large and liquid debt outstanding, support a single-name CDS market at all.

The named instrument is normally a senior unsecured obligation, but it is a benchmark rather than a boundary. Coverage extends to any obligation of the borrower ranking equal to or above the reference obligation in the priority of claims. That breadth has a direct consequence for the payoff. Because several qualifying instruments may exist, the settlement amount is fixed by the cheapest-to-deliver obligation: the qualifying instrument that can be bought most cheaply while still matching the seniority of the reference obligation. A protection buyer holding a more expensive qualifying bond is nonetheless paid on the basis of the cheap one.

Example 1 · Worked

A company with several issues trading in the market files for bankruptcy, which is a credit event. A CDS on this company names a five-year senior unsecured bond as its reference obligation. Three instruments are quoted.

Quoted instruments after the filing

Choice	Instrument	Price
A	Subordinated unsecured bond	20% of par
B	Five-year senior unsecured bond	50% of par
C	Two-year senior unsecured bond	45% of par

Which instrument is the cheapest-to-deliver obligation for this contract?

Solution. C, the two-year senior unsecured bond at 45% of par. Work in two steps.

Step 1. Filter on seniority. The reference obligation is senior unsecured, so only instruments ranking equal or higher qualify. Choice A is subordinated. It carries the lowest price of the three at 20% of par, but it is not covered by the contract and therefore cannot be the cheapest-to-deliver obligation.

Step 2. Take the lowest price among the qualifiers. Both remaining bonds are senior unsecured, so both qualify despite their different maturities. At 45% of par, C is cheaper than B at 50% of par.

The practical consequence matters more than the arithmetic. A holder of the five-year bond, the very instrument named in the contract, is compensated on the basis of the two-year bond at 45, not on the basis of the bond actually held.

Index CDS and credit correlation

The second structure bundles single-name exposures into a portfolio, allowing a participant to take a view on a group of credits at once, much as an index fund allows a view on a group of equities. Two families dominate: the North American indexes, labelled CDX, and the European, Asian and Australian indexes, labelled iTraxx.

What makes a portfolio of credits behave differently from the sum of its parts is the tendency of defaults to arrive together. In an index CDS this shows up as credit correlation, and it is the central determinant of value. Modelling how one company’s failure is connected to another’s is a specialist discipline in its own right, but the direction of the effect is easy to state. The more tightly defaults are correlated, the more expensive it is to buy protection on the combination, because the bad outcomes cluster. Spread the exposure across companies whose fortunes are only loosely linked and protection becomes considerably cheaper.

Tranche CDS

The third structure covers a group of borrowers but only between specified loss thresholds, in the same way that an asset-backed structure carves a pool into layers with each layer absorbing a defined slice of the losses. A tranche CDS therefore isolates a band of the loss distribution rather than the whole of it.

The CDS market is large, global and unusually well organised for an over-the-counter market. The body that supplies that organisation is the International Swaps and Derivatives Association, the ISDA, which publishes the conventions the market has agreed to follow. Counterparties sign an ISDA Master Agreement, and their individual contracts conform to ISDA specifications. Europe uses the Standard Europe Contract; the United States and Canada use the Standard North American Contract. Equivalent standardised documents cover Asia, Australia, Latin America and a handful of individual countries.

Notional and maturity

Every contract specifies a notional amount, the size of the protection bought. One consequence surprises newcomers: the total notional of CDS written on a reference entity can exceed that entity’s outstanding debt. Nothing prevents this, because a protection buyer does not have to be a creditor. A party with no exposure at all can buy protection purely because it expects credit quality to change.

Like any derivative, a CDS expires. Coverage runs to that date and no further. Maturities of one to ten years are typical, and the five-year contract is by a wide margin the most actively traded, although the two parties may negotiate whatever term they wish. Maturity dates cluster on the twentieth day of March, June, September and December, and of those the March and September dates are the most liquid because that is when index contracts roll.

The CDS spread and the standardised coupon

The premium the buyer pays is quoted as the CDS spread, a return over a market reference rate demanded in exchange for bearing credit risk. Conceptually it is the same object as the credit spread on a bond: the compensation for taking the risk that the borrower fails.

Historically the coupon written into the contract simply equalled that spread. A credit judged to need 4% of compensation produced quarterly payments adding to 4% a year. Standardisation replaced this. Contracts now carry one of two conventional annual coupons.

Standardised CDS coupons

Coupon	Typically applied to
1%	CDS on an investment-grade company or index
5%	CDS on a high-yield company or index

Note that the reference bond makes its own payments, referred to collectively as its coupon, while the CDS written on that bond carries a separate coupon rate of its own. Do not conflate the two.

Why an upfront premium is needed

Two conventional rates cannot possibly compensate a seller correctly across every borrower. Investment-grade companies differ widely among themselves, and so do high-yield companies. Any given contract will therefore carry a coupon that is either too generous or too mean relative to the risk actually being assumed. The mismatch is settled at inception with a single cash payment, the upfront premium, equal to the present value of the difference between the credit spread the borrower deserves and the standard coupon the contract pays.

The direction follows from the sign. A credit spread wider than the standard coupon means the seller is being underpaid over the life of the contract, so the buyer hands over cash at the start. A credit spread narrower than the standard coupon means the seller is being overpaid, so the seller pays the buyer at the start.

Value moves even when nothing defaults

Whether or not an upfront payment changes hands, credit quality moves afterwards, and the contract moves with it. Take a high-yield borrower whose credit spread is 5% against a CDS coupon of 5%. The two match, so no upfront payment is made and the buyer simply pays 5% of notional a year. Suppose the borrower then deteriorates. The buyer is now paying 5% for protection against a risk that merits more than 5%. Nothing about the coverage or its cost has changed, but the risk being covered has grown, so the contract has become more valuable to the buyer, who may unwind and bank the gain. The seller has correspondingly lost, since 5% no longer compensates for what is now being insured. Absent any other exposure to the borrower, deterioration in credit quality is a gain for the protection buyer and a loss for the protection seller, and the market value of the contract records exactly that.

Why long and short mean opposite things for single-name CDS and for index CDS

In equities and bonds the buyer is long and the seller is short. Single-name CDS invert this: the buyer of protection is short credit exposure and the seller of protection is long credit exposure. That is internally consistent, because a short position is meant to profit when things go badly, and the protection buyer does exactly that when credit quality deteriorates. Index positions then invert it back again: buying a CDX means going long credit exposure, and selling a CDX means going short. The safest habit is to abandon the words buy and sell for the instrument altogether and speak instead of buying protection or selling protection, which never changes meaning.

A credit event is the trigger: the occurrence that obliges the protection seller to pay the protection buyer. Everything about the contract depends on this definition being unambiguous. The question must admit a clean answer, occurred or did not occur, because a market cannot function on a trigger that is open to argument.

The three principal credit events

Credit events recognised in standard CDS contracts

Event	What it means	Note
Bankruptcy	A legal procedure provided for by national law that compels creditors to defer their claims	Universally treated as a credit event
Failure to pay	A scheduled payment of principal or interest is missed after any grace period, with no bankruptcy filing	Defined uniformly in ISDA contracts, less so in bespoke ones
Restructuring	Reduction or deferral of principal or interest, a change in seniority, or a change in the currency of payment	Must be involuntary or coercive to qualify

Bankruptcy erects a temporary barrier around the company that creditors cannot cross. Inside it, the defaulting party works with its creditors and the court on a plan to repay. If that plan fails, full liquidation is the likely outcome and the court decides who is paid what. Until liquidation, the company usually keeps trading, and many companies never liquidate at all but emerge from the process.

Restructuring requires a further test. It counts only if it is either involuntary, meaning imposed on the borrower by its creditors, or coercive, meaning imposed on the creditors by the borrower. Jurisdiction matters here more than anywhere else in the contract. Restructuring is not a credit event in the United States, where distressed issuers generally reorganise through bankruptcy, which is a credit event. In countries where the bankruptcy court is a less usual route to reorganisation, restructuring is recognised. The Greek debt crisis produced a well-known restructuring that triggered credit events.

Sovereign and municipal markets add a further category. A government may declare a moratorium on payments falling due, or, more drastically, repudiate the obligation by disputing the validity of the entire debt. Other, less common events are defined in ISDA’s Credit Derivatives Definitions and are not considered here.

Who decides

The judgement is not left to the counterparties. Each region of the world has a Determinations Committee within ISDA, a body of 15 members made up of 10 sell-side CDS dealer banks and 5 buy-side non-bank end users. Declaring a credit event requires a supermajority of 12 of those 15 votes.

Composition of a Determinations Committee

Element	Number
CDS dealer banks, sell side	10
Non-bank end users, buy side	5
Total members	15
Votes needed to declare a credit event	12

Succession events

The same committees rule on a second question. A succession event arises when the corporate structure of the reference entity changes in a way that clouds who is ultimately responsible for the debt: a merger, a divestiture, a spinoff or something similar. A clean case gives no trouble. If one company acquires all the shares of another, it normally assumes the target’s debt too. Many transactions are messier. Partial share acquisitions, spinoffs and divestitures can leave genuine doubt about which entity now stands behind a particular obligation, and for a CDS holder that doubt is not academic.

Such questions go to a Determinations Committee, whose resolution frequently turns on detailed readings of contract provisions and of the law in the relevant country. Where a succession event is declared, the CDS contract is amended to reflect the committee’s view of who has become the obligor. In some cases the contract ends up divided across more than one entity.

Once a Determinations Committee has declared a credit event, the two parties acquire the right to settle, but not the obligation to do so. Settlement generally takes place 30 days after the declaration, by one of two methods.

Physical settlement, the less common route, has the protection buyer deliver the debt instrument itself and the protection seller pay the full notional amount in exchange. Cash settlement replaces the delivery with a payment from seller to buyer. Determining how large that payment should be is the difficult part, because reasonable parties can disagree about how much has actually been lost.

Recovery rate, loss given default and the payout

Default does not wipe out a claim. Some portion of the amount owed is normally recovered, and that portion, expressed as a percentage, is the recovery rate. In most models the recovery rate is applied to principal only. Its complement is the loss given default, which is in effect the estimate of the credit loss.

Loss given default is one minus the recovery rate, in percentage terms.

Why the industry runs an auction

Actual recovery on a defaulted claim can take years and will usually arrive long after the CDS has been settled. Waiting is not an option. The industry therefore fixes the number by auction: major banks and dealers submit bids and offers for the cheapest-to-deliver defaulted debt, and the clearing level of that auction reveals the market expectation of the recovery rate and hence the loss given default. Both parties agree in advance to accept the auction result. That agreement carries a real consequence. The eventual recovery may turn out to be materially different from the auction level, and a protection buyer who also owns the underlying debt bears the difference.

Example 2 · Worked

A French company files for bankruptcy, triggering CDS contracts. It has two series of senior bonds outstanding. Two investors each hold EUR 10 million of protection alongside EUR 10 million of one of the bonds.

Positions after the bankruptcy filing

Investor	Bond held	Bond price	Bond face	CDS protection
X	Bond A	30% of par	EUR 10 million	EUR 10 million
Y	Bond B	40% of par	EUR 10 million	EUR 10 million

1. What recovery rate applies to the two CDS contracts?

Solution. 30%. Both bonds are senior, so both qualify, and the payoff is fixed by the cheapest of them. Bond A trades at 30% of par against Bond B at 40%, so Bond A is the cheapest-to-deliver obligation and its price sets the recovery rate for both contracts. Note that Investor Y is paid on Bond A even though Investor Y holds Bond B.

2. Would Investor X prefer cash settlement, physical settlement, or neither?

Solution. Investor X is indifferent. Compare the two routes.

Cash settlement. The payout is loss given default multiplied by notional: (1 − 30%) × EUR 10 million = EUR 7 million. Investor X keeps Bond A and sells it in the market for 30% of EUR 10 million = EUR 3 million. Total proceeds are EUR 7 million + EUR 3 million = EUR 10 million.

Physical settlement. Investor X delivers the full EUR 10 million face amount of Bond A and receives the notional in cash, EUR 10 million.

The two routes give the same EUR 10 million, which is precisely what one would expect: Investor X holds the cheapest-to-deliver bond, so nothing is left on the table either way.

3. Would Investor Y prefer cash settlement, physical settlement, or neither?

Solution. Investor Y prefers cash settlement.

Cash settlement. The CDS payout is set by the cheapest-to-deliver bond, so Investor Y also receives (1 − 30%) × EUR 10 million = EUR 7 million. But the bond actually held is Bond B, which sells for 40% of EUR 10 million = EUR 4 million. Total proceeds are EUR 7 million + EUR 4 million = EUR 11 million.

Physical settlement. Delivering Bond B produces only the face amount, EUR 10 million.

Cash settlement is worth EUR 1 million more. The general rule is visible in the comparison: an investor holding debt worth more than the cheapest-to-deliver obligation should settle in cash and sell the better bond separately, rather than surrender it for par.

A CDS index is no more a traded instrument than a stock index is. What trades is a contract built on the index, and the indexes themselves come largely from a firm called Markit. The traded instruments generate a payoff whenever any entity covered by the index defaults.

The four main index families

Markit classifies its indexes first by region and then by credit quality. North America and Europe are the two most heavily traded regions, with CDX covering North America and iTraxx covering Europe, Asia and Australia. Each region carries an investment-grade and a high-yield version.

Principal CDS index families

Index	Region	Credit quality	Number of entities
CDX IG	North America	Investment grade	125
iTraxx Main	Europe, Asia, Australia	Investment grade	125
CDX HY	North America	High yield	100
iTraxx Crossover	Europe, Asia, Australia	High yield	Up to 75

Quoting convention splits along the same line. Investment-grade index CDS are normally quoted as spreads, while high-yield index CDS are normally quoted as prices. Both use standardised coupons. If that dual convention looks awkward, recall that the bond market does the same thing, describing a government bond sometimes by a price of 120 and sometimes by a yield of 2.68%, with both descriptions pointing at the same instrument.

Equal weights, rolls and defaults

Every CDS index is equally weighted. In a 125-name index each constituent accounts for one one-hundred-and-twenty-fifth of the notional, so settlement on a single default touches that fraction of the position. Markit refreshes the membership of each index every six months, launching a new series while keeping the old ones alive. The newest series is the on-the-run series and the earlier ones are off-the-run; moving a position from one series to the next is called a roll.

When a constituent defaults it is removed from the index and settled exactly as a single-name CDS would be, sized on its share of the index. The index then continues with a correspondingly smaller notional. That mechanism is the key to the next example.

Example 3 · Worked

An investor sells USD 500 million of protection using the CDX IG index, which contains 125 reference entities. Worried about a handful of the names, the investor hedges part of the exposure to each. For Company A the investor buys USD 3 million of single-name CDS protection. Company A then defaults.

1. What is the investor’s net notional exposure to Company A?

Solution. USD 1 million, long. The index is equally weighted, so the exposure to any single name is the total notional divided by the number of entities:
USD 500,000,000 ÷ 125 = USD 4 million long credit exposure through the index.
The single-name hedge is USD 3 million of protection bought, which is USD 3 million short credit exposure. Netting:
USD 4 million − USD 3 million = USD 1 million long.

2. What proportion of the exposure to Company A has been hedged?

Solution. 75%. The hedge covers USD 3 million of a USD 4 million exposure:
3 ÷ 4 = 0.75.

3. What notional remains on the index CDS trade?

Solution. USD 496 million. Company A has defaulted, so it is removed from the index and settled separately at its index share of USD 4 million. The index carries on with the remainder:
USD 500 million − USD 4 million = USD 496 million.
Note that the USD 3 million single-name hedge does not enter this calculation at all. It is a separate contract and does not change the size of the index position.

How the market came about

Banks intermediate between savers and borrowers, and corporate lending sits at the core of what they do. Every corporate loan carries two distinct risks: that the borrower fails to repay principal and interest, which is credit risk or default risk, and that market rates move so that the loan yields less than comparable instruments now available, which is interest rate risk. Techniques for handling the second have existed for a long time. The first, until roughly the mid-1990s, was handled by traditional analysis of the borrower, its industry and the wider economy, supported by controls such as credit limits, monitoring and collateral. In effect a lender had three choices: decline the loan, lend against collateral whose value is itself uncertain, or lend and watch closely in the hope of spotting trouble early.

Credit derivatives, created around 1995, added a fourth. They let credit risk be handed to another party, which in turn separates credit risk from interest rate risk. A bank can then keep doing the thing it exists to do, lend, in the knowledge that the credit component can be transferred if it wishes. Because lending underpins economic activity generally, that transferability has real economic value. The instruments turned out to work better in bond markets, where terms and conditions are far more standardised, than in the loan market, and among the four types of credit derivative the CDS has become so dominant that it is now close to the only one used at any scale.

Trading, clearing and market size

Execution happens over the counter, over the telephone, by instant message, or across the Bloomberg messaging system. Details of each trade go to the Depository Trust and Clearinghouse Corporation, a United States institution supplying post-trade clearing, settlement and reporting services to a wide range of securities markets. Regulation now requires central clearing of many CDS contracts, meaning the contracts pass through clearinghouses that collect and distribute payments, impose margin requirements and mark positions to market. Central clearing has grown sharply since 2010: slightly more than half of all CDS are now centrally cleared, against just 10% in 2010.

The market is markedly smaller than it was before the 2008 financial crisis.

Gross notional amounts reported by the Bank for International Settlements

Measure	Amount
CDS gross notional, December 2019	About USD 7.6 trillion
CDS market value, December 2019	USD 199 billion
CDS gross notional, December 2007	USD 57.9 trillion
Interest rate contracts notional, December 2019	About USD 449 trillion

Interest rate contracts here cover forward rate agreements, swaps and options.

The 2007 figure is roughly 7.6 times the 2019 figure, so the contraction over that period was close to eight-fold. Set against interest rate derivatives the CDS market is small: USD 7.6 trillion against about USD 449 trillion of notional. Activity is also highly concentrated. More than 90% of CDS market activity now comes from trading in five indexes: iTraxx Europe, iTraxx Europe Crossover, iTraxx Europe Senior Financials, CDX IG and CDS HY.

Standardisation is what produced that concentration. Single-name trading is limited by the sheer diversity of the entities involved, whereas an index built on a fixed, well-identified portfolio gives participants something uniform to trade. They have responded in volume, and index CDS are now typically more liquid than single-name CDS, with average daily turnover several times as large.

The general recipe for pricing a derivative is to find the cost of a position that exactly offsets the underlying exposure and therefore earns the risk-free rate. Applied to a CDS, that cost is the credit spread, or equivalently the upfront payment attached to a given contractual coupon. Although the instrument is called a swap, its economics are those of an option, because the seller’s payment is contingent on an event that the ISDA Determinations Committee must declare.

Two features make this harder than pricing a currency forward. First, the settlement amount after a credit event is far less clear than for derivatives whose underlying trades actively. Credit does not trade in its own right; it exists implicitly inside bond and loan prices. Second, every reference entity has its own debt structure, which complicates the relationship between a CDS contract and any particular bond or loan of that borrower. Full credit models lie outside this reading, but the factors that drive the price do not.

Credit valuation adjustment as the organising idea

The credit valuation adjustment, or CVA, is the present value of the credit risk attaching to a loan, bond or derivative obligation. In principle it should approximate what a hedge would have to cost to leave an investor earning the risk-free rate, which is exactly the CDS position described above. The calculation assembles five components.

Components of the credit valuation adjustment

Component	Meaning	Relationship
Expected exposure (EE)	Total projected exposure should default occur; for a CDS this reflects the notional	Input
Recovery rate (RR)	Percentage of the loss recovered in default	Input
Loss given default (LGD)	Amount lost if default occurs	EE × (1 − RR) = LGD
Probability of default (POD)	Conditional probability of default, assuming no prior default	Input
Expected loss (EL)	Probability-weighted loss	LGD × POD = EL

Each period’s expected loss is discounted at the risk-free rate and the results are summed.

The probability of default drives the spread

Strip the problem to one period, ignore the time value of money, assume default can happen only at maturity, and assume no upfront payment. The fair price of protection for that period collapses to a product of two numbers.

With a probability of default of 2% and a recovery rate of 60%, the estimated spread for the period is (1 − 0.60) × 0.02 = 0.0080, or 80 bps. On a notional of USD 100 over one year, the fair value of the contract is the present value of USD 0.80.

Conditional probabilities and the hazard rate

Probability of default is a conditional quantity. In a two-period setting, the chance of defaulting in period 2 is conditional on having survived period 1. Real models treat default as arriving in continuous time; the discrete treatment here is a simplification that gives the same intuition.

Take a two-year loan of USD 1,000 paying 5%, with one interest payment of USD 50 due after one year and USD 1,050 of interest and principal due after two. Suppose the probability of defaulting on the first payment is estimated at 2% and on the second at 4%. To find the probability of default across the life of the loan, first build the probability of survival. Surviving the first year has probability 100% − 2% = 0.98, and surviving the second, conditional on having reached it, has probability 100% − 4% = 0.96. Multiplying:

So survival over the two years is approximately 94.08%, and the probability of default over the life of the loan is 100% − 94.08% = 5.92%.

This conditional probability of default has a name: the hazard rate, the probability that an event occurs given that it has not occurred already. Its cumulative effect over long horizons is the part candidates consistently underestimate. Consider a 10-year bond with a constant hazard rate of 2% a year. The probability of surviving all ten years is 0.98 raised to the tenth power, which is 0.817, so the probability of default at some point in the decade is 1 − 0.817 = 0.183, or 18.3%. A risk that looks negligible in any single year compounds into something substantial across a decade. The constant hazard rate assumed here is itself a simplification.

Figure 2: Survival probability under a constant 2% hazard rate

The curve is drawn through the eleven period-end values from 0 to 10, and the six round markers sit on the even-numbered periods. Survival compounds rather than subtracts, each period keeping 98% of what is left, so 0.817 survives after ten periods and the cumulative probability of default is 18.3%. Over a decade at this hazard rate the compounding is mild enough that the path still looks almost straight.

Example 4 · Worked

A company has a constant hazard rate of 8% a year, equivalent to 2% a quarter. An investor sells five-year CDS protection on the company, with premiums paid quarterly over the five years.

1. What is the probability of survival for the first quarter?

Solution. 98%. The hazard rate for the quarter is 2%, so survival is 100% − 2% = 98%.

2. What is the conditional probability of survival for the second quarter?

Solution. 98% again. The hazard rate is constant at 2% a quarter, so conditional on having survived the first quarter, the probability of defaulting during the second is 2% and the conditional probability of surviving it is 98%. A constant hazard rate means the conditional figure never changes.

3. What is the probability of survival through the second quarter?

Solution. 96.04%. This is a cumulative rather than a conditional figure, so the two quarterly survival probabilities multiply:
98% × 98% = 96.04%.
Equivalently, the probability of defaulting at some point during the first two quarters is 1 − 96.04% = 3.96%. Note that 3.96% is not simply 2% + 2%, because the second quarter’s 2% applies only to the 98% of outcomes that reached it.

The two legs of the contract

Pricing becomes much easier to think about once the contract is split into its two sides. The protection leg is the contingent payment the seller may have to make. The premium leg is the series of payments the buyer promises. Each is valued the same way: establish the cash flow, weight it by the relevant probability, and discount at the risk-free rate.

Building the two legs

Step	Protection leg	Premium leg
1	Establish loss given default on the reference obligation	Establish the standardised coupon payments
2	Apply the probability of default, contingent on survival	Apply the hazard rates, contingent on survival
3	Discount expected loss at the risk-free rate	Discount the contingent coupons at the risk-free rate
Result	Sum of the present values of expected loss	Sum of the present values of contingent coupons

The difference between the two present values is what changes hands at inception.

A positive result is paid by the protection buyer; a negative result is paid by the protection seller.

Figure 3: The upfront payment as the gap between the two legs

Here the protection leg is worth more than the premium leg, so the gap between the bar tops is paid by the protection buyer to the protection seller. Reverse the heights and the payment reverses direction.

Production pricing models are considerably more elaborate than this, but they are built on exactly this framework.

The credit spread on a debt instrument is the amount above a market reference rate that investors require in order to hold it. The reference rate is not itself free of credit risk, since it reflects the rate at which commercial banks lend to one another. As a rough decomposition, the credit spread is the probability of default multiplied by loss given default expressed as a percentage.

Collect a borrower’s credit spreads across a range of maturities and the result is that borrower’s credit curve. It is the credit analogue of the term structure of interest rates, with two differences: it applies to non-government borrowers, and credit risk is embedded in every point on it.

What determines the shape

The CDS market for a borrower and that borrower’s credit curve are not two separate things. Given how the CDS market has developed and how efficiently it prices, the credit curve is in practice determined by CDS rates. Hazard rates are the key driver of its shape.

Reading the slope of a credit curve

Shape	What it implies	Frequency
Upward-sloping	Default is more likely in later years	The common case
Flat	Associated with a constant hazard rate	Intermediate
Downward-sloping	Default is more likely in the earlier years	Less common, often signals severe near-term stress

Figure 4: Three shapes of the credit curve

Spread is measured up the vertical axis of each panel and maturity along the horizontal. The middle panel is drawn tilting very slightly downward rather than perfectly level, because once the recovery rate is above zero, discounting alone eases the spread a little as maturity lengthens even when the hazard rate is held constant.

That last qualification is worth spelling out. Even with hazard rates held constant, the curve does not come out perfectly flat, because of discounting. Imagine a company issuing both a 5-year and a 10-year zero-coupon bond with equally likely probabilities of default and therefore equal expected payoffs. The present values of those payoffs differ because the horizons differ, so the discount rates that equate present value to expected payoff cannot be the same at both maturities.

Example 5 · Worked

Two points on a company’s credit curve are observable. At the 5-year maturity the CDS trades on a 300 bp credit spread, and at the 10-year maturity it trades on 500 bps. Consider two separate movements in the curve.

1. The 5-year spread is unchanged and the 10-year spread widens by 100 bps. What does this imply?

Solution. The curve steepens, from a 200 bp gap between the two points to a 300 bp gap, with the entire move at the long end. The reading is that the market sees no additional near-term risk but has become less comfortable about the company further out. A plausible story is that liquidity is adequate for now, but that a repayment schedule beginning after five years is expected to strain cash flow. Nothing about the short-term credit view has changed.

2. The 10-year spread is unchanged and the 5-year spread widens by 500 bps. What does this imply?

Solution. The 5-year spread moves from 300 bps to 800 bps while the 10-year stays at 500 bps, so the curve inverts and becomes downward-sloping. Near-term credit risk has risen sharply. The corollary is more interesting than it first appears: the probability of default actually falls if the company survives the next five years, because the market is pricing an immediate problem rather than a permanent one. The likely story is a liquidity issue that has to be resolved soon, with default following if it is not.

Prices, spreads and the upfront premium

Corporate bonds can be described by price or by spread, and spread is the more informative of the two. A high-yield bond issued with a coupon equal to its yield prices at par. An investment-grade bond of the same maturity issued the same way also prices at par. On the offering date the two prices are identical, and they may stay close for much of the life of the bonds, yet the instruments are nothing alike. The price says almost nothing. The spread, measured against a market reference rate or the risk-free rate, tells an investor how much credit risk is implied by the price, the maturity and the coupon. The same argument applies to CDS: they have prices, but their spreads are far more informative.

Because the reference entity’s own debt will rarely carry a spread equal to the conventional 1% or 5% coupon, the present value of the buyer’s promised payments will differ from the present value of the coupons on the entity’s debt. That difference is the upfront premium.

The industry works with a quick approximation rather than the full present value calculation.

The duration used here is effective duration, because the cash flows on the coupon leg are contingent on the reference entity not defaulting and are therefore uncertain. Converting the premium into a price is then a matter of subtraction from 100.

Example 6 · Worked

Two independent situations. Assume high-yield companies carry 5% coupons on their CDS and investment-grade companies carry 1%.

1. A high-yield company has a 10-year credit spread of 600 bps and the CDS has a duration of 8 years. What approximate upfront premium is required to buy 10-year protection?

Solution. Approximately 8% of the notional.

Step 1. Identify the shortfall in the coupon. Buying protection means paying the standard 500 bp coupon, but the market demands 600 bps for this credit. The buyer is therefore underpaying by 600 − 500 = 100 bps every year, and must make that up at the start.

Step 2. Convert the annual shortfall into a present value using duration.
100 bps × 8 = 800 bps = 8% of the notional, paid by the protection buyer to the protection seller.

The sign is intuitive. The credit spread exceeds the fixed coupon, so the seller is being underpaid over the life of the deal and is compensated at inception.

2. Protection was sold for five years on an investment-grade name, and the seller had to hand over an upfront premium of 2% to the party buying protection. Take the duration of the contract to be four years. Find the credit spread of the company and the price of the CDS per 100 par.

Solution. Credit spread 50 bps; price 102.

Step 1. Fix the sign of the upfront premium. The seller is paying rather than receiving, so the premium enters as −2%.

Step 2. Amortise it over the duration to get an annual rate.
−2% ÷ 4 = −50 bps.

Step 3. Add it to the fixed coupon. The investment-grade coupon is 100 bps:
100 bps + (−50 bps) = 50 bps.

This is the reverse of question 1, and the check is that the credit spread of 50 bps is below the fixed coupon of 100 bps. That is exactly the case in which the protection seller pays the protection buyer, which is what happened.

Step 4. Convert to a price. Price is 100 minus the upfront premium percentage, and the premium here is negative:
100 − (−2) = 102.

A CDS has a value that moves throughout its life, set by the market. Participants continuously reassess the current credit quality of the reference entity, and from that reassessment come a current value and an implied credit spread. Several inputs move at once. Duration shortens simply by the passage of time. New information moves the default probability, the expected severity of loss in default, and the slope of the credit curve, all at once. Nothing about the valuation procedure changes, though: it is identical to the procedure used at inception, run with updated inputs. The resulting market value records the gains and losses of the two parties.

A worked narrative

Consider a five-year CDS with a fixed 1% coupon written on a reference entity whose credit spread is 2.5%. The buyer is promising 1% a year for coverage on a credit that merits 2.5%, so the present value of the protection leg exceeds that of the premium leg, and the difference is paid upfront by the buyer to the seller.

Now suppose credit quality improves during the life of the contract, so that the spread narrows to 2.1%. Price a freshly created CDS with the same remaining maturity and the same 1% coupon. Its premium leg is still worth less than its protection leg, because 1% is still below 2.1%, but the gap is smaller than it was, because the risk is smaller. The original contract is therefore worth less than what was paid for it. The seller has gained and the buyer has lost, and the size of that transfer is the difference between the original upfront premium and the new one.

Two approximations turn this into numbers quickly.

The parallel with bonds is exact and worth holding on to. A bond moves in percentage price terms by roughly its modified duration times the shift in its yield. Substitute the spread shift for the yield shift, and the duration of the swap for the duration of the bond it references, and the CDS relationship falls out unchanged.

Example 7 · Worked

USD 10 million of five-year protection is bought, on a contract whose duration is four years. The reference company started out on a credit spread of 500 bps, which then widens to 800 bps.

1. Does the protection buyer gain or lose from this change in the credit spread?

Solution. The buyer gains. Owning protection is being short the credit exposure. A widening spread means credit quality has deteriorated, which is the outcome a short position is designed to profit from, so the protection owned has become more valuable.

2. Estimate the percentage price change on the CDS and the profit to the investor.

Solution. Price change 12%; profit USD 1.2 million.

Step 1. Measure the spread change.
800 bps − 500 bps = 300 bps.

Step 2. Multiply by duration to get the percentage price change.
300 bps × 4 = 1,200 bps = 12%.

Step 3. Apply that to the notional.
12% × USD 10,000,000 = USD 1,200,000.

The gain is unrealised until the investor does something about it, which brings us to monetisation.

Three ways to realise a gain or a loss

Turning a change in market value into cash is called monetising the gain or loss. Start from the economics. The protection seller has effectively insured the debt of the reference entity in exchange for a stream of promised payments and possibly an upfront premium, so the seller is more or less long the company’s bonds. The protection buyer is more or less short them. As credit quality moves, so does the market value of the contract, and the counterparties can crystallise the result.

Routes to a realised profit or loss on a CDS

Route	Mechanism	Frequency
Credit event	The contract effectively pays off in response to a default	Rare in any single contract
Unwind	Enter an offsetting CDS in the market on matching terms	The usual route
Hold to expiry	No default occurs; the seller keeps every premium and pays nothing	Less common as a deliberate choice

Return to the contract whose spread narrowed from 2.5% to 2.1%. The implied upfront premium on a new CDS matching the original terms, with maturity adjusted for time elapsed, is the market value of the original CDS, and it is smaller than the original premium. The original protection buyer who wishes to exit enters a new CDS as a protection seller and receives that newly calculated premium, which is less than what was paid at the start. The original protection seller who wishes to exit enters a new CDS as a protection buyer and pays a premium smaller than the one received at the start. The buyer monetises a loss; the seller monetises a gain. The unwinding trade does not have to be done with the original counterparty, though there are advantages to doing so, and central clearing has made the whole process easier.

The third route needs a word of explanation. If no default occurs and the contract simply runs to expiry, the seller has collected every premium and made no payment, and the obligation ends. The spread of the CDS converges to zero as maturity approaches, in the same way that a bond price converges to par. The seller has clearly won: payment was received for bearing a risk that grew steadily less likely to materialise. The buyer has clearly lost on the contract itself.

Why the protection buyer’s loss at expiry may not be a loss at all

The CDS position, taken alone, is a loss: premiums were paid and nothing came back. But if the buyer is a creditor of the reference entity, the position was never meant to stand alone. The premiums are the price of removing an exposure the creditor did not want, and a homeowner does not treat an insurance premium as a loss merely because the house did not burn down. The distinction matters when evaluating a hedging programme: judging it on the profit and loss of the hedge alone, rather than on the combined position, will make every successful hedge look like a mistake.

Derivatives generally serve two purposes. The first is to act on an expected movement in the underlying. A derivative usually needs less capital, is usually an easier way to create a short economic exposure, and sits in a market that can react to information faster and with more liquidity than the market for the underlying itself. The second is to act on a valuation difference between the derivative and the underlying: take the appropriate position in one and the offsetting position in the other, and if the assessment is right and other investors reach the same view, the two converge and the return is essentially free of risk because the underlying exposure has been hedged. Whether that works depends on how efficient the market is and how good the valuation model is. Differences can also arise between two derivatives on the same underlying.

Applied to CDS, the first purpose is managing credit exposures, taking on or shedding credit risk as expectations change. The second concerns valuation disparities and is taken up in the final section.

Buying and selling protection

The simplest application is a lender buying protection to cut its exposure to a borrower. The lender may hold more credit risk than it wants without wishing to sell the bond or loan, because transaction costs are significant, because it may want the asset back later, or because the market for that asset is illiquid. Where the concern is temporary, reducing risk through a CDS is almost always easier than selling. Nor is this confined to financial institutions: any organisation carrying credit exposure is a candidate.

Selling protection needs more explanation. Some sellers are CDS dealers whose business is to make markets and profit from doing so. A dealer manages its book either by diversifying credit risks or by laying the risk off with another party, for instance by shorting the debt or equity of the reference entity, often placing the resulting funds in a repurchase agreement, or repo. Done well, the payment received for assuming the risk exceeds the cost of removing it, which requires sophisticated credit modelling.

Dealers are not the only sellers. Any bondholder has bought both credit risk and interest rate risk. An investor who wants the credit component alone can obtain it by selling protection, which requires far less capital, may involve lower total transaction costs than buying the bond, and gives a position that is often more liquid and therefore easier to unwind.

Naked credit default swaps

A party with no exposure at all to the reference entity may also buy protection. That position is a naked credit default swap, and it has attracted political and regulatory criticism. The objection is that a party with nothing at stake should not be permitted to speculate that a borrower’s condition will worsen, an argument that gained force during the financial crisis of 2008 to 2009 when many investors who owned no underlying debt profited from the collapse.

The counterargument is that equivalent bets are made routinely elsewhere through long puts, short futures and short sales of shares and bonds, all of which are accepted as ways of protecting oneself against poor market performance. Credit protection does the same job. Supporters add that naked positions bring liquidity to the credit market, which may make it more stable rather than less. The compromise reached in practice is narrow: naked CDS on sovereign debt are banned in Europe, while naked positions are generally permitted otherwise.

Long/short credit trades

Instead of taking a directional view on one credit, a participant can sell protection on one reference entity and buy protection on another. This is a long/short credit trade, and it is a bet on relative rather than absolute credit quality: that one entity will improve relative to the other. The two entities are usually connected in some way, perhaps competitors or producers of substitute goods. A view that competitive shifts in the luxury car industry will favour one manufacturer over another would be expressed by selling protection on the favoured name and buying protection on the other.

Environmental, social and governance factors provide another source of such views, since weak practices at one company relative to a peer can be expected to show up in credit spreads. The trade is then to buy protection on the company with weak ESG practices and sell protection on the company with strong ones.

Example 8 · Worked

An analyst covers two United States apparel companies. Atelier is large, focused on high-end brands, and profitable despite a high cost structure. Trapp is smaller and less profitable, focused on less expensive brands, and determined to keep costs low. Both buy merchandise from suppliers worldwide, and both are exposed to a recent fire at the factory of Global Textiles, a major supplier to each, which caused multiple casualties and unfavourable headlines.

The two responded very differently. Atelier signed an Accord on Fire and Building Safety, a legally binding agreement among global apparel manufacturers, retailers and trade unions in the country where the fire occurred, and then invested in fixing and upgrading machinery in its suppliers’ factories, with the aim of reducing lost employee time and the rate of accidents and fatalities. Investors regard Atelier’s governance favourably: management and stakeholder interests are strongly aligned, and the board has a high proportion of independent directors and is notably diverse. Trapp’s founder is majority owner, chief executive and chairman, and the board consists largely of people with minimal industry expertise, leaving it unprepared to respond to the fire. Investors regard Trapp’s governance as poor. Consistent with its low-cost emphasis and its inexperienced board, Trapp declined to sign the accord.

Single-name CDS trade on both, though Trapp’s is less liquid.

Five-year CDS spreads, before and after the fire

Company	Spread before the fire	Widening	Spread after the fire
Atelier	150 bps	60 bps	210 bps
Trapp	250 bps	75 bps	325 bps

The initial 100 bp gap reflects Trapp’s thinner trading liquidity and its weaker perceived creditworthiness, itself a function of smaller size and lower profitability.

The analyst expects the consequences of the fire to be more damaging for Trapp than for Atelier over the longer term, because of Trapp’s greater ESG-related risks, notably weaker factory safety and weaker governance. Specifically, the analyst expects Trapp’s spread to stay wider than its pre-fire 250 bps while Atelier’s returns to its pre-fire 150 bps.

Describe how the analyst can use CDS to exploit this view, and quantify the outcome on the analyst’s stated assumptions.

Solution. Buy five-year protection on Trapp and sell five-year protection on Atelier, a gain of 35 bps on the analyst’s assumptions.

Step 1. Set the legs from the view. Buying protection on Trapp is shorting Trapp’s credit, which profits if Trapp’s spread stays elevated. Selling protection on Atelier is going long Atelier’s credit, which profits as Atelier’s spread returns to its pre-fire level. The trade expresses relative credit quality, not the direction of the sector.

Step 2. Measure the differential today. Right after the fire:
325 bps − 210 bps = 115 bps.

Step 3. Measure the differential at the analyst’s target. Assume Atelier returns fully to 150 bps but Trapp narrows only to 300 bps from 325 bps:
300 bps − 150 bps = 150 bps.

Step 4. Take the difference.
150 bps − 115 bps = 35 bps, the profit on the long/short trade, excluding trading costs.

Note that the trade makes money even though Trapp’s own spread narrows by 25 bps. What matters is that Atelier’s narrows by more.

Long/short trades using indexes

The same structure works with index CDS. An investor expecting the economy to weaken can buy protection using a high-yield index and sell protection using an investment-grade index, profiting as high-yield spreads widen relative to investment-grade spreads. A trader expecting Asia to strengthen relative to Europe can buy protection using a European index and sell protection using an Asian index, profiting as Asian spreads narrow relative to European ones.

Curve trades

A curve trade is a long/short trade along a single credit rather than across two. Protection is bought at one maturity and sold on the same reference entity or index at another. Take the common case of an upward-sloping credit curve, where long-term CDS rates and credit spreads exceed short-term ones. Any change in shape makes the curve either steeper or flatter. Steeper means long-term credit risk has risen relative to short-term credit risk; flatter means it has fallen.

Figure 5: A steepening credit curve and the trade that expresses it

Both curves start from almost the same short-maturity spread and separate as maturity lengthens, which is what steepening means. The trade that profits from this move buys long-maturity protection and sells short-maturity protection.

An investor who expects long-term credit risk to rise relative to short-term credit risk, that is, who expects the curve to steepen, buys protection at the long end and sells it at the short end. In single-name terms that means buying a long-term CDS and selling a short-term CDS. In index terms the wording flips, as always: the same economic position is achieved by selling a long-term CDS index and buying a short-term CDS index.

The near-term reading of these two trades is worth memorising, because the labels are counterintuitive. A curve-steepening trade is bullish in the short run: it says the near-term outlook for the reference entity is better than the long-term outlook. A curve-flattening trade is bearish in the short run: it says the short-run outlook looks worse than the long-run outlook and anticipates trouble soon.

Example 9 · Worked

An investor owns intermediate-term bonds issued by a company and has become worried about a default in the near term, while remaining relaxed about the long term. The company’s two-year CDS trades at 350 bps and its four-year CDS at 600 bps.

1. Describe a curve trade that hedges the default risk the investor is worried about.

Solution. Buy two-year single-name protection and sell four-year single-name protection.

The investor’s view is that near-term spreads will rise while long-term spreads will not, so the curve flattens from its current upward slope of 600 − 350 = 250 bps. Protection is therefore bought where the risk is thought to be rising, at the two-year point, and sold further out on the curve at the four-year point, where the investor is comfortable. The short leg is not a hedge; it is a funding decision.

2. Why might the investor prefer this to simply buying protection on the reference entity?

Solution. Cost. The premium received on the four-year protection sold offsets part of the premium paid on the two-year protection bought, so near-term cover is obtained more cheaply than by buying it outright. The offset is not free. It works only while the investor’s view of near-term risk relative to long-term risk turns out to be right; if long-term risk rises instead, the sold leg produces losses that the bought leg was never intended to cover.

Parallel shifts

Not every move in a credit curve changes its shape. Sometimes the whole curve moves up or down by roughly the same amount. Exactly as long-duration bonds move more than short-duration bonds, longer-term CDS move more than shorter-term CDS for a given spread change. A trader who expects all spreads to rise therefore wants to be a buyer of protection, but recognises that the long end will respond more. One way to express this is to buy protection at the long end of the curve and hedge by selling protection at the short end, sizing the two legs so that the volatility of the leg expected to gain exceeds that of the other. If more risk is wanted, the trader can simply trade the more volatile leg on its own.

Investors do not agree about the price of credit risk, and disagreement produces valuation disparities. In principle only one price eliminates credit risk correctly, but nobody knows what it is. Whoever estimates it best can profit at the expense of whoever estimates it worst, and that advantage is captured by trading the CDS against the reference entity’s debt, its equity, or derivatives on either. Such trading depends heavily on models that isolate the credit component of a return. The models belong to specialists; the ideas do not.

Where the basis comes from

The yield on a bond issued by a reference entity contains a component compensating for credit risk. In principle that component should equal the credit spread on a CDS referencing the same entity, since both are payment for bearing the same risk, whether the risk is borne by a bondholder or by a protection seller. In practice the two can differ, for several reasons: honest differences of opinion, differences in the models used in the two markets, differences in liquidity, and supply and demand in the repo market, which is a primary source of financing for bond purchases. That gap is the foundation of the basis trade.

To measure it, decompose the bond yield into three parts.

Taken together, the first two terms amount to the market reference rate.

Whatever the bond yields above that reference rate is therefore its credit spread, and it is that figure which is set against the spread quoted in the CDS market.

Naming the basis

Condition	Name
Spread higher in the bond market than in the CDS market	Negative basis
Spread higher in the CDS market than in the bond market	Positive basis

The decomposition is not always this clean. Embedded options complicate it, as with callable and convertible bonds, and so does a bond trading well away from par. Those factors have to be handled in the calculation.

How the trade works

Most basis trades rest on the belief that any such mispricing is temporary and that the two spreads will converge once the market notices. Suppose the bond market implies a 5% credit risk premium while the CDS market implies 4%. The trader has no way of knowing which figure is right, and does not need to. Viewed from the CDS, its premium is too low relative to the bond. Viewed from the bond, its premium is too high, which is to say its price is too low. Either the CDS market is pricing too little credit risk, or the bond market too much, or both. The trade is the same either way: buy the bond at a price that appears to overstate its credit risk, and simultaneously buy protection at a premium that appears unjustifiably low, hedging the interest rate exposure with a duration strategy or with interest rate derivatives. Default risk on the bond is covered by the CDS, so the position is balanced. If convergence occurs, the 1% differential is captured.

Example 10 · Worked

An investor wants to be long the credit risk of a company. The company’s bond yields 6% and matures in five years. A comparable five-year CDS has a credit spread of 3.25%. The investor can borrow at the market reference rate, currently 2.5%.

1. Calculate the bond’s credit spread.

Solution. 3.5%. Strip the market reference rate out of the bond yield:
6.00% − 2.50% = 3.50%.

2. Identify a basis trade that exploits the situation.

Solution. Buy the bond and buy protection in the CDS market, netting 25 bps.

Step 1. Compare the two measures of the same risk. The bond market pays 3.50% for this credit risk; the CDS market charges 3.25% to remove it.

Step 2. Identify which market is cheap. Credit risk is cheaper in the CDS market at 3.25% than in the bond market at 3.50%, so protection is the thing to buy.

Step 3. Compute the net. Go long the bond and earn its 3.50% credit spread, pay 3.25% for protection:
3.50% − 3.25% = 0.25% = 25 bps retained, with the credit risk hedged.

Trading across the capital structure

A second family of trades stays within one issuer. Credit risk is embedded in virtually every unsecured debt instrument a company issues, and in its capital leases, and each is priced to reflect that risk. An investor can use the CDS market as a benchmark to identify which of these instruments is mispriced relative to the swap, then buy the cheap one and sell the expensive one, again assuming the market will adjust. This is considerably more difficult than a bond-versus-CDS basis trade, because priority of claims means the instruments do not pay out equally in default.

The same logic extends to equity. Because a CDS spread responds to changes in leverage, an anticipated corporate action that changes the capital structure can be traded through the credit and the equity at the same time.

Example 11 · Worked

An investor believes a company will be taken private in a leveraged buyout: it will issue a large amount of debt and use the proceeds to repurchase all of its publicly traded equity, leaving it owned by management and a small group of insiders.

1. Why might the CDS spread change?

Solution. The transaction loads a great deal of new debt onto the same asset base, which will almost certainly raise the probability of default. A higher probability of default means a wider CDS spread, and therefore a higher price for protection.

2. What equity-versus-credit trade would anticipate this corporate action?

Solution. Buy the stock and buy credit protection. Both legs profit if the buyout happens. The share price rises because the company is repurchasing all of its outstanding equity, typically at a premium. The CDS price rises because the spread widens to reflect the increased probability of default. This is one of the few trades in which a long equity position and a bearish credit position are complementary rather than contradictory, and the reason is that a leveraged buyout transfers value from creditors to shareholders.

Index against components

CDS indexes support one further arbitrage. If the cost of the index differs from the aggregate cost of its components, an investor can go long the cheaper of the two and short the more expensive, on the implicit assumption that convergence will occur. If it does, the gain is captured with the risk essentially neutralised. The practical obstacle is cost: transaction costs on this kind of trade can be large enough to eliminate the profit for everyone except the very largest investors.

Pulling the reading together

A CDS transfers the credit risk of a third party from a protection buyer, who is short that credit, to a protection seller, who is long it. Coverage attaches to the reference obligation and to everything ranking equal or above it, and the payoff is set by the cheapest of those instruments. A credit event, declared by a Determinations Committee, triggers settlement, normally in cash, at a recovery rate discovered by auction. Pricing rests on hazard rates and loss given default: the protection leg and the premium leg are each valued as probability-weighted, discounted cash flows, and the difference between them is the upfront payment attached to a standardised 1% or 5% coupon. Once the contract is live, its value tracks the credit spread, and the quick approximation, spread change in basis points multiplied by duration, converts a credit view into a profit or loss. The applications follow directly: shed or acquire credit exposure, express a relative view between two credits, express a view on the shape of a single credit curve, or arbitrage the price of the same credit risk between the CDS market, the bond market and the equity market.

Check yourself

1. A CDS names a five-year senior unsecured bond as its reference obligation. After a bankruptcy filing, three instruments trade: a senior unsecured bond at 55 of par, a senior secured bond at 70 of par, and a subordinated bond at 15 of par. Which sets the payout, and what is the recovery rate?

The senior unsecured bond at 55, giving a recovery rate of 55% and a payout of 45% of notional. Coverage extends to obligations ranking equal to or above the reference obligation, so the senior secured bond qualifies but is more expensive at 70. The subordinated bond is cheapest at 15 but ranks below the reference obligation, so it does not qualify at all. Cheapest-to-deliver means cheapest among the qualifying instruments, not cheapest overall.

2. An investment-grade reference entity has a credit spread of 40 bps. What upfront payment convention applies, and who pays whom?

Investment-grade contracts carry a standardised coupon of 1%, or 100 bps. The credit spread of 40 bps is below that, so the seller is receiving more than the risk warrants and must compensate the buyer at inception. The protection seller pays the upfront premium to the protection buyer. Approximating with a duration of 4 years, the premium is (40 − 100) bps × 4 = −240 bps, or 2.4% of notional paid by the seller, and the price per 100 par is 100 − (−2.4) = 102.4.

3. A borrower has a constant hazard rate of 3% a year. What is the probability of default at some point over four years, and why is it not 12%?

Survival over four years is 0.97 raised to the fourth power, which is 0.8853, so the probability of default is 1 − 0.8853 = 0.1147, or about 11.5%. It is not 12% because the hazard rate is conditional: the 3% in year 2 applies only to the 97% of outcomes that survived year 1, the 3% in year 3 only to those that survived years 1 and 2, and so on. Adding the annual rates double counts the paths that have already defaulted.

4. An investor sells USD 20 million of five-year protection on a company whose spread then narrows from 400 bps to 250 bps. The CDS duration is 4.5 years. Estimate the investor’s profit or loss.

A gain of approximately USD 1.35 million. The spread change is 400 − 250 = 150 bps of narrowing. The percentage price change is 150 bps × 4.5 = 675 bps, or 6.75%, and 6.75% × USD 20,000,000 = USD 1,350,000. Because narrowing spreads benefit the party who is long the credit, and the protection seller is long the credit, the move is a gain for this investor and an equal loss for the protection buyer.

5. A company’s two-year CDS trades at 700 bps and its ten-year CDS at 400 bps. What does this shape say, and is a curve-flattening trade here bullish or bearish in the short run?

The curve is downward-sloping, which implies a greater probability of default in the earlier years than the later ones and usually reflects severe near-term stress. A flattening trade, which buys near-dated protection and sells longer-dated protection, is bearish in the short run: it says the short-run outlook is worse than the long-run outlook. A steepening trade would be the bullish one, since it says the near term is the safer period.

6. A five-year bond yields 8.25%, the market reference rate is 3.00%, and the five-year CDS spread is 5.75%. Is the basis positive or negative, and what trade follows?

The bond credit spread is 8.25% − 3.00% = 5.25%, which is below the CDS spread of 5.75%, so the spread is higher in the CDS market and the basis is positive. Credit risk is expensive in the CDS market and cheap in the bond market, so the trade is the reverse of the standard negative-basis trade: sell protection at 5.75% and short the bond, giving up its 5.25% credit spread, for a net 50 bps if the two converge.

7. An investor sells USD 250 million of protection on an equally weighted 125-name investment-grade index. One constituent defaults with a recovery rate of 35%. What is paid out, and what notional remains?

Each name accounts for USD 250,000,000 ÷ 125 = USD 2 million of notional. Loss given default is 1 − 35% = 65%, so the payout is 65% × USD 2,000,000 = USD 1,300,000, paid by this investor as the protection seller. The defaulted name is removed from the index and the position continues on a notional of USD 250 million − USD 2 million = USD 248 million.

8. Why does the industry settle CDS on an auction-determined recovery rate rather than waiting for the actual recovery, and who bears the difference?

Actual recovery on defaulted debt can take years and would arrive long after the CDS was due to settle, so the contract would be unusable as a hedge. The auction, in which major banks and dealers bid for the cheapest-to-deliver defaulted debt, produces the market’s expectation of recovery immediately, and both parties agree in advance to accept it. The difference between the auction level and the eventual recovery is borne by whoever ends up holding the defaulted debt. That is a real exposure for a protection buyer who also owns the underlying bonds, because the CDS has already been settled at the auction level.

End of lesson.

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