CDS Spread and Bond Yield Spread: Why They Disagree
The same issuer defaulting is priced twice. Once in the bond market, as a yield spread over a benchmark curve, and once in the credit default swap market, as a premium in basis points of notional. A replication argument says the two numbers should be the same, and they routinely are not.
The gap is the CDS-bond basis, and it is one of the more useful numbers in credit because of what it is made of. Almost none of it is disagreement about the probability of default. It is the price of funding a bond, the value of a delivery option, the cost of a protection seller who might not pay, and the balance sheet of whoever is holding the paper.
Key Takeaways
- Basis = CDS spread minus bond spread, so a negative basis means the cash bond is cheap relative to the derivative.
- The replication argument holds that a risky bond plus purchased protection is a risk-free position, which is why the two spreads should agree.
- A bond at a Z-spread of 280 basis points against protection at 195 gives a basis of minus 85, with the bond the cheap side.
- Factors that make the CDS contract worth more than a pure default hedge, such as a cheapest to deliver option, push the basis positive.
- Factors that make holding the physical bond expensive, principally funding and balance sheet cost, push the basis negative.
- A negative basis trade earning 55 basis points of net carry returns 11.0% on capital only because a 5% haircut supplies twenty times leverage.
- What closes the trade out is funding, mark to market on the CDS leg, and counterparty risk, not a default by the issuer.
- A large negative basis across many issuers at once is a funding signal rather than a credit view.
Two prices for the same credit risk
An issuer’s credit risk is priced in two separate markets. In the cash bond market it appears as a yield spread over a benchmark curve: the extra yield an investor demands for holding the issuer rather than a government or a swap. In the credit default swap market it appears as a premium, quoted in basis points of notional per year, paid by the buyer of protection to the seller.
Both numbers are compensation for the same event, a default by the same issuer. There is no obvious reason for them to differ, and in practice they usually do.
| Bond yield spread | CDS spread | |
|---|---|---|
| What it is | Yield on the bond less the benchmark curve, usually measured as a Z-spread or an asset swap spread | Annual premium for protection against default, in basis points of notional |
| Paid by | Nobody; it is embedded in the price the investor pays | The protection buyer, quarterly, to the protection seller |
| Requires funding | Yes, the bond must be bought and financed | No, the position is unfunded at inception |
| Exposure to the issuer | Long credit | Short credit if buying protection, long credit if selling it |
The third row is the one that ends up explaining most of the disagreement, and it is worth carrying forward. A bond has to be paid for. A credit default swap does not.
The replication argument
The reason the two should agree is a construction rather than an assertion.
Take a floating rate bond from the issuer, trading at par, paying the reference rate plus a spread. Buy it, and buy default protection on the same issuer for the same maturity and the same notional. If the issuer defaults, the protection pays the loss on the bond. If it does not, the bond redeems at par. Either way the holder receives the reference rate, and holds a position with no credit exposure left in it.
risky bond + protection bought ≈ risk-free asset
so the spread earned on the bond should equal the premium paid for the protection, otherwise a risk-free position pays more or less than the risk-free rate
If the bond spread exceeded the CDS premium, that combination would earn more than the risk-free rate with no credit risk, and capital would flow into it until the gap closed. If the CDS premium exceeded the bond spread, the reverse trade would do the same. The argument is clean, and the assumptions it quietly makes are exactly where the residual gap comes from.
The basis, and what its sign means
The difference is called the CDS-bond basis, and it is defined in one direction.
basis = CDS spread − bond spread
a negative basis means the bond spread is the wider of the two, so the bond is cheap relative to the derivative
An issuer’s five-year bond trades at a Z-spread of 280 basis points. Five-year protection on the same issuer trades at 195 basis points. What is the basis, and which instrument is cheap?
- Basis = 195 − 280 = −85 basis points.
- The basis is negative, so the cash bond is paying 85 basis points a year more than the cost of insuring it.
- Buying the bond and buying protection therefore leaves 85 basis points a year of spread, before any financing cost, on a position with the issuer default risk hedged.
Answer: a basis of −85 basis points, with the bond cheap relative to the CDS. Note what has and has not been hedged. Default risk has been transferred to the protection seller. The financing of the bond, the risk that the protection seller fails, and the risk that the basis widens further before the position is unwound are all still held.
The sign convention is worth committing to memory in the form of its consequence rather than its formula. Negative basis means the bond is cheap, and the trade that harvests it is long the bond and long protection. Positive basis means protection is expensive relative to the bond, and the trade is the mirror image, which is harder to put on because it requires shorting a cash bond.
Why the basis is not zero
The replication argument assumes a par floating rate bond, costless funding at the reference rate, a protection seller who always pays, and a credit event definition that matches the bond exactly. Each assumption that fails moves the basis, and the direction is predictable.
| Driver | Effect on the basis | Why |
|---|---|---|
| Cheapest to deliver option | More positive | Where settlement allows a choice of deliverable obligation, the protection buyer holds an option, and pays for it in the premium |
| Difficulty of shorting bonds | More positive | Buying protection is often the only practical way to be short a credit, so that demand lands entirely on the CDS |
| Restructuring as a credit event | More positive | The contract can be triggered by events that do not impair the bond holder, which is extra protection and carries a price |
| Funding above the reference rate | More negative | A leveraged holder finances the bond at a spread, so the bond must yield more to be worth holding |
| Counterparty risk on the seller | More negative | Protection from a seller who might not pay is worth less, so buyers pay less for it |
| New issue supply | More negative | Concessions on new bonds widen cash spreads without touching the derivative |
| Balance sheet and capital cost | More negative | Holding the bond consumes capacity that the unfunded position does not |
Read the table as two groups rather than seven items. Everything that makes the CDS contract more valuable than a pure default hedge pushes the basis positive. Everything that makes holding the physical bond more expensive than the replication assumes pushes it negative. In calm markets the two groups roughly offset and the basis sits in a modest range. In stressed markets the funding and balance sheet items dominate, because that is precisely when financing is scarce, and the basis goes sharply negative across whole markets at once.
That is the pattern observed in late 2008, when basis levels that had been tens of basis points moved to hundreds for many issuers. The trade that looked risk-free was not: it was short funding liquidity, and it was carrying that exposure in a form the label did not disclose.
The negative basis trade, and what breaks it
The trade itself is simple to state. Buy the bond, buy protection on the same issuer for the same maturity, finance the bond in the repo market, and collect what remains.
An investor puts 10 million of notional into that trade. The repo lender applies a 5% haircut, so 500,000 of the investor’s own capital is committed. What does the position earn, and what is the return on the capital tied up?
- Net carry = 280 − 195 − 30 = 55 basis points a year.
- On 10 million of notional, 0.0055 × 10,000,000 = 55,000 a year.
- Capital committed = 5% × 10,000,000 = 500,000.
- Return on capital = 55,000 / 500,000 = 11.0% a year.
Answer: 55,000 a year, or 11.0% on the capital committed. That headline return is entirely a product of the leverage. The underlying position earns 55 basis points, and the twenty times leverage implied by a 5% haircut turns it into 11%. Any account of this trade that reports the 11% without the haircut has described the return and omitted the risk.
Three things break it, and none of them is a default by the issuer.
The first is funding. The repo haircut can be raised and the repo spread can widen, and both happen when markets are stressed. A trade whose net carry is 55 basis points is wiped out by a 55 basis point increase in the financing spread, and the position was sized on the assumption that the earlier number would hold.
The second is the mark to market on the CDS leg. The two legs are hedged for default but not for daily valuation, and margin is called on the derivative in cash while the bond leg cannot be monetised at the same speed. A position that is correct at maturity can still require more cash today than the holder has.
The third is the protection seller. If the seller fails at the same time the issuer does, the hedge that justified the position is not there. Correlation between the reference entity and the protection seller is the thing that turns a hedged position into an unhedged one at the worst possible moment, and it is not visible anywhere in the basis figure.
Describing a negative basis trade as arbitrage. It is a relative value position financed with borrowed money, and it carries funding risk, liquidity risk, counterparty risk and mark to market risk. The default risk has been hedged, which is the one risk everybody names, and it is not the one that closes the position out.
Reading the basis
For a risk manager rather than a trader, the basis is most useful as an indicator, and it carries different information at different levels.
A basis of a few tens of basis points, in either direction, is ordinary. It reflects the contractual and funding differences described above and does not say anything about the issuer.
A large negative basis on one issuer, when its peers are unaffected, usually points to something specific in the cash market for that name: a forced seller, a new issue, or a bond that has become difficult to finance. It is a statement about the bond rather than about the credit.
A large negative basis across many issuers at once is a funding signal. It says that capital is unwilling or unable to hold cash bonds, and that is a market-wide liquidity condition rather than a credit view. The historical usefulness of the measure is precisely this: the basis moved before many of the credit indicators that were being watched more closely, because it prices the cost of holding an asset rather than the probability of the issuer failing.
Questions on this material usually take one of three forms. Compute the basis and identify which instrument is cheap, where the trap is the direction of the subtraction. Identify which listed factor would widen or narrow the basis, which is answered from the two groups in the table rather than by memorising seven items. Or explain why a negative basis trade is not risk-free, where the expected answer names funding, counterparty risk and mark to market rather than default risk.
The short version
- Two markets price the same default event, and the difference between them is the CDS-bond basis.
- Negative basis means the bond is cheap, and the harvesting trade is long the bond and long protection.
- The drivers fall into two groups: contract features that make protection more valuable push the basis positive, and the cost of holding a physical bond pushes it negative.
- In stressed markets the funding group dominates and the basis goes sharply negative across whole markets, as it did in late 2008.
- The negative basis trade is not arbitrage. It hedges the one risk everybody names and retains funding, liquidity, counterparty and mark to market risk.
- As an indicator, a wide basis on a single name says something about that bond, while a wide basis across many names says something about the availability of funding.
Frequently Asked Questions
What is the CDS-bond basis?
The basis is the CDS spread minus the bond yield spread for the same issuer and maturity, with the bond spread usually measured as a Z-spread or an asset swap spread. A negative basis means the bond spread is the wider of the two, so the cash bond is cheap relative to the derivative. A positive basis means protection is expensive relative to the bond.
Why should a CDS spread and a bond yield spread be equal?
Because buying a par floating rate bond from an issuer and buying default protection on the same issuer for the same maturity leaves a position with no credit exposure. If the issuer defaults the protection covers the loss, and if it does not the bond redeems at par. That combination should therefore earn the risk-free rate, which requires the spread earned on the bond to equal the premium paid for the protection.
What makes the basis positive or negative?
Anything that makes the CDS contract more valuable than a pure default hedge pushes the basis positive: a cheapest to deliver option, restructuring as a credit event, and the fact that buying protection is often the only practical way to be short a credit. Anything that makes holding the physical bond more expensive than the replication assumes pushes it negative: funding above the reference rate, counterparty risk on the protection seller, new issue supply, and the balance sheet cost of holding the asset.
What is a negative basis trade?
Buying the cash bond, buying protection on the same issuer and maturity, and financing the bond in the repo market, so the remaining spread is collected as carry. On a bond at 280 basis points, protection at 195 and a repo spread of 30, the net carry is 55 basis points a year, which is 55,000 on 10 million of notional.
Why is a negative basis trade not arbitrage?
Because only the default risk has been hedged. The position still carries funding risk, since the repo spread can widen and the haircut can be raised; mark to market risk, since margin is called in cash on the derivative leg while the bond cannot be monetised at the same speed; and counterparty risk, since a protection seller that fails at the same time as the reference entity leaves the position unhedged at the worst moment.
What does a large negative basis across many issuers indicate?
A funding condition rather than a credit view. It says that capital is unwilling or unable to hold cash bonds, which is why basis levels moved from tens of basis points to hundreds for many issuers in late 2008. A large negative basis on a single issuer while its peers are unaffected points instead to something specific in the cash market for that name, such as a forced seller or a new issue.
How does leverage affect the return on a basis trade?
Entirely. A trade earning 55 basis points of net carry on 10 million of notional produces 55,000 a year. If the repo haircut is 5%, the capital committed is 500,000, and the return on that capital is 11.0%. The underlying position still earns 55 basis points, and the headline figure is the product of roughly twenty times leverage, so a 55 basis point widening in the financing spread eliminates it.
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