Define the CDS-bond basis and explain what it means.
The idea
The CDS-bond basis is the CDS spread minus the bond's yield spread over the risk-free benchmark, written: Basis = CDS spread − (bond yield − risk-free rate). If the two markets priced the same default risk, owning the bond and buying CDS protection would be a risk-free combination earning the risk-free rate, and the basis would be zero. A negative basis means protection is cheap relative to the bond. A negative basis trade buys the bond and buys CDS protection. Its net annual return, before other costs, is: Carry = bond yield − CDS spread − funding cost. Basis values drift away from zero for several reasons. Counterparty risk in the CDS pushes the CDS spread down. The cheapest-to-deliver option and broad credit event definitions push it up. Other drivers are bond illiquidity, funding costs and the choice of risk-free benchmark. The trade is not riskless when funding costs exceed the risk-free rate.
Formulas
CDS-bond basis
basis = CDS spread − (bond yield − risk-free rate)
- CDS spread
- the CDS spread on the issuer
- bond yield
- the bond's yield
- risk-free rate
- the matching risk-free benchmark rate
Negative means protection is cheap relative to the bond. Reversing the subtraction flips the sign.
Net carry of a negative basis trade
net return = bond yield − funding cost − CDS spread
- bond yield
- the bond's yield
- funding cost
- the rate paid to fund the bond
- CDS spread
- the premium paid for protection
Funded at the risk-free rate it equals minus the basis. Funding above the risk-free rate eats the profit.
A practice question
How is the CDS-bond basis defined?
- The CDS spread minus the bond's yield spread over the risk-free benchmark. - correct
- The bond's yield spread over the risk-free benchmark minus the CDS spread.Why not: Reverses the sign convention of the basis.
- The sum of the CDS spread and the bond's yield spread.Why not: Adds the two spreads rather than comparing them.
- The CDS spread minus the bond's absolute yield, with no risk-free adjustment.Why not: Compares a spread with a yield level; the bond yield must first be reduced by the risk-free rate.
Basis = CDS spread - (bond yield - risk-free rate). A negative basis means protection looks cheap relative to the bond.
A harder one
A 5-year bond yields 5.10% when the matching risk-free rate is 3.00%. The 5-year CDS spread on the issuer is 95 basis points. What is the CDS-bond basis?
- +115 basis pointsWhy not: Reverses the sign by taking bond spread minus CDS spread.
- +305 basis pointsWhy not: Adds the CDS spread to the bond spread.
- -115 basis points - correct
- -210 basis pointsWhy not: Subtracts only the bond spread and leaves the CDS leg out of the comparison.
Bond spread = 5.10% - 3.00% = 210 bp; basis = 95 - 210 = -115 bp.
The hardest tier
Which of the following would tend to make the CDS-bond basis more negative?
- Counterparty risk in the protection seller, which lowers the spread that protection buyers are willing to pay. - correct
- The cheapest-to-deliver option held by protection buyers, which raises the CDS spread.Why not: This raises the CDS spread and so pushes the basis up, not down.
- A credit event definition that includes restructuring, which gives buyers wider protection.Why not: Broader protection raises the CDS spread, making the basis less negative.
- A strong investor bid for the bond that compresses its yield spread.Why not: A lower bond spread raises the basis, since the bond spread is subtracted.
Basis = CDS spread - bond spread. Counterparty risk lowers what buyers pay for protection and so lowers the CDS spread; the other three raise the CDS spread or lower the bond spread.
In the app: 6 practice questions on this outcome, spaced review that brings it back before you forget it.
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