4: CDS Bond Basis

Mini Chapter Four

CDS Bond Basis

Credit default swap spread oftentimes is used interchangeably with the credit spread on a corporate bond. In theory bonds can be delivered on CDS contracts in case of a default which should imply that credit spreads and CDS spreads should not diverge as that could create arbitrage opportunities. For instance, if Credit spreads widen a lot but CDS doesn’t, arbitrageurs could buy the bond and buy CDS protection to earn the basis till maturity. In case of default, they can sell the bond at recovery value and get compensated for their loss by the CDS, earning the risk-free locked-in basis of the trade.

CDS vs Cash Bond basis can persist – Though simply described above, this arbitrage (CDS spreads tighter than bond credit spreads is called negative basis) is not easy to lock in for reasons like a) it’s expensive to source matching tenors on the bond and the CDS b) balance sheet constraints i.e. shortage of capital/higher funding costs eats into the arbitrage opportunity c) different investor playfields or mandates/market accessibility. Similarly, if CDS trades wider than bond credit spread (called positive basis), the inability to short the bond/borrow it on repo in a timely manner would make it challenging to lock in this basis and even if the repo is secured the risk of the bond going ‘special’ needs to be monitored.

Also, terms around reference obligations in a CDS contract are crucial in determining its level as a wider spectrum of cheapest to deliver instruments many of which could be illiquid would trade at a deeper concession to the liquid ones nudging the CDS spread higher.

Credit spread risk of a portfolio is typically denoted as CS01 i.e. the change in the present value of the portfolio due to a basis point change in the credit spread. One could think of this sensitivity as the change in the price of a floating rate bond due to a basis point change in credit spread. If you recall, we assumed above that the credit spread of a risky bond has a multiplicative effect over the risk-free discount rate for computing PV of its cash flows. For instance if R_f is the risk free interest rate and s is the credit spread for the corporate bond, the discount rate to arrive at the bond’s present value is

\[ ( 1 + R_f ) \times ( 1 + s) \]

In practice, since market professionals denote the difference between the fixed rate risky yield and fixed rate risk free yield as the credit spread, they effectively assume an additive impact of s on R_f i.e. the discount rate denoted as

\[ ( 1 + R_f + s ) \]

Mathematically then the dollar value of change in yield (DV01) would be less than the dollar value of change in credit spread when the assumption is for a multiplicative spread over risk free rate to discount cashflows, while it would be the same if the spread is additive.