The negative basis: buy the bond or sell credit default swap protection?

The difference between the credit spread associated with a bond and the par spread associated with selling credit default swap (CDS) protection on the bond issuer is known as the bond’s negative basis. It is an important quantity for credit investors in order to decide whether it is more lucrative to buy a bond or to sell CDS protection. This definition, however, constitutes an inaccurate measurement devoid of a rigorous backing by classical arbitrage pricing theory, since it implicitly ignores the possibility of a credit event and also does not accurately take into account potential differences regarding the cash requirements of bond and CDS. We provide an accurate definition for the negative basis, generalizing an idea originated in Mai (2019). While the latter reference still hinges on a no arbitrage assumption in an implicit market model that is not always satisfied, we adopt a logic that is valid without restrictive assumptions but universally valid in practice. Our definition is shown to be identical in the case when the implicit no arbitrage assumption in Mai (2019) happens to hold. We thereby complete a sound theoretical framework that clarifies and justifies how the negative basis must be defined. Furthermore, our framework is general enough to deal with discrete and floating rate bond coupons, and also adapts to the situation when bond and CDS have different currency denomination, so that all cases of practical relevance are included.