• Credit Derivatives

    The negative basis conditioned on default

    The negative basis is an annualized earnings figure that measures the expected excess return of a bond investment over a reference discounting rate, after credit risk has been hedged away via credit default swap (CDS) protection. Unfortunately, the most appropriate measurement of the negative basis is in terms of a root of a non-trivial decreasing function. The goal of the present article is to derive closed proxy formulas for the negative basis, at least in special situations. Under the assumption that a credit event before maturity of bond (and CDS) is certain, i.e. conditioned on default before maturity, we are able to derive a very simple formula. Furthermore, a small enhancement of the formula provides a proxy formula for the (unconditional) negative basis. The availability of such closed formulas allows to study qualitative properties of the negative basis, such as dependence on the recovery rate assumption or leg prices