Markets for credit default swaps (CDS) and bonds of the same reference entity and maturity are bound by no-arbitrage conditions. Indeed, using a large data set we show that CDS premia and par asset swap spreads are mostly cointegrated. Nonetheless, the average CDS-bond basis (i.e. the difference between both measures) is positive in the period 2004-2005. We detect fourteen different economic basis drivers, which make the basis firm-specific and time-dependent. Furthermore, we describe the basis smile, and illustrate that the average basis is the lowest for five year maturities of corporate credits denominated in euro.