We explore the relationship between CDS premia and bond asset swap spreads on the same reference entity. As Duffie (1999) shows, there is a clear theoretical link between CDS premia and bond prices if the two quantities are viewed as a pure measure of credit risk. However, many studies provide evidence that factors other than credit risk seem to affect bond prices and CDS premia, and these factors may partially obscure the relationship. We focus on the difference between the yield spread and the CDS premium, the bond-CDS basis, and show that the basis is highly sensitive to firm-specific and market wide credit risk and liquidity. If CDS and bonds are used in a dynamic hedging strategy or in a basis trading strategy that depends on the convergence of CDS and bond markets, it is necessary to correctly quantify the associated risks of these strategies.