Irreducible Risks of Hedging a Bond with a Default Swap

This paper analyzes the effectiveness of hedging a defaultable bond, that may not be at par, with a credit default swap (CDS) by quantifying the variance of the hedging errors and determining the optimal hedge ratio. The static hedging framework uses bond recovery and time to default, which are correlated, to calculate the variance of the hedging errors and the optimal hedge ratio for the bond-CDS trade. The results show that there are irreducible risks when hedging a defaultable bond with a CDS; these irreducible risks increase with the magnitude of the premium/discount of the bond and decrease as the correlation between default time and recovery increase. The results also show that the optimal hedging ratio was closer to the bond price than the par value of the bond. This paper provides a framework distinct from the risk neutral framework by transparently showing the residual risks and their drivers.