Basis Risk When Hedging a Global Credit Portfolio

The calculation of the capital charge for CVA risk, as required by the Basel Committee on Banking Supervision, is usually rather unstable due to the volatility of CDS spreads. Since credit derivatives on single names are not very liquid, the implied adjustments in capital charges could be reduced by hedging a credit derivative portfolio with a contrary position in a credit index. We examine the efficiency of such hedge in the face of decreased correlations between single name CDSs and CDS indices, and we also evaluate the level of basis risk still remaining under the hedge. We address several questions: Is there enough diversification of risk in a global credit portfolio to allow for a good hedge? Is basis risk higher in North America than in Europe? Does the effectiveness of the hedge increase when we take credit quality into account? Do conditional second order moments provide a better hedge than least squares?