A five year corporate bond trades at 250 basis points over the government curve with an assumed 40% recovery. What annual default probability does that imply, what does it become at 20% recovery, and why does the figure overstate the real default rate?

A five year corporate bond trades at 250 basis points over the government curve with an assumed 40% recovery. What annual default probability does that imply, what does it become at 20% recovery, and why does the figure overstate the real default rate?

Approach: Use the credit triangle that sets the spread equal to the hazard rate times loss given default, then ask what else is priced into a traded spread beyond default itself.

4.17%. The credit triangle sets spread = hazard rate * (1 - recovery), so h is 0.025/0.60, which is 4.17%. At a 20% recovery rate the same spread implies h of 0.025/0.80, or 3.125%, which shows that a spread pins down the product of the hazard rate and loss given default rather than either one alone. The figure is a risk-neutral probability, so it carries a risk premium for default timing and correlation on top of a liquidity premium for holding a corporate bond against a government one. Realised default rates on investment grade credit have run at roughly a third to a half of the risk-neutral figure, so quoting 4.17% as the expected default frequency overstates it by a factor of two or three.

Follow-up: The five year spread is 250 basis points and the one year is 80. What forward hazard rate does the curve imply for years two to five?

Key concepts: credit triangle, hazard rate, recovery rate, risk-neutral probability.