Credit Spreads and Default Probability Extraction

A CDS spread and a recovery assumption together imply a hazard rate, and that hazard rate is the market's default probability.

A credit spread compensates a bond or credit default swap investor for the possibility that the borrower defaults before the instrument matures, and that spread can be inverted to extract the market's implied probability of default given an assumption about how much would be recovered if default occurred. The extraction is mechanical once the recovery assumption is fixed, but the recovery assumption itself is the part that requires judgment.

A credit spread is the extra yield an investor demands over a comparable risk-free rate for holding exposure to a borrower that might not repay in full. For a bond, that spread is embedded in the bond's yield relative to a government bond of similar maturity. For a credit default swap, the spread is quoted directly as an annual premium, paid periodically by the protection buyer to the protection seller in exchange for compensation if the reference entity defaults.

In either case, the spread reflects the market's combined view of two things: how likely default is over the relevant horizon, and how much would actually be recovered on the defaulted debt. A wider spread can mean the market sees a higher chance of default, a lower expected recovery, or some combination of both, which is exactly why extracting a clean default probability requires separating those two effects rather than reading the spread as a probability directly.

The standard method models default as arriving according to a constant hazard rate, meaning a constant instantaneous probability of default per unit of time, conditional on no default having happened yet. Under a simplified but commonly used approximation, the annual CDS spread is roughly equal to the hazard rate multiplied by the loss given default, where loss given default is one minus the assumed recovery rate.

Take a five year CDS spread of 100 basis points and an assumed recovery rate of 40 percent, giving a loss given default of 60 percent. Solving the approximation for the hazard rate gives 100 basis points divided by 60 percent, which comes to a hazard rate of approximately 1.67 percent per year. That figure is the market-implied annual probability of default conditional on survival to that point, not a cumulative probability over the full five years.