Implied Default Probability
Approximate annual default probability implied by a credit spread, using the standard reduced-form approximation: spread ≈ default probability × loss given default. Inverting gives the probability the market is pricing in.
When to use: Use to translate a credit spread into a more interpretable default-rate equivalent. A 200 bp spread on a corporate bond with 40% recovery implies roughly a 3.3% annual default probability — useful sanity check against historical default rates by rating bucket.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| DefaultProb | Default Probability | Implied annual probability of default as a decimal | % |
| Spread | Yield Spread | Difference between a bond yield and a benchmark yield, in decimal form | % |
| Recovery | Recovery Rate | Expected fraction of par recovered in default, as a decimal | % |
Real-Life Examples
Example 1: 200 bp Spread, 40% Recovery
A corporate bond yields 200 bps over Treasuries. Standard senior-unsecured recovery assumption is 40%.
Given
Step-by-Step
The market is pricing in ~3.3% annual default risk. Compare to historical default rates: this is consistent with a low-BBB / high-BB profile. If actual rated default risk is meaningfully lower, the bond may be cheap.
Example 2: High-Yield 600 bp Spread
High-yield bond yielding 600 bps over Treasuries; assume 40% recovery.
Given
Step-by-Step
10% implied annual default probability — typical of single-B / CCC names. Wide spreads carry both fundamental default risk and a risk premium, so realized defaults often run 2-3 percentage points below implied figures.
Frequently Asked Questions
Risk-neutral. The figure includes a risk premium for default uncertainty; actual ("real-world") default rates are typically lower than what spreads imply. The gap is what credit investors earn for bearing default risk.
A simplified continuous-time hazard-rate model: spread ≈ λ(1 − R), where λ is the default intensity and R is recovery. Solving for λ gives the formula. The approximation is good for short horizons and small spreads.
Standard assumptions: 40% for senior unsecured corporates, 60% for senior secured, 25% for subordinated. Sovereign and EM debt vary widely. Moody's and S&P publish historical recovery statistics by seniority and sector.