How to use the credit spread calculator
Credit spread compares two yields:
- Corporate bond yield. The yield to maturity from your broker’s quote or our bond yield calculator.
- Treasury yield of similar maturity. Use the Treasury closest in maturity to the bond. A 7-year corporate bond is compared with the 7-year Treasury, not the 10-year.
- Recovery rate, used for a quick estimate of the default risk the spread implies.
Implied default probability goes further. Enter a spread in basis points, a recovery rate and a horizon, usually the bond’s remaining maturity. The results show the annual hazard rate, the probability of default in the first year and over the whole horizon. The table repeats the calculation for spreads from 50 to 800 basis points.
The formulas
If the spread pays only for expected default losses, it equals the annual default rate times the share of face value lost in a default:
Probability of default within t years = 1 − e−λts is the spread as a decimal, R the recovery rate and t the horizon in years. λ is the default intensity, the instantaneous annual rate of default for a bond that has survived so far.
This is the standard “credit triangle” approximation used for quick estimates. It treats the hazard rate as constant over the horizon.
A worked example
A corporate bond yields 5.6% and the Treasury of similar maturity yields 4.2%. The credit spread is 140 bp, which is $140.00 a year of extra income for every $10,000 invested.
For the default calculation, take a spread of 250 bp and a recovery rate of 40%. The implied hazard rate is 4.17% a year, a 4.08% chance of default in the first year. Over 5 years the cumulative implied probability of default is 18.8%, leaving a survival probability of 81.2%.
How the spread translates into risk
At a 40% recovery rate and a five-year horizon:
| Spread | Annual hazard rate | 5-year implied default probability |
|---|---|---|
| 100 bp | 1.67% | 8.0% |
| 250 bp | 4.17% | 18.8% |
| 500 bp | 8.33% | 34.1% |
The relationship is close to proportional for small spreads and bends as the probability accumulates, since a bond can only default once. Recovery matters too: the lower the recovery, the less often defaults need to happen to justify the same spread.
Why implied probabilities overstate real defaults
A spread is not a pure price of default. It also compensates investors for:
- Liquidity. Most corporate bonds trade far less than Treasuries, and selling quickly can mean accepting a worse price.
- Risk aversion. Defaults cluster in recessions, exactly when losses hurt most, so investors demand more than the expected loss.
- Taxes and other features. In the US, Treasury interest is exempt from state income tax and corporate interest is not; call options and other features also add to the yield.
Because the formula assigns all of this to default, the probabilities it produces are market-implied, risk-neutral figures that generally exceed the default rates that actually occur. They are still useful for comparing bonds, and for seeing how much the market’s fear has changed when spreads widen.
What this calculator does not include
- Exact benchmark matching. Professional spread measures such as the Z-spread or option-adjusted spread compare against the whole Treasury curve and adjust for embedded options. A simple yield difference is a close approximation for plain bullet bonds.
- A term structure of default risk. The hazard rate is assumed constant. Real issuers can have very different short-term and long-term risk.
- Price effects. To see how a change in spread moves the price of a bond, reprice it at the new yield with the bond price calculator; the bond duration calculator gives the sensitivity directly.