Tools › Investing › Bonds › Credit Spread and Default Risk › Example
What a 250 bp credit spread says about default: rule of thumb, exact one-year and constant-hazard forms at 40 % recovery
| Tool | Credit Spread and Default Risk |
| Source | Closed forms of risk-neutral pricing; the pairing spread = hazard rate × loss given default as used in Gibson, M. S. (2004). Understanding the Risk of Synthetic CDOs. Finance and Economics Discussion Series 2004-36, Board of Governors of the Federal Reserve System, Washington, DC (60 bp, 40 % recovery, 1 % a year). Merton, R. C. (1974), Journal of Finance 29(2), for the Advanced section. |
| Level | Undergraduate |
Problem
A five-year bond yields 6.5 % while a risk-free bond of the same maturity yields 4.0 % (effective yearly rates). Assuming that a default returns 40 % of the promised amount, find the credit spread, the default probability it implies by the rule of thumb, exactly for one year and at a constant hazard rate to maturity, the chance of surviving five years, and the spread that would pay for the same hazard rate if recovery were 20 %.
Inputs to Enter
- Bond yield 6.5 %, risk-free yield 4.0 %, maturity 5 years, recovery rate 40 % (the default inputs; press Submit)
Answers
- Spread = 0.065 − 0.040 = 0.025 (250 bp); loss given default = 1 − 0.40 = 0.60
- Rule of thumb: hazard = 0.025 / 0.60 = 0.04167 (4.17 % a year)
- One year, exact: p = 0.025 / (1.065 · 0.60) = 0.03912
- To maturity: Q = [1 − (1.04 / 1.065)^5] / 0.60 = 0.1866; survival 0.8134; hazard = −ln(0.8134) / 5 = 0.04132; within one year 1 − exp(−0.04132) = 0.04048
- Break-even spread for that hazard at 20 % recovery: 342 bp (0 % recovery 439 bp, 60 % 163 bp, 80 % 79 bp)
- Advanced defaults: Merton with equity 500, equity volatility 40 %, debt 500 due in 5 years gives asset value 902.575, asset volatility 23.01 %, distance to default 1.272, default probability 10.17 %, spread 41 bp; a 6 % semi-annual bond at the implied hazard prices at 97.7883 against 109.1681 with no default risk
Notes
The tool's default inputs are this case. The probabilities are risk-neutral: they include a premium for bearing risk and overstate the frequency at which such bonds have defaulted. Checked by hand, against the spread and hazard pairs printed in Gibson (2004) and against scipy (brentq, fsolve) in test_credit_spread_default_risk.php; not a worked example printed in a publication. A calculator for education and analysis, not investment advice.