What a credit spread pays for
A spread covers the losses you should expect, plus a premium for bearing the risk. Split it, and run it backwards to the default rate the market is pricing.
- Calculate the credit spread and the expected loss
- Split the spread into expected loss and risk premium
- Back out the breakeven default rate
- Show how the recovery assumption changes both
The intuition
An insurer covering houses expects a few to burn down each year. Its premiums must cover those expected claims, and then some: it also wants paying for the risk that a bad year brings far more claims than average, all at once.
A corporate bond's credit spread, its yield above the risk-free rate, works like that premium. Part of it is expected loss: the chance the issuer defaults in a year × what you lose if it does. The rest is the risk premium: pay for defaults that cluster in recessions, and for holding something harder to sell than a government bond.
Spread = yield − risk-free rate. Loss given default = 1 − recovery. Expected loss = probability of default × loss given default. Risk premium = spread − expected loss. Breakeven default rate = spread ÷ loss given default.
Why it works
- The conventions here: everything annual and simple. Expected loss = probability of default × (1 − recovery). The risk premium is whatever part of the spread expected loss does not explain.
- Most of a spread is usually premium. Corporate bonds have historically paid well above their default losses, which is why credit has beaten its losses over time.
- The breakeven default rate is the default rate at which the spread exactly pays for the losses, leaving no premium.
- State a credit view as a default rate: not 'the spread is wide' but 'the market is pricing more defaults than I believe'.
- Recovery is the harder input. Default probabilities rest on decades of data; recovery depends on where the bond ranks and what the assets fetch on the day.
- The premium can go negative at the top of a credit cycle, when spreads no longer cover a normal year of defaults.
| Spread: 8.0% − 4.0% | 400bp |
| Loss given default: 1 − 40% | 60% |
| Expected loss: 2% × 60% | 120bp |
| Risk premium: 400 − 120 | 280bp, 70% of the spread |
| Breakeven default rate: 400bp ÷ 60% | 6.67% a year |
| Against your 2% estimate: 6.67% ÷ 2% | 3.3 times |
At 20% recovery instead: expected loss is 2% × 80% = 160bp, and the breakeven default rate falls to 400bp ÷ 80% = 5.00%.
The formulas
What the bond pays for its credit risk.
The actuarial cost of default.
Pay for bearing the risk.
The default rate the spread just covers.
Worked example
The spread first. Expected loss is the default probability times what you lose in a default; the rest is premium.
See it move
Same bond. Change the spread, your default probability, the recovery you expect and the risk-free rate.
- Raise your default probability. Expected loss rises and the premium shrinks; the breakeven default rate does not move.
- Raise the recovery. Expected loss falls, and both the premium and the breakeven default rate rise.
- Widen the spread. The premium and the breakeven default rate both rise.
- Raise the risk-free rate. The bond's yield rises; the premium does not move.
Run it backwards
Same bond, reversed: suppose there is no risk premium at all. What annual default rate is the spread pricing in?
With no premium, the whole spread is expected loss: spread = default rate × (1 − recovery). Divide the spread by the loss given default.
Set that against your own estimate. The gap is the risk premium expressed as defaults: losses the market is paid for that you do not expect.
Traps
Say it in the interview
“A bond yields 400 basis points over Treasuries. What is that spread paying you for?”
Check yourself
4 fresh questions, with new numbers. Answer each one correctly to finish the chapter. Get one wrong and you will see the full working, then you can try it again with new numbers.
Answers within 1% are marked right. Type the number; $, %, x and M are fine. First tries count toward Learned: the topic is Learned once every chapter is done and 75% of first tries were right.
- Spread = yield − risk-free rate.
- Expected loss = default probability × (1 − recovery).
- Risk premium = spread − expected loss.
- Breakeven default rate = spread ÷ (1 − recovery).