Credit · C2 · 9 min
Ratings, default and expected loss
Read a credit rating, work out the loss you should expect on a loan, and see what default rate a bond’s extra yield implies.
In the news: “S&P cuts the company to BB+”: one notch, and its bonds drop out of investment grade, so many holders have to sell.
The essentials
- Credit ratings
- Letter grades from agencies such as S&P, Moody’s and Fitch for how likely a borrower is to pay. From safest to riskiest: AAA, AA, A, BBB, BB, B and CCC. Default rates rise steeply down the scale.
- The investment-grade line
- AAA to BBB− (Baa3 at Moody’s) is ; BB+ and below is . A bond cut across the line is a , which funds limited to investment grade must sell.
- PD and LGD
- (PD) is the chance a borrower fails to pay within a year. (LGD) is the share lost if it does: one minus the recovery, so 60% at 40% recovery.
- Expected loss
- The average loss a year: PD times LGD times the amount lent. £100 lent at a 2% PD and a 60% LGD loses £1.20 a year on average; some years nothing, some years much more.
- The credit triangle
- A spread pays for the expected loss, so dividing it by the LGD gives the default rate it implies: 300bp at 40% recovery implies about 5% a year. Spreads also pay for uncertainty, so the implied rate usually exceeds history.
Expected loss and the credit triangle
EL = PD × (1 − R) × N; spread ≈ PD × (1 − R)
- PD
- probability of default in a year
- R
- recovery rate (40% = 0.4); 1 − R is the loss given default
- N
- the amount lent
How it works
1. Grading borrowers
Before lending, you want to know how likely the borrower is to pay. Rating agencies such as S&P, Moody’s and Fitch publish that view as a letter grade, a . From safest to riskiest: AAA, AA, A, BBB, BB, B and CCC.
2. The investment-grade line
Each grade has notches: BBB+, BBB, BBB−. Everything from AAA down to BBB− is ; BB+ and below is . Moody’s writes the same grades as Aaa, Aa, A, Baa, Ba, B and Caa, with 1, 2 and 3 in place of +, nothing and −. So BBB− is Baa3, and B+ is B1.
3. Fallen angels
Many funds and insurers may hold only investment grade. So when a company is cut from BBB− to BB+, they must sell its bonds, often at the same time, and prices tend to drop. A bond cut below the line is a . Agencies often warn first by putting a rating on watch, and prices tend to fall before the cut.
4. The chance of default
Say a company has a 2% chance of failing to pay within a year. That is its , or PD. The agencies’ records show default rates rising steeply as ratings fall: defaults are rare at A and above and far more common at B and CCC.
5. How much you lose
A default rarely wipes you out: lenders usually get part of their money back. If you recover 40p in the pound, the is 40% and you lose 60%. That 60% is the , or LGD: one minus the recovery rate.
6. Expected loss
Lend £100 to a borrower with a 2% PD and a 60% LGD. On average you lose 2% × 60% × £100 = £1.20 a year. That average is the : PD × LGD × the amount lent. Some years you lose nothing, some years much more.
7. Spread, in basis points
A risky bond has to pay more than a safe government bond of the same length. The extra is its spread. Traders quote it in (bp), hundredths of a percentage point: a spread of 1.2% is 120bp.
8. The credit triangle
To break even, the spread must at least cover the expected loss each year. So spread ≈ PD × (1 − recovery): a 2% PD with 40% recovery needs 2% × 60% = 1.2%, or 120bp. Run it backwards to read the PD a spread implies: PD ≈ spread ÷ (1 − recovery). This is the .
9. Why real spreads are wider
Spreads usually imply more defaults than history shows. Investors also want paying for uncertainty, for defaults bunching together in recessions, and for bonds that can be hard to sell. So the triangle tells you what the market is pricing, not what will happen.
Try it
Move the chance of default and the recovery to see the spread that covers the expected loss. Or switch, set a spread, and read the default chance it implies.
spread ≈ PD × (1 − recovery)
- Spread that pays for it
- 120bp
- Expected loss a year on £10m
- £120,000
- Chance of default within 5 years
- 9.6%
| Annual default probability | Spread |
|---|---|
| 1% | 60bp |
| 2% | 120bp |
| 5% | 300bp |
| 10% | 600bp |
Worked example
A 5-year BB bond pays a spread of 300bp (3%). You hold £20m and assume 40% recovery if the company defaults.
- Loss given default: 1 − 40% = 60%.
- Implied PD: 3% ÷ 60% = 5% a year.
- Expected loss a year: £20m × 5% × 60% = £600,000.
- Check: 300bp of £20m is also £600,000, the extra income the spread pays you.
About 5% a year priced in: a 300bp spread pays for a 5% default rate at 40% recovery.
Check yourself
9 quick questions on the explanation above.
Practice
New numbers every set. Misses and guesses go into your review deck.
In the interview
Answer out loud in under a minute, then compare.
What’s a fallen angel, and why does it matter for flows?
A bond trades 400bp over with 40% recovery. What default rate is priced in?
Do you trust ratings? What do they miss?
Remember
PD ≈ spread ÷ (1 − recovery)
A spread is the market’s price for default and loss: divide it by the loss on default to see the default rate it implies.
Sources
Definitions and maths are standard textbook material; dated facts link to the sources above. Worked numbers are illustrative.