How do you turn a default probability into basis points?

The expected-loss component of a spread is not a matter of opinion. It is arithmetic, and it fits on one line.

The formula

Expected loss = probability of default × loss given default

and

Loss given default (LGD) = 1 − recovery rate

The recovery rate is the fraction of your claim you get back after a default — through a restructuring, an asset sale, or a bankruptcy process. If a defaulted bond eventually returns 40 cents on the dollar, the recovery rate is 40% and the LGD is 60%.

A fuller version used in bank risk management adds exposure at default: EL = PD × LGD × EAD. For a bond held near par, EAD is simply the notional, so it drops out of the intuition.

A worked example

An illustrative issuer with a 2% annual probability of default and an expected 40% recovery:

• LGD = 1 − 0.40 = 0.60
• Expected loss = 0.02 × 0.60 = 0.012 = 1.2% = 120bp per year

So 120bp of whatever this bond pays over the benchmark is not income — it is a reserve against the losses that arithmetic says will arrive. If the bond quotes at 300bp, the other 180bp is risk premium and liquidity premium.

Both inputs move the answer

Hold everything else and vary one input at a time:

• PD 2%, recovery 70% → LGD 0.30 → EL = 60bp
• PD 2%, recovery 40% → LGD 0.60 → EL = 120bp
• PD 4%, recovery 40% → LGD 0.60 → EL = 240bp
• PD 4%, recovery 20% → LGD 0.80 → EL = 320bp

Notice that recovery is not a footnote. Two issuers with an identical default probability can face expected losses that differ by a factor of two, purely because of where in the capital structure your claim sits. Unit 3 is entirely about that.

Running the formula backwards

Because the relationship is so simple, practitioners invert it to ask what the market is implying. Rearranged:

Implied default probability ≈ spread ÷ LGD

A bond at 300bp with an assumed 40% recovery implies 0.0300 ÷ 0.60 = 5% per year.

Now be careful, because this is where people overclaim. That 5% is a risk-neutral figure: it is what you get if you pretend the entire spread is expected loss. But lesson 2 showed the spread also contains risk and liquidity premiums. So the implied number systematically exceeds the default rate actually observed in history — often by a wide multiple for higher-quality credits.

The honest reading of "the market implies a 5% default probability" is: the market is charging as much as a 5% annual default rate would justify, for reasons that include but exceed default risk. It is a price statement, never a forecast.

In the data

Practitioners keep a lookup from rating to typical spread. Aswath Damodaran publishes one every year for government borrowers, and six of its buckets are below. It starts at exactly 0 for Aaa, the benchmark itself, and widens as the letters fall.

The values are fractions rather than basis points: A1 reads 0.005993, meaning 60bp. Read them as basis points and every spread is out by a factor of 10,000.

Try it now

Run the math both directions:

1. Take the spread you computed in lesson 1, or rebuild it from the two tables below: the high-quality corporate 5-year yield for August 2026 minus the average of the three Treasury 5-year readings from the same month. Divide it by an assumed LGD of 0.60. That is the implied default rate the price is charging for.

2. Now go forward instead, using the rating lookup in the section above. Take two buckets, A1 and Ba2, and give each an illustrative annual default probability, 0.1% and 1% respectively. Run expected loss forward at the same 0.60 LGD for both.
3. Compare each expected loss with its bucket's default spread in basis points. The gap between them is the risk-and-liquidity premium, the same quantity you isolated last lesson, arrived at from the other side. Note which bucket leaves the larger share of its spread unexplained by expected loss.