FRM Exam Part I · Corporate Bonds

Default Risk, Recovery Rates and Expected Loss on Corporate Bonds

Updated 11 October 2026 · Fact-checked

Expected loss on a corporate bond is the probability of default (PD) times the loss given default (LGD) times the exposure at default (EAD). LGD equals 1 minus the recovery rate. Find PD for the right horizon, set LGD from seniority, apply EAD, and multiply.

Understand Default Risk, Recovery Rates and Expected Loss

A corporate bond can fail to pay interest or principal. That event is default. Credit risk analysis splits the damage into three parts: how likely default is, how much you lose if it happens, and how much you are owed at that moment.

Probability of default (PD) is the chance the issuer defaults over a stated horizon, usually one year. Exposure at default (EAD) is the amount owed when default occurs. For a bond this is usually the face value plus any accrued interest, depending on how the question defines it. Loss given default (LGD) is the fraction of EAD you lose. It equals 1 minus the recovery rate.

Recovery depends on seniority. Senior secured creditors are paid first from collateral. Senior unsecured come next, then subordinated, then junior subordinated. Equity holders come last. Historical average recoveries fall as you move down this ladder, so a subordinated bond has a higher LGD than a senior unsecured bond from the same issuer. Recovery is also lower in recessions, when defaults cluster. Recovery rates are usually quoted as a percentage of face value, often measured from the market price shortly after default.

PD over several years needs care. Cumulative PD is the chance of default at any time up to year t. Marginal PD (unconditional) is the chance of default in a specific year, as seen today. Conditional PD (hazard rate) is the chance of default in a year given survival to its start. Survival probability is 1 minus cumulative PD. With a constant annual conditional PD of h, survival to year t is (1 − h)^t.

Expected loss is the average loss you should plan for. It is not the worst case. Unexpected loss, the variability around that average, is a separate topic and is the reason capital is held.

Key formulas to remember

Expected loss: EL = PD × LGD × EAD; PD, LGD and EAD must refer to the same horizon and the same exposure. Assumes PD and LGD are independent.
Loss given default: LGD = 1 − Recovery rate; Recovery rate is a fraction of exposure. Recovered amount = RR × EAD.
Expected loss rate: EL rate = PD × LGD; Divide EL by EAD to get a percentage.
Survival probability: S(t) = 1 − Cumulative PD(t); Chance of no default up to time t.
Marginal PD: Marginal PD(t) = Cum PD(t) − Cum PD(t−1); Unconditional chance of default in year t only.
Conditional PD: Conditional PD(t) = Marginal PD(t) ÷ S(t−1); Chance of default in year t given survival to the start of year t.
Constant hazard cumulative PD: Cum PD(t) = 1 − (1 − h)^t; h is the constant annual conditional default probability.
Approximate credit spread: Spread ≈ PD × LGD; Rough link under risk neutrality for small PD; ignores risk premium and liquidity.

How to solve Default Risk, Recovery Rates and Expected Loss questions

Use this order for any question on default risk, recovery and expected loss.

1Identify what is asked: EL in currency, EL rate, LGD, recovery, or a PD for a specific year.
2Write down the horizon. Check that PD, and any spread, match it.
3Convert recovery to LGD: LGD = 1 − RR. If the question gives LGD, skip this.
4Set EAD. Use the face value or exposure stated in the question. Do not use market price unless told to.
5For multi-year PD, build survival probabilities first, then get marginal or conditional PD by the formulas.
6Multiply PD × LGD × EAD. For several bonds, compute each EL and add them.
7Check the answer: EL must be less than EAD × LGD, and the EL rate must be less than LGD.
8Match the units asked for: currency, percent or basis points.

Quickest way: Three-number shortcut

When to use it: Use for single-period EL questions with clear PD, recovery and exposure.

Write LGD = 1 − RR in your head.
Compute EL rate = PD × LGD in decimals.
Multiply by EAD.
For multi-year PD, ask only whether you need marginal or conditional. Marginal uses a difference; conditional divides that difference by prior survival.

Common mistakes in Default Risk, Recovery Rates and Expected Loss

Using the recovery rate in place of LGD in the EL formula.
Both numbers appear in the question and recovery is easy to grab.
Fix: Always compute LGD = 1 − RR first and write it down.
Treating cumulative PD as the PD for one year.
The question gives a 5-year figure and the student applies it to year 5 alone.
Fix: Marginal PD for year t is the difference between cumulative PDs. Check which type is asked.
Forgetting to divide by survival probability for conditional PD.
Marginal and conditional PD sound alike.
Fix: Conditional PD(t) = Marginal PD(t) ÷ S(t−1). It is always at least as large as the marginal PD.
Ranking recovery rates in the wrong order.
Confusing bond seniority with equity ownership priority.
Fix: Remember the order paid: senior secured, senior unsecured, subordinated, junior, equity. Higher rank means higher recovery and lower LGD.
Mixing horizons, such as using a one-year PD on a two-year exposure.
Numbers are used without checking the time label.
Fix: Label each input with its horizon before multiplying.
Treating expected loss as the worst-case loss.
Loss and risk are blurred together.
Fix: EL is an average. Worst-case or unexpected loss relates to the variability of losses and is a separate measure.

Worked examples

Example 1

A bank holds a senior unsecured corporate bond with exposure at default of $4,000,000. The one-year PD is 2.5% and the expected recovery rate is 40%. Calculate the one-year expected loss.

Show the solution

LGD = 1 − 0.40 = 0.60.
EL rate = PD × LGD = 0.025 × 0.60 = 0.015, or 1.5%.
EL = 0.015 × $4,000,000 = $60,000.

Answer: $60,000

Example 2

A bond issuer has cumulative default probabilities of 3% by year 1 and 7% by year 2. What is the probability that the issuer defaults in year 2, given that it survived year 1?

Show the solution

Marginal PD for year 2 = 7% − 3% = 4%.
Survival to end of year 1 = 1 − 0.03 = 0.97.
Conditional PD = 0.04 ÷ 0.97 = 0.04124.
This is about 4.12%.

Answer: About 4.12%

Exam tips

Read whether the question gives recovery rate or LGD. Many wrong options are built from using the wrong one.
For cumulative, marginal and conditional PD, write the three labels on your scratch sheet and decide which is asked before computing.
A calculator helps with (1 − h)^t using the y^x key. Keep at least four decimals until the final step.
Expect conceptual questions on seniority, collateral and why recovery falls in downturns. Know the payment order cold.
Check that your EL is smaller than the loss if default occurs. This catches inverted formulas quickly.

Practice questions from Corporate Bonds

Default Risk, Recovery Rates and Expected Loss in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Default Risk, Recovery Rates and Expected Loss: frequently asked questions

What is the expected loss formula in FRM Part I?

EL = PD × LGD × EAD. LGD is 1 minus the recovery rate. All three inputs must refer to the same exposure and horizon.

How do I calculate the recovery rate on a defaulted bond?

Divide the amount recovered by the exposure, or use the post-default market price as a percentage of face value. If a bond trades at 35 per 100 face after default, the recovery rate is 35%, and LGD is 65%.

How does seniority affect recovery rates?

Higher-ranking claims are paid first, so they recover more on average. Senior secured bonds typically recover more than senior unsecured, which recover more than subordinated debt. Actual recovery varies by issuer and economic conditions.

What is the difference between cumulative and marginal default probability?

Cumulative PD is the chance of default at any time up to a date. Marginal PD is the chance of default in one specific year, measured from today. Conditional PD is the marginal PD divided by the survival probability to the start of that year.