FRM Exam Part II · Fundamentals of Credit Risk

Credit Risk Components: PD, LGD, EAD and Expected Loss

Updated 11 October 2026 · Fact-checked

Expected loss is the average credit loss you anticipate over a set horizon. Multiply three inputs: probability of default (PD), exposure at default (EAD) and loss given default (LGD). EL = PD × LGD × EAD. LGD = 1 − recovery rate. Check that PD and EAD use the same horizon.

Understand Credit Risk Components: PD, LGD, EAD and Expected Loss

Credit risk is the risk that a borrower or counterparty fails to pay. Banks break it into three parts so each can be measured on its own.

Probability of default (PD) is the chance the borrower defaults within a stated horizon, usually one year. It is a percentage. Under Basel, a default is generally defined by unlikeliness to pay or being more than 90 days past due on a material obligation.

Exposure at default (EAD) is the amount you expect to be owed at the moment of default. For a term loan it is the outstanding balance. For a credit line it is the drawn amount plus a share of the undrawn amount expected to be drawn before default. That share is the credit conversion factor (CCF). Borrowers in distress tend to draw down their lines, so EAD is often higher than today's drawn balance.

Loss given default (LGD) is the share of EAD you lose if default happens, after recoveries and costs. The recovery rate (RR) is the share you get back. LGD = 1 − RR. Both are fractions of EAD, so they always add to 100%.

Expected loss (EL) combines the three: EL = PD × LGD × EAD. It is the average loss, so banks treat it as a cost of doing business. They price it into loan spreads and cover it with provisions. Unexpected loss (UL) is the variability of loss around EL. Capital is held against UL, not EL. The product formula assumes PD, LGD and EAD are independent, which often fails in downturns when all three rise together.

Key formulas to remember

Expected loss: EL = PD × LGD × EAD; EL is in currency. PD and EAD must refer to the same horizon. LGD is a fraction of EAD.
LGD and recovery rate: LGD = 1 − RR and RR = 1 − LGD; Both are stated as a share of EAD. Recovery rate is often quoted per 100 of face value.
EAD for a credit line: EAD = Drawn + CCF × Undrawn; CCF is the expected share of the undrawn limit that is drawn by default. It lies between 0% and 100%.
Expected loss rate: EL% = EL ÷ EAD = PD × LGD; Useful for comparing loans of different size.
Portfolio expected loss: EL(portfolio) = Σ ELᵢ; Expected losses add up across exposures. Unexpected losses do not add up, because of diversification.
Unexpected loss for one exposure, fixed EAD and LGD: UL = EAD × LGD × √(PD × (1 − PD)); Applies when EAD and LGD are fixed and default is a Bernoulli event. Standard deviation of loss.

How to solve Credit Risk Components: PD, LGD, EAD and Expected Loss questions

Use this order for any question on PD, LGD, EAD and EL.

1Identify what is given: PD, recovery rate or LGD, drawn and undrawn amounts, CCF, and the horizon.
2Convert recovery rate to LGD if needed: LGD = 1 − RR.
3Compute EAD. For a term loan use the outstanding balance. For a line use Drawn + CCF × Undrawn.
4Check that PD matches the horizon asked for. Adjust only if the question tells you how.
5Multiply: EL = PD × LGD × EAD. Convert percentages to decimals first.
6For a portfolio, compute EL for each exposure and add them.
7State the meaning: EL is the average loss, covered by pricing and provisions. Variability is UL, covered by capital.

Quickest way: Three-number product with a sanity check

When to use it: Use when the question gives PD, LGD or recovery, and a loan or line size, and asks for EL or a ranking.

Write LGD = 1 − RR first if recovery is given.
Compute EAD in one line if there is an undrawn amount.
Multiply PD × LGD to get the loss rate, then multiply by EAD.
Sanity check: EL must be smaller than EAD × LGD, and smaller than EAD × PD.
Scan the options. Wrong answers often come from using RR instead of LGD, or ignoring the undrawn part.

Common mistakes in Credit Risk Components: PD, LGD, EAD and Expected Loss

Using the recovery rate in place of LGD in the EL formula.
Both numbers appear in the question and look alike.
Fix: Always convert first: LGD = 1 − RR. A high recovery means a low LGD.
Using only the drawn balance as EAD for a credit line.
The undrawn limit feels like it is not a real exposure.
Fix: Add CCF × Undrawn. If the question gives a CCF, it is telling you to use it.
Applying CCF to the whole limit instead of the undrawn part.
The word 'limit' appears and students apply CCF to it.
Fix: CCF applies to undrawn only. Drawn counts in full.
Treating expected loss as the amount of capital needed.
Both are called loss measures.
Fix: EL is the average and is met by pricing and provisions. Capital covers UL, the loss above the average up to a chosen confidence level.
Adding unexpected losses across loans like expected losses.
EL adds, so students assume UL does too.
Fix: EL is additive. UL is a standard deviation or tail measure and depends on default correlation, so portfolio UL is less than the sum when correlation is below 1.
Mixing horizons, such as a five-year PD with a one-year question.
Cumulative and annual PDs are both quoted in tables.
Fix: Underline the horizon in the question and pick the matching PD.

Worked examples

Example 1

A bank has a USD 10 million term loan to a corporate. One-year PD is 2%. If default occurs, the bank expects to recover 40% of exposure. Calculate the one-year expected loss.

Show the solution

EAD = USD 10 million, since it is a fully drawn term loan.
LGD = 1 − 0.40 = 0.60.
EL = PD × LGD × EAD = 0.02 × 0.60 × 10,000,000.
0.02 × 0.60 = 0.012. 0.012 × 10,000,000 = 120,000.

Answer: Expected loss = USD 120,000 (a 1.2% loss rate).

Example 2

A bank grants a EUR 20 million revolving credit line, of which EUR 12 million is drawn. The CCF on the undrawn part is 50%. One-year PD is 3% and LGD is 45%. Calculate EAD and the one-year expected loss.

Show the solution

Undrawn = 20 − 12 = EUR 8 million.
EAD = 12 + 0.50 × 8 = 12 + 4 = EUR 16 million.
Loss rate = PD × LGD = 0.03 × 0.45 = 0.0135.
EL = 0.0135 × 16,000,000 = 216,000.

Answer: EAD = EUR 16 million; expected loss = EUR 216,000.

Exam tips

When recovery rate is given, convert to LGD before anything else. Distractors are built on this slip.
For credit lines, look for the undrawn amount and CCF. EAD is often the hidden step.
Know the roles: EL is priced and provisioned, UL is capitalised. Conceptual questions test this.
Remember LGD and PD tend to rise together in downturns, so a simple product can understate stressed loss.
Check that the horizon of PD matches the question before multiplying.

Practice questions from Fundamentals of Credit Risk

Credit Risk Components: PD, LGD, EAD 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.

Credit Risk Components: PD, LGD, EAD and Expected Loss: frequently asked questions

What is the expected loss formula in FRM Part II?

EL = PD × LGD × EAD. PD is the probability of default over the horizon, LGD is the fraction of exposure lost on default, and EAD is the exposure at default. All three must be consistent in horizon and currency.

What is the difference between recovery rate and LGD?

Recovery rate is the share of exposure you get back after default. LGD is the share you lose. They add to 100%, so LGD = 1 − recovery rate.

What is the difference between expected loss and unexpected loss?

Expected loss is the average credit loss and is covered by pricing and provisions. Unexpected loss is the variability of loss around that average. Banks hold capital against unexpected loss.

How is exposure at default calculated for a credit line?

EAD = drawn amount + CCF × undrawn amount. The CCF reflects how much of the unused limit a borrower is expected to draw before default. It is applied only to the undrawn part.