FRM Exam Part II · Credit Risk

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

Updated 11 October 2026 · Fact-checked

Credit risk is the risk of loss when a borrower or counterparty fails to pay. Expected loss is the average loss you plan for: EL = PD × LGD × EAD. Unexpected loss is the variability of loss around that average, usually measured as a standard deviation or as a tail loss minus EL.

Understand Credit Risk Fundamentals and Expected Loss

Credit risk is the chance that a borrower or counterparty does not meet its obligations in full and on time. Every credit loss estimate is built from a few simple parts.

Probability of default (PD) is the chance the borrower defaults within a set horizon, usually one year. Loss given default (LGD) is the share of exposure you lose if default happens. LGD = 1 − recovery rate, so a 40% recovery means a 60% LGD. Exposure at default (EAD) is the amount owed at the moment of default. For a drawn loan it is the outstanding balance. For a credit line, EAD includes the expected drawn part of the undrawn commitment, often through a credit conversion factor. Maturity (M) is the remaining life of the exposure. Longer maturity gives more time for credit quality to fall, so it raises risk and capital under Basel IRB.

Expected loss (EL) is the average loss over the horizon. Multiply the three parameters: EL = PD × LGD × EAD. Banks treat EL as a cost of doing business. They cover it through loan pricing and through provisions or reserves, not through capital.

Unexpected loss (UL) is the uncertainty around EL. Actual losses in a bad year can be far above average. UL is commonly the standard deviation of the loss distribution. Economic capital is then the loss at a high confidence level (the credit VaR) minus EL. Capital is held for this gap.

For a single exposure with fixed LGD and EAD, default is a Bernoulli event. The standard deviation of loss is then EAD × LGD × √(PD × (1 − PD)). For a portfolio, UL depends strongly on default correlation, so portfolio UL is less than the sum of individual ULs unless correlation is perfect.

Key formulas to remember

Expected loss: EL = PD × LGD × EAD; Use the same horizon for PD and EAD. EL is in currency units. EL rate = PD × LGD.
Loss given default: LGD = 1 − Recovery rate; Recovery is expressed as a share of exposure. Check whether the question gives recovery or LGD.
EAD for a credit line: EAD = Drawn + CCF × Undrawn; CCF is the credit conversion factor, the expected share of the undrawn limit that is drawn by default.
Unexpected loss, single exposure (fixed LGD and EAD): UL = EAD × LGD × √(PD × (1 − PD)); This is the standard deviation of loss. It assumes LGD is a known constant.
Unexpected loss with random LGD: σ² of loss = EAD² × [PD × σ_LGD² + LGD² × PD × (1 − PD)]; Assumes LGD is independent of default and EAD is fixed. UL is the square root.
Portfolio expected loss: EL_portfolio = Σ EL_i; EL is additive across exposures, whatever the correlation.
Portfolio UL, two exposures: UL_p = √(UL₁² + UL₂² + 2ρ × UL₁ × UL₂); ρ is the correlation of losses. UL is not additive unless ρ = 1.
Economic capital (credit VaR basis): Economic capital = Credit VaR at confidence level − EL; Credit VaR is the quantile loss. Capital covers only the unexpected part.

How to solve Credit Risk Fundamentals and Expected Loss questions

Use this order for any EL or UL question. It keeps units, horizons and definitions straight.

1Identify what is asked: EL, UL, capital, or a single parameter such as LGD or EAD.
2List the inputs and convert them to decimals: PD, LGD or recovery, drawn and undrawn amounts, CCF, horizon.
3Build EAD first. For a credit line add CCF × undrawn to the drawn balance.
4Convert recovery to LGD if needed: LGD = 1 − recovery.
5Compute EL = PD × LGD × EAD. Check that PD matches the horizon asked for.
6For UL, choose the right formula: fixed LGD, random LGD, or portfolio with correlation. Take the square root at the end.
7If capital is asked, subtract EL from the quantile loss. Do not hold capital for EL itself.
8Sanity check: EL should be much smaller than EAD, and UL for one exposure is usually larger than EL when PD is small.

Quickest way: Three-number shortcut

When to use it: Use for single-exposure EL and UL questions with fixed LGD, where options are far apart.

Compute EAD × LGD once. Call it the loss severity S.
EL = PD × S.
UL = S × √(PD × (1 − PD)). For small PD, √(1 − PD) is close to 1, so UL ≈ S × √PD.
For portfolio EL, just add. For portfolio UL, only add directly if the question says perfect correlation; otherwise use the correlation formula.
Reject options that are above S, because loss cannot exceed severity for a single exposure.

Common mistakes in Credit Risk Fundamentals and Expected Loss

Using LGD as the recovery rate, or the reverse.
Questions often give recovery and the formula needs LGD.
Fix: Always write LGD = 1 − recovery before you multiply.
Forgetting the undrawn commitment when finding EAD.
Students take the drawn balance as the full exposure.
Fix: For lines of credit use Drawn + CCF × Undrawn. If no CCF is given, check whether the question states a draw assumption.
Adding unexpected losses across exposures.
EL is additive, so students assume UL is too.
Fix: UL is a standard deviation. Add variances with correlation terms, then take the square root.
Holding capital against expected loss.
EL and UL are mixed up as 'the loss number'.
Fix: EL is covered by pricing and provisions. Economic capital covers credit VaR minus EL.
Mismatching horizons, for example using a 5-year cumulative PD with a one-year question.
Tables often show several horizons.
Fix: Read the horizon in the question and pick the PD for that same period.
Dropping the (1 − PD) term in UL or using PD(1 − PD) without the square root.
Students recall the Bernoulli variance but forget to convert to standard deviation.
Fix: Remember UL is a standard deviation: √(PD × (1 − PD)) × EAD × LGD.

Worked examples

Example 1

A bank has a $10 million term loan to a corporate borrower and an undrawn $4 million revolving line to the same borrower. The one-year PD is 2%. The CCF on the undrawn line is 50%. Recovery in default is expected to be 45%. Find the one-year expected loss.

Show the solution

EAD = drawn + CCF × undrawn = 10,000,000 + 0.5 × 4,000,000 = $12,000,000.
LGD = 1 − 0.45 = 0.55.
EL = PD × LGD × EAD = 0.02 × 0.55 × 12,000,000.
0.02 × 0.55 = 0.011. 0.011 × 12,000,000 = 132,000.

Answer: Expected loss = $132,000.

Example 2

A single exposure has EAD of €5 million, LGD of 60% (treated as fixed) and one-year PD of 4%. Calculate the expected loss and the unexpected loss (standard deviation of loss).

Show the solution

Severity S = EAD × LGD = 5,000,000 × 0.60 = €3,000,000.
EL = PD × S = 0.04 × 3,000,000 = €120,000.
PD × (1 − PD) = 0.04 × 0.96 = 0.0384.
√0.0384 = 0.19596 (since 0.196² = 0.038416).
UL = 3,000,000 × 0.19596 ≈ €587,880.

Answer: EL = €120,000 and UL ≈ €588,000 (about €587,900). UL is nearly five times EL, which is typical for a low-PD single name.

Exam tips

Read whether the question gives recovery or LGD, and whether PD is annual or cumulative, before touching a calculator.
Expect conceptual items too: who covers EL (pricing, provisions) and who covers UL (capital).
When a portfolio question mentions correlation, the answer is a UL below the sum of individual ULs. Eliminate options that simply add them.
Know that Basel IRB uses PD, LGD, EAD and maturity as inputs to risk weights, and that maturity adjustments raise capital for longer exposures.
If an option shows EL larger than EAD × LGD, discard it at once.

Practice questions from Credit Risk

Credit Risk Fundamentals 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 Fundamentals and Expected Loss: frequently asked questions

What is the expected loss formula in FRM Part II?

EL = PD × LGD × EAD. PD is the default probability over the horizon, LGD is the share lost on default, and EAD is the exposure at default. Use the same horizon for all inputs.

What is the difference between expected loss and unexpected loss?

Expected loss is the average loss you anticipate and cover through pricing and provisions. Unexpected loss is the variability of loss around that average, and capital is held against it. Economic capital is typically credit VaR minus EL.

Is maturity part of the expected loss formula?

Not in the basic formula. Maturity is a fourth credit risk component that matters for risk, since longer exposures have more time to deteriorate. Basel IRB uses it as an input to the capital requirement.

How is EAD calculated for a credit line?

Add the drawn balance to the expected drawn part of the undrawn limit: EAD = Drawn + CCF × Undrawn. The CCF reflects that borrowers tend to draw more as they approach default.