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FRM Exam Part II · Credit Value at Risk

PD, LGD and EAD: Expected Loss Calculation

Updated 11 October 2026 · Fact-checked

PD is the probability a borrower defaults over a horizon. EAD is the amount owed at default. LGD is the share of EAD lost after recoveries. Expected loss = PD × LGD × EAD. Solve by matching the horizon, converting recovery to LGD, and estimating EAD including undrawn limits.

Understand Credit Risk Parameters: PD, LGD and EAD

Every credit loss model rests on three inputs. Probability of default (PD) is the chance that a borrower defaults within a stated horizon, usually one year. Exposure at default (EAD) is how much you are owed at the moment of default. Loss given default (LGD) is the fraction of that exposure you lose after recoveries and costs.

The link between LGD and recovery is simple: LGD = 1 − recovery rate. Recovery is measured as a share of exposure, and should be net of workout costs and discounted to the default date. A 40% recovery means a 60% LGD.

EAD is easy for a term loan: it is close to the outstanding balance. It is harder for revolving lines and commitments. Borrowers tend to draw more as their credit worsens, so the undrawn part of a limit matters. You model this with a credit conversion factor (CCF), the share of the undrawn amount expected to be drawn by default. For derivatives, EAD depends on future market values and is covered under counterparty exposure.

The three inputs combine into expected loss (EL). EL is the average loss you expect and should be covered by pricing and provisions. The variation around that average is unexpected loss, which capital covers. Under Basel's internal ratings-based approach, banks estimate PD, and under the advanced approach also LGD and EAD. Regulators require LGD to reflect downturn conditions, because recoveries fall when defaults rise.

Key formulas to remember

Expected loss
EL = PD × LGD × EAD
Use the same horizon for PD, usually one year. Assumes PD, LGD and EAD are independent for the point estimate.
LGD and recovery rate
LGD = 1 − Recovery rate
Recovery is a fraction of exposure, ideally net of costs and discounted to default.
Exposure at default with undrawn limit
EAD = Drawn + CCF × Undrawn
CCF is between 0% and 100%. Undrawn = Limit − Drawn.
Expected loss rate
EL rate = EL ÷ EAD = PD × LGD
Useful for comparing loans of different size.
Portfolio expected loss
EL(portfolio) = Σ PDᵢ × LGDᵢ × EADᵢ
Expected losses add up across exposures, with no diversification effect.
Multi-year PD
Cumulative PD over n years = 1 − (1 − PD)ⁿ
Valid only if the annual PD is constant and defaults are independent across years.

How to solve Credit Risk Parameters: PD, LGD and EAD questions

Use this sequence for any question on PD, LGD, EAD or expected loss.

  1. 1Identify what is given: PD, LGD or recovery, drawn amount, limit, CCF.
  2. 2Check the horizon of the PD. Convert to the horizon asked if needed.
  3. 3Convert recovery rate to LGD using LGD = 1 − recovery. Watch for costs of workout.
  4. 4Compute EAD. For a revolver, use drawn plus CCF times undrawn, not the limit.
  5. 5Multiply PD × LGD × EAD, or sum across exposures for a portfolio.
  6. 6Check units and size: EL must be less than EAD, and PD × LGD is a rate below PD.
  7. 7Interpret: EL is covered by pricing and provisions, while unexpected loss is covered by capital.

Quickest way: Rate first, then amount

When to use it: Use under time pressure for single-loan or small portfolio expected loss questions.

  1. Write EAD first, since it is the most often mistaken input.
  2. Turn recovery into LGD in one line.
  3. Compute PD × LGD as a percentage.
  4. Multiply by EAD.
  5. Eliminate options larger than EAD or equal to PD × EAD, which ignores LGD.

Common mistakes in Credit Risk Parameters: PD, LGD and EAD

  • Using the full limit as EAD on a revolving facility

    Candidates forget the undrawn part is only partly drawn at default.

    Fix: Use EAD = drawn + CCF × undrawn, and read the limit and drawn amounts carefully.

  • Using the recovery rate as LGD

    Both are percentages and appear in the same sentence.

    Fix: Always write LGD = 1 − recovery before multiplying.

  • Mismatching horizons

    A multi-year PD is paired with a one-year question, or the reverse.

    Fix: State the horizon and convert using 1 − (1 − PD)ⁿ when annual PD is constant.

  • Treating expected loss as the capital requirement

    Both are described as loss measures.

    Fix: EL is the mean loss covered by pricing and provisions. Capital covers unexpected loss beyond EL.

  • Ignoring that LGD and PD move together

    The formula multiplies them as if independent.

    Fix: Recall that recoveries fall in downturns, so use downturn LGD for regulatory purposes and note the correlation in interpretation.

Worked examples

Example 1

A bank has a revolving credit line of USD 10 million to a corporate. USD 6 million is drawn. The CCF is 50%. The one-year PD is 2% and the recovery rate on a default is 35%. Calculate the one-year expected loss.

Show the solution
  1. Undrawn = 10 − 6 = USD 4 million.
  2. EAD = 6 + 0.50 × 4 = USD 8 million.
  3. LGD = 1 − 0.35 = 65%.
  4. EL = 0.02 × 0.65 × 8,000,000 = USD 104,000.

Answer: Expected loss is USD 104,000.

Example 2

A portfolio has two loans. Loan A: EAD USD 5 million, PD 1%, LGD 40%. Loan B: EAD USD 3 million, PD 4%, LGD 75%. Find the portfolio expected loss and which loan contributes more.

Show the solution
  1. Loan A: 0.01 × 0.40 × 5,000,000 = USD 20,000.
  2. Loan B: 0.04 × 0.75 × 3,000,000 = USD 90,000.
  3. Portfolio EL = 20,000 + 90,000 = USD 110,000.
  4. Loan B is larger: it has the higher PD and LGD despite a smaller EAD.

Answer: Portfolio expected loss is USD 110,000, and Loan B contributes more (USD 90,000).

Exam tips

  • Questions often hide EAD in a limit and drawn amount. Compute EAD before anything else.
  • If a recovery rate is given, convert it to LGD before multiplying.
  • Expect conceptual items on downturn LGD, CCF behaviour and why EL differs from unexpected loss.
  • Know which inputs a bank estimates under foundation and advanced IRB approaches.
  • Sanity check: expected loss should be far below EAD, and a PD of a few percent gives a small EL rate.

Practice questions from Credit Value at Risk

Credit Risk Parameters: PD, LGD and EAD 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 Parameters: PD, LGD and EAD: frequently asked questions

How do you calculate expected loss from PD, LGD and EAD?

Multiply the three: EL = PD × LGD × EAD. Make sure PD covers the same horizon you want, usually one year. For a portfolio, sum the expected losses of each exposure.

How is LGD related to the recovery rate?

LGD = 1 − recovery rate, with recovery measured as a share of exposure. Better estimates net off workout costs and discount recoveries to the default date. A 30% recovery gives a 70% LGD.

How do you estimate exposure at default for a credit line?

Add the drawn balance to a share of the undrawn limit: EAD = drawn + CCF × undrawn. The CCF reflects that borrowers draw more as they approach default. For derivatives, EAD depends on modelled future exposure instead.

What is the difference between expected loss and unexpected loss?

Expected loss is the average credit loss, covered by pricing and provisions. Unexpected loss is the volatility of losses around that average, and capital is held against it. Credit VaR is often described as the loss at a high percentile minus expected loss.