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FRM Exam Part II · Introduction to Credit Risk Modeling and Assessment

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

Updated 11 October 2026 · Fact-checked

Expected loss is the average credit loss you expect over a set horizon. You get it by multiplying three inputs: probability of default (PD), loss given default (LGD) and exposure at default (EAD). So EL = PD × LGD × EAD. To solve questions, align the horizon, convert recovery to LGD, then multiply.

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

Credit risk is the risk that a borrower or counterparty fails to pay what it owes. To measure it, risk managers break it into three questions. How likely is default? How much is owed when it happens? How much of that is lost after recoveries?

The three answers are the building blocks. Probability of default (PD) is the chance the borrower defaults over a stated horizon, usually one year. Exposure at default (EAD) is the amount outstanding at the time of default. For a loan with an undrawn limit, EAD includes the part of the limit you expect the borrower to draw before default. Loss given default (LGD) is the share of EAD you lose after recoveries and costs. It equals 1 minus the recovery rate.

Expected loss (EL) combines them: EL = PD × LGD × EAD. It is the mean of the loss distribution. Banks treat it as a normal cost of lending. They price it into loan spreads and cover it with provisions.

Unexpected loss (UL) is different. It is the variation of losses around EL, often measured as the standard deviation of the loss distribution. Capital is held against unexpected loss, not expected loss. Under the Basel IRB approach, risk-weighted assets are driven by PD, LGD, EAD and maturity.

Keep the units straight. PD is a probability, LGD is a percentage, and EAD is a currency amount. Only EL and UL come out in currency.

Key formulas to remember

Expected loss
EL = PD × LGD × EAD
PD and LGD as decimals, EAD in currency. The PD horizon sets the EL horizon.
Loss given default from recovery
LGD = 1 − Recovery rate
Recovery rate is a share of EAD recovered, net of costs if the question says so.
Exposure at default with undrawn limit
EAD = Drawn amount + CCF × Undrawn commitment
CCF is the credit conversion factor, the share of the undrawn limit expected to be drawn at default.
Expected loss rate
EL ÷ EAD = PD × LGD
Useful when exposure is not given or you compare loans.
Portfolio expected loss
EL(portfolio) = Σ EL(i)
Expected loss is additive across exposures. No correlation is needed.
Unexpected loss of one exposure with fixed LGD and EAD
UL = EAD × LGD × √(PD × (1 − PD))
Standard deviation of loss when LGD is certain, treating default as a Bernoulli event. UL does not add across exposures unless defaults are perfectly correlated.

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

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

  1. 1Identify the horizon of the PD (one year, or cumulative over several years) and the horizon the question asks for.
  2. 2Find EAD. If there is an undrawn commitment, add CCF × undrawn to the drawn balance.
  3. 3Find LGD. If you are given a recovery rate, compute 1 − recovery. If collateral is given, work out the loss after collateral first.
  4. 4Convert all percentages to decimals.
  5. 5Multiply: EL = PD × LGD × EAD.
  6. 6For a portfolio, compute each EL and add them.
  7. 7If the question asks about unexpected loss or capital, remember EL is the mean and UL is the spread. Say which one the answer measures.
  8. 8Check the answer is below EAD and has the right currency.

Quickest way: Rate first, then amount

When to use it: Use this for multiple-choice questions with several loans or answer options that differ by a factor of 10 or 100.

  1. Compute the loss rate PD × LGD in your head, for example 2% × 40% = 0.8%.
  2. Multiply that rate by EAD.
  3. Sanity check the size: 0.8% of ₹10,00,00,000 is ₹8,00,000.
  4. If the question gives recovery, subtract from 1 before anything else.
  5. Eliminate options larger than EAD or that use PD × EAD alone.

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

  • Using the recovery rate as LGD

    Both are percentages and the question may give only recovery.

    Fix: Always write LGD = 1 − recovery. A 35% recovery means a 65% LGD.

  • Ignoring the undrawn part of a credit line

    Students take the drawn balance as EAD.

    Fix: Check for a limit and a CCF. EAD = drawn + CCF × undrawn.

  • Confusing expected loss with unexpected loss

    Both appear in credit VaR and economic capital discussions.

    Fix: EL is the mean loss, priced and provisioned. UL is the variability, covered by capital.

  • Mismatching horizons

    A multi-year cumulative PD is used in a one-year question, or the reverse.

    Fix: Match the PD horizon to the loss horizon before multiplying.

  • Adding unexpected losses across loans

    Students assume EL additivity applies to UL.

    Fix: EL adds. UL depends on default correlation and is generally less than the sum unless correlation is perfect.

  • Entering percentages as whole numbers

    Rushing under time pressure.

    Fix: Convert to decimals. 2% is 0.02, not 2.

Worked examples

Example 1

A bank has a term loan with ₹20,00,00,000 outstanding. The one-year PD is 1.5%. Expected recovery is 45% of the exposure. Find the one-year expected loss.

Show the solution
  1. EAD = ₹20,00,00,000.
  2. LGD = 1 − 0.45 = 0.55.
  3. Loss rate = PD × LGD = 0.015 × 0.55 = 0.00825.
  4. EL = 0.00825 × ₹20,00,00,000 = ₹16,50,000.

Answer: The one-year expected loss is ₹16,50,000.

Example 2

A bank grants a corporate a USD 10 million credit line. USD 6 million is drawn. The CCF on the undrawn part is 50%. The one-year PD is 2% and LGD is 40%. Calculate EAD and the one-year expected loss.

Show the solution
  1. Undrawn amount = 10 − 6 = USD 4 million.
  2. EAD = 6 + 0.50 × 4 = USD 8 million.
  3. EL = 0.02 × 0.40 × 8,000,000.
  4. 0.02 × 0.40 = 0.008, and 0.008 × 8,000,000 = USD 64,000.

Answer: EAD is USD 8 million and the expected loss is USD 64,000.

Exam tips

  • Read for a hidden step: a recovery rate, an undrawn limit or collateral that changes LGD or EAD.
  • Check which horizon the PD covers. Questions often give a cumulative multi-year PD.
  • When a question mentions capital, it is usually testing unexpected loss, not expected loss.
  • Know the Basel link: IRB risk weights use PD, LGD, EAD and maturity as inputs.
  • Estimate the rate PD × LGD first. It lets you reject wrong options quickly.

Practice questions from Introduction to Credit Risk Modeling and Assessment

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?

Expected loss equals PD × LGD × EAD. PD and LGD are used as decimals and EAD is the currency exposure. The result is the average loss over the PD horizon.

What is the difference between expected loss and unexpected loss?

Expected loss is the mean of the credit loss distribution. It is priced into spreads and covered by provisions. Unexpected loss is the variability around that mean, and capital is held against it.

How is LGD related to the recovery rate?

LGD = 1 − recovery rate. If you recover 30% of the exposure, LGD is 70%. Some questions net recovery costs, so read the wording.

Is expected loss additive across a portfolio?

Yes. The portfolio expected loss is the sum of the individual expected losses, whatever the correlation. Unexpected loss does not add in this way.