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Risk Management in Banking and Insurance · Credit Risk Management

PD, LGD and EAD: Expected Loss and Credit VaR

Updated 11 October 2026 · Fact-checked

PD is the chance a borrower defaults in a period. LGD is the share of exposure lost on default. EAD is the amount owed at default. Expected loss = PD × LGD × EAD. Unexpected loss is the variability of loss around this mean, and credit VaR models estimate it.

Understand Measurement of Credit Risk: PD, LGD and EAD

Credit risk is the risk that a borrower fails to pay as agreed. To measure it, a bank breaks it into three parts. Each part answers one question.

Probability of default (PD) asks: how likely is the borrower to default over a set horizon, usually one year? It comes from internal rating grades, historical default rates or market-based models. A higher-rated borrower has a lower PD.

Exposure at default (EAD) asks: how much will the bank be owed when default happens? For a term loan it is the outstanding amount. For a cash credit or overdraft limit, the borrower may draw more as trouble grows, so EAD = drawn amount + a share of the undrawn limit. That share is called the credit conversion factor.

Loss given default (LGD) asks: what fraction of EAD is lost after recoveries from collateral, guarantees and the workout process? LGD = 1 − recovery rate. Secured loans usually have lower LGD than unsecured ones.

Expected loss (EL) is the average loss you expect: EL = PD × LGD × EAD. Banks price it into interest spreads and cover it through provisions. Unexpected loss (UL) is the standard deviation of credit loss around EL. It is the surprise part, and economic capital is held against it. Credit VaR is the loss at a chosen confidence level (say 99.9%) minus EL, so it is a measure of unexpected loss.

Three well-known portfolio models estimate credit VaR. CreditMetrics is based on rating migration: it values the portfolio under each possible rating change or default, using transition probabilities and correlations. KMV (Moody's KMV) treats the firm's equity as a call option on its assets and derives an expected default frequency from asset value, asset volatility and the debt level (distance to default). CreditRisk+ is an actuarial model: it treats defaults as rare events following a Poisson distribution and models only default, not migration.

Key rules to remember

Expected loss
EL = PD × LGD × EAD
Use PD and LGD as decimals. EL is in rupees. All three must refer to the same horizon.
Loss given default
LGD = 1 − Recovery rate
Recovery rate is net of workout costs if the question says so.
Exposure at default
EAD = Drawn amount + CCF × Undrawn commitment
CCF is the credit conversion factor, given in the question.
Portfolio expected loss
EL(portfolio) = Σ EL of each exposure
Expected losses add up simply, whatever the correlation.
Unexpected loss, single exposure with fixed LGD and EAD
UL = EAD × LGD × √[PD × (1 − PD)]
Assumes LGD is certain and default is a yes/no event. Sound only under this simplification.
Credit VaR
Credit VaR = Loss at chosen confidence level − EL
Some texts define credit VaR as the loss quantile itself. Follow the definition in the question.
Net loss rate or EL rate
EL rate = EL ÷ EAD = PD × LGD
Useful to compare pricing across loans.

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

Use this order for any numerical on PD, LGD, EAD and loss measures.

  1. 1List the data given: PD, LGD or recovery rate, drawn amount, limit, CCF, horizon.
  2. 2Find EAD first. If there is an undrawn limit, add CCF × undrawn amount to the drawn amount.
  3. 3Find LGD. If recovery or collateral is given, LGD = 1 − recovery rate. If collateral value is given in rupees, loss = EAD − net recovery, then divide by EAD.
  4. 4Check that PD is in decimals and for the same period as the question asks.
  5. 5Compute EL = PD × LGD × EAD for each exposure.
  6. 6For a portfolio, add the ELs. Do not add ULs unless the question says correlation is 1 or asks for simple addition.
  7. 7If asked for UL, use the formula given or the standard form, and show the substitution.
  8. 8State the result in rupees and add one line of meaning, such as the provision or pricing implication.

Quickest way: EAD, then LGD, then multiply

When to use it: For 2-mark MCQs and for the first part of a long numerical where only EL is needed.

  1. Write EAD, LGD and PD as three numbers on one line.
  2. Multiply PD × LGD first to get the loss rate, for example 2% × 40% = 0.8%.
  3. Multiply the loss rate by EAD.
  4. Scan the options for common traps: EL computed on the limit instead of EAD, or PD used as a percentage number.

Common mistakes in Measurement of Credit Risk: PD, LGD and EAD

  • Using the sanctioned limit as EAD instead of drawn amount plus CCF × undrawn.

    Students treat the whole limit as certain to be drawn, or ignore the undrawn part.

    Fix: Always compute EAD = drawn + CCF × undrawn. Use the CCF given in the question.

  • Taking LGD as the recovery rate.

    The two numbers are complements and are easy to swap when a question states only recovery.

    Fix: Write LGD = 1 − recovery before any multiplication.

  • Confusing expected loss with unexpected loss.

    Both are called 'loss' and both appear in capital discussions.

    Fix: Remember: EL is the mean, covered by pricing and provisions. UL is the variability, covered by capital.

  • Adding unexpected losses of loans to get the portfolio UL.

    Students copy the rule that works for EL.

    Fix: Only EL is additive. Portfolio UL depends on correlation and is generally less than the simple sum when correlation is below 1.

  • Mixing up the three models, for example saying CreditRisk+ uses rating migration.

    The names sound alike and the notes are brief.

    Fix: Link each to one key idea: CreditMetrics = migration, KMV = asset value option, CreditRisk+ = Poisson default only.

  • Entering PD as 2 instead of 0.02.

    Rushing under time pressure.

    Fix: Convert percentages to decimals as the first step and check that EL is smaller than EAD.

Worked examples

Example 1

A bank has granted a cash credit limit of ₹10,00,000 to a borrower, of which ₹6,00,000 is drawn. The credit conversion factor for the undrawn part is 50%. The one-year PD is 3%. Collateral is expected to yield a net recovery of 60% of EAD on default. Calculate EAD, LGD and the expected loss.

Show the solution
  1. Undrawn amount = ₹10,00,000 − ₹6,00,000 = ₹4,00,000.
  2. EAD = ₹6,00,000 + 50% × ₹4,00,000 = ₹6,00,000 + ₹2,00,000 = ₹8,00,000.
  3. LGD = 1 − 0.60 = 0.40, or 40%.
  4. EL = PD × LGD × EAD = 0.03 × 0.40 × ₹8,00,000.
  5. 0.03 × 0.40 = 0.012, and 0.012 × ₹8,00,000 = ₹9,600.

Answer: EAD = ₹8,00,000; LGD = 40%; expected one-year loss = ₹9,600. The bank should cover this through pricing and provisioning.

Example 2

A bank holds two unrelated term loans. Loan A: EAD ₹50,00,000, PD 2%, LGD 45%. Loan B: EAD ₹30,00,000, PD 5%, LGD 60%. Calculate the expected loss of each loan and of the portfolio, and the unexpected loss of Loan A using UL = EAD × LGD × √[PD × (1 − PD)].

Show the solution
  1. EL of A = 0.02 × 0.45 × ₹50,00,000 = 0.009 × ₹50,00,000 = ₹45,000.
  2. EL of B = 0.05 × 0.60 × ₹30,00,000 = 0.03 × ₹30,00,000 = ₹90,000.
  3. Portfolio EL = ₹45,000 + ₹90,000 = ₹1,35,000.
  4. For A: EAD × LGD = ₹50,00,000 × 0.45 = ₹22,50,000.
  5. PD × (1 − PD) = 0.02 × 0.98 = 0.0196. Its square root = 0.14.
  6. UL of A = ₹22,50,000 × 0.14 = ₹3,15,000.

Answer: EL of A = ₹45,000; EL of B = ₹90,000; portfolio EL = ₹1,35,000. UL of Loan A = ₹3,15,000, about seven times its EL, which shows why capital is held against unexpected loss and not only provisions against expected loss.

Exam tips

  • In MCQs, the usual traps are using the limit as EAD, taking recovery as LGD and mixing up the three credit VaR models. Check each before marking.
  • Write the formula, then the substitution, then the answer in rupees. Marks follow the working even if the final figure slips.
  • For descriptive questions on models, give one line each on the core idea, the inputs and the main limitation, such as CreditRisk+ ignoring rating migration.
  • Always say which part of loss is met by provisions and pricing (EL) and which by capital (UL).
  • If the question does not give a formula for UL, state the one you are using and its assumption.

Practice questions from Credit Risk Management

Measurement of Credit Risk: 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.

Measurement of Credit Risk: PD, LGD and EAD: frequently asked questions

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

Multiply the three: EL = PD × LGD × EAD. Convert PD and LGD to decimals first. Compute EAD as drawn amount plus CCF times the undrawn limit if a limit is given.

What is the difference between expected loss and unexpected loss?

Expected loss is the average credit loss over a period and is covered by pricing and provisions. Unexpected loss is the volatility of loss around that average. Banks hold capital against it.

What is the difference between CreditMetrics, KMV and CreditRisk+?

CreditMetrics values a portfolio under rating migrations and defaults. KMV derives default probability from the firm's asset value and volatility using an option view of equity. CreditRisk+ uses a Poisson-based actuarial approach and models default only.

Is credit VaR the same as unexpected loss?

They are closely linked. Credit VaR is the loss at a chosen confidence level, and unexpected loss is often measured as that figure minus expected loss. Check the definition given in the question.