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FRM Exam Part II · Credit Scoring and Retail Credit Risk Management

Retail Portfolio Risk: PD, LGD and Loss Forecasting

Updated 11 October 2026 · Fact-checked

Retail portfolio risk measurement estimates losses on large pools of small loans. You estimate PD, LGD and EAD for each homogeneous pool, then compute expected loss as PD × LGD × EAD. Roll rates and vintage curves forecast how delinquent balances and new cohorts will turn into defaults and losses over time.

Understand Retail Portfolio Risk Measurement: PD, LGD and Loss Forecasting

A retail portfolio holds thousands or millions of small loans: cards, auto loans, mortgages, personal loans. You cannot rate each borrower like a corporate. So banks group loans into pools with similar risk, based on score band, product, delinquency status or origination date. Risk is then measured on the pool.

Three parameters drive loss. PD is the probability that a loan defaults over a horizon, usually one year. LGD is the share of exposure lost after default, net of recoveries and costs. EAD is the exposure at default. Expected loss (EL) is PD × LGD × EAD. EL is the average loss and is covered by pricing and provisions. Unexpected loss (UL) is the variability around EL. Capital is held against it.

Retail pools are granular, so idiosyncratic risk diversifies away. What is left is systematic risk, such as unemployment or house prices. That is why Basel IRB uses a supervisory formula with an asset correlation for each retail class instead of a full portfolio model. Basel IRB retail classes are residential mortgages, qualifying revolving retail exposures and other retail. Retail PD, LGD and EAD are all estimated by the bank, with no foundation approach. Retail risk is assessed at pool level, and default under Basel is often defined at the facility level, with 90 days past due as the usual trigger.

Roll rate analysis tracks the share of balances that move from one delinquency bucket to the next in a period, for example current to 30 days, 30 to 60, and 60 to 90. Multiplying the roll rates along the chain gives the share of current accounts that eventually reach default or charge-off. It is a short-term forecasting tool.

Vintage analysis groups loans by origination period, such as the 2023 Q1 cohort. You plot cumulative default or loss rate against loan age for each vintage. Comparing curves shows whether newer vintages are worse than older ones, and older vintages give a template to project the losses of young ones. It separates seasoning effects from underwriting quality and from the macro environment.

Key formulas to remember

Expected loss
EL = PD × LGD × EAD
Average loss over the horizon. Express PD and LGD as decimals. EL rate = PD × LGD.
LGD from recovery
LGD = 1 − Recovery rate
Recovery must be net of collection costs and discounted to default date for economic LGD.
Unexpected loss (standard deviation form)
UL = EAD × √(PD × σLGD² + LGD² × PD × (1 − PD)), with LGD treated as a fixed mean and independent of default
If LGD is fixed, UL = EAD × LGD × √(PD × (1 − PD)). Applies to a single exposure.
Roll rate chain
P(current → default) ≈ r(C→30) × r(30→60) × r(60→90) × r(90→charge-off)
Assumes the rates are stable and each step is a one-period transition. Rates are measured on balances or accounts.
Cumulative default rate for a vintage
Cumulative default rate at age t = defaults to age t ÷ original number of loans (or balance)
Use the original cohort size as denominator, not surviving loans.
Capital requirement (IRB)
Capital = EAD × (Unexpected-loss capital rate K)
K = LGD × [conditional PD at 99.9% − PD], with a supervisory correlation. Expected loss is covered separately by provisions.

How to solve Retail Portfolio Risk Measurement: PD, LGD and Loss Forecasting questions

Use this order for any retail loss question, whether it gives parameters, a delinquency table or vintage data.

  1. 1Identify the pool and the horizon. Check whether data are on accounts or on balances.
  2. 2Decide which tool the question wants: EL formula, roll rate chain, or vintage projection.
  3. 3Write down PD, LGD and EAD. Convert percentages to decimals. Convert recovery into LGD if needed.
  4. 4For roll rates, list each bucket transition rate and multiply along the path to default or charge-off.
  5. 5For vintages, align curves by loan age, not calendar date, and compare each cohort at the same age.
  6. 6Compute the number, then state the unit: rupees, USD, or a loss rate in percent.
  7. 7Interpret: compare EL with provisions or pricing, and UL with capital. Note any assumption such as stable roll rates.
  8. 8Check the answer for size. A retail EL rate above PD signals an error, because LGD is at most 100%.

Quickest way: Multiply, then sanity-check

When to use it: Use when the question gives the three parameters or a chain of roll rates and has four numeric options.

  1. Convert everything to decimals.
  2. Multiply PD × LGD first to get the loss rate, then multiply by EAD.
  3. For roll rates, multiply the chain and apply it to the starting balance.
  4. Eliminate options that exceed EAD or that ignore LGD.
  5. If the question says recovery, subtract it from 1 before multiplying.

Common mistakes in Retail Portfolio Risk Measurement: PD, LGD and Loss Forecasting

  • Using recovery rate in place of LGD in the EL formula.

    The question gives a recovery percentage and it looks like the number to use.

    Fix: Compute LGD = 1 − recovery first. A 35% recovery means a 65% LGD.

  • Multiplying only some roll rates, or using the wrong starting bucket.

    Students rush and skip a transition, or start from 30 days past due when the question starts from current.

    Fix: Write the chain of buckets first and match each rate to a transition. Start where the question's balance sits.

  • Reading vintage curves by calendar date instead of loan age.

    Charts often show time on the axis and students compare cohorts at different ages.

    Fix: Compare cohorts at the same months on book. A young vintage with a higher loss at month 12 than an older one at month 12 is truly worse.

  • Treating expected loss as the capital requirement.

    Both are loss measures, so they blur together.

    Fix: EL is covered by pricing and provisions. Capital covers UL, the extra loss in a bad tail.

  • Dividing vintage defaults by surviving loans rather than original loans.

    Pool size shrinks as loans pay off or default, so the current count feels natural.

    Fix: For a cumulative rate, use the original cohort as denominator. Surviving-loan denominators give a hazard-type rate instead.

  • Assuming retail IRB capital depends on a bank's portfolio-specific correlation.

    Corporate credit models use estimated correlations.

    Fix: In Basel IRB, retail correlations come from supervisory formulas by retail class. Banks estimate PD, LGD and EAD only.

Worked examples

Example 1

A bank has a pool of credit card balances of USD 80 million. The one-year PD is 4%, LGD is 70% and the pool's EAD equals the balance. Compute the expected loss, and the unexpected loss treating LGD as fixed.

Show the solution
  1. EL = PD × LGD × EAD = 0.04 × 0.70 × 80,000,000.
  2. 0.04 × 0.70 = 0.028. 0.028 × 80,000,000 = USD 2,240,000.
  3. UL with fixed LGD = EAD × LGD × √(PD × (1 − PD)).
  4. PD × (1 − PD) = 0.04 × 0.96 = 0.0384. √0.0384 ≈ 0.19596.
  5. UL = 80,000,000 × 0.70 × 0.19596 = 56,000,000 × 0.19596 ≈ USD 10,974,000.

Answer: EL is USD 2.24 million. UL is about USD 10.97 million. This UL is the standard deviation for a single exposure. In a granular pool the diversified UL is much smaller, so it overstates pool risk.

Example 2

A lender has ₹200 crore of current auto loans. Monthly roll rates are: current to 30 days 3%, 30 to 60 days 40%, 60 to 90 days 60%, 90 days to charge-off 80%. Assume the rates are stable and each step is a one-period transition. How much of the current balance is expected to be charged off along this path?

Show the solution
  1. Write the chain: current → 30 → 60 → 90 → charge-off.
  2. Multiply the rates: 0.03 × 0.40 × 0.60 × 0.80.
  3. 0.03 × 0.40 = 0.012.
  4. 0.012 × 0.60 = 0.0072.
  5. 0.0072 × 0.80 = 0.00576.
  6. Apply to the balance: 0.00576 × ₹200 crore = ₹1.152 crore.

Answer: About 0.576% of current balances, or ₹1.152 crore, is expected to be charged off along this path. This ignores cures, where delinquent accounts return to current, so it is a rough estimate.

Exam tips

  • Read whether the question gives recovery or LGD. This swap is the most common trap.
  • For vintage questions, find the same loan age on each curve before ranking cohorts.
  • Know that Basel IRB retail has no foundation approach and that PD, LGD and EAD are bank estimates, with supervisory correlations.
  • Separate EL from UL in your answer. EL goes to provisions and pricing, UL to capital.
  • If a roll rate question mentions cures, say the simple chain overstates losses.

Practice questions from Credit Scoring and Retail Credit Risk Management

Retail Portfolio Risk Measurement: PD, LGD and Loss Forecasting in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Retail Portfolio Risk Measurement: PD, LGD and Loss Forecasting: frequently asked questions

What is vintage analysis in retail credit?

Vintage analysis groups loans by origination period and tracks each group's cumulative default or loss against loan age. You use it to compare underwriting quality across cohorts and to project losses on young vintages from older ones.

What is roll rate analysis in delinquency?

It measures the share of balances or accounts that move from one delinquency bucket to the next, such as 30 to 60 days past due. Multiplying the rates along the chain estimates how many current accounts end in default or charge-off.

How do I estimate expected loss for retail loans?

Group loans into homogeneous pools, estimate PD, LGD and EAD for each, and multiply them. Sum the pool results for the portfolio. Use through-the-cycle or stressed inputs where the question or regulator asks for it.

How are retail exposures treated under Basel IRB?

A bank using IRB estimates its own PD, LGD and EAD for retail pools. The risk-weight function uses supervisory correlations set for each retail class, such as mortgages, qualifying revolving and other retail. There is no foundation approach for retail.