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FRM Exam Part II · Portfolio Credit Risk

Industry Credit Portfolio Models: CreditMetrics, CreditRisk+, KMV

Updated 11 October 2026 · Fact-checked

Industry credit portfolio models estimate a loan portfolio's loss distribution and credit VaR. CreditMetrics uses rating migration and asset-value correlation. KMV uses Merton-based distance to default and expected default frequency. CreditRisk+ uses Poisson defaults with gamma-distributed rates. CreditPortfolioView links default rates to macroeconomic factors.

Understand Industry Credit Portfolio Models

A bank holds many loans. It needs one number for how much it could lose on the whole portfolio at a high confidence level. Industry credit portfolio models produce that number. All four models give a loss distribution, from which you read expected loss, unexpected loss and credit VaR. They differ in what drives losses and what data you feed in.

CreditMetrics (J.P. Morgan) is a mark-to-market model. It starts from each borrower's rating and a transition matrix. Over the horizon, usually one year, a borrower can stay, upgrade, downgrade or default. Each outcome gives a revalued loan, using forward credit spreads, or a recovery value in default. Correlation comes from equity or asset returns, typically through a multi-factor model, with a Merton-style link between asset value and rating thresholds. Joint outcomes are usually found by Monte Carlo simulation.

KMV Portfolio Manager is also structural. It uses the Merton idea: default occurs when asset value falls below the default point. The firm's distance to default is converted into an expected default frequency (EDF) using KMV's own empirical default database, not a normal-distribution table. EDFs are driven by equity prices, so they move continuously and quickly. Asset correlations come from a factor model. Like CreditMetrics, it simulates the portfolio, and it can include migration of EDF.

CreditRisk+ (Credit Suisse First Boston) is an actuarial, default-only model. It ignores rating migration and asset values. Each obligor has a small default probability, and the number of defaults is treated as Poisson. Default rates are made random, usually gamma distributed, using sector factors, which creates correlation and fat tails. Exposures are grouped into bands. The loss distribution comes out analytically through a recursion, so no simulation is needed.

CreditPortfolioView (McKinsey) is a macroeconomic, econometric model. Default rates by country and industry are linked to macro variables such as GDP growth and unemployment through a logit function. Shocks to those variables are simulated. Default rates are higher in recessions, so correlation comes from the shared economic cycle. It is explicitly conditional on the economy. CreditMetrics, which uses average through-the-cycle transition matrices, and CreditRisk+ are largely unconditional. KMV EDFs are point-in-time, because they respond to equity prices, but they are not built from macro variables.

Key formulas to remember

Expected loss
EL = PD × LGD × EAD
Common to all models. The portfolio EL is the sum of individual ELs.
Unexpected loss and credit VaR
Credit VaR = loss at chosen percentile − expected loss
Check whether the question defines VaR relative to expected loss or as the total loss quantile.
Poisson probability of n defaults
P(n) = e^(−μ) × μ^n ÷ n!
CreditRisk+ building block. μ is the expected number of defaults. Mean = variance = μ.
Merton distance to default (simplified)
DD = (asset value − default point) ÷ (asset value × asset volatility)
KMV maps DD to EDF empirically, not through the normal distribution.
CreditPortfolioView default rate
p = 1 ÷ (1 + e^(y)), where y is the macro health index
Here y is a health index built from macro variables. A lower y (a weak economy) gives a higher default rate p, and a higher y (a strong economy) gives a lower p. The logit keeps p between 0 and 1.

How to solve Industry Credit Portfolio Models questions

Most exam questions ask you to identify a model from its features, compare models, or do a small calculation inside one model.

  1. 1Identify the risk driver the question mentions: ratings and transitions, equity-based asset value, Poisson or gamma default rates, or macroeconomic variables.
  2. 2Match it to the model: ratings and migration to CreditMetrics, asset value and EDF to KMV, Poisson to CreditRisk+, macro factors to CreditPortfolioView.
  3. 3Decide the loss definition: mark-to-market (migration counts) or default-only (only default losses count).
  4. 4Note where correlation comes from: asset or equity factors, gamma sector factors, or the macro cycle.
  5. 5Note the solution method: Monte Carlo simulation or analytical recursion.
  6. 6If a calculation is needed, compute expected loss first, then apply the model's formula such as Poisson probabilities.
  7. 7Check the answer against the options: is it in the correct unit, and is credit VaR measured from the mean or from zero?

Quickest way: Keyword-to-model matching

When to use it: For descriptive comparison questions where you have under a minute.

  1. Rating transition matrix or forward spreads: CreditMetrics.
  2. Distance to default, EDF or equity volatility: KMV.
  3. Poisson, gamma or exposure bands: CreditRisk+.
  4. GDP, unemployment or the business cycle: CreditPortfolioView.
  5. CreditRisk+ is the default-only (actuarial) model. CreditMetrics is mark-to-market with rating migration. KMV can include EDF migration. CreditPortfolioView models default rates conditional on the macro state.
  6. Analytical solution points to CreditRisk+. Simulation points to the other three.

Common mistakes in Industry Credit Portfolio Models

  • Saying CreditRisk+ includes rating migration.

    Students assume every portfolio model revalues loans after downgrades.

    Fix: CreditRisk+ is a default-only model. Only default or no default matters, and losses are the exposure net of recovery.

  • Saying KMV uses the normal distribution to turn distance to default into default probability.

    The textbook Merton model does so, and the two get blended.

    Fix: KMV maps distance to default to EDF using its empirical default history. The pure Merton model uses N(−d2).

  • Treating CreditRisk+ default correlation as coming from asset returns.

    CreditMetrics and KMV use asset correlations, so students assume all do.

    Fix: In CreditRisk+, correlation arises because default rates are random and share common sector factors, usually gamma distributed.

  • Calling CreditPortfolioView a structural model.

    It sounds like a firm-level model because it is built on ratings and segments.

    Fix: It is an econometric, macro-conditional model. Default rates are driven by macroeconomic variables, so they rise in recessions.

  • Claiming the Poisson model allows only one default per obligor and so is exact.

    Poisson allows multiple events in principle.

    Fix: CreditRisk+ uses Poisson as an approximation when default probabilities are small. It can in principle count more than one default per obligor, which is negligible for small PDs.

  • Forgetting to subtract expected loss when asked for unexpected loss.

    Students read the percentile off the distribution and stop.

    Fix: Unexpected loss at a percentile is that percentile loss minus expected loss, unless the question defines credit VaR otherwise.

Worked examples

Example 1

A CreditRisk+ portfolio has 200 obligors, each with a one-year default probability of 1%. Treating the number of defaults as Poisson, what is the probability of exactly 2 defaults? Use e^(−2) = 0.1353.

Show the solution
  1. Expected number of defaults μ = 200 × 0.01 = 2.
  2. P(2) = e^(−2) × 2² ÷ 2!
  3. = 0.1353 × 4 ÷ 2
  4. = 0.1353 × 2 = 0.2706.

Answer: About 27.1%.

Example 2

A risk manager has a portfolio loss distribution from simulation. Expected loss is $12 million and the 99.9th percentile loss is $95 million. The model values each loan after possible rating upgrades and downgrades using forward spreads. Which model is described, and what is the credit VaR measured from the mean?

Show the solution
  1. Rating changes and revaluation with forward spreads is the mark-to-market feature of CreditMetrics.
  2. Credit VaR from the mean is the percentile loss minus expected loss.
  3. $95 million − $12 million = $83 million.

Answer: CreditMetrics, with credit VaR (unexpected loss) of $83 million at 99.9%.

Exam tips

  • Exams often list four features and ask which belongs to which model. Learn the keyword for each model cold.
  • Expect a question on what drives correlation in each model. The answers are asset factors, gamma sector factors, and macro variables.
  • Know which models are default-only and which are mark-to-market.
  • Watch the wording: EDF is KMV, transition matrix is CreditMetrics, Poisson is CreditRisk+.
  • For Poisson questions, compute μ first, then substitute carefully.

Practice questions from Portfolio Credit Risk

Industry Credit Portfolio Models: frequently asked questions

What is the main difference between CreditMetrics and CreditRisk+?

CreditMetrics is a mark-to-market model using rating migration, with correlation from asset returns and simulation. CreditRisk+ is a default-only actuarial model using Poisson defaults with random gamma default rates and an analytical solution.

How does KMV Portfolio Manager differ from CreditMetrics?

Both are structural and use asset correlations. KMV derives default probability as an EDF from distance to default using equity market data and its own default database. CreditMetrics relies on agency-style ratings and a transition matrix.

Why does CreditRisk+ use a Poisson distribution?

For many obligors with small default probabilities, the count of defaults is well approximated by a Poisson distribution. It needs only the mean default rate, and making that rate random adds correlation and fat tails.

What makes CreditPortfolioView different?

It links default rates directly to macroeconomic variables, so the loss distribution depends on the state of the economy. CreditMetrics, with average through-the-cycle transition matrices, and CreditRisk+ are largely unconditional on the cycle. KMV EDFs are point-in-time because they move with equity prices, but they are not built from macro variables.