FRM Exam Part II · Credit Value at Risk

CreditMetrics Approach to Credit VaR Explained

Updated 11 October 2026 · Fact-checked

CreditMetrics is a portfolio credit risk model. It uses a rating transition matrix to give the probability that a bond ends the horizon in each rating or in default. It revalues the bond in each state, builds a value distribution, and reads credit VaR as expected value minus the percentile value.

Understand CreditMetrics Approach

A bond's value changes for credit reasons even without default. If its rating is downgraded, its credit spread widens and its price falls. CreditMetrics measures this. It is a mark-to-market model, so it captures both migration and default.

The model works over a horizon, usually one year. You start with the bond's current rating. The transition matrix gives the probability of ending the year in each rating, including default. For each end rating you revalue the bond. You discount the remaining cash flows using the forward zero curve for that rating. In default you use the recovery rate times face value.

This gives a discrete distribution of bond values with one probability per rating state. The expected value is the probability-weighted average. Credit VaR at a confidence level is the expected value minus the value at the chosen percentile. This is a loss relative to the mean, not relative to the current value.

For a portfolio you need joint moves. CreditMetrics links each obligor to a latent asset return, assumed normal. Rating thresholds are set from the transition probabilities. Asset-value correlations, usually estimated from equity returns and factor models, set the joint migration probabilities. Because the portfolio distribution has no simple form, it is usually found by Monte Carlo simulation.

CreditMetrics differs from CreditRisk+. CreditMetrics is a mark-to-market, migration-based model. CreditRisk+ is an actuarial, default-only model where default rates are random and the loss distribution is found analytically.

Key formulas to remember

Expected bond value: E(V) = Σ pᵢ × Vᵢ; pᵢ is the transition probability to state i, including default. Vᵢ is the revalued bond in that state.
Value in default: V_default = Recovery rate × Face value; Recovery is often stated as a percentage of face value. Check whether the question includes accrued coupon.
Revalued bond if it survives: Vᵢ = Σ CFₜ ÷ (1 + fᵢ,ₜ)ᵗ; Use the forward zero rates for the end rating i, for the remaining cash flows, including the coupon paid at the horizon.
Credit VaR (relative to mean): Credit VaR = E(V) − V at the (1 − c) percentile; Measured from the expected value. Some questions ask for loss from the current value, so read the wording.
Asset return thresholds: Z_k = N⁻¹(cumulative probability from default up to and including state k); Order the states from worst (default) upward. The default threshold is Z_default = N⁻¹(PD). The threshold for the next state up is N⁻¹(PD + p of that state), and so on. Each threshold is the standard normal quantile of the running total of transition probabilities.
Standard deviation of value: σ = √[Σ pᵢ × (Vᵢ − E(V))²]; Used for single-bond volatility and sometimes for approximating VaR.

How to solve CreditMetrics Approach questions

Follow these steps for any CreditMetrics question, single bond or portfolio.

1Identify the starting rating, horizon and confidence level.
2Read the row of the transition matrix for the starting rating. Check that the probabilities sum to 100%.
3Revalue the bond in each end rating using that rating's forward curve. Use the recovery value for default.
4Multiply each value by its probability and sum to get the expected value.
5Sort the states from worst to best value and add probabilities from the worst until you reach the tail of 1 − c.
6Credit VaR = expected value minus the percentile value. For a discrete distribution, apply the interpolation or rule the question states.
7For a portfolio, state the correlation input. Joint probabilities come from the bivariate normal on asset returns. Add the position values in each joint state and then repeat the percentile step.
8Interpret the result. Say what loss is not exceeded with the given confidence over the horizon.

Quickest way: Cumulative-tail shortcut for single-bond credit VaR

When to use it: Use it when the question gives the state values and probabilities for a single bond and asks for credit VaR at a stated confidence.

List the values from lowest to highest next to their probabilities.
Add probabilities from the bottom until the total reaches or passes the tail (for example 1% for 99%).
Take the value of the state where the cumulative probability first reaches the tail.
Compute E(V) quickly as the weighted sum. Mostly one or two states differ much from the par value.
Subtract: E(V) minus the tail value. Check that the sign and the reference point match the question.

Common mistakes in CreditMetrics Approach

Measuring credit VaR from the current bond value when the question defines it from the mean.
Market VaR is often shown against current value, so students carry the habit over.
Fix: Read the definition in the question. CreditMetrics classically uses the expected value as the reference.
Discounting with one curve for all states.
It is simpler to reuse the original spread.
Fix: Revalue with the forward curve of the end rating. The change in spread is what drives the value change.
Leaving out default or using face value instead of recovery.
Default has a tiny probability, so it feels ignorable.
Fix: Include default with recovery times face value. It often defines the far tail.
Confusing CreditMetrics with CreditRisk+.
Both give credit loss distributions.
Fix: CreditMetrics is mark-to-market with migration and asset correlations. CreditRisk+ is actuarial and default-only with random default rates.
Thinking that portfolio VaR is the sum of the single-bond VaRs.
Adding is easier than the joint distribution.
Fix: The sum ignores diversification. Imperfect asset correlation makes portfolio VaR lower than the sum.
Using a percentile that is not in the table without comment.
The discrete distribution has jumps.
Fix: Use the rule given in the question. If none is given, choose the state where the cumulative tail probability first reaches the tail.

Worked examples

Example 1

A one-year horizon bond has these end states: A with probability 90%, value 108; BBB with probability 8.5%, value 104; Default with probability 1.5%, value 50. Compute the expected value, and the credit VaR at 98% confidence measured from the expected value.

Show the solution

Expected value = 0.90 × 108 + 0.085 × 104 + 0.015 × 50.
= 97.2 + 8.84 + 0.75 = 106.79.
The tail is 2%. Starting from the worst state, default has a cumulative probability of 1.5%, which is below the tail.
Adding BBB gives a cumulative probability of 10%, which passes the tail. The 2% percentile falls in the BBB state.
The percentile value is 104.
Credit VaR = 106.79 − 104 = 2.79.

Answer: Expected value is 106.79. Credit VaR at 98% is 2.79.

Example 2

A bond has end states: A with probability 95%, value 100; BB with probability 4%, value 90; Default with probability 1%, value 40. Find the expected value, and the credit VaR at 99% confidence measured from the expected value.

Show the solution

Expected value = 0.95 × 100 + 0.04 × 90 + 0.01 × 40.
= 95 + 3.6 + 0.4 = 99.0.
The tail is 1%. Default has a cumulative probability of 1%, which equals the tail.
The percentile value is 40.
Credit VaR = 99.0 − 40 = 59.0.

Answer: Expected value is 99.0. Credit VaR at 99% is 59.0.

Exam tips

Check whether the question measures VaR from the expected value or from the current value. The answers differ.
Questions often test the concept, not the arithmetic: migration, mark-to-market, asset correlation and Monte Carlo.
Know the contrast with CreditRisk+: migration vs default-only, and simulation vs analytical loss distribution.
Remember that correlation drives portfolio tails. Higher asset correlation reduces diversification, so it generally fattens the portfolio loss tail and raises credit VaR.
Write down the sorted values and cumulative probabilities before computing. It avoids picking the wrong state.

Practice questions from Credit Value at Risk

CreditMetrics Approach: frequently asked questions

What is the main difference between CreditMetrics and CreditRisk+?

CreditMetrics is a mark-to-market model. It values bonds after rating migration and default. CreditRisk+ is an actuarial model that looks at default only and treats default rates as random.

How are correlations handled in CreditMetrics?

Each obligor has a latent asset return that is normally distributed. Transition probabilities set the rating thresholds. Asset correlations then give joint migration probabilities across obligors.

How do I use a transition matrix for credit VaR?

Take the row for the starting rating. Each cell is the probability of ending in a given rating. Revalue the bond in each state and combine the values with those probabilities to get the distribution.

Why is credit VaR from CreditMetrics often measured from the mean?

The model produces a distribution of future values. Expected loss is already priced and provisioned, so the unexpected part is measured as the gap from the mean to the percentile.