FRM Exam Part II · Credit Risk

Credit Portfolio Risk and Credit VaR Explained

Updated 11 October 2026 · Fact-checked

Credit portfolio risk is the risk of loss from defaults across a whole loan book, driven by default correlation and concentration. Credit VaR is the loss at a chosen confidence level minus expected loss. Solve it by finding the loss quantile, subtracting expected loss, and reading the result as unexpected loss.

Understand Credit Portfolio Risk and Credit VaR

A single loan has a probability of default (PD), a loss given default (LGD) and an exposure at default (EAD). Expected loss is PD × LGD × EAD. You can price and provision for it. The real danger is the loss that is worse than expected.

In a portfolio, losses depend on how defaults move together. If defaults were independent, a large book would have a very stable loss. In practice borrowers share economic conditions, so defaults cluster. Default correlation is what fattens the right tail of the loss distribution. Higher correlation means the same expected loss but a much higher tail loss. Concentration (by name, sector or region) works the same way.

Credit VaR is the loss quantile at a confidence level (say 99.9%) over a horizon (usually one year), measured relative to expected loss. So Credit VaR = quantile loss − expected loss. This is unexpected loss at that confidence and is the basis for economic capital. The loss distribution is skewed with a long right tail, so it is not normal.

CreditMetrics is a mark-to-market model. It uses a rating transition matrix to revalue each bond at the horizon in every rating state, including default, and uses an equity-based asset correlation to link borrowers. It captures migration and spread changes, usually via simulation. CreditRisk+ is an actuarial default-only model. It treats the number of defaults as Poisson, with default rates that vary with sector factors. It gives a closed-form loss distribution and needs only PDs, exposures and recoveries.

The Vasicek single-factor model underpins Basel IRB capital. Each borrower's asset value has a common systematic factor and an idiosyncratic factor. For a large homogeneous portfolio, the idiosyncratic risk diversifies away. The default rate then depends only on the systematic factor, which gives a closed-form worst-case default rate.

Key formulas to remember

Expected loss: EL = PD × LGD × EAD; Per exposure. Portfolio EL is the sum of individual ELs, with no correlation effect.
Credit VaR (unexpected loss at confidence level): Credit VaR = Loss quantile at α − Expected loss; Some texts quote the quantile itself as the VaR. Read the question for which definition applies.
Two-asset default correlation from joint default: ρD = (p12 − p1·p2) ÷ √[p1(1 − p1) × p2(1 − p2)]; p12 is the joint default probability. Default correlations are usually small, even when asset correlations are high.
Vasicek worst-case default rate: WCDR = N[ (N⁻¹(PD) + √ρ × N⁻¹(α)) ÷ √(1 − ρ) ]; N is the standard normal CDF, ρ the asset correlation, α the confidence level. Conditional on the systematic factor at its (1 − α) tail. Large homogeneous portfolio assumed.
Vasicek loss at confidence level: Loss = EAD × LGD × WCDR; Subtract EL = EAD × LGD × PD to get unexpected loss. Basel IRB capital is of this form, with further adjustments.
Poisson default probability (CreditRisk+): P(n defaults) = e^(−μ) × μⁿ ÷ n!; μ is the expected number of defaults. Mean and variance both equal μ.
Portfolio loss variance (two exposures): σ² = σ1² + σ2² + 2ρ·σ1·σ2; Loss standard deviation rises with correlation. Used for unexpected loss.

How to solve Credit Portfolio Risk and Credit VaR questions

Use this order for most credit portfolio questions.

1Identify the model asked about: CreditMetrics (mark-to-market, migration), CreditRisk+ (default-only, Poisson) or Vasicek (single factor, large portfolio).
2List the inputs given: PD, LGD, EAD, correlation, confidence level and horizon.
3Compute expected loss first as PD × LGD × EAD, summed over exposures.
4Compute the loss at the required confidence level. For Vasicek, find the worst-case default rate with the formula. For simulation, take the percentile of the loss distribution.
5Subtract expected loss from that loss to get Credit VaR (unexpected loss), unless the question defines VaR as the quantile.
6Check the direction: higher correlation or concentration raises Credit VaR but leaves EL unchanged.
7State the interpretation: the loss that is exceeded with probability 1 − α over the horizon, and the capital it implies.

Quickest way: Vasicek WCDR shortcut

When to use it: Use when a question gives PD, asset correlation and a confidence level for a large homogeneous portfolio.

Get N⁻¹(PD) and N⁻¹(α) from the z-values given. Common: N⁻¹(0.999) = 3.09, N⁻¹(0.99) = 2.33.
Compute the numerator: N⁻¹(PD) + √ρ × N⁻¹(α).
Divide by √(1 − ρ).
Convert to a probability with N(·). That is the WCDR.
Multiply by LGD × EAD, then subtract PD × LGD × EAD for unexpected loss.
Sanity check: WCDR must exceed PD, and it rises as ρ rises.

Common mistakes in Credit Portfolio Risk and Credit VaR

Treating Credit VaR as the full loss quantile when the question asks for unexpected loss.
Market VaR is usually quoted as a quantile, so students carry the habit over.
Fix: Check the wording. If the question says relative to expected loss, subtract EL.
Assuming credit losses are normally distributed.
Parametric market VaR uses a normal distribution.
Fix: Remember the loss distribution is skewed with a fat right tail. Normal approximations understate the tail.
Confusing asset correlation with default correlation.
Both are called correlation, but default correlation is typically much lower than asset correlation.
Fix: Vasicek and CreditMetrics use asset correlation as input. The default correlation formula uses joint default probabilities.
Using N⁻¹(1 − α) instead of N⁻¹(α) in the Vasicek formula.
Sign confusion between the factor's tail and the confidence level.
Fix: The standard form uses +√ρ × N⁻¹(α) with α near 99.9%. A bad outcome gives a high WCDR.
Saying CreditRisk+ captures rating migration.
Both models are called industry credit models and get blurred.
Fix: CreditRisk+ is default-only and Poisson based. Migration and mark-to-market belong to CreditMetrics.
Thinking diversification lowers expected loss.
Diversification lowers risk, so students assume EL falls too.
Fix: EL is additive. Diversification lowers unexpected loss and Credit VaR only.

Worked examples

Example 1

A bank holds a large homogeneous loan portfolio with total EAD of USD 500 million, PD 2%, LGD 50% and asset correlation 0.20. Using the Vasicek model at 99.9% confidence, with N⁻¹(0.02) = −2.054, N⁻¹(0.999) = 3.090, and N(−0.39) ≈ 0.348... compute the worst-case default rate, Credit VaR relative to expected loss.

Show the solution

Compute √ρ = √0.20 = 0.4472 and √(1 − ρ) = √0.80 = 0.8944.
Numerator = −2.054 + 0.4472 × 3.090 = −2.054 + 1.382 = −0.672.
Divide: −0.672 ÷ 0.8944 = −0.751.
WCDR = N(−0.751) ≈ 0.226, or about 22.6%.
Loss at 99.9% = 500 × 0.50 × 0.226 = USD 56.5 million.
EL = 500 × 0.50 × 0.02 = USD 5 million.
Credit VaR = 56.5 − 5 = USD 51.5 million.

Answer: WCDR is about 22.6%. Loss at 99.9% is about USD 56.5 million. Credit VaR (unexpected loss) is about USD 51.5 million. The N(−0.39) hint in the problem is not used.

Example 2

Two borrowers each have a one-year PD of 4%. The joint default probability is 0.0016 + 0.0012 = 0.0028. What is the default correlation, and what does it imply?

Show the solution

p1 = p2 = 0.04, p12 = 0.0028.
Independent joint probability = 0.04 × 0.04 = 0.0016.
Covariance = 0.0028 − 0.0016 = 0.0012.
Variance of each default indicator = 0.04 × 0.96 = 0.0384.
Denominator = √(0.0384 × 0.0384) = 0.0384.
ρD = 0.0012 ÷ 0.0384 = 0.03125, about 3.1%.

Answer: Default correlation is about 3.1%. It is positive, so joint defaults are more likely than under independence (0.28% versus 0.16%), which raises the portfolio's tail loss. Expected loss is unchanged.

Exam tips

Know which model uses what: CreditMetrics uses transition matrices, asset correlation and revaluation. CreditRisk+ uses Poisson defaults and sector factors. Vasicek uses one systematic factor.
Expect conceptual questions on what raises Credit VaR: higher PD, LGD, correlation or concentration. Expected loss moves only with PD, LGD and EAD.
Do the arithmetic of the Vasicek formula slowly. Wrong order of operations is the most common lost mark.
Read whether the question asks for the loss quantile, unexpected loss, or economic capital. They are different numbers.
Remember that Vasicek assumes a large, homogeneous portfolio. A small or concentrated book breaks the diversification assumption.

Practice questions from Credit Risk

Credit Portfolio Risk and Credit VaR in other exams

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

Credit Portfolio Risk and Credit VaR: frequently asked questions

What is the difference between CreditMetrics and CreditRisk+?

CreditMetrics is a mark-to-market model. It values each exposure after possible rating changes or default and links borrowers through asset correlation. CreditRisk+ is a default-only actuarial model. It uses Poisson default counts with sector factors and gives a closed-form loss distribution.

How do I calculate credit VaR?

Find the portfolio loss at your confidence level, for example the 99.9th percentile of the loss distribution. Then subtract expected loss. The result is unexpected loss, which is the Credit VaR used for economic capital.

Why does default correlation matter so much?

It controls how often many borrowers default together. Expected loss stays the same, but higher correlation fattens the right tail. That raises the loss at high confidence levels and the capital needed.

What does the Vasicek single factor model assume?

Each borrower's asset value depends on one common systematic factor and an independent idiosyncratic factor, with the same PD and correlation across borrowers. In a very large portfolio, the idiosyncratic part diversifies away, so only the systematic factor drives the default rate.