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FRM Exam Part II · Credit Risk Management

Credit Portfolio Risk and Concentration for FRM Part II

Updated 11 October 2026 · Fact-checked

Credit portfolio risk is the risk of loss from defaults across a pool of loans, driven by PD, LGD, exposure size and default correlation. Concentration raises tail loss. To find credit VaR with Vasicek, compute the stressed PD with the normal CDF, then multiply by LGD and EAD and subtract expected loss for unexpected loss.

Understand Credit Portfolio Risk and Concentration

A single loan has expected loss (EL) = PD × LGD × EAD. A portfolio's expected loss is just the sum of the individual ELs. Correlation does not change it. What correlation changes is the spread of losses, and so the tail.

Default correlation is the tendency of borrowers to default together. It comes from shared drivers such as the economic cycle, sector shocks or a common region. If defaults were independent, a large portfolio would have a loss close to EL and tail risk would fade. With positive correlation, bad years bring many defaults at once, and the loss distribution is skewed with a fat right tail.

Diversification reduces risk that is specific to a borrower (idiosyncratic risk). It cannot remove systematic risk, the part driven by the common factor. Concentration risk arises when exposure is heavy to a single name, sector, country or collateral type. Name concentration means a few large exposures. Sector concentration means many exposures with high correlation. Both push up unexpected loss (UL) and economic capital.

The Vasicek single-factor model gives a clean formula. Each borrower's asset value is driven by one systematic factor and one idiosyncratic factor, with asset correlation ρ. A borrower defaults when its asset value falls below a threshold N⁻¹(PD). Conditional on the systematic factor, defaults are independent. For a large homogeneous portfolio, the loss rate in a bad scenario at confidence level X is the worst-case default rate (WCDR). This is the basis of the Basel IRB capital formula.

Credit VaR is the loss at a chosen confidence level over a horizon (usually one year) minus nothing, or minus EL when you want unexpected loss. In exams, read carefully whether the question asks for VaR (total loss quantile) or UL / economic capital (VaR − EL).

Key formulas to remember

Expected loss
EL = PD × LGD × EAD
Portfolio EL is the sum of individual ELs. It does not depend on correlation.
Vasicek worst-case default rate
WCDR(X) = N[ (N⁻¹(PD) + √ρ × N⁻¹(X)) ÷ √(1 − ρ) ]
N is the standard normal CDF, N⁻¹ its inverse. X is the confidence level, e.g. 99.9%. Valid for a large homogeneous portfolio with one factor.
Credit VaR (Vasicek)
Credit VaR = WCDR × LGD × EAD
This is the total loss quantile, assuming LGD is fixed and known.
Unexpected loss / capital
UL = Credit VaR − EL = (WCDR − PD) × LGD × EAD
Basel IRB capital follows this idea, with extra adjustments for maturity.
Asset correlation and default correlation
Asset value Aᵢ = √ρ × M + √(1 − ρ) × Zᵢ
M is the systematic factor, Zᵢ is idiosyncratic. Both are standard normal. Default correlation is lower than asset correlation for typical PDs.
Two-asset default correlation
ρ_D = (P(both) − PD₁ × PD₂) ÷ √(PD₁(1 − PD₁) × PD₂(1 − PD₂))
P(both) is the joint default probability.
Herfindahl-Hirschman Index
HHI = Σ wᵢ²
wᵢ is each exposure's share of the portfolio. Higher HHI means more concentration. 1/HHI is the effective number of equal-sized exposures.

How to solve Credit Portfolio Risk and Concentration questions

Use this order for most portfolio credit risk questions, whether they are numeric or conceptual.

  1. 1Identify what is asked: EL, VaR (total loss), UL (VaR − EL), or a concentration measure.
  2. 2List PD, LGD, EAD, ρ and the confidence level. Check that PD and the horizon use the same period.
  3. 3Compute EL = PD × LGD × EAD first. It is often needed later.
  4. 4For Vasicek, find N⁻¹(PD) and N⁻¹(X). Combine them in the WCDR formula, then convert back with N.
  5. 5Multiply WCDR by LGD and EAD to get credit VaR. Subtract EL if the question asks for unexpected loss or capital.
  6. 6For concentration, compute weights, then HHI = Σ w², or compare sector and name exposures to limits.
  7. 7Sanity check: WCDR must be above PD, and higher ρ must raise WCDR. Then state the interpretation in one line.

Quickest way: Direction and rank shortcuts for MCQs

When to use it: Use when options are far apart or the question is conceptual. It saves time on a 4-hour, 80-question paper.

  1. Remember WCDR > PD always, for ρ > 0 and X > 50%. Eliminate any answer below PD.
  2. If ρ rises with all else fixed, VaR and UL rise. EL stays the same.
  3. If correlation is zero, WCDR collapses to PD and UL is zero in the large-portfolio limit.
  4. For concentration questions, pick the answer that raises tail loss without raising EL, such as adding sector or name overlap.
  5. For numeric Vasicek, compute only N⁻¹ values and one division. Use the standard normal table values you know: N⁻¹(99%) = 2.326, N⁻¹(99.9%) = 3.090.

Common mistakes in Credit Portfolio Risk and Concentration

  • Saying correlation changes portfolio expected loss

    Students link correlation with 'more risk' and apply it to every measure.

    Fix: EL is additive. Correlation changes only the shape and tail of the loss distribution, so it affects UL and VaR.

  • Forgetting to subtract EL when UL or capital is asked

    The Vasicek formula gives a loss number and students stop there.

    Fix: Read the last line of the question. Capital under Basel IRB covers UL, so use (WCDR − PD) × LGD × EAD.

  • Using N⁻¹(X) with the wrong sign

    Mixing up the confidence level with the tail probability.

    Fix: Use N⁻¹(0.999) = +3.090 for a 99.9% worst case. A positive sign raises the default rate.

  • Assuming diversification removes all risk

    Textbook independence examples suggest risk vanishes as names increase.

    Fix: Diversification removes idiosyncratic risk only. Systematic risk, captured by ρ, stays in a large portfolio.

  • Treating asset correlation and default correlation as the same

    Both are called correlation and sit in the same chapter.

    Fix: Vasicek ρ is correlation of asset values. Default correlation is of the 0/1 default events and is usually much smaller. Use the right one in each formula.

  • Reading a low HHI as low risk overall

    HHI measures only name concentration.

    Fix: A portfolio with many equal names can still be concentrated in one sector or region. Check sector and geographic exposure too.

Worked examples

Example 1

A large homogeneous loan portfolio has total EAD of USD 500 million, PD = 2%, LGD = 50% and asset correlation ρ = 0.20. Using the Vasicek model at 99.9% confidence, the worst-case default rate is closest to which of the following? (A) 2.0% (B) 10.4% (C) 14.2% (D) 21.7%

Show the solution
  1. N⁻¹(0.02) = −2.054. N⁻¹(0.999) = 3.090.
  2. √ρ = √0.20 = 0.4472. √(1 − ρ) = √0.80 = 0.8944.
  3. Numerator = −2.054 + 0.4472 × 3.090 = −2.054 + 1.382 = −0.672.
  4. Divide by 0.8944: −0.672 ÷ 0.8944 = −0.751.
  5. WCDR = N(−0.751) ≈ 0.226 using the normal table, so about 22.6%. Re-check: N(−0.75) = 0.2266.
  6. Closest option is 21.7%. The other options are far from 22.6% and 2.0% equals PD, which cannot be right since WCDR > PD.

Answer: (D) about 21.7%, as the nearest option to the computed 22.6%.

Example 2

Using the same portfolio data, suppose WCDR = 22.6%. Compute the credit VaR and the unexpected loss in USD.

Show the solution
  1. EL = PD × LGD × EAD = 0.02 × 0.50 × 500 million = USD 5 million.
  2. Credit VaR = WCDR × LGD × EAD = 0.226 × 0.50 × 500 million = USD 56.5 million.
  3. UL = Credit VaR − EL = 56.5 − 5 = USD 51.5 million.
  4. Interpretation: with 99.9% confidence, one-year loss should not exceed USD 56.5 million. Capital held against unexpected loss is USD 51.5 million.

Answer: Credit VaR is USD 56.5 million and unexpected loss is USD 51.5 million.

Exam tips

  • Look for the phrase 'unexpected loss' or 'capital'. It signals that you must subtract EL.
  • Check the sign and level of N⁻¹(X). Most Vasicek errors are here, not in the algebra.
  • In concept questions, tie each answer back to systematic versus idiosyncratic risk. That distinction decides many MCQs.
  • When options include a value below PD for WCDR, discard them at once.
  • Concentration questions often ask which change increases tail risk most. Choose the one that adds correlated exposure, not merely more names.

Practice questions from Credit Risk Management

Credit Portfolio Risk and Concentration 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 Concentration: frequently asked questions

What is the Vasicek single-factor model in simple terms?

It says every borrower's asset value depends on one common factor and one borrower-specific factor. Given the common factor, defaults are independent. This lets you compute the default rate of a large portfolio in a bad economy with a closed-form formula.

How do I calculate credit VaR for a portfolio in the exam?

Find EL, then use the Vasicek WCDR formula at the stated confidence level. Credit VaR is WCDR × LGD × EAD. If the question wants unexpected loss, subtract EL.

What is the difference between diversification and concentration in credit risk?

Diversification spreads exposure across many borrowers, sectors and regions to cut idiosyncratic risk. Concentration is heavy exposure to one name or a group of correlated names. Concentration raises unexpected loss without changing expected loss.

Does higher correlation increase expected loss?

No. Expected loss depends only on PD, LGD and EAD. Higher correlation fattens the tail of the loss distribution, so credit VaR and unexpected loss rise.