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FRM Part II · FRM Exam Part II

Credit Value at Risk for FRM Part II

Credit Value at Risk is the loss on a credit portfolio that will not be exceeded at a chosen confidence level over a set horizon. Expected loss is PD × LGD × EAD. Unexpected loss is the standard deviation of losses. Economic capital is credit VaR minus expected loss, a separate measure. Estimate the loss distribution, then read off the loss at the chosen confidence level.

What this chapter covers

This chapter shows how to measure credit risk for a whole portfolio, not one loan. You start with the loss distribution and its three inputs: probability of default (PD), loss given default (LGD) and exposure at default (EAD). Expected loss is the mean of the distribution. Credit VaR looks far into the tail. Economic capital is the gap between that tail loss and expected loss.

The core of the chapter is the set of models that build the distribution. Merton and KMV link default to asset value falling below debt. CreditMetrics uses rating migrations and revaluation. CreditRisk+ uses an actuarial approach with default counts, usually Poisson-based. The single-factor model and Vasicek formula give a closed-form tail default rate, which links to the Basel internal-ratings-based capital approach. Default correlation sits behind all of them.

The chapter connects to the rest of Part II in several ways. It sits next to counterparty credit risk and structured credit, which reuse PD, LGD and correlation. It shares tail-risk thinking with market risk VaR and expected shortfall. It also feeds capital and stress testing questions, and the private credit reading in Current Issues. Expect applied questions: compute a number, then say what it means or which model fits.

Credit risk is one of the six Part II topics, and the exam is 80 equally weighted multiple-choice questions. This chapter gives you both calculation questions and concept questions, and the same ideas (PD, LGD, correlation, tail loss) recur in other chapters. The formulas are short, so careful practice turns them into reliable marks. Candidates who only memorise model names lose marks on questions that ask what drives a result or why a model fails.

Credit Value at Risk: topics in the order to study them

  1. 1Credit VaR Fundamentals and Loss DistributionStart here to learn expected loss, unexpected loss, tail loss and economic capital, since every later model produces this distribution.
  2. 2Credit Risk Parameters: PD, LGD and EADThese are the inputs to every model, so you need them clear before building a portfolio view.
  3. 3Portfolio Credit Risk and Default CorrelationCorrelation turns a sum of loan losses into a fat-tailed portfolio distribution, which explains why models differ.
  4. 4Structural Models: Merton and KMVThis is the first model of default, and its asset-value logic also underpins the single-factor model.
  5. 5CreditMetrics ApproachIt extends the structural idea to rating migrations and value changes, so it builds directly on Merton.
  6. 6CreditRisk+ and Actuarial ModelsStudy it after CreditMetrics to see the contrast: default-only, count-based and not tied to asset values.
  7. 7Single-Factor Model and Vasicek Credit VaRIt gives the closed-form tail default rate and needs the structural and correlation ideas already in place.
  8. 8Model Comparison, Validation and LimitationsFinish with comparison and backtesting, which only make sense once you know each model's inputs and assumptions.

How to prepare Credit Value at Risk

Aim to link each model to its inputs, its output and its main weakness. Practise by calculation, then by explaining the result in one sentence.

  1. Read the fundamentals and write the chain in your own words: EL = PD × LGD × EAD, then UL, then credit VaR and economic capital.
  2. Do small calculations for EL on single loans and portfolios until you get them right without notes.
  3. Learn default correlation with a two-name example, and note how higher correlation fattens the tail without changing expected loss.
  4. Make a one-page table of Merton, KMV, CreditMetrics, CreditRisk+ and Vasicek: default driver, inputs, what is modelled, main limitation.
  5. Practise the Vasicek formula with several PD and correlation values until you can do it with a calculator and check the direction of the answer.
  6. Take timed mixed question sets, since the exam is 80 questions in 4 hours, and write down why each wrong option was wrong.
  7. In the last days, revisit validation topics: backtesting difficulty, data scarcity, model risk and the effect of the credit cycle.

Common mistakes in Credit Value at Risk

  • Treating credit VaR as the same as expected loss or as the capital figure.

    Fix: Check the wording. Credit VaR is the tail loss; economic capital is credit VaR minus expected loss.

  • Thinking higher correlation raises expected loss.

    Fix: Expected loss depends only on PD, LGD and EAD. Correlation changes the shape and the tail.

  • Mixing up what CreditMetrics and CreditRisk+ model.

    Fix: CreditMetrics is mark-to-market with migrations. CreditRisk+ is default-only and count-based.

  • Putting the wrong quantile into the Vasicek formula.

    Fix: Use +√ρ × N⁻¹(q) with q = 0.999, so N⁻¹(0.999) is about +3.09. Do not use N⁻¹(1 − q), which is about −3.09 and gives a tail default rate that is too low. Then check that the result exceeds the PD.

  • Using risk-neutral and real-world PDs interchangeably.

    Fix: Note the source of each PD. Risk-neutral PDs from spreads usually exceed real-world PDs because of risk premia.

  • Ignoring limitations when asked to evaluate a model.

    Fix: For each model, know one key assumption and one weakness, such as constant correlation or the scarcity of default data.

Last-day revision: Credit Value at Risk

  • Expected loss = PD × LGD × EAD; it is the mean of the loss distribution.
  • Unexpected loss (UL) is the standard deviation of losses. Economic capital (sometimes called unexpected loss at the tail) is credit VaR minus expected loss. They are different measures.
  • Credit VaR is a high quantile of a skewed loss distribution with a fat right tail.
  • LGD = 1 − recovery rate, and recovery is often uncertain and tied to the credit cycle.
  • Higher default correlation leaves expected loss unchanged but raises tail loss.
  • Merton: equity is a call option on firm assets; default occurs if assets fall below debt at maturity.
  • KMV uses distance to default and maps it to an empirical expected default frequency.
  • CreditMetrics uses a rating migration matrix and revalues the portfolio at the horizon, usually one year.
  • CreditRisk+ models default counts with a Poisson-type distribution and ignores migration.
  • Vasicek tail default rate = N[(N⁻¹(PD) + √ρ × N⁻¹(q)) ÷ √(1 − ρ)], where q is the confidence level.
  • In the Vasicek formula, for a high confidence level (e.g., 99.9%) and a typical low PD, a higher ρ raises the tail default rate.
  • Credit models are hard to backtest because defaults are rare and horizons are long.

Credit Value at Risk practice questions

Credit Value at Risk in other exams

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

Credit Value at Risk: frequently asked questions

What is the difference between expected loss and unexpected loss?

Expected loss is the average loss, equal to PD × LGD × EAD. Unexpected loss is the standard deviation of losses around that average. Economic capital is a separate, quantile-based measure: credit VaR minus expected loss, sometimes called unexpected loss at the tail.

Do I need to memorise the Vasicek formula?

Yes, you should know it and be able to compute it with a calculator. Also know what it implies: for a high confidence level such as 99.9% and a typical low PD, the tail default rate rises with correlation. It also rises with the confidence level. Understanding the direction helps you check your answer.

Which model is easiest to confuse with others?

CreditMetrics and CreditRisk+ are most often mixed up. Remember that CreditMetrics values the portfolio after rating changes, while CreditRisk+ only counts defaults and uses an actuarial method.

How much calculation should I expect in this chapter?

Expect some short calculations, such as expected loss, a Vasicek tail rate or a distance to default, along with conceptual questions. Practise both types, because the exam is applied and case-like.