FRM Part I · FRM Exam Part I

Measuring Credit Risk for FRM Part I

Measuring credit risk means estimating how much you could lose when a borrower or counterparty fails to pay. You start with expected loss = PD × LGD × EAD, then add unexpected loss, ratings migration, structural and reduced-form default models, and portfolio credit VaR. Solve questions by writing the formula first, then the numbers.

What this chapter covers

This chapter turns the idea of credit risk into numbers. You learn how to split a loss into three parts: the probability the borrower defaults (PD), the share of exposure you lose if it does (LGD), and the amount owed at default (EAD). From there you move to expected loss, unexpected loss, and the capital held against it.

The middle of the chapter covers how default probabilities are estimated. Ratings and transition matrices give you a historical, agency-based view. The Merton model treats equity as a call option on the firm's assets and gives a market-based, structural view. Reduced-form models treat default as a random event with a hazard rate and link it to credit spreads. The last topic scales everything up to a portfolio, where correlation and concentration decide how fat the loss tail is.

The chapter connects to much of the rest of Part I. It uses probability and distributions from Quantitative Analysis, option pricing ideas from Financial Markets and Products, and VaR thinking from Valuation and Risk Models. It also links to the Foundations of Risk Management material on capital and risk governance. Time spent here pays back across the paper.

The FRM Part I exam has 100 equally weighted multiple-choice questions in 4 hours, and credit risk questions are mostly short calculations you can win with a clear method. Expected loss, survival probabilities from a transition matrix, the Merton distance to default and the spread-to-hazard-rate link all follow repeatable steps. Candidates who know the formulas and the conditions behind them pick up quick marks. Candidates who only memorise definitions often lose them on small traps such as mixing up annual and cumulative probabilities. GARP revises the curriculum every year, so check the current Study Guide and Learning Objectives for exact scope.

Measuring Credit Risk: topics in the order to study them

1Expected and Unexpected Credit LossesStart here because PD, LGD and EAD are the vocabulary every later topic uses.
2Credit Risk Mitigation and Recovery RatesCollateral, netting and guarantees change EAD and LGD, so you study them right after the loss formula.
3Credit Ratings and Transition MatricesThis gives you the first practical source of PD and teaches multi-period probability calculations.
4Structural Models of Default (Merton Model)It builds on option ideas and shows how a firm's asset value and leverage drive default probability.
5Reduced-Form Models and Credit SpreadsYou compare it with the Merton view and link hazard rates to spreads and recovery, which needs the earlier loss concepts.
6Portfolio Credit Risk, Credit VaR and CorrelationLeave it for last because it combines single-name PD and LGD with correlation to measure the portfolio tail.

How to prepare Measuring Credit Risk

Treat this chapter as a set of formulas with conditions. Learn each one, then practise until the steps are automatic.

Write the core formulas on one page: EL = PD × LGD × EAD, LGD = 1 − recovery rate, and the survival probability link. Say each one aloud with its meaning.
For each topic, solve at least five numerical questions by hand. Always write the formula, substitute the numbers, then state the answer with its units.
Practise transition matrices until you can multiply them for two periods without error. Check that each row sums to 1 and that default is an absorbing state.
Work through the Merton model in order: asset value, debt face value, volatility, then d2 and N(−d2) as the risk-neutral default probability. Know what each input does to the result.
Practise the approximate spread relation: spread ≈ hazard rate × (1 − recovery). Then solve for any one variable when given the other two, and note when the approximation is acceptable.
Finish with portfolio questions. Compare how higher correlation changes the loss tail while expected loss stays the same.
Do timed mixed sets. Aim for a steady pace across the 100 questions, and mark long calculations to return to later.

Common mistakes in Measuring Credit Risk

Using the recovery rate where LGD is needed, or the reverse.
Fix: Convert straight away: LGD = 1 − recovery rate. Write LGD on your scratch line before you calculate anything.
Adding annual default probabilities to get a multi-year probability.
Fix: Use survival probabilities. Cumulative default = 1 − product of annual survival probabilities, or use matrix multiplication for a transition matrix.
Reading the Merton default probability as a real-world probability.
Fix: Note that N(−d2) under the standard setup is risk-neutral. Real-world versions use the asset drift in place of the risk-free rate.
Mixing up expected loss and unexpected loss when reading capital questions.
Fix: Expected loss is the mean and is priced or provisioned for. Unexpected loss is the variability beyond it and drives capital.
Ignoring the direction of correlation effects at portfolio level.
Fix: Remember that correlation does not change the mean loss on the portfolio. It widens the spread and makes extreme losses more likely.
Skipping matrix and logarithm arithmetic checks on a calculator.
Fix: Re-enter key steps once. Use the calculator's memory and exponent keys, and sanity-check that probabilities lie between 0 and 1.

Last-day revision: Measuring Credit Risk

Expected loss = PD × LGD × EAD.
LGD = 1 − recovery rate, with both stated on the same exposure basis.
Unexpected loss is the variability of loss around its expected value, usually measured as a standard deviation.
Credit VaR is a loss quantile minus expected loss when you measure unexpected loss, so read the question's definition.
Netting, collateral and guarantees reduce exposure or loss given default.
In a transition matrix, each row sums to 1 and default is absorbing.
Multi-year migration probabilities come from multiplying the matrix, not from adding annual numbers.
Merton model: equity is a call option on firm assets, and debt equals a risk-free bond minus a put.
In the Merton model, N(−d2) is the risk-neutral probability that assets end below the debt face value.
Higher asset volatility or higher leverage raises Merton default probability.
Reduced-form models treat default as a random event driven by a hazard rate.
Spread ≈ hazard rate × (1 − recovery rate) as a rule of thumb.
Higher default correlation leaves expected loss unchanged but fattens the tail of the loss distribution.

Measuring Credit Risk practice questions

Measuring Credit Risk in other exams

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

Measuring Credit Risk: frequently asked questions

What is the first thing to learn in credit risk for FRM Part I?

Learn expected loss: PD × LGD × EAD. Every other topic in the chapter either estimates one of those three inputs or shows how losses behave across a portfolio.

Do I need to memorise the full Merton model derivation?

You should understand the setup and be able to use the formulas and inputs, rather than reproduce a derivation. Focus on what d2 means, how leverage and volatility affect default probability, and how equity and debt map to options.

How are credit spreads linked to default probability?

In a reduced-form view, the credit spread is roughly the hazard rate multiplied by (1 − recovery rate). With any two of the three values, you can estimate the third. It is an approximation, so use it as the question directs.

Is a financial calculator useful for this chapter?

Yes, mainly for exponentials, powers and multi-step arithmetic such as survival probabilities and Merton inputs. Practise with the calculator allowed in the exam so you are quick and accurate on the day.