Credit Risk Expected Loss: PD, LGD and EAD Notes for FRM Part 1 [2026]

Credit risk expected loss is the average loss a lender expects to absorb on a loan, bond or portfolio over a fixed horizon, usually one year. It comes from one multiplication: expected loss equals probability of default times loss given default times exposure at default. EL = PD x LGD x EAD. FRM Part 1 tests each ingredient separately, then the combinations: EAD on a partly drawn credit line, recovery rate converted into LGD, cumulative default probabilities built from marginal ones, and the split between the expected loss a bank provisions for and the unexpected loss it holds capital against. This note defines each term, shows how it is estimated, runs the arithmetic in full, and finishes with the summary table, traps and revision box.

Planning your FRM revision around work? Lay out the remaining topics with our free study timetable generator. This note completes a set of three calculation-heavy FRM Part 1 notes, with duration and convexity and option greeks explained.

Table of Contents

• Credit risk expected loss: the three building blocks
• PD: probability of default, and how it is estimated
• LGD: loss given default and the recovery rate
• EAD: exposure at default and the credit conversion factor
• Credit risk expected loss: putting EL together
• Unexpected loss and credit VaR
• Credit risk expected loss: summary table
• Exam traps
• One-page revision: credit risk expected loss
• Frequently asked questions
• Wrapping up

Credit risk expected loss: the three building blocks

Credit risk expected loss is the average loss a lender expects on an exposure over a set horizon, calculated as probability of default times loss given default times exposure at default. Expected loss is a cost of doing business in lending, priced into interest rates and covered by loan loss provisions.

Each ingredient answers a different question. PD asks: how likely is this borrower to default within the horizon? LGD asks: if default happens, what fraction of the exposure is lost after recoveries? EAD asks: how much will be owed at the moment of default? Multiply the three and you get the loss the lender should expect on average. It is a mean, not a worst case, and actual losses in any single year scatter around it. That scatter is the unexpected loss covered later in this note. One discipline runs through every exam question here: PD, LGD and EAD must share the same horizon and the same exposure, or the multiplication quietly produces a plausible-looking wrong answer.

PD: probability of default, and how it is estimated

PD is the likelihood that an obligor defaults within the horizon, expressed as a percentage. A PD of 3% means that, across a large pool of similar borrowers, about 3 in 100 are expected to default within the year. Estimators build PD three ways. Historical approaches track past default rates for similar borrowers. Ratings-based approaches map credit ratings to the default rates historically observed for each grade. Market-based approaches back PD out of bond spreads or equity prices, most famously the Merton model, which treats firm equity as a call option on its assets and infers default risk from asset value and volatility.

Two PD distinctions appear in exam questions every cycle. Through-the-cycle PD averages default behavior across good and bad years and moves slowly; point-in-time PD reflects current conditions and swings with the economy. And marginal PD is the default probability for one specific future year, while cumulative PD covers default at any point up to that year. The two connect through survival:

Worked example. Year 1 marginal PD is 2%. For borrowers who survive year 1, the year 2 marginal (conditional) PD is 3%. Survival over two years = 0.98 x 0.97 = 0.9506. Cumulative 2-year PD = 1 – 0.9506 = 4.94%. Simply adding the marginal PDs gives 5%, a small overstatement that grows with horizon and PD level. The multiplication route is the correct one.

LGD: loss given default and the recovery rate

LGD is the fraction of EAD lost when a default occurs, after recoveries from collateral, guarantees and workout collections, and after the costs of collecting them. It connects to the recovery rate by one identity:

LGD = 1 – recovery rate

A recovery rate of 40% means an LGD of 60%: of every dollar exposed at default, 60 cents is expected to be lost and 40 cents recovered. What drives LGD: seniority (senior secured debt recovers most, subordinated debt least), the quality and liquidity of collateral, the borrower industry, and the state of the economy. Recoveries fall in recessions precisely when defaults rise, a pattern called downturn LGD, and that link between default rates and LGD is one reason realized credit losses cluster so violently in crises.

Estimation mirrors PD: banks average realized recoveries on their own defaulted loans (workout LGD), use market prices of defaulted bonds just after default (market LGD), or apply supervisory values. The key exam skills: convert between recovery rate and LGD without a sign error, and apply LGD to EAD, not to the amount originally lent.

EAD: exposure at default and the credit conversion factor

EAD is the amount owed at the moment of default. For a fully drawn term loan it is close to the outstanding balance. For revolving facilities it is genuinely uncertain, because stressed borrowers draw down their lines before they fail. The standard model splits the facility:

EAD = amount drawn + CCF x amount undrawn

The credit conversion factor (CCF) is the share of the undrawn commitment expected to be drawn by the time of default. Worked example. A borrower has a USD 500,000 revolving line, of which USD 300,000 is drawn and USD 200,000 is undrawn, with a CCF of 50%. EAD = 300,000 + 0.50 x 200,000 = USD 400,000. Using only the drawn 300,000 understates the exposure; the CCF, estimated from how past defaulters behaved on similar facilities, is the empirical middle ground.

Credit risk expected loss: putting EL together

The three ingredients combine in the single most tested formula in credit risk:

Expected loss = PD x LGD x EAD

Worked example 1. A corporate loan segment has EAD of USD 2,000,000, a one-year PD of 3% and an LGD of 45%. EL = 0.03 x 0.45 x 2,000,000 = USD 27,000. As a rate, that is 27,000 / 2,000,000 = 1.35% of exposure per year, and it sets the floor under loan pricing: the spread on such lending must at least cover 1.35% before funding and operating costs and any return on capital.

Worked example 2. A bond position has exposure at default of USD 500,000, an expected recovery rate of 40% and a one-year PD of 5%. First convert: LGD = 1 – 0.40 = 60%. Then EL = 0.05 x 0.60 x 500,000 = USD 15,000. The example is deliberately built so the recovery conversion is the step that decides the answer: candidates who plug 40% in as LGD get USD 10,000 and find it waiting among the answer choices.

Read the two examples together and the intuition locks in. Expected loss rises in direct proportion to each ingredient, so a borrower twice as likely to default, on an exposure twice as loss-heavy, costs four times as much to carry. A low-PD secured loan can therefore carry a smaller EL than a high-PD unsecured one, even when the secured loan is far larger.

Unexpected loss and credit VaR

Expected loss is an average, and averages do not bankrupt banks; deviations do. Unexpected loss (UL) measures the volatility of loss around the expected level. In the simplified single-loan model used in FRM teaching, with default a yes-or-no event and LGD treated as fixed, UL takes a clean form:

UL = EAD x LGD x square root of (PD x (1 – PD))

Worked example. For the loan segment in worked example 1: UL = 2,000,000 x 0.45 x square root of (0.03 x 0.97) = 900,000 x 0.17059 = about USD 153,500. Compare the two numbers: EL of USD 27,000 is the routine cost of a normal year, covered by provisions. UL of roughly USD 153,500 is the scale of a bad surprise, and surprises of that kind are what bank capital exists to absorb. Real portfolios complicate the formula: LGD itself varies, and defaults correlate through the economy, driven largely by one systematic factor, so portfolio UL falls far more slowly than EL as a portfolio grows.

Credit VaR extends the same idea to a chosen confidence level: the loss at a high quantile of the loss distribution, often 99.9% over one year, minus the expected loss. Illustrative example: if a portfolio has a 99.9% one-year loss estimate of USD 410,000 and an EL of USD 27,000, credit VaR is about 410,000 – 27,000 = USD 383,000. The subtraction matters: EL is already provided for, so the capital question covers only the excess. The quantile logic is identical to market VaR; our FRM value at risk cheat sheet covers the market-risk version.

Credit risk expected loss: summary table

Term	Meaning	Typical drivers	Watch out for
PD	Probability of default within the horizon	Borrower quality, rating, leverage, economy	Marginal vs cumulative; same horizon as LGD and EAD
LGD	Fraction of EAD lost if default occurs	Seniority, collateral, downturn conditions	LGD = 1 – recovery rate; applies to EAD
EAD	Amount owed at the moment of default	Drawn balance, CCF on undrawn commitments	CCF applies to the undrawn part only
EL	PD x LGD x EAD	All three ingredients, proportionally	It is a mean, not a worst case
UL	Volatility of loss around EL	PD level, LGD volatility, default correlation	Covered by capital, not by provisions
Credit VaR	Quantile loss minus EL	Confidence level, horizon, loss distribution	Subtract EL; EL is already provided for

Exam traps

• Recovery rate plugged in as LGD. The conversion LGD = 1 – recovery rate is the single most tested step. A 40% recovery means a 60% LGD, never 40%.
• CCF on the whole limit. The conversion factor applies only to the undrawn commitment. The drawn part enters EAD at full value.
• Mismatched horizons. A one-year PD with a multi-year LGD, or an EL compared against provisions for a different period, produces nonsense. Align the horizon first.
• Provisions versus capital. Provisions cover expected loss; capital covers unexpected loss. Swapping the two is a classic theory-question trap.

One-page revision: credit risk expected loss

Quantity	Formula	Example result from this note
LGD	1 – recovery rate	Recovery 40% gives LGD 60%
EAD (revolver)	Drawn + CCF x undrawn	300,000 + 0.5 x 200,000 = 400,000
Expected loss	PD x LGD x EAD	0.03 x 0.45 x 2,000,000 = 27,000
Cumulative PD	1 – product of (1 – marginal PD)	1 – 0.98 x 0.97 = 4.94% over 2 years
Unexpected loss (simple)	EAD x LGD x sqrt(PD x (1 – PD))	About 153,500 for the example loan
Credit VaR	Quantile loss – EL	410,000 – 27,000 = 383,000

• EL is priced into loans and covered by provisions; UL is covered by capital.
• EL rate on the example segment: 27,000 / 2,000,000 = 1.35% of exposure.
• Downturn LGD: recoveries fall when defaults rise, so EL and UL spike together in crises.
• Same horizon, same exposure: the alignment check before any EL multiplication.

Frequently asked questions

Is expected loss the most a lender can lose?

No. Expected loss is the average outcome across many similar exposures and many possible years. On a single loan the worst case is losing nearly the whole exposure at default, which is why the loss distribution, unexpected loss and credit VaR exist alongside EL.

Why hold capital if expected loss is already provisioned?

Because provisions are sized for the average year and losses do not arrive in average years. Capital absorbs the deviation between realized losses in a bad year and the expected level. Regulators size that capital using unexpected loss and credit VaR concepts.

What pushes LGD up or down?

Subordination pushes LGD up, because subordinated lenders are paid last. Strong, liquid collateral pushes it down. Downturns push it up across the board, since collateral values fall and workout recoveries shrink exactly when defaults multiply.

Does a higher PD always mean a higher expected loss?

Not on its own. EL multiplies all three ingredients, so a high-PD loan with heavy collateral (low LGD) can carry a smaller expected loss than a low-PD unsecured loan. Exam questions exploit this by changing two ingredients at once and asking which exposure has the larger EL.

Credit risk expected loss: wrapping up

The exam routine is: align the horizon, convert recovery to LGD, build EAD with the CCF if the facility is partly drawn, multiply for EL, then ask the second question the examiners always ask: is this number an average (provision for it) or a deviation (hold capital against it)? Round out the set with duration and convexity and option greeks explained, and find every note in the series on the FRM notes hub.

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