Credit Risk Events and Loss Components

What Makes a Loss a Credit Loss?

A lender or other counterparty faces credit risk when it may not receive the contractual payment it is owed. The resulting loss depends on more than whether the counterparty defaults: it also depends on how much is exposed when the event occurs and how much of that exposure is ultimately lost. Keeping these elements separate makes assumptions visible and helps prevent unlike quantities from being combined.

The event used to identify default must be specified for the analysis, as must the time horizon. For this tutorial, take the default event as defined by the hypothetical contract or risk model in each example. The exact boundaries of a default event can vary with the purpose and governing rules of an analysis.

Definition: Credit risk is the risk of loss arising when a borrower or other counterparty fails to meet a contractual obligation. For an exposure over a specified horizon, the main loss components are the probability of default (PD), the exposure at default (EAD), and the loss given default (LGD). PD is the probability of the specified default event during that horizon. EAD is the amount exposed when default occurs. LGD is the fraction of EAD that is lost, after allowing for recoveries and, when the model specifies, relevant costs.

EAD is measured in money, while PD and LGD are proportions between zero and one. If EAD is $E$ dollars and LGD is $L$, the loss conditional on default is $EL$ dollars. Equivalently, if the net recovery is $R$ dollars and the recovery and exposure use the same basis, then $L=(E-R)/E$. The loss conditional on default is $E-R$.

\text{Loss given default in dollars} = \text{EAD}\times\text{LGD}

The three components answer different questions. PD concerns whether default occurs within the chosen horizon; EAD concerns the amount at risk at the event time; LGD concerns the fraction of that amount not recovered. They must refer to a consistent exposure, event definition, and horizon. A one-year PD, for example, should not be paired without adjustment with an exposure or severity defined for a different period.

From Components to Expected Loss

For a simple model, suppose a single exposure has fixed EAD $E$ and fixed LGD $L$ if default occurs during a specified period. Let $D$ equal 1 if default occurs in that period and 0 otherwise, with $P(D=1)=p$. The modeled loss is $X=DEL$. If there is no default, the modeled default loss is zero; if default occurs, it is $EL$. Therefore, the expected loss is $pEL$.

E[X]=E[DEL]=EL\,E[D]=ELp

Here $E[\cdot]$ denotes expectation, while $E$ without brackets in the formula denotes the fixed exposure amount. This familiar product is valid under the stated fixed-component model. If EAD or LGD varies, the product of a marginal PD, an average EAD, and an average LGD is not automatically the correct expected loss. Dependence matters: for example, a counterparty may be most likely to default when exposure is unusually large, or when recovery is unusually poor.

Key result: With fixed EAD and LGD and a PD measured over the same horizon, expected credit loss is $p\times EAD\times LGD$. More generally, expected loss is the probability-weighted average of the losses across possible outcomes; use the simple product only when its assumptions fit the model.

The reasoning is direct: loss is zero when $D=0$, and equals $EL$ when $D=1$. Thus the average over outcomes is $0(1-p)+EL(p)=pEL$. This derivation also shows why the formula is an expectation, not a prediction that the actual loss will equal that amount. In a single period, the realized loss in this simple model is either zero or $EL$.

Worked Example: Calculating Loss and Expected Loss on a Loan

A hypothetical lender has a loan with a balance of $800,000 at the start of a one-year risk horizon. Assume the balance remains the EAD if default occurs during that year. The estimated net recovery after default is $280,000. The one-year PD is 2.5%. Calculate the loss given default in dollars, LGD, and expected credit loss for the year. Assume no discounting, no additional costs, and no variation in EAD or recovery. No interest-rate or mortality assumption is needed.

Method. First calculate the loss conditional on default by subtracting net recovery from EAD. Then express that loss as a fraction of EAD and apply the fixed-component expected-loss formula.

Step 1: Loss in dollars if default occurs. The EAD is $800,000 and the net recovery is $280,000:

\text{Loss given default}=\$800{,}000-\$280{,}000=\$520{,}000

Step 2: Calculate LGD.

LGD=\frac{\$520{,}000}{\$800{,}000}=0.65=65\%

Step 3: Calculate expected credit loss. The PD is $0.025$, the EAD is $800,000, and LGD is $0.65$:

E[X]=0.025\times\$800{,}000\times0.65 =\$20{,}000\times0.65 =\$13{,}000

The results are internally consistent: if default occurs, the modeled loss is $520,000; a 2.5% chance of that loss gives an expected loss of $13,000 over the year. The common mistake this method avoids is treating the $280,000 recovery as the loss severity. It is the recovered amount; the loss is the $520,000 shortfall.

Exposure at Default Is Not Always the Current Balance

For a term loan with no further drawings, the current balance may be a reasonable assumption for EAD. For a revolving facility or a commitment that can be drawn before default, the exposure at the event may exceed the amount already drawn. A simplified estimate can add an assumed fraction of the undrawn commitment to the current drawn amount. That fraction is an assumption about future drawings, not a recovery rate or a probability of default.

EAD=\text{drawn amount}+ (\text{undrawn commitment}\times\text{assumed fraction drawn})

This calculation is only as suitable as its inputs and purpose. It does not establish that the assumed fraction is correct for every borrower or facility. The estimated EAD must then be paired with a severity assumption defined for that same exposure basis.

Worked Example: Two Commitments With Different Drawings and Severity

A hypothetical lender assesses two facilities over the next year. Facility A has $400,000 drawn and $200,000 undrawn; the model assumes 50% of the undrawn amount is drawn before default. Its one-year PD is 3% and its LGD is 40%. Facility B has $250,000 drawn and $150,000 undrawn; the assumed fraction drawn is 20%, its one-year PD is 1.5%, and its LGD is 55%. Calculate the EAD and expected loss for each facility and the combined expected loss. Assume fixed model inputs over the horizon, no discounting, and no additional costs.

Method. Estimate each EAD separately, calculate its conditional loss, then multiply by that facility’s PD. Add the expected losses. No independence assumption is required to add expectations.

Facility A, EAD. The assumed additional drawing is $0.50\times\$200{,}000=\$100{,}000$, so:

EAD_A=\$400{,}000+\$100{,}000=\$500{,}000

Facility A, conditional loss and expected loss.

\text{Loss if default}_A=\$500{,}000\times0.40=\$200{,}000

E[X_A]=0.03\times\$200{,}000=\$6{,}000

Facility B, EAD. The assumed additional drawing is $0.20\times\$150{,}000=\$30{,}000$, so:

EAD_B=\$250{,}000+\$30{,}000=\$280{,}000

Facility B, conditional loss and expected loss.

\text{Loss if default}_B=\$280{,}000\times0.55=\$154{,}000

E[X_B]=0.015\times\$154{,}000=\$2{,}310

Combined expected loss.

E[X_A+X_B]=\$6{,}000+\$2{,}310=\$8{,}310

The combined result is $8,310. The method avoids applying each LGD to the drawn balance alone, which would omit the assumed pre-default drawings. It also avoids using a single severity or PD for both facilities despite their different stated assumptions.

Credit Losses and Market-Value Changes

A default loss and a change in market value are different measurements. A default loss is tied to a failure to meet an obligation and the resulting shortfall after recovery. A market-value change measures the difference between an asset’s values at two dates under a valuation basis. A bond’s value can fall because investors demand a higher yield or because their assessment of the issuer’s credit quality worsens, even if no default has occurred.

A credit-related market-value decline is relevant to risk management, but it is not, by itself, a realized default loss. Conversely, a position held at a value close to its initial value can still incur a substantial loss if default later occurs and recovery is low. An analysis should state whether it is measuring a default-related cash shortfall, a change in market value, or a broader measure that explicitly combines effects.

Worked Example: Separating a Default Loss From a Price Decline

A hypothetical institution holds a bond with a face claim of $2,000,000. Its market value falls from $1,960,000 to $1,900,000 over a quarter as required yields rise. The issuer has not defaulted during the quarter. For a separate one-year credit-loss assessment, assume a PD of 1.8%, an EAD of $2,000,000, and net recoveries of $1,000,000 if default occurs. Calculate the quarter’s market-value change, LGD, and one-year expected default loss. Assume no discounting, no additional costs beyond those reflected in net recovery, and fixed one-year credit-loss inputs.

Method. Calculate the change in quoted market value separately from the loss conditional on default. Use the stated face claim as EAD for the credit-loss calculation; do not substitute the quarter-end market price.

Step 1: Market-value change.

\$1{,}900{,}000-\$1{,}960{,}000=-\$60{,}000

The market-value decline is $60,000. Since no default occurred in the stated quarter, this decline is not a realized default shortfall in this scenario.

Step 2: Loss conditional on default and LGD.

\text{Loss if default}=\$2{,}000{,}000-\$1{,}000{,}000=\$1{,}000{,}000

LGD=\frac{\$1{,}000{,}000}{\$2{,}000{,}000}=0.50=50\%

Step 3: One-year expected default loss.

E[X]=0.018\times\$2{,}000{,}000\times0.50 =\$36{,}000\times0.50 =\$18{,}000

The one-year expected default loss is $18,000, while the observed quarter’s market-value decline is $60,000. They answer different questions and should not be added or substituted for one another unless a specified measure is designed to combine them. The common mistake avoided here is using the $60,000 price decline as LGD, or treating it as proof that a default loss has occurred.

Common Traps in Component Calculations

The product of PD, EAD, and LGD is compact, but it is easy to use incorrectly. Check the units and definitions before multiplying:

Subtracting in the wrong direction. Net recovery is not the loss. For consistent exposure and recovery amounts, loss conditional on default is EAD minus net recovery.
Mixing a dollar amount and a percentage. LGD is a fraction of EAD. If the loss is already stated in dollars, do not multiply that dollar loss by EAD again.
Using an inconsistent horizon. PD, EAD assumptions, and severity must match the period and event basis being assessed.
Ignoring possible drawings. For a commitment, the amount currently drawn need not equal EAD if additional drawings are assumed before default.
Calling every credit-related price decline a default loss. A valuation decline can occur without default; identify which quantity the question asks for.
Assuming averages can always be multiplied. If EAD or LGD varies with default or with each other, the simple product of separately averaged inputs may not give the correct expected loss.

Key takeaway: State the horizon and event first. Then identify PD, EAD, and LGD on consistent bases. Under fixed-component assumptions, conditional loss is $EAD\times LGD$, and expected loss is $PD\times EAD\times LGD$. Keep that default-loss calculation distinct from market-value changes.

Check Your Understanding

For each problem, use only the assumptions stated and keep default losses distinct from market-value changes.

A hypothetical receivable has EAD $360,000 and net recovery of $126,000 if default occurs. Its one-year PD is 4%. Find LGD, the loss if default occurs, and expected loss. (Answer: LGD = 65%; loss if default = $234,000; expected loss = $9,360.)
A hypothetical revolving facility has $180,000 drawn and $120,000 undrawn. Assume 25% of the undrawn commitment is drawn before default. If LGD is 40% and the one-year PD is 2%, calculate EAD and expected loss. (Answer: EAD = $210,000; expected loss = $1,680.)
A lender has two unrelated fixed exposures. Exposure A has EAD $500,000, LGD 30%, and one-year PD 2%; exposure B has EAD $200,000, LGD 60%, and one-year PD 5%. Find the expected loss for each and the total. (Answer: A = $3,000; B = $6,000; total = $9,000.)
A hypothetical bond’s market value declines from $740,000 to $715,000, with no default during the measurement period. Separately, its one-year credit model uses EAD $800,000, net recovery $440,000, and PD 3%. Calculate the market-value decline and one-year expected default loss. (Answer: market-value decline = $25,000; expected default loss = $10,800.)
A hypothetical exposure has fixed EAD $1,200,000 and LGD 45% if default occurs during the year. The one-year PD is 1.25%. Calculate the conditional loss and expected loss, and state whether either calculation requires an interest-rate or mortality assumption. (Answer: conditional loss = $540,000; expected loss = $6,750; neither calculation requires an interest-rate or mortality assumption.)

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