PD, LGD and EAD Explained for Mortgage Credit Risk

If a $300,000 mortgage defaults, how much does the lender lose? The answer is not a single number. It depends on three separate quantities: the probability of default (PD), the loss given default (LGD) and the exposure at default (EAD). Multiplied together, they give the expected loss on a loan.

The expected loss identity

Each of the three quantities answers its own question. How likely was the loan to default in the first place? If it defaulted, how much of the outstanding balance does the lender actually lose once the workout is finished? And how much was outstanding at the moment of default?

Expected loss equals probability of default times loss given default times exposure at default: EL = PD x LGD x EAD.

This is the basic identity of credit risk modeling. It shows up wherever a lender or investor faces credit risk, including mortgages, credit cards, commercial loans and corporate bonds. If you multiply only PD by LGD, you get an expected loss rate rather than a dollar figure.

There are three caveats:

• The identity is approximate at the loan level. In practice, expected loss is estimated over a chosen horizon, 12 months for some uses and the loan's lifetime for others. Discount factors make losses far in the future worth less today than losses in the near term. The simple product is good for intuition, but production models add more machinery around it.
• All three factors are random variables. PD is a probability by definition. The words "given default" and "at default" mean LGD and EAD are distributions over the loans that actually default. Treating each one as a single point estimate makes the vocabulary easier, but real modeling treats each as a distribution and carries that through the calculation.
• The factors are not independent. This matters enough to get its own section below.

The international Basel capital framework formalizes these three quantities and uses them as the primary inputs to the internal ratings-based (IRB) capital calculation. The US implementation follows the same structure. Because of that, PD, LGD and EAD are the shared vocabulary across product types, even though each product has its own modeling issues. For example, mortgage LGD is dominated by housing market dynamics, while credit card LGD is driven by behavioral and demographic factors.

Probability of default (PD)

PD is the probability that a loan will default within a specified horizon: the next month, the next 12 months or the loan's remaining lifetime. It always falls between zero and one. The modeler estimates it from the loan's attributes and the macro environment around it. Put simply, PD asks: what is the chance the borrower will not pay as agreed? Across a portfolio, it tells you how many of a group of similar loans you should expect to default over the horizon you care about. That makes it the driver of expected default counts in capital planning, stress testing and reserve estimation.

Where PD lives in the data

The Freddie Mac loan-level data (SF-LLD) does not store PD. It records observed default events. The performance file tracks every loan month by month. The current loan delinquency status column runs from 0 for current, through 1 for 30 days past due, up to 6 for 180 days past due or more. Zero balance codes record how a loan terminated, such as foreclosure, REO disposition, short sale, repurchase or note sale. A loan that reaches a chosen delinquency threshold or ends in foreclosure counts as an observed default. The rate of those events in a cohort is the observed default rate, and PD models are calibrated against it.

Why PD is hard to model

1. Default is a chosen threshold, not a natural event. The modeler picks the definition, such as 60, 90 or 180 days past due, foreclosure, charge-off or some combination. That choice affects every modeling decision that follows.
2. Prepayment removes loans from the at-risk population before they have a chance to default. A naive PD calculation that ignores prepayment understates the risk. This is a competing risks problem.
3. Vintage and macro conditions shift the baseline. A 2006 vintage PD is meaningfully different from a 2014 vintage PD.
4. The horizon matters. A 12-month PD and a lifetime PD are different quantities with different uses, such as capital versus CECL.

There are two common ways to estimate PD. One is a logistic regression scorecard built with weight of evidence and information value. The other is a survival model using Kaplan-Meier curves, Cox regression, parametric survival and competing risks. Both target the same quantity, and regulated practice tends to use both.

What PD is not

• It is not prepayment probability. Prepayment is a separate quantity with its own modeling methods, and it is not a credit event.
• It is not the delinquency rate. Delinquency is a point-in-time snapshot of payment status. PD is the probability of reaching a chosen default state over a chosen horizon.
• It is not the charge-off rate. Charge-off is an accounting concept tied to when a lender writes off a loss, which happens after the credit event PD tries to predict.

Loss given default (LGD)

LGD is the fraction of the loan's exposure that the lender actually loses when default happens, after recoveries are netted out. By convention it falls between zero and one, though edge cases can push it outside that range. PD asks whether the borrower will default. LGD asks: if they do, how much of the outstanding balance is gone? For example, if a borrower defaults on a $200,000 balance and the lender recovers $140,000 after foreclosure costs, the property sale and legal expenses, the loss is $60,000 and the LGD is 30%.

Where LGD lives in the data

The LGD inputs appear in the performance file at the disposition month of a defaulted loan:

• net_sales_proceeds: what the property sold for at disposition.
• expenses: costs the lender incurred during the workout, including legal fees, maintenance fees and taxes.
• actual_loss_calculation: the loss figure the GSE computes from the inputs.
• mi_recoveries: what the mortgage insurance provider paid, if applicable.
• non_mi_recoveries: any other recovered amount.

For loans that did not default, these fields are empty.

Why LGD is hard to model

• The distribution is bimodal. Many defaults resolve with very little or no loss, for example through a successful modification or a short sale near the balance. Others resolve with very high losses, such as a long-delayed foreclosure in a depressed local housing market. Few outcomes fall in the middle, so linear models fit poorly. Practitioners use beta regression and two-stage decomposition instead.
• Property value dominates. House price movements drive LGD far more than borrower attributes do, which is why the mark-to-market loan-to-value ratio matters.
• Timing matters. A workout can take months to years. The timing of cash flows affects the realized loss, so discounting is important.

LGD is not credit card severity, which has a different distribution and different drivers. In the simplest framing it is one minus the recovery rate. It is also not the charge-off amount: charge-off is an accounting recognition of loss, while LGD follows the actual workout cash flows through to final resolution.

Exposure at default (EAD)

EAD is the outstanding principal balance on the day of default, the dollar amount actually at risk. It is the dollar figure that PD times LGD gets multiplied by. For a 30-year mortgage that has been on the books for five years, EAD is almost always less than the original loan amount, because the borrower has been paying down principal.

In SF-LLD, the current_actual_upb field tracks the outstanding balance month by month. Its value in the month of default is the EAD, and over the loan's life it shows the amortization path you would expect on a fixed rate mortgage.

For fixed rate mortgages, EAD is relatively well behaved, because the payment, rate and term set a fairly predictable balance path. The main complication is curtailment, when a borrower pays extra principal beyond the scheduled payment. Curtailment varies by borrower and changes with the rate environment, the borrower's equity position and seasoning. Some borrowers never curtail, some pay down aggressively in the early years and others make a single lump-sum payment.

Revolving products are much harder. A borrower with a $15,000 credit line might carry a $2,000 balance for a long time, then run it up to $12,000 or $13,000 weeks before default. For those products the industry uses credit conversion factors. EAD is not the loan amount at origination, not the authorized credit line and not the current balance of a loan that has not defaulted. It is the answer to a hypothetical: if this loan defaults, what will be outstanding?

Why PD, LGD and EAD are not independent

Multiplying the three factors is only fully correct if they are independent, and they are not. A loan with a high loan-to-value ratio at origination has a higher PD, because the borrower has less equity and less margin to absorb a shock to income or home value. The same loan also has a higher LGD, because the lender has less property value to recover from in foreclosure. Both are driven partly by the same property value and borrower quality factors.

The macro environment links them too. When house prices fall, more borrowers default and losses on each default rise. Treating the factors as independent and multiplying point estimates systematically underestimates dollar losses in a stress scenario, which is exactly when loss estimates matter most. Two-stage default plus severity models, which model the joint distribution, and scenario-conditional modeling for CECL are structural ways to handle this.

Key takeaways

• Expected loss equals PD times LGD times EAD, estimated over a chosen horizon, with discounting in production models.
• PD is a probability between zero and one. The data records default events, not PD itself.
• LGD is the share of exposure lost after recoveries. It is bimodal and driven mainly by property value.
• EAD is the unpaid principal balance at the moment of default. Curtailment is the main complication for mortgages.
• Keep the definitions separate. Default is not delinquency, LGD is not charge-off, and EAD is not the credit line.
• PD and LGD move together through loan-to-value and house prices, so multiplying independent point estimates understates stress losses.