How to Calculate Expected Loss: PD, EAD, and LGD

To calculate expected loss, multiply three inputs: the probability of default (PD), the loss given default (LGD), and the exposure at default (EAD). In dollar terms, Expected Loss = PD × LGD × EAD. As a percentage of the exposure, drop the EAD and multiply PD by LGD. Convert each percentage to a decimal before multiplying. A loan with a 10% probability of default, a 50% loss given default, and a $100,000 exposure gives 0.10 × 0.50 × $100,000 = $5,000 of anticipated credit loss over the measurement horizon. The Bank for International Settlements codified this relationship in its Basel II internal ratings-based framework, and it now sits under credit-risk capital rules worldwide.¹

The formula is simple. The work is in the three inputs. Each one has its own definition, its own estimation method, and its own room for error.

Probability of Default

Probability of default is the likelihood a borrower fails on a debt obligation within a set window, almost always twelve months for regulatory purposes. Lenders estimate it from historical payment data on borrowers with similar credit profiles, internal scorecards, or external ratings from agencies like Moody’s and S&P Global. Values range from a fraction of a percent for highly rated sovereigns to double digits for speculative-grade corporates.

How you estimate PD matters as much as the number itself. A through-the-cycle approach smooths out short-term swings and reflects long-run credit quality, which makes estimates stable but slow to react to deteriorating conditions. A point-in-time approach incorporates current macroeconomic data and produces estimates that move with the credit cycle, tracking actual default rates more closely from quarter to quarter. Older Basel II guidance leaned toward through-the-cycle. Both IFRS 9 and the U.S. CECL standard now push institutions toward point-in-time projections that account for where the economy is heading, not just where it has been.

Exposure at Default

Exposure at default is the total dollar amount the lender would be owed at the moment the borrower stops paying. For a standard term loan, that is the outstanding principal plus accrued but unpaid interest and fees.² For revolving credit lines and other commitments, the calculation gets more complicated, because borrowers in financial distress tend to draw down available credit before they default.

Regulators handle this with credit conversion factors that estimate what percentage of an undrawn commitment will be drawn by the time of default. Under the U.S. standardized approach:

0% for commitments the lender can cancel unconditionally at any time
20% for commitments with an original maturity of one year or less that the lender cannot cancel unconditionally
50% for commitments with an original maturity of more than one year that the lender cannot cancel unconditionally

Apply the factor to the undrawn portion and add it to the current balance.³ A borrower with $60,000 drawn on a $100,000 line with more than a year remaining has an estimated EAD of $60,000 plus 50% of the $40,000 undrawn portion, or $80,000.

Loss Given Default

Loss given default is the fraction of the exposure the lender actually loses once recovery efforts are exhausted. Recover $55,000 on a $100,000 default and LGD is 45%.⁴

Recovery is not free, and LGD reflects that. It captures three categories of loss: the lost principal and interest, the carrying cost of a non-performing loan while it sits on the books, and the workout expenses of collecting, including legal fees, court costs, and collections staff time.⁵ A foreclosure that takes eighteen months and requires litigation eats heavily into whatever the property eventually sells for.

Collateral and Seniority

Two factors dominate recovery. The first is whether the loan is secured and how much the collateral is worth at the time of default. A residential mortgage backed by a property worth more than the loan balance has a far lower LGD than an unsecured credit card. The second is where the lender sits in the borrower’s capital structure. Senior secured creditors get paid before subordinated lenders, who get paid before equity holders.

Under the Basel Foundation internal ratings-based approach, when a bank does not model its own estimates, supervisory LGD values apply:

40% for senior unsecured claims on non-financial corporates
45% for senior unsecured claims on banks, sovereigns, and financial institutions
75% for all subordinated claims

These figures set a floor for banks that have not developed their own advanced recovery models.⁶

LGD Moves With the Economy

Recovery rates tend to drop during recessions, precisely when default rates are rising. Collateral values fall, buyers are scarce, and courts are congested. That positive correlation between default frequency and loss severity means LGD estimates set during benign conditions can seriously understate the losses that actually materialize in a downturn. Institutions that mark LGD to current market conditions rather than long-run averages will capture this cyclicality more accurately.

Working a Single Loan

For any individual loan, the calculation is mechanical. Take a $250,000 commercial loan with a 3% PD and a 40% LGD:

$250,000 × 0.03 × 0.40 = $3,000

That $3,000 is what the lender should, on average, set aside or price into the interest rate to cover credit risk on that loan.

Scaling to a Portfolio

Portfolio expected loss is the sum of the individual expected losses across every exposure. Each loan carries its own PD, LGD, and EAD, and the products are added together.¹ A book of 500 loans produces 500 expected-loss figures that aggregate into a single portfolio number, which is what makes the calculation useful for capital planning.

Precision matters at scale. A one-percentage-point error in LGD across a $10 billion loan portfolio shifts the expected loss estimate by tens of millions of dollars, which flows directly into how much capital the institution holds and how it prices new lending.

Expected Loss Versus Unexpected Loss

Expected loss is only the average. It is a cost of doing business, much like shrinkage in retail, and banks cover it through loan loss provisions and allowances that reduce earnings but are planned for. Unexpected loss is the risk that actual losses exceed the average, sometimes by a wide margin, and it is covered with capital rather than provisions.⁷

The two sit on different parts of the same loss distribution. Expected loss is at the center. Unexpected loss captures the tail, measured as a standard deviation or a value-at-risk figure at a stated confidence level. Regulatory capital minimums are calibrated above and beyond whatever the bank provisions for expected loss, so that a bad year doesn’t turn into insolvency.

Forward-Looking Adjustments Under IFRS 9 and CECL

Both IFRS 9 and the U.S. CECL standard require institutions to incorporate forward-looking information rather than relying only on historical loss rates. In practice, that means feeding macroeconomic forecasts into the model. GDP growth, unemployment, interest rate paths, housing prices, and consumer spending all influence how PD and LGD will behave in the near future.

Most institutions run multiple economic scenarios, typically a baseline, an optimistic case, and a recessionary case. Each produces its own expected loss estimate, and the final figure is a probability-weighted blend. This is where the most judgment enters, and where two banks holding identical portfolios can report meaningfully different expected loss numbers based on how pessimistic or optimistic their assumptions are.

The two standards differ in when the number gets recognized. IFRS 9 uses a three-stage model: a twelve-month expected credit loss for assets whose credit risk has not increased significantly since origination, and a lifetime expected credit loss once credit risk has increased significantly or the asset is credit-impaired.⁸ IFRS 9 includes a rebuttable presumption that credit risk has increased significantly when a payment is more than 30 days past due.⁹

CECL takes a different approach. Under Accounting Standards Update 2016-13, U.S. institutions recognize lifetime expected credit losses from the moment a loan is originated, even when the risk of loss is remote.¹⁰ There is no staging. Every financial asset measured at amortized cost gets a lifetime loss estimate on day one, adjusted for expected prepayments. The change was deliberate: the prior incurred-loss model recognized losses only after they were probable, and banks entered the 2008 crisis with reserves that turned out to be far too thin.

A Note on Tax Treatment

The reserve a bank builds under CECL or IFRS 9 is not a tax deduction. Federal tax law requires an actual economic loss, not a statistical estimate of future loss. A wholly worthless debt is deductible in the year it becomes worthless, and a partially worthless debt can be deducted to the extent it is charged off during the taxable year.¹¹ The reserve method was repealed in 1986 for most taxpayers. The CECL allowance on the balance sheet is a book expense, not a tax expense, until the debt is actually written off or charged down, which creates a permanent timing difference and the need for deferred tax asset planning.

1
Bank for International Settlements (BIS). An Explanatory Note on the Basel II IRB Risk Weight Functions
2
Office of the Comptroller of the Currency. Exposure at Default of Unsecured Credit Cards
3
eCFR. 12 CFR 217.33 Off-Balance Sheet Exposures
4
Federal Reserve Bank of Chicago. Loss Given Default and Economic Capital
5
Federal Reserve Bank of New York. What Do We Know About Loss-Given-Default?
6
Bank for International Settlements (BIS). CRE32 – IRB Approach: Risk Components
7
Bank for International Settlements (BIS). Forecasting Expected and Unexpected Losses
8
Bank for International Settlements (BIS). IFRS 9 Financial Instruments
9
IFRS Foundation. Expected Credit Losses Slides
10
FDIC. Current Expected Credit Losses (CECL)
11
Office of the Law Revision Counsel. 26 U.S. Code 166 – Bad Debts