Expected Loss Calculator (PD × LGD × EAD)
Calculate the expected credit loss of a loan or portfolio from probability of default (PD), loss given default (LGD) and exposure at default (EAD), plus the unexpected loss and risk-adjusted margin.
How it works
EL = PD × LGD × EAD · EL rate = PD × LGD · loss in default = EAD × LGD · unexpected loss (fixed LGD) = EAD × LGD × √(PD × (1 − PD)) · risk-adjusted margin = margin − PD × LGD
Expected loss is the average credit loss a lender should plan for on a loan over one year: the chance the borrower defaults (PD) times the share of the exposure that is lost after recoveries (LGD) times the amount outstanding at default (EAD). It is the core of the Basel internal-ratings-based approach and of IFRS 9 / CECL loan-loss provisions, and it should be covered by pricing; the unexpected loss — the volatility around that average — is what bank capital is held against.
Worked example
A loan with 100,000 exposure at default, a 2% one-year probability of default and a 45% loss given default has an expected loss of 100,000 × 0.02 × 0.45 = 900.00, or 0.90% of the exposure. If it does default, 45,000 is lost; the unexpected loss (one standard deviation) is 45,000 × √(0.02 × 0.98) = 6,300.00. With a 3% interest margin the risk-adjusted margin is 3% − 0.90% = 2.10%, and a 2% PD sits in the moderate default-risk band.
Sources: BIS — Basel Framework, CRE31 IRB risk weight functions · BIS — An Explanatory Note on the Basel II IRB Risk Weight Functions
Frequently asked questions
What is the difference between expected and unexpected loss?
Expected loss is the average you should price in and provision for. Unexpected loss is how far actual losses can swing above that average; banks hold capital against it rather than covering it through pricing.
What LGD should I use?
Under the Basel foundation approach, senior unsecured corporate loans use 45% and subordinated claims 75%. Secured loans have lower LGDs depending on the collateral; mortgages are often 10%–25%.
How does this relate to IFRS 9 and CECL?
Both standards build loan-loss allowances from PD, LGD and EAD. IFRS 9 uses 12-month expected loss for performing loans and lifetime expected loss once credit risk has increased significantly; CECL uses lifetime loss from the start.
How do I use the risk-adjusted margin?
If the loan’s margin is smaller than PD × LGD, the loan is expected to lose money on credit alone, before operating costs and capital charges.
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Educational estimate, not credit, accounting or investment advice. Lenders, auditors and rating agencies adjust these ratios with their own definitions — use the exact definitions in your loan agreement or reporting framework.