Credit risk math: PD, LGD, EAD, Expected Loss, Unexpected Loss

Credit risk on a loan portfolio doesn't get priced by gut feel; it gets priced by breaking the question "how much might we lose" into a small number of measurable components, then combining them into a single expected figure and a separate tail-risk figure. Almost every institutional credit model, from bank capital requirements to private credit fund reserving, runs through the same handful of terms.

How it works

Probability of default (PD) is the likelihood that a given borrower, or a given cohort of similar borrowers, fails to meet its obligations within a defined period, usually expressed as an annualized percentage. PD is estimated from historical default rates on comparable loans, adjusted for borrower-specific factors: credit history, industry, macro conditions, collateral quality.

Loss given default (LGD) is what actually gets lost if a default happens, expressed as a percentage of the exposure. LGD is rarely 100%, because collateral, guarantees, and recovery processes typically claw back some portion of the loss. A well-collateralized loan might carry an LGD of 20-30%; an unsecured loan can run much higher.

Exposure at default (EAD) is simply how much is actually outstanding at the moment of default, which can differ from the original loan amount if the facility is revolving or partially drawn.

Multiply the three together and you get Expected Loss: EL = PD x LGD x EAD. This is the loss a lender should plan for as a matter of course, the number that gets built into pricing (interest rates need to cover it) and reserving (provisions get set aside for it). Expected Loss isn't a worst case. It's the average outcome across a large enough portfolio.

Unexpected Loss is the harder number: the additional loss that could occur beyond the expected figure during a genuinely bad period, driven by the volatility and correlation of defaults across the portfolio, not just their average rate. A portfolio of 500 uncorrelated small loans has much lower Unexpected Loss, relative to its size, than 5 large loans to correlated borrowers in the same industry, even if both portfolios carry an identical Expected Loss. Unexpected Loss is what capital reserves and equity cushions are actually sized against, because it's the loss that shows up unpredictably rather than reliably.

Why it matters

Expected Loss belongs in pricing; Unexpected Loss belongs in capital structure. Conflating the two is a common and expensive mistake: a lender that only reserves for Expected Loss, and treats any capital cushion as a rounding error, is unprepared for the exact scenario capital is supposed to protect against, a correlated bad quarter, not an average one.

The math also explains why diversification is a risk management tool and not just a platitude. Spreading exposure across uncorrelated borrowers, industries, and geographies doesn't change a portfolio's Expected Loss much, but it can meaningfully compress Unexpected Loss, because uncorrelated defaults are statistically less likely to cluster in the same period.

Where this shows up in Rekord

Rekord underwrites every deal type against these same PD, LGD, and EAD inputs, and portfolio-level Unexpected Loss is what drives concentration limits across originators and deal types. For how correlation specifically gets measured across a portfolio, see Portfolio correlation, concentration, and the HHI index.