Loss given default measures severity after default. Calculate a recovery ledger, account for costs and timing, and separate LGD from default probability and expected loss.
Loss given default
Loss given default (LGD) is the proportion of an exposure at default lost after allowing for recovery on a specified valuation basis. It measures the severity of a default. A lender can face a low chance of default and still suffer a large loss if the event occurs, so a credit model needs a severity assumption as well as a probability.
For a positive exposure and net recovery value measured in the same currency at the same date,
LGD=EADEAD−net recovery value.
“Net” matters: recovery receipts may arrive after a lengthy collection process, and obtaining them can cost money. The denominator also matters: the relevant claim can differ from the original loan advance, bond purchase price or derivative notional.
A loss percentage needs a recovery ledger
Consider a wholly fictional loan with fixed EAD of USD 1,000,000. After default, stipulate USD 400,000 of net recovery value, measured at the default date. This is already the value after collection costs and any discounting of delayed recoveries; it is not necessarily cash received immediately. Any collateral proceeds are included in that amount, and there are no additional recoveries or costs.
Synthetic USD 1,000,000 exposure divided into USD 400,000 net recovery, 40%, and USD 600,000 loss, 60%, on one default-date valuation basis. No default probability is assigned.
Original synthetic ledger in USD. Widths represent shares of the same fixed exposure. Recovery is net of costs and measured at the default date; the example supplies conditional severity, with no default probability or issuer calibration.
The recovery rate is 40%, so LGD is its complement, 60%, under this same denominator and valuation convention. A quoted bond price after default and eventual cash collected through a workout are different recovery measurements. Substituting one for the other changes the question.
LGD is also distinct from a trading return. An investor who bought the loan below its claim amount would compare proceeds with that purchase price when calculating investment performance; the LGD ledger above compares recovery with EAD.
Why the dates and costs change the answer
Here is a separate fictional workout on the same USD 1,000,000 EAD. Stipulate one gross receipt of USD 440,000 exactly one year after default, collection costs of USD 55,000 paid on that same future date, and a 10% effective annual discount rate for both cash flows. This chosen rate is an arithmetic assumption, not a prescribed regulatory or market rate.
Default-date valuation
USD
Gross receipt: 440,000 / 1.10
400,000
Collection costs: 55,000 / 1.10
50,000
Net recovery value
350,000
Loss relative to EAD
650,000
This workout has LGD of 65%. Counting the gross future receipt as net recovery would overlook both collection costs and the time value of money. The stipulated nominal net receipt is USD 385,000; its default-date value is USD 350,000.
The Basel Framework's CRE36.76 defines loss for IRB LGD estimation economically, including material discount effects and direct and indirect collection costs. Its guidance on recovery discounting, §§30.12–30.15, also addresses the risk in uncertain recovery streams. These banking-supervision conventions do not make the illustrative 10% rate appropriate for another purpose.
What belongs in an LGD assumption
A recovery assumption describes a particular facility and claim, rather than the borrower alone. Relevant features include:
Collateral and enforceability. What can the creditor actually control and sell, in which currency, at what cost and after what delay? A collateral appraisal is not automatically a realised recovery.
Legal rank. Which other claims have priority, and how do security rights, guarantees and the applicable insolvency process affect the amount available to this creditor?
Economic conditions. Asset-sale proceeds and workout times can deteriorate in the same conditions that produce more defaults. A benign-period recovery average may give an unsuitable stress assumption.
Keep the exposure and recovery conventions consistent. If collateral has already reduced the exposure denominator in a model, deducting the same collateral again through recovery can count its benefit twice.
A realised LGD is measured from a completed default and recovery process. An estimated LGD predicts severity before the outcome is known; unfinished workouts require assumptions about outstanding receipts and costs. For IRB capital, CRE36.83–36.85 addresses downturn conditions, borrower–collateral dependence and the limitations of using collateral market value alone. An individual realised loss, a forecast and a regulatory downturn parameter therefore need not agree.
In a simple ledger with no extra costs and recovery between zero and EAD, LGD lies between 0% and 100%. Economic-loss conventions that include costs can produce losses above EAD; do not impose a universal cap without specifying the model or framework.
From severity to expected loss
LGD does not supply a default probability. Neither the 60% severity above nor its 40% recovery tells us how likely the default was.
For a chosen horizon, let D denote default. In a default-loss model with zero loss outside D and all amounts on a consistent valuation basis,
E[L]=P(D)E[EAD×LGD∣D].
This conditional expression assumes default has positive probability; if default is impossible, the model’s default loss is zero. Fixed EAD and fixed LGD give the familiar product of exposure, PD and LGD. When severity and exposure vary together within default states, multiplying their separate averages can miss their dependence. A historical physical-risk estimate and an assumption used in market pricing also serve different purposes; the recovery number should be identified accordingly.
Alexander J. McNeil, Rüdiger Frey and Paul Embrechts, Quantitative Risk Management: Concepts, Techniques and Tools, revised edition (Princeton University Press, 2015), §10.1.5, pp. 372–373: EAD, PD, recovery severity and dependence.
Basel Committee, Basel Framework, CRE36, version effective 1 January 2023, §§36.76 and 36.83–36.85: economic loss, collection costs, downturn LGD and collateral considerations.
Basel Committee, Consolidated Guidelines, CRI30, §§30.12–30.15: discounting recovery and workout-cost streams, including their risk. The examples here are stipulated ledgers, not estimates for a real borrower.
