Loss given default is the share of an exposure a lender expects to lose if the borrower defaults, after everything that can be recovered has been recovered and the cost and delay of recovering it have been accounted for. It is one of three parameters that together produce expected credit loss, alongside probability of default and exposure at default. This calculator builds LGD from its components rather than asking you to guess it, and then combines it with a probability of default to give the expected loss.
Arb Digital built this page as a teaching aid for the structure of the calculation. It publishes no supervisory haircut, no conversion factor and no downturn adjustment, because those are defined by the applicable rulebook and by each institution's approved models. Every parameter here is one you enter, with the reason it matters stated next to it.
What This Loss Given Default Calculator Does
Enter the drawn balance and undrawn commitment with a credit conversion factor to derive exposure at default, then the collateral value with its haircut, the recovery costs as a proportion of gross recovery, the length of the workout and the discount rate applied to it. The hero figure is LGD as a percentage. The grid shows the exposure at default the inputs imply, the effective recovery rate after costs and discounting, the loss amount if default occurs, and the expected credit loss once your probability of default is applied.
Recovery is capped at exposure. Collateral worth more than the exposure does not produce a negative loss, because a lender recovers what it is owed and no more. That cap matters on over-collateralised facilities, where a naive calculation would otherwise show a recovery rate above one hundred per cent.
How to Use It
- Build exposure at default first. Drawn balance plus the undrawn commitment multiplied by a conversion factor, because facilities are typically drawn down further on the way into default.
- Value the collateral and haircut it. The haircut should reflect a forced sale in poor conditions, not an orderly one in good conditions.
- Add the cost of recovering. Legal fees, agents, servicing and internal workout resource all reduce what actually reaches the lender.
- Set the workout period and discount rate. Recovery cash arrives late, and late money is worth less.
- Enter a probability of default and press Calculate to see LGD, exposure, recovery rate, loss amount and expected loss update together.
The Formula and How It Is Calculated
Exposure at default is drawn + undrawn × CCF. Gross recovery is the haircut collateral value, capped at exposure. Net recovery is gross recovery less recovery costs, discounted back over the workout period. The recovery rate is that discounted amount divided by exposure, and LGD = 1 − recovery rate. Expected credit loss is PD × LGD × EAD.
Work the defaults through by hand. Exposure at default is 8,000,000 + 4,000,000 × 0.50 = 10,000,000. Collateral of 7,000,000 with a 25% haircut gives 5,250,000, which is below exposure so no cap applies. Recovery costs of 10% take 525,000, leaving 4,725,000. Discounting that over 1.5 years at 8% divides by 1.08 raised to the power 1.5, which is 1.12237, giving 4,209,846. The recovery rate is 4,209,846 ÷ 10,000,000 = 42.10%, so LGD is 57.90%. The loss if default occurs is 5,790,154, and with a 2% probability of default the expected credit loss is 0.02 × 5,790,154 = 115,803.
Notice how much work the discounting does. Undiscounted, the recovery rate would be 47.25% and LGD 52.75%. Eighteen months of delay at 8% moved LGD by more than five percentage points on this exposure — over half a million in loss on a ten million facility, purely from timing.
Why the Framework Treats These as Parameters, Not Facts
Under the internal ratings-based approach, the Basel Framework's credit risk chapter on risk components sets out the calculation of the risk components used in the risk-weight functions — probability of default, loss given default, exposure at default and maturity — for each asset class. What those components may be, how they must be estimated, which floors apply and whether a bank may use its own estimates at all are all determined by supervisory rules and by model approval, not by arithmetic.
That is why nothing on this page is published as a figure. Conversion factors, collateral haircuts, eligibility criteria for collateral, minimum LGD floors and downturn requirements are rulebook matters that differ by jurisdiction and are revised. A calculator that hard-coded any of them would teach the wrong thing confidently. The mechanism is stable; the parameters are not.
A specific requirement worth knowing about: supervisory frameworks generally require LGD estimates to reflect economic downturn conditions rather than a long-run average, because defaults cluster in downturns and collateral is worth least exactly when it is most needed. A long-run average LGD applied to a downturn portfolio systematically understates loss. Whether and how a downturn adjustment applies to you is a rulebook question.
Collateral Is Worth Less Than You Think in Default
The largest and most common error in LGD estimation is valuing collateral as though it will be sold in normal conditions by a willing seller with time to negotiate. Default recovery is none of those things. The sale is forced, the timing is not chosen, the buyer knows why the asset is on the market, and the asset class is frequently under pressure for the same macroeconomic reason the borrower defaulted. Property collateral behind a property developer is the textbook case of correlated exposure.
Legal enforceability is the second issue. Collateral that cannot be perfected, seized or sold in the relevant jurisdiction contributes nothing regardless of its appraised value, and the same asset pledged to multiple lenders contributes only the share your security ranking actually reaches. Recovery costs are the third: enforcement is expensive, and on smaller exposures fixed enforcement costs can consume a large fraction of what is recovered.
The practical implication for the haircut field is that it should be estimated from your institution's own realised recovery data where that exists, or from a defensible external source where it does not — never from an appraisal value with a round number subtracted.
Expected Credit Loss and the Accounting Angle
The product of the three parameters is expected credit loss, and it appears in two different contexts that are easy to confuse. In the prudential context it feeds regulatory capital through the risk-weight functions. In the accounting context, IFRS 9 Financial Instruments sets out impairment requirements based on expected credit losses on financial assets and commitments to extend credit, which drives the loss allowance in the financial statements.
The two use similar language and different definitions. Accounting expected credit loss is forward-looking, probability-weighted across scenarios, and may cover twelve months or the lifetime of the instrument depending on whether credit risk has increased significantly. Regulatory parameters carry floors, downturn requirements and conservatism that accounting estimates do not. Numbers from one framework should never be dropped into the other without adjustment.
Where LGD Sits Among the Other Ratios
LGD is a severity measure and says nothing about likelihood. A facility with a 90% LGD and a 0.01% probability of default is a lower expected loss than one with a 20% LGD and a 5% probability. The two must be read together, which is exactly what the expected loss figure in the grid does. It also says nothing about liquidity — for the funding-stress side of the prudential framework, our liquidity coverage ratio calculator covers the LCR and NSFR.
On the pricing side, expected loss is one component of what a lender needs to charge, alongside funding cost, capital cost and operating cost. Our cost of debt calculator and bond yield calculator look at the same relationship from the borrower's and the investor's side, the NPV calculator handles the discounting of the recovery stream directly, and the debt to equity ratio calculator and credit utilization calculator cover leverage and drawdown behaviour.
Arb Digital builds free calculators and explainers for specialist audiences, without overstating what a model output means.
Browse the free tools hub Talk to Arb DigitalCommon Mistakes to Avoid
- Skipping the discounting. Recoveries arrive years after default, and treating them at face value understates LGD by a material margin.
- Valuing collateral at appraised value. Default recovery is a forced sale in poor conditions, often in the same downturn that caused the default.
- Ignoring the undrawn commitment. Borrowers approaching default draw down available lines, so exposure at default usually exceeds today's balance.
- Using a long-run average where a downturn estimate is required. Defaults cluster, and average recoveries overstate what is achievable when they do.
- Mixing accounting and regulatory parameters. IFRS 9 expected credit loss and the prudential parameters answer different questions under different rules.
Related Free Tools From Arb Digital
For the liquidity side of the prudential framework use the liquidity coverage ratio calculator. For pricing and discounting see the cost of debt calculator, bond yield calculator and NPV calculator. For borrower leverage and utilisation, the debt to equity ratio calculator and credit utilization calculator apply, and the free tools hub lists the rest.
Frequently Asked Questions
It is the proportion of an exposure a lender expects to lose if the borrower defaults, after recoveries, recovery costs and the delay in collecting them. It is expressed as a percentage of exposure at default and is one of three parameters that combine to give expected credit loss.
Because recovery cash arrives long after default and is worth less when it does. Discounting an eighteen-month recovery at eight per cent moves LGD by several percentage points, which on a large exposure is a substantial amount of loss created purely by timing rather than by any change in what is recovered.
It is the assumed proportion of an undrawn commitment that will have been drawn by the time default occurs. Borrowers in difficulty typically use available lines, so exposure at default is usually larger than the current balance. The applicable factor is a supervisory or model parameter rather than an observation.
No. A lender recovers what it is owed and no more, so recovery is capped at exposure at default in this calculator. Over-collateralised facilities produce an LGD of zero rather than a negative loss, and surplus collateral value returns to the borrower or to junior creditors.
Because they are defined by the applicable supervisory rulebook and by each institution's approved models, they differ by jurisdiction and asset, and they are revised. Publishing them would present a moving target as settled fact. The mechanism is what this page teaches; the parameters are yours to supply.
No. The prudential framework applies floors, downturn requirements and other conservatism that accounting estimates do not, while IFRS 9 requires probability-weighted, forward-looking estimates over either twelve months or the instrument's lifetime. The two share vocabulary but not definitions, and figures should not be transferred between them.
Not on its own. LGD measures severity, not likelihood. An unsecured facility to a very strong borrower can carry a high LGD and a very low expected loss, while a secured facility to a weak borrower can carry a low LGD and a higher expected loss. The two parameters only mean something together.
This tool is provided for educational use only and is not credit, regulatory or financial advice. It publishes no haircut, conversion factor or supervisory parameter — every figure applied is one you entered. Regulatory credit risk parameters are governed by the applicable supervisory rulebook and by approved internal models, and a qualified risk professional should determine any figure used in practice.
