IFRS 9 ECL calculator. 12-month, lifetime, probability-weighted.
One exposure, three macro scenarios. Change a weight, a multiplier or the remaining maturity and watch the allowance move. Every formula is written out below the calculator. Runs in your browser; nothing you enter leaves the page.
| Scenario | PD used | 12-month ECL | Lifetime ECL | Weight | Weighted |
|---|
Year by year, base case
Lifetime build-up| Year | Exposure | Survival to start | Marginal PD | Expected loss | Discount | Present value |
|---|
What a weight shift alone does
Same PDs, different probabilities| Weights U / B / D | Weighted ECL | Coverage | vs current |
|---|
The formulas, in the order the calculator applies them.
- Scenario PD. Each scenario's annual PD is the base 12-month PD times that scenario's multiplier, capped at 100 percent.
PDs = min(1, PDbase × ms) - Survival and marginal default. With a constant annual hazard, the probability that the borrower is still performing at the start of year t is the survival, and the probability of defaulting during year t is the marginal PD.
St−1 = (1 − PDs)t−1 · MPDt = St−1 × PDs - Exposure profile. Bullet keeps the full exposure to maturity. Straight line reduces the exposure at the start of each year by one equal instalment.
EADt = EAD × (1 − (t − 1) / T) for straight line; EADt = EAD for bullet - Expected loss in year t, discounted. Default is assumed at the end of year t and the shortfall is discounted at the effective interest rate.
ELt = MPDt × LGD × EADt / (1 + EIR)t - 12-month and lifetime ECL. 12-month ECL is year one only. Lifetime ECL is the sum to maturity.
ECL12m = EL1 · ECLlife = Σt=1..T ELt - Stage. Stage 1 reports 12-month ECL, Stage 2 lifetime ECL. Stage 3 is credit-impaired: PD is 100 percent, so the allowance is the exposure times LGD and the scenario multipliers no longer apply.
- Probability weighting. The reported ECL is the weighted sum of the scenario ECLs, using the weights normalised to 100 percent. The weighting is applied to the loss outcome, not to the PD.
ECL = Σs ws × ECLs
Sources: IFRS 9 Financial Instruments, section 5.5 (impairment) and appendix B5.5, IFRS Foundation. Scenario weight presets from the Riskweise 16-scenario stress testing matrix on the tools page. For the model-governance side of ECL see Beyond the black box and the IFRS 9 ECL implementation service.
Expected credit loss, asked and answered.
What is the difference between 12-month and lifetime expected credit loss?
A 12-month ECL is the portion of lifetime ECL that results from default events possible within twelve months of the reporting date: the probability of default in year one, times the loss given default, times the exposure, discounted. Lifetime ECL sums that calculation over every year to maturity, with each year weighted by the probability that the borrower has survived to the start of it. IFRS 9 requires 12-month ECL for Stage 1 exposures and lifetime ECL for Stage 2 and Stage 3. The move from Stage 1 to Stage 2 therefore multiplies the allowance without any change in the borrower, which is why the size of the lifetime-to-12-month ratio, driven by remaining maturity and the PD level, is the number a risk committee should know for each portfolio.
Why does the calculator weight the ECL of each scenario rather than weighting the PD?
IFRS 9 requires the expected credit loss to reflect an unbiased and probability-weighted amount determined by evaluating a range of possible outcomes. The weighting is applied to the loss outcome under each scenario, not to an input. When the loss is a linear function of PD the two approaches give the same answer, but they diverge as soon as anything is non-linear, for example when a downside multiplier pushes the PD to its cap of 100 percent, or when the LGD itself varies by scenario. Weighting the outcomes is the approach that is correct in every case, so it is the one used here.
What discount rate does IFRS 9 require for expected credit losses?
The effective interest rate determined at initial recognition, or an approximation of it, for financial assets that are not purchased or originated credit-impaired. The cash shortfalls in each future period are discounted back to the reporting date at that rate. This calculator discounts each year's expected loss from the end of the year in which the default is assumed to occur, which is a simplification most portfolio models refine to a mid-year convention; the direction and order of magnitude are the same.
How do macroeconomic scenarios enter the IFRS 9 ECL calculation?
Through the forward-looking information IFRS 9 requires. In practice a bank builds a base case from its economic forecast and at least one upside and one downside case, converts each into a PD adjustment through a satellite model, and assigns each a probability. The calculator represents that with a PD multiplier and a weight per scenario. The preset weight sets, 30/40/30, 10/40/50 and 0/25/75 for upside, base and downside, are the three severities of the macro weight shift scenario in the Riskweise stress testing matrix, so the calculator shows how a reallocation of probability alone moves the allowance before any PD changes.
Is this calculator an IFRS 9 model?
No. It is a transparent illustration of the mechanics for a single exposure, using a constant annual hazard rate, a single LGD and a simple amortisation profile. A production ECL model works at facility or segment level with PD term structures that vary by rating and time, LGDs that depend on collateral and cure rates, exposure profiles that include undrawn commitments, and staging rules driven by significant increase in credit risk criteria. The calculator is useful for checking an order of magnitude, explaining a result to a committee, or testing what a change in weights or maturity does to the allowance. It is not a substitute for the model, and it is not a regulatory output.
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