Expected Loss Calculator
The formula
What the expected loss tells you
The Basel and IFRS 9 workhorse: what a credit portfolio statistically loses per year, as the product of who might fail (PD), how much the failure costs (LGD) and how much is at stake (EAD). Pricing must clear EL; capital exists for everything above it.
Calculation: EL = EAD × PD × LGD. Enter your inputs and every substitution is shown below the result.
Reading the result
A loan priced 20bp above its EL is thin once funding, operating cost and the UL capital charge are added.
Rules of thumb: Prime mortgages historically EL 5–15bp · unsecured consumer 1–3%/yr · corporate performing ~15–60bp
Limitations and best practice
Through-the-cycle vs point-in-time PDs differ enormously; downturn LGD can double the base case. Expected loss is a mean — credit damage lives in the tail.
This calculator gives an estimate based on standard formulas; it is not professional financial, medical, legal or engineering advice. Verify anything you plan to act on with a qualified professional and your own records.
Frequently asked questions
Is expected loss the same as provisions?
Who actually uses expected loss?
Source & methodology
Basel II/III IRB framework; IFRS 9 (2014) expected credit losses.
Expected Loss explained: formula, worked example and honest limits
This page was written for one job: turning your own inputs into a defensible figure, with the working shown. Expected Loss is the kind of number people argue about from memory. This page ends that argument with arithmetic you can watch happen: enter your figures, get Expected loss (annual) in real time, and see every substitution printed below.
Return and risk arrive as a package in Expected Loss. A result of $2,014 means little until you ask what variance sits behind it, how it compares with the boring alternative (the companion tools above compute exactly that comparison), and whether the inputs assume the good scenario or the expected one.
What makes Expected Loss worth calculating is not precision but position: it tells you which side of a threshold you are on, and by how much. A rough figure that settles the direction beats an elaborate one that never commits.
Nothing below is stock text pasted around a number: the worked example computes expected loss (annual) = $2,014 from this tool’s own defaults, and the sensitivity section ranks the inputs that move the result — Exposure at default first, at ≈10.0 % of the headline for a ten-percent error either way in that input. Work down the page and by the end you could re-derive the result in a spreadsheet from memory.
Inside the Expected Loss calculation: formula and every input
The engine implements a single stated model: EL = EAD × PD × LGD. There is no hidden coefficient and no login-gated precision — the formula printed is the formula executed, which is also what makes the result citable.
Exposure at default ($) (example value 238,008) is a measured number in the unit named by the label; the formula does not convert for you. This input feeds the formula directly; a defensible figure here is worth more than false precision anywhere else.
Probability of default (%) (example value 2) is a plain measured quantity — the unit shown in the label is the unit the formula expects. Rates are the most mis-transcribed input on any page like this; copy it from the document rather than retyping from memory.
Loss given default (%) (example value 47) is a measured number in the unit named by the label; the formula does not convert for you. Enter it exactly as your document states it — quoted annual, monthly and effective rates are three different numbers.
Expected Loss on the example inputs: the complete substitution
Abstract formulas are hard to trust, so here is the complete substitution using the default inputs, written the way an examiner would want it. Starting figures: Exposure at default ($), Probability of default (%), Loss given default (%). The computed expected loss (annual) comes out at $2,014, which the interpretation band labels “≈ 85 bp of exposure — the number pricing must clear”.
- EL = $238,008 × 1.8% × 47% = $2,014
EL as % of EAD — 0.846 %. If your inputs change, this is usually the first companion figure to move.
Basis points — 84.6 bp. Compare it against the main result of $2,014 before drawing conclusions.
Credit spread needed (EL + capital charge ≈ +60bp) — 60.85 bp. Read next to the headline, this is the figure that shows the shape of the trade-off.
Unexpected loss proxy (√(PD(1−PD))×LGD×EAD) — $14,872. This is the number experienced users quote when the headline alone would mislead.
Overwrite any input above and every line of this example updates with it — the substitution is live, not a screenshot of somebody else’s numbers.
How far Expected Loss can reasonably move
The honest version of any estimate is a corridor, and this one is cheap to produce: Expected Loss was recomputed at 5 points along the dominant input, with every other field left untouched.
| Exposure at default setting | Expected loss (annual) |
|---|---|
| 80 % of the example value | $1,611 |
| 90 % of the example value | $1,812 |
| example inputs | $2,014 |
| 110 % of the example value | $2,215 |
| 120 % of the example value | $2,416 |
The corridor runs from $1,611 to $2,416 across that band — which is the range worth planning inside rather than the single $2,014 point estimate. Reproduce it in the form above by editing Exposure at default alone; the substitution steps will follow your figures exactly.
Where Expected Loss is fragile — and where it is not
Generic advice says “it depends on your inputs”; this section says exactly how much. Each field was perturbed by ±10 % in isolation and the expected loss (annual) recomputed, so the ranking below is measured rather than asserted. For Expected Loss the ranking is measured rather than guessed, and it belongs to these defaults: shift the starting point and the order can shift with it.
- Nudge Exposure at default by ±10 % and Expected Loss lands between $1,812 and $2,215 (sensitivity ≈10.0 %)
- Probability of default: ten percent up gives $2,215, ten percent down gives $1,812 — ≈10.0 % of the expected loss (annual) either way
- Nudge Loss given default by ±10 % and Expected Loss lands between $1,812 and $2,215 (sensitivity ≈10.0 %)
Exposure at default is the dominant lever here: ten percent either way moves the result by about 10.0 %, from $1,812 to $2,215. Measure that input from a document rather than from memory, and Probability of default is effectively tied with it (≈10.0 % for the same nudge), so verify the pair together. The rest of the inputs earn only a rounding-error of attention, and that asymmetry is the practical payoff of measuring rather than asserting.
Is your Expected Loss good — reading the result bands
The value above only becomes useful the moment you know what it is being measured against. On the example inputs the band reads “≈ 85 bp of exposure — the number pricing must clear”; your own figures place you on a different rung of the same ladder. Before treating the band as fact, note its width: ten percent either way on Exposure at default already spans $1,812 to $2,215. The practical reading rules: read the band as a starting hypothesis, then test it: change the two dominant inputs by ten percent and see whether the verdict survives. Verdicts that survive stress are the ones worth acting on.
Related measures answer related questions, and the distinctions matter: Expected Loss is the quantity, Expected loss (annual) is this tool’s reading of it, and the decision that follows belongs to neither of them separately.
Why Expected Loss results go wrong — and how to prevent it
Through-the-cycle vs point-in-time PDs differ enormously; downturn LGD can double the base case. Expected loss is a mean — credit damage lives in the tail. This calculator gives an estimate based on standard formulas; it is not professional financial, medical, legal or engineering advice. Verify anything you plan to act on with a qualified professional and your own records.
Stopping at the first plausible answer. If the result surprises you, the productive question is which input would have to be wrong for the surprise to disappear — then go check that input.
One mistake is specific to this engine: assuming every input matters equally. The computation above shows Exposure at default dominating — a careful figure there beats false precision everywhere else.
A final trap is presentation: reporting Expected Loss to more decimal places than the inputs support. The tool prints what the arithmetic gives; you should quote only what your least precise field justifies.
Six things to confirm before acting on Expected Loss
- Recompute once with the dominant input deliberately set low, and see whether the decision changes.
- Compare the result with one independent method or published benchmark.
- Re-verify Exposure at default against a source document — ten percent of error there moves the headline by ≈10.0 %.
- Record the date and the inputs alongside the number so future-you knows what was assumed.
- Check that every field the formula needs actually arrived from a document, not from recollection.
- Confirm the answer against one independent method or published benchmark for Expected Loss.
Step by step: getting a trustworthy Expected Loss out of this tool
Using a calculator well sounds trivial, but the difference between a decision-grade figure and a throwaway one lives entirely in the routine. The routine for Expected Loss takes a minute to learn and applies to every input above.
Step 1 — gather before you type. Expected Loss depends on exposure at default ($), probability of default (%), loss given default (%). Collect them from a source document — a statement, a report, an invoice, a log — rather than from memory, because recalled inputs are the single largest cause of wrong results. Estimates improve most when the worst case is written down in ink.
Step 2 — baseline before exploration. Get one defensible Expected loss (annual) on screen before you start nudging numbers. Without a baseline, every variation looks interesting and none of them means anything. If the verdict changes with a ten-percent nudge, report the nudge alongside the number.
Step 3 — play with the inputs on purpose. Ten percent up, ten percent down, one field at a time. Within a few minutes you will know this calculation better than most people who quote its results. Note the assumption you are least sure about; that is where the real risk lives.
Step 4 — stress before you commit. A decision that survives a ten-percent squeeze on its two biggest inputs needs no luck to be sound. One that does not survive is a decision about hope, not about arithmetic. A calculation you cannot explain to somebody else is a calculation you cannot defend.
Step 5 — record the context, not just the number. Note today’s date and the inputs alongside the $2,014 output. Six months from now the context is what turns this figure into a trend. Say the answer out loud before you save it; if it sounds wrong, the model did not change, your understanding did.
Where Expected Loss matters in practice
Most Fixed Income disagreements are arithmetic disagreements in disguise. When Expected loss (annual) of $2,014 sits on the table with its working shown, the conversation stops being about who sounds more confident and starts being about which input is wrong. Precision is a promise you make about your data; make sure your inputs can keep it.
The audience for this page is people who need one trustworthy number before their next decision. In professional Fixed Income practice the pattern is always the same — screen with Expected Loss, then invest slow analysis only in whatever survives the screen. The test of a good estimate is not that it feels right but that it changes what you do.
There is a personal-administration use people overlook: periodic self-checking. Expected Loss quietly drifts as life changes — rates move, bodies change, costs compound — and re-running it a few times a year catches drift while correction is still cheap. A figure nobody can reproduce is a figure nobody will act on twice.
The questions that come up most about Expected Loss
What affects Expected Loss the most?
The short answer: Exposure at default. The longer answer is the sensitivity table on this page, where every numeric input was probed by ten percent and the expected loss (annual) recalculated — Exposure at default moved it furthest, by roughly 10.0 % ($1,812 to $2,215).
Do probability of default and exposure at default matter equally?
Expected Loss here is co-driven: Exposure at default and Probability of default produced ≈10.0 % and ≈10.0 % responses, which is a tie for practical purposes. Everything below those two is a rounding error by comparison.
What is a typical Expected Loss?
On the worked example above Expected Loss comes out at $2,014. Treat that as one point on a distribution rather than a norm: the bands, the companion outputs and the sensitivity ranking tell you how wide the plausible range really is.
How do I calculate Expected Loss by hand?
Use the stated model — EL = EAD × PD × LGD — and substitute in the order the tool prints (it starts from EL = $238,008 × 1.8% × 47% = $2,014). On the example inputs the hand route lands on $2,014, exactly what the calculator shows. A spreadsheet reproduces it in two or three cells; doing it once by hand is what makes the automated answer trustworthy.
What happens to Expected Loss if exposure at default changes by 10 %?
On these inputs a ±10 % change in exposure at default takes Expected Loss to $2,215 against the $2,014 example — around 10.0 % of the headline. The same test on every other field is in the sensitivity section.
Is the Expected Loss result of $2,014 good or bad?
The tool answers “what”, not “whether”: $2,014 carries the verdict “≈ 85 bp of exposure — the number pricing must clear” for the default case, which is a starting interpretation rather than a verdict on your situation. Re-run with your own figures and compare the bands.
Can I predict future returns with Expected Loss?
No tool predicts; Expected Loss computes implications. Use it to ask "if these inputs hold, what follows" — then stress the assumptions.
How often should I check Expected Loss?
Whenever an input changes by more than a few percent, and otherwise on the rhythm of your decisions — before a purchase, a review, a renewal. Expected Loss is a snapshot, not a subscription; stale snapshots are the most common silent error in Investing & Markets planning.
Is expected loss the same as provisions?
IFRS 9 "ECL" is related but lifetime-adjusted and forward-looking; regulatory EL multiplies 12-month PD by LGD — same family, different horizons.
Who actually uses expected loss?
Banks under Basel IRB capital rules, lenders pricing loans and credit cards, and insurers setting reserves — anywhere the portfolio's average loss must be priced or provisioned.
Can this tool see the numbers I type?
It cannot. There is no submission step: the calculation happens in your browser and the result disappears when you close the page. Treat the fields above as a scratchpad rather than a form.
Glossary for Expected Loss
- EL as % of EAD
- 0.846 % in the default Expected Loss calculation — one of the secondary figures an experienced reader checks before trusting the primary number.
- Basis points
- 84.6 bp on the example inputs — a companion figure printed beside the headline of Expected Loss so that no result is read in isolation.
- Credit spread needed (EL + capital charge ≈ +60bp)
- 60.85 bp on the example inputs — a companion figure printed beside the headline of Expected Loss so that no result is read in isolation.
- Expected loss (annual)
- The primary output of this tool: $2,014 for the default inputs, computed exactly from EL = EAD × PD × LGD.
- Worked example
- Every substitution in order, from the example inputs to $2,014 — the audit trail for the headline figure.
- Verdict band
- The interpretation attached to a result (“≈ 85 bp of exposure — the number pricing must clear” on these inputs), which turns a bare number into a position on a scale.
- Sensitivity (±10 %)
- How far the Expected Loss moves when a single input is nudged ten percent either way; the ranked list on this page is computed live from this engine.
Method, sources and what this tool cannot tell you
Everything above runs on one stated formula, applied without hidden coefficients: EL = EAD × PD × LGD. Source of record: Basel II/III IRB framework; IFRS 9 (2014) expected credit losses. Any other implementation of this model should return the same figure for the same inputs. If one does not, the difference is in its assumptions — which this page prints and that one probably does not.
Nothing here replaces a qualified professional, and nothing here is approximate either — the arithmetic is exact, and the honesty is in the inputs you supply. The design constraint was set by usefulness rather than by comfort: an estimate you can interrogate beats an answer you have to trust.
Turning this Expected Loss into a decision
Re-run the calculation with your own figures, stress the two most sensitive inputs by ±10 %, and only then act on the result.
The audience here is people who need one trustworthy number before their next decision. Everything you need to defend the result — formula, substitution, sensitivity, source — is printed above, so the only remaining variable is the honesty of your inputs.