Vose SoftwareModelRisk example · Corporate finance
Credit Portfolio Losses
How much could the loan book lose in a bad year? Default correlation, loss given default and the capital it needs.
From the model’s saved run
How much could the loan book lose in a year?
One-year credit loss (US$m), correlated and independent defaults, at the confidence on the Inputs sheet.
| Measure | Correlated defaults | Independent defaults |
|---|---|---|
| Mean loss | 11.0 | 10.9 |
| Value at risk at 99.0% | 47.3 | 15.6 |
| Expected shortfall at 99.0% | 58.3 | 16.3 |
| Chance the loss exceeds the expected loss + capital held | 1.9% | 0.0% |
| Mean defaults | 46 | 45 |
| Defaults at 99.0% | 185 | 62 |
| Measure | Unit | Value |
|---|---|---|
| Expected loss | US$m | 10.9 |
| Capital held (Inputs sheet) | US$m | 30.0 |
| Capital needed: value at risk − expected loss | US$m | 36.4 |
| Capital needed if defaults were independent | US$m | 4.6 |
| Capital held − capital needed | US$m | −6.4 |
| Verdict | Short: the capital held does not cover this confidence |
S-curve (cumulative probability) of Correlated defaults, Independent defaults from the saved simulation.
Histogram of Correlated defaults from the saved simulation.
The business question
A regional bank has lent US$1.4 billion to 2,000 small and medium-sized companies, rated A to E. History gives each grade's one-year default rate, from 0.3% for grade A to 9% for grade E, and the bank recovers on average a little over half of what a defaulting borrower owes. Multiplying these together, the bank expects to lose about US$11 million a year.
But defaults do not happen independently: a recession raises every borrower's chance of default at once, and in a bad year many default together. The model draws the state of the economy each year, the defaults it causes in every grade, and the loss on each default, and compares the result with independent defaults.
- Who it is for
- Credit risk managers, bank treasurers and CFOs, trade-credit insurers, lenders with concentrated books.
- Main outputs
- One-year credit loss: expected loss, value at risk and expected shortfall at a chosen confidence, the capital needed against the capital held with a verdict, and the chance of exceeding it — with correlated and with independent defaults · loss by rating grade against its expected loss.
How the model works
Three sheets after this one, read from left to right. Each one feeds the next.
Inputs sheet
For each grade, the number of loans, the exposure per loan and the long-run one-year default probability. The mean and spread of the loss given default; the asset correlation between borrowers; the capital held.
Loan book sheet
A Normal draw represents the economy. Each grade's default probability for the year moves with it (the Vasicek formula); VoseBinomial draws the defaults, and VoseAggregateMC adds up a Beta-distributed loss for each one. The same book with independent defaults is drawn beside it.
Results sheet
Mean loss, value at risk and expected shortfall, the capital needed above the expected loss and the chance of exceeding the capital held — correlated and independent — and the losses by grade.
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The results in detail
Where the losses come from
Loss by grade (US$m): expected by formula, simulated on average, and in a bad year. The first two agree: a built-in check.
| Grade | Expected loss | Mean simulated | At the confidence |
|---|---|---|---|
| Grade A | 0.54 | 0.54 | 4.28 |
| Grade B | 1.73 | 1.76 | 10.26 |
| Grade C | 2.70 | 2.71 | 12.94 |
| Grade D | 3.54 | 3.59 | 14.33 |
| Grade E | 2.43 | 2.43 | 7.98 |
| Measure | Unit | Value |
|---|---|---|
| Rank correlation of the loss with the economy | −0.97 |
How to read these results
- Every borrower's chance of default moves with the same economy. In a good year few default. In a bad year many default together. The expected loss is the same either way, but the bad years are far worse with correlated defaults.
- With independent defaults the loss would hardly vary from year to year, and the capital the book needs would be a fraction of the true figure: ignoring default correlation is the classic way to under-capitalise a loan book.
- The riskiest grade is not where most money is lost in a bad year. The larger books in the middle grades, with modest default rates, lose more when the economy turns.
- Regulatory capital uses 99.9%, far in the tail: 10,000 samples give only a rough estimate of it. Set the confidence on the Inputs sheet and run 100,000 samples before relying on it.
See it move. Open the workbook, change an input on the Inputs sheet and run the simulation: every table and chart on this page updates in Excel.
Inputs and assumptions
Every assumption in the model, with its uncertainty and where it comes from. The figures are illustrative.
Losses and correlation 3 inputs
What a default costs, and how defaults move together.
| Assumption | Unit | Value |
|---|---|---|
| Loss given default: meanWorkout history: recoveries average 55%. | of the exposure | 45% |
| Loss given default: standard deviationFrom loan to loan. | 20% | |
| Asset correlationRegulatory formula for small companies: 12% to 24%. | 12% |
Capital 2 inputs
Held against unexpected losses on this book.
| Assumption | Unit | Value |
|---|---|---|
| Capital heldAbove the expected loss, which provisions cover. | US$m | 30 |
| Confidence the capital must coverRegulators use 99.9%: run 100,000 samples for it; 10,000 give a rough estimate. | 99.0% |
The loan book by grade 5 inputs
Long-run one-year default probabilities from the bank's rating history.
| Grade | Loans | Exposure per loan, US$m | Default probability |
|---|---|---|---|
| Grade AEstablished companies, strong cover. | 400 | 1.00 | 0.3% |
| Grade B | 600 | 0.80 | 0.8% |
| Grade C | 500 | 0.60 | 2.0% |
| Grade D | 350 | 0.50 | 4.5% |
| Grade EWatch list. | 150 | 0.40 | 9.0% |
Units and conventions
- Money
- US$ million (US$m); a loss is positive.
- Default probability
- The chance that a borrower defaults within the year.
- Loss given default
- The share of the exposure lost when a borrower defaults, after recoveries.
- Capital needed
- The loss at the confidence level less the expected loss, which pricing and provisions cover.
Key assumptions and limitations
- Defaults
- One economic factor drives all grades (one asset correlation); within a grade, borrowers are alike.
- Losses
- Exposure at default equals the loan; loss given default is independent of the economy.
- Horizon
- One year; no new lending or repayments during the year.
- Data
- The bank and all figures are invented for this example.
How to use it
- Enter your book by grade, your loss-given-default experience and the capital you hold.
- Set the asset correlation: regulatory formulas give 12% to 24% for corporate loans.
- Run a simulation from the ModelRisk ribbon (10,000 samples with a fixed seed are set; use 100,000 for the 99.9% level).
- Compare the capital needed at your confidence level with the capital held; test limits by grade.
ModelRisk functions used
- VoseNormal
- The state of the economy this year: the single factor behind correlated defaults.
- VoseBinomial
- The number of defaults in each grade, at this year's default probability.
- VoseAggregateMC, VoseBetaObject
- The sum of a Beta-distributed loss given default for every default.
- NORM.S.DIST, NORM.S.INV (Excel)
- The Vasicek formula for the default probability given the economy.
- VoseSimCVARp, VoseSimPercentile, VoseSimMean
- Expected shortfall, value at risk and the other statistics on the Results sheet.
Further reading
- Monte Carlo simulation explained (Vose guide)
- Vasicek, O. (2002). The distribution of loan portfolio value. Risk 15(12), 160–162.
- Vose, D. (2008). Risk Analysis: A Quantitative Guide, 3rd edition. Wiley — credit risk.
Download the workbook and run it yourself. It opens in Excel with ModelRisk. The free trial runs every example model.
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An illustrative example: the figures are invented for teaching and do not describe a real company, project or asset. Last updated 9 October 2026.