Vose SoftwareModelRisk example · Corporate finance
Currency and Interest-Rate Exposure
How much cash could currency and interest-rate moves cost, and how much does hedging half of it save?
From the model’s saved run
Cash flow at risk
Cash flow over the three years (€m). Cash flow at risk = mean − 5th percentile.
| Policy | Mean | 5th pct | Cash flow at risk | Chance of a negative quarter | 95th pct |
|---|---|---|---|---|---|
| Unhedged | 35.6 | −23.2 | 58.8 | 45.3% | 99.9 |
| Hedging policy | 30.4 | 1.1 | 29.4 | 24.5% | 62.6 |
| Unhedged, if the markets were independent | 35.7 | −37.8 | 73.4 | 53.4% | 115.0 |
| Measure | Unit | Value |
|---|---|---|
| Cash flow over 3 years at today's rates | €m | 32.7 |
S-curve (cumulative probability) of Unhedged, Hedging policy, Independent markets from the saved simulation.
The business question
A European engineering company invoices its US customers about US$45 million a quarter. It makes most of what it sells in a UK plant whose costs are about £20 million a quarter, has €12 million of other costs, and pays Euribor plus 1.75% on a €250 million loan.
At today's rates the business generates about €2.7 million a quarter — thin enough that a weaker dollar or a stronger pound could turn a quarter negative. The dollar and the pound tend to move together against the euro, which partly protects the company: its dollar revenue and sterling costs move in the same direction.
The board is considering a policy of hedging half of each exposure: forward contracts for the currencies and an interest-rate swap for the loan. The model simulates the three markets together for twelve quarters.
- Who it is for
- Treasurers, CFOs and risk committees setting a hedging policy; FP&A teams forecasting cash in several currencies.
- Main outputs
- Cash flow over three years, unhedged and hedged: mean, 5th percentile and cash flow at risk · the chance of a negative quarter · the effect of the correlation between the dollar and the pound · quarterly cash flow fan · drivers.
How the model works
Three sheets after this one, read from left to right. Each one feeds the next.
Inputs sheet
The dollar sales, sterling and euro costs and the loan. Today's exchange rates and interest rates; the annual volatility of each market and the correlations between them. The share of each exposure hedged and the swap rate.
Cash flow sheet
VoseTimeMultiGBM draws twelve quarters of the three markets together from their covariance matrix. Each quarter, the dollar sales and sterling costs are converted at that quarter's rates, and the loan pays Euribor plus its margin. The hedged version fixes half of each at today's forward rates and the swap rate.
Results sheet
Cash flow over three years — its mean, 5th percentile and cash flow at risk — unhedged, hedged and with independent currencies. The chance of a negative quarter; quarter by quarter; the drivers.
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The results in detail
Which hedge share?
Every share from the unhedged run, exactly: in every future the hedged cash flow is (1 − share) × unhedged + share × fully hedged (€m over 3 years).
Line chart: 90th percentile, Median, Mean, 10th percentile.
| Share hedged | Mean | 5th pct | Cash flow at risk | Cost of the hedge |
|---|---|---|---|---|
| 0% | 35.6 | −23.2 | 58.8 | 0.0 |
| 25% | 33.0 | −11.0 | 44.1 | 2.6 |
| 50% | 30.4 | 1.1 | 29.4 | 5.2 |
| 75% | 27.8 | 13.2 | 14.7 | 7.8 |
| 100% | 25.3 | 25.3 | 0.0 | 10.4 |
Cost of the hedge: the mean cash flow given up against no hedge. The policy row above is the row at the share on the Inputs sheet.
Quarter by quarter
How many of the twelve quarters turn negative.
| Measure | Unit | 5th pct | Median | 95th pct | Mean |
|---|---|---|---|---|---|
| Negative quarters, unhedged | of 12 | – | – | 10.0 | 2.3 |
| Negative quarters, hedged | of 12 | – | – | 6.0 | 1.0 |
The dollar
EUR/USD by quarter: the further ahead, the wider the range.
Line chart: 90th percentile, Median, Mean, 10th percentile.
| Measure | Unit | 10th pct | Median | 90th pct | Mean |
|---|---|---|---|---|---|
| Average EUR/USD over the 3 years | USD/EUR | 0.983 | 1.097 | 1.225 | 1.101 |
What drives the cash flow
Lowest and highest mean cash flow over ten equal groups of each market's average (VoseSimSensitivityMean), drawn from the overall mean.
Tornado chart: the inputs ranked by how far the mean output moves across each input’s range.
The ranking as a table 3 inputs
| Input (ranked by influence) | Lowest mean | Highest mean | Rank |
|---|---|---|---|
| EUR/USD level | −18.0 | 98.8 | 1 |
| Euribor level | 27.3 | 41.3 | 2 |
| EUR/GBP level | 30.5 | 42.1 | 3 |
How to read these results
- A weaker dollar (a higher EUR/USD) cuts the euro value of the sales. A weaker pound (a higher EUR/GBP) cuts the euro cost of the UK plant. Unhedged, the cash flow over three years can fall far below what today's rates promise, and the chance of at least one negative quarter is close to one half.
Hedging half of each exposure halves the cash flow at risk and nearly halves the chance of a negative quarter, but it is not free. Dollar and sterling interest rates are above Euribor, so the forward rates are above today's rates and the dollars sold forward buy fewer euros: the hedge costs about €5 million of average cash flow over the three years.
The rest is the business's own exposure, which the hedge share sets. The hedge-share table shows every choice at once: the cash flow at risk shrinks in proportion to the share left unhedged, and the cost grows with the share hedged.
- The dollar and the pound tend to move together against the euro, so the sales and the UK costs partly offset: with independent markets the cash flow at risk would be clearly larger. A hedge that ignored this correlation would over-hedge.
The tornado chart shows EUR/USD as the driver: the mean cash flow runs from about €99 million in the tenth of futures with the weakest euro down to about −€18 million in the tenth with the strongest.
The bar for EUR/GBP is small, and it is mostly EUR/USD's effect: a strong euro against the pound comes with a strong euro against the dollar, so the cash flow is lower there, although a cheaper pound lowers the UK costs. A tornado measures association, not cause, when inputs are correlated. Euribor matters little: the loan costs much less than the currency swings.
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.
Exposures 5 inputs
Each quarter.
| Assumption | Unit | Value |
|---|---|---|
| Sales in US dollarsUS customers, invoiced in dollars. | US$m per quarter | 45.0 |
| UK plant costs | £m per quarter | 20.0 |
| Other costs | €m per quarter | 12.0 |
| Floating-rate loan | €m | 250.0 |
| Loan margin over Euribor | per year | 1.75% |
Markets today 5 inputs
Spot rates and the interest rates that set the forward rates.
| Assumption | Unit | Value |
|---|---|---|
| EUR/USD | USD per EUR | 1.1000 |
| EUR/GBP | GBP per EUR | 0.8500 |
| Euribor | per year | 2.50% |
| US dollar interest rateFor the forward rates. | per year | 4.00% |
| Sterling interest rate | per year | 3.75% |
Market risk 5 inputs
Annual volatilities of the log changes, and their correlations.
| Assumption | Unit | Value |
|---|---|---|
| Volatility of EUR/USDThree years of weekly changes. | per year | 8.0% |
| Volatility of EUR/GBP | per year | 6.0% |
| Volatility of Euribor (relative)Of the log of the rate. | per year | 20.0% |
| Correlation: EUR/USD vs EUR/GBPThe dollar and the pound tend to move together against the euro. | -1 to 1 | 0.50 |
| Correlation: exchange rates vs Euribor | -1 to 1 | 0.00 |
Hedging policy 2 inputs
Applied to every quarter from today.
| Assumption | Unit | Value |
|---|---|---|
| Share of each exposure hedgedForwards for the currencies, a swap for the loan. | 50% | |
| Swap rate (fixed, replaces Euribor)Three-year swap quote. | per year | 2.70% |
Units and conventions
- Money
- € million (€m); dollar and sterling amounts in US$m and £m.
- Exchange rates
- Units of foreign currency per euro: a higher EUR/USD is a weaker dollar.
- Cash flow at risk
- The mean cash flow less its 5th percentile: how much worse than expected one year in twenty could be.
- Quarters
- Quarter 1 is the next quarter; twelve quarters, three years.
Key assumptions and limitations
- Markets
- Log changes are Normal and their volatilities and correlations constant; today's rates are the median forecast.
- Hedging
- Forwards and the swap are agreed today for all twelve quarters; no credit risk or margin calls.
- Business
- Volumes and local-currency prices are fixed: only the markets move the cash flow.
- Data
- The company and all figures are invented for this example.
How to use it
- Enter your quarterly exposures, today's market rates and your hedging policy on the Inputs sheet.
- Set the volatilities and correlations from market data (for example three years of weekly changes).
- Run a simulation from the ModelRisk ribbon (10,000 samples with a fixed seed are set).
- Choose the hedge share whose cash flow at risk the company can carry.
Simulate this model with ModelRisk’s classic engine: it does not run in Turbo mode yet.
ModelRisk functions used
- VoseTimeMultiGBM
- EUR/USD, EUR/GBP and Euribor for twelve quarters, drawn together from a covariance matrix.
- VoseInput, VoseOutput
- Name the drivers and the cash flows as outputs.
- VoseSimMean, VoseSimPercentile
- Statistics of the simulation for the tables and charts on the Results sheet.
- VoseSimSensitivityMean
- The tornado chart: every VoseInput ranked by how far the mean unhedged cash flow moves across its range.
Further reading
- Sensitivity analysis in Excel: a tornado chart step by step (Vose guide)
- Coyle, B. (2000). Hedging Currency Exposures. Global Professional Publishing.
- Vose, D. (2008). Risk Analysis: A Quantitative Guide, 3rd edition. Wiley — correlated time series.
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.