Translating a euro investment in a dollar fund, splitting the gain two ways, and keeping the quarterly split consistent with the cumulative one.
Split a foreign-currency investment's dollar gain into a valuation part, the local gain translated at the closing rate, and a currency part, the cost translated at the change in rate. A EUR 50.0m investment bought at 1.10 and valued at EUR 60.0m at 1.05 shows a $8.00m unrealised gain: $10.50m from the company and minus $2.50m from the euro. The two parts must sum to the total, and the convention must not change from quarter to quarter.
Worked in full in The Private Equity Fund Controller Playbook by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
A dollar-denominated fund that owns a European company reports one number to its investors, the dollar fair value. The investment committee wants to know how much of the movement is the business and how much is the currency, and so does every limited partner reading the quarterly report. The arithmetic is simple. Getting it consistent is not.
| Date | Fair value, EUR m | EUR/USD | Value, $m |
|---|---|---|---|
| Acquisition (cost) | 50.0 | 1.10 | 55.00 |
| Prior quarter end | 54.0 | 1.08 | 58.32 |
| Current quarter end | 60.0 | 1.05 | 63.00 |
Cumulative unrealised gain = 60.0 × 1.05 − 50.0 × 1.10 = 63.00 − 55.00 = 8.00
In local currency the company is up 20.0 per cent, a multiple of 1.20x. In dollars it is up 14.5 per cent, 1.15x. The difference is the euro, and the split assigns it.
Valuation = (60.0 − 50.0) × 1.05 = 10.50
FX = 50.0 × (1.05 − 1.10) = −2.50
Total = 10.50 − 2.50 = 8.00
Valuation = (60.0 − 50.0) × 1.10 = 11.00
FX = 60.0 × (1.05 − 1.10) = −3.00
Total = 11.00 − 3.00 = 8.00
In Excel, convention A: =(FV_EUR-Cost_EUR)*Rate_now and =Cost_EUR*(Rate_now-Rate_cost).
Both are defensible and both tie. They differ by the cross term, the local gain times the change in rate: 10.0 × (−0.05) = −0.50. Convention A leaves it in the valuation line; convention B puts it in FX. This article uses convention A because it answers the investor's question directly: what the company earned, at today's money, and what the currency did to the money originally invested.
The quarter's dollar change is 63.00 − 58.32 = $4.68m. There are two ways to split it, and they give different answers that both tie.
| Method | Valuation | FX | Total |
|---|---|---|---|
| Cumulative split this quarter less cumulative split last quarter | 6.18 | −1.50 | 4.68 |
| Periodic: local change at closing rate, FX on opening fair value | 6.30 | −1.62 | 4.68 |
Last quarter's cumulative split under convention A was $4.32m of valuation and minus $1.00m of FX. Taking the difference gives 6.18 and minus 1.50. The periodic method treats the opening fair value as the new base and gives 6.30 and minus 1.62. A controller who reports quarters on the periodic method and inception-to-date on the cumulative method will find that the quarterly valuation and FX lines do not add up to the inception-to-date lines, even though every total ties. Pick one, document it, and keep it.
| EUR/USD | Value | Total gain | Valuation | FX | USD multiple |
|---|---|---|---|---|---|
| 0.95 | 57.00 | 2.00 | 9.50 | −7.50 | 1.04x |
| 1.00 | 60.00 | 5.00 | 10.00 | −5.00 | 1.09x |
| 1.05 | 63.00 | 8.00 | 10.50 | −2.50 | 1.15x |
| 1.10 | 66.00 | 11.00 | 11.00 | 0.00 | 1.20x |
| 1.15 | 69.00 | 14.00 | 11.50 | 2.50 | 1.25x |
Under convention A the valuation line itself moves with the rate, because the local gain is translated at today's rate. The whole dollar gain disappears at 0.917 dollars per euro, the dollar cost divided by the euro fair value.
The mistake is to mix the conventions: take the valuation at one rate and the FX on the other base. Valuation at the closing rate plus FX on fair value gives 10.50 − 3.00 = $7.50m, $0.50m short of the real gain. Valuation at the historical rate plus FX on cost gives 11.00 − 2.50 = $8.50m, $0.50m too much. The error is small here; on a large portfolio in a year when the dollar moves sharply it is not, and it shows up as an unexplained difference in the NAV bridge.
If the fund hedges the currency, the hedge result belongs alongside the FX line, not inside the valuation. A forward that gains when the euro falls offsets part of the negative FX component, and reporting the two next to each other shows investors what the hedge actually did. Netting the hedge into the valuation line hides both the currency loss and the hedge gain. Why a hedge that shows a loss has not necessarily failed is worked, from the corporate side, in did my currency hedge fail if it lost money.
The control. Valuation plus FX must equal the change in dollar fair value, for each investment, every quarter, and the quarterly splits must add to the inception-to-date split. If either test fails, the conventions have been mixed.
The NAV build that this split feeds is worked in how to calculate the NAV of a private equity fund, and the book's question set, including its currency translation exercises, is in the free workbooks for the book.
While the investment is held it is part of the unrealised change in fair value. In the worked case the cumulative unrealised gain is $8.00m, of which minus $2.50m is currency. On exit the whole difference between dollar proceeds and dollar cost becomes realised, and the split is kept only for analysis and investor reporting.
Divide the dollar cost by the local fair value. The investment cost $55.00m and is worth EUR 60.0m, so the dollar gain is zero at 0.917 dollars per euro. At that rate the euro's fall has wiped out the whole 20.0 per cent local gain; below it the position shows a dollar loss.
Many accounting frameworks allow an investment company to present the currency effect within the change in fair value rather than as a separate line. The split is still expected in investor reporting and performance attribution, so the controller should compute it every quarter with one documented convention.
Currency translation is covered in chapter 12 of The Private Equity Fund Controller Playbook. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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