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How do exchange rates change a private equity fund's IRR?

A euro fund measured in US dollars, flow by flow, and why the currency cost more than its own annual fall.

Julian R. Sterling · from Private Markets Performance

Convert every capital call and distribution at the exchange rate on its own date, convert the NAV at the measurement-date rate, and compute the IRR on the converted series. On an illustrative euro fund earning 14.57 per cent in euros, a US dollar investor whose euro fell 10 per cent over eight years earns 12.71 per cent. The currency cost 1.86 points of IRR, more than the 1.31 per cent a year the euro actually fell, because the euro was weakest when the money came back.

Worked in full in Private Markets Performance by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →

Most private funds report in their own currency, and many of their investors measure in another. The manager's return and the investor's return are then two different numbers, and both are correct. What is not correct is any shortcut that converts the fund's IRR rather than the fund's cash flows.

The fund and the exchange rate

An illustrative euro fund per 100 committed, year-end flows, and the US dollar price of one euro. NAV of 40.0 at year 8.

Year	Calls, €	Distributions, €	USD per EUR	Net flow, €	Net flow, $
0	20	0	1.20	−20.0	−24.00
1	25	0	1.18	−25.0	−29.50
2	25	0	1.14	−25.0	−28.50
3	15	5	1.10	−10.0	−11.00
4	10	15	1.08	5.0	5.40
5	5	25	1.06	20.0	21.20
6	0	35	1.05	35.0	36.75
7	0	40	1.06	40.0	42.40
8, with NAV	0	30	1.08	70.0	75.60
Total	100	150		90.0	88.35

The calculation, step by step

The dollar investor paid 114.60 for its calls and received 202.95. The currency took 0.13x off the multiple and 1.86 points off the IRR.

Why the cost is larger than the currency's fall

From 1.20 to 1.08 the euro fell 10.0 per cent over eight years, 1.31 per cent a year. A quick estimate would take that off the euro IRR: (1.1457 × (1 − 0.0131)) − 1 = 13.07 per cent. The true figure is 12.71, 0.36 points lower.

The reason is the path. The dollar investor bought euros for its calls at an average of 1.1460 and sold the euros it received back at an average of 1.0682 across distributions and NAV, 6.8 per cent less. The euro bottomed at 1.05 to 1.06 in years 5 to 7, exactly when the largest distributions were paid, and recovered only for the final distribution and the NAV. A currency's money-weighted effect, like the fund's own return, depends on when the money moves, not on where the rate started and ended.

The check makes the point: had the euro fallen from 1.20 to 1.08 in a straight line at 1.31 per cent a year, the dollar IRR would be 13.07 per cent, exactly the shortcut. The shortcut is right only for a currency that moves smoothly, which no currency does.

What if: the rate on the measurement date

Only the year 8 rate changes; it applies to the last distribution and to the 40.0 NAV.

Year 8 rate	Versus base	Dollar IRR	Dollar TVPI	Gap to euro IRR, points
0.97	−10%	11.95%	1.70x	−2.62
1.08	0%	12.71%	1.77x	−1.86
1.19	+10%	13.44%	1.84x	−1.13
Flat at 1.20 throughout		14.57%	1.90x	0.00

A 10 per cent move on the last day alone shifts the dollar IRR by about three quarters of a point, because the NAV is still 21.1 per cent of the fund's value. For a younger fund, with most of its value in NAV, the measurement-date rate can dominate the reported return. The euro IRR is unaffected by any of it.

Hedging changes the series, not the method. If the investor hedges, the hedge's gains and losses are part of its cash flows and belong in the dollar series on their dates. A fund-level hedge is already inside the fund's euro flows. Either way, the return is computed on what actually moved through the investor's account.

The common mistake

The common mistake is to convert the whole history at today's rate, usually because the reporting system holds one rate per reporting date. Multiplying every euro flow by 1.08 scales the series without changing its shape, so the dollar IRR comes out at 14.57 per cent and the TVPI at 1.90x, identical to the euro figures, and the 1.86 points the currency actually cost disappear. The second mistake is to adjust the IRR by the currency's annual change: compounded it misses the path by 0.36 points here, simply subtracted (13.26 per cent) by more, and in a more volatile period it can miss by more than the fund's alpha.

Takeaway

Convert each flow at its own date's rate, the NAV at the measurement date's rate, then compute the IRR and multiples on the converted series: 12.71 per cent and 1.77x for the dollar investor here, against 14.57 per cent and 1.90x in euros. Report both, and say which is which. The cash flow series and the reconciliation tests that should come before any return are in the free workbooks for this book; how a fund's accounts separate the currency gain from the investment gain is in how to split FX gain from investment gain.

Questions readers ask

Can you convert a fund's IRR into another currency by adding the FX change?

Only approximately, and only if the currency moved smoothly. On the illustrative euro fund, compounding the euro's 1.31 per cent annual fall into the 14.57 per cent euro IRR gives 13.07 per cent, and simple subtraction 13.26; converting each flow at its own rate gives 12.71 per cent, because the euro was weakest when the largest distributions were paid.

Which exchange rate should be used for the NAV in a private equity return?

The rate on the measurement date, the same date as the NAV. In the illustrative fund the 40.0 euro NAV is 21.1 per cent of total value, so a 10 per cent move in the year 8 rate alone shifts the dollar IRR from 12.71 to 11.95 or 13.44 per cent.

Why does my dollar TVPI differ from the fund's euro TVPI?

Because calls and distributions were converted at different rates. The illustrative dollar investor bought euros for its calls at an average of 1.1460 and received distributions and NAV worth an average of 1.0682, 6.8 per cent less, so a 1.90x euro TVPI becomes 1.77x in dollars.

Also on this site

• How do you split FX gains from investment gains in a fund's NAV?Valuation gain at the closing rate, FX on cost: a EUR 50.0m deal now worth 60.0 shows a $8.00m gain, $10.50m from the company and minus $2.50m from the euro.
• IRR vs XIRR: which should a private equity fund use?XIRR, on actual value dates. The same fund gives 11.33 per cent with XIRR and 12.43 per cent with IRR on annual buckets: 1.10 points of pure date error.
• Can you average fund IRRs to get a portfolio return?No. Three funds at 11.52, 10.12 and 19.51 per cent average to 13.72 per cent. The pooled return is 11.78 per cent, 194 basis points lower.
• How much does a NAV markdown cut a private equity fund's IRR?It depends on the fund's age: a 20 per cent markdown takes 9.7 points off a year-4 IRR of 10.1 per cent, 2.6 points at year 7 and 0.5 points at year 10.
• How do you benchmark private equity against an index plus 3%?Run a PME on the index grown at index plus 3 per cent, not the IRR against a CAGR. A fund that misses by 0.08 points on the CAGR beats it with a PME of 1.040.
• How do you calculate a horizon IRR for a private equity fund?Open with the NAV as a call, add the window's flows, close with the NAV. Here the five-year horizon IRR is 13.98 per cent against 11.07 since inception.

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