A private fund's money goes in and comes out over a decade, so the inflation that matters is the inflation suffered while each dollar was invested.
Divide each call and distribution by the price index at its own date, then take the IRR of the deflated flows. On an illustrative fund with a 12.62 per cent nominal IRR and ten years of inflation averaging 3.44 per cent, the deflated flows give a real IRR of 8.23 per cent, not the 8.88 per cent the Fisher shortcut gives on the ten-year average. The shortcut is exact only when inflation is constant; here an inflation spike landed while most of the capital was out, and the shortcut overstated the real return by 0.65 points.
Worked in full in Alternative Investments by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Endowments and foundations set their targets in real terms: a spending rule of, say, 5 per cent a year plus inflation, so that the purchasing power of the fund survives. Private fund reports are nominal. The conversion looks like a one-line formula, and for a listed portfolio held through a fixed period it nearly is. For a private fund, whose money goes in and comes out over a decade, the inflation that matters is the inflation suffered while each dollar was invested, and an average over the calendar does not measure that.
| Year | Net flow | Inflation in the year | Price index | Real flow |
|---|---|---|---|---|
| 0 | −25 | 1.000 | −25.00 | |
| 1 | −25 | 2.0% | 1.020 | −24.51 |
| 2 | −20 | 2.0% | 1.040 | −19.22 |
| 3 | −15 | 2.0% | 1.061 | −14.13 |
| 4 | 10 | 7.0% | 1.135 | 8.81 |
| 5 | 20 | 6.0% | 1.204 | 16.62 |
| 6 | 30 | 5.0% | 1.264 | 23.74 |
| 7 | 35 | 3.0% | 1.302 | 26.89 |
| 8 | 30 | 2.5% | 1.334 | 22.48 |
| 9 | 25 | 2.5% | 1.368 | 18.28 |
| 10 | 20 | 2.5% | 1.402 | 14.27 |
The fund calls 85 and distributes 170, a TVPI of 2.00x. Prices rise 40.2 per cent over the ten years, a compound average of 3.44 per cent, but unevenly: 2 per cent a year while capital is being called, then 7, 6 and 5 per cent in years 4 to 6, when the fund is fully invested and has barely begun to distribute.
Σ CFt ÷ (1 + IRR)t = 0
On the eleven nominal flows, =IRR(B2:B12) returns 12.62 per cent.
The Fisher relation converts a nominal rate to a real one: (1 + nominal) ÷ (1 + inflation) − 1. With the ten-year average, 1.1262 ÷ 1.0344 − 1 = 8.88 per cent. Simply subtracting gives 9.18 per cent. Both use one inflation figure for the whole decade, which treats a dollar called in year 0 and a dollar called in year 3 as if they had lived through the same prices.
Real flowt = CFt ÷ CPIt, with CPI0 = 1; real IRR = IRR(real flows)
Year 4: 10 ÷ 1.135 = 8.81. Year 7: 35 ÷ 1.302 = 26.89. On the eleven real flows, =IRR(E2:E12) returns 8.23 per cent.
In Excel, with years in column A, flows in B, inflation in C, set D2 to 1 and build the index as =D2*(1+C3) down the column, the real flow as =B2/D2 in column E, and run IRR or XIRR on the result. With monthly or quarterly data, use the index at each flow's date.
In real terms the fund called 82.87 and returned 131.08, a real multiple of 1.58x rather than 2.00x. The nominal and real IRRs together imply that the fund's own money suffered inflation of 4.05 per cent a year, not the 3.44 per cent calendar average, because the expensive years fell when the most capital was outstanding and distributions had not yet started.
| Method | Real IRR | Margin over a 5% real target |
|---|---|---|
| Nominal IRR minus average inflation | 9.18% | |
| Fisher on the ten-year average | 8.88% | 3.88 |
| IRR of deflated flows | 8.23% | 3.23 |
The fund clears a 5 per cent real target comfortably either way, but the shortcut adds 0.65 points to the margin. In a programme review that compares several funds against the spending rule, an error of that size moves managers across the line.
| Inflation path | Ten-year average | Fisher shortcut | Deflated flows | Shortcut error |
|---|---|---|---|---|
| Spike in years 4 to 6 (base) | 3.44% | 8.88% | 8.23% | 0.65 |
| Flat at the same average | 3.44% | 8.88% | 8.88% | 0.00 |
| Late: 3, 5, 6, 7% in years 7 to 10 | 3.44% | 8.88% | 9.64% | −0.76 |
| Early: 6, 7, 5, 4% in years 1 to 4 | 3.54% | 8.77% | 8.48% | 0.29 |
The shortcut is right only on the flat path. When inflation arrives late, after most of the money has come home, the investor escaped it and the true real return, 9.64 per cent, is higher than the shortcut says. The same ten-year price rise can push the error either way by three quarters of a point. It is not a rounding question; it is a timing question, the same one that separates an IRR from a time-weighted return.
Which index? Use the index your target is written in. A foundation whose spending rule is defined against consumer prices should deflate by consumer prices at each flow date; one with a cost-based target, such as a university's own cost index, should use that. Mixing a nominal benchmark with a real target is the most common error in an annual review.
Taking the fund's nominal IRR, subtracting a headline inflation figure for the reporting period, and comparing the result with the real target. The subtraction overstates by 0.95 points here, and the reporting-period average is the wrong inflation for a fund whose capital came and went inside the period. The fix costs one column in the spreadsheet. The simpler conversion for a single holding period, without interim flows, is set out in how to calculate real return after inflation.
Deflate each flow by the index at its date and take the IRR: 8.23 per cent real here, against 8.88 by Fisher and 9.18 by subtraction. The fund's own investors lived through 4.05 per cent inflation a year, not 3.44, because of when their money was out. The free workbooks for the book carry the same call and distribution engine; add a price index row to the flows and the real return of the fund, and of the investor's sleeve around it, follows directly. The further gap between the fund's return and what the whole commitment earned is worked in how much of the IRR reaches the investor.
Only if inflation was constant over the fund's life. On an illustrative fund with a 12.62 per cent nominal IRR, Fisher on the 3.44 per cent ten-year average gives 8.88 per cent, while deflating each flow gives 8.23 per cent when inflation spiked mid-life, and 9.64 per cent when it came late.
No. Divide each call and distribution by the price index at its date. In the illustrative case the fund calls 85 and returns 170, a 2.00x nominal multiple, but in real terms it calls 82.87 and returns 131.08, a real multiple of 1.58x after prices rose 40.2 per cent over ten years.
At least its spending rate plus costs, in real terms, measured on deflated flows. Against an illustrative 5 per cent real target, a fund with an 8.23 per cent real IRR clears it by 3.23 points; the Fisher shortcut would report 3.88, overstating the margin by 0.65 points.
This article is one calculation from Alternative Investments. 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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