How to measure how long a fund actually holds the investor's money, and the shortcut that turns any multiple into an IRR.
The duration of a private equity fund is the dollar-weighted average date of its distributions minus the dollar-weighted average date of its capital calls: the length of time the investor's money is actually out. On an illustrative ten-year buyout fund that calls 95 and returns 180, calls centre on year 1.68 and distributions on year 6.72, a duration of 5.04 years. That single number turns a multiple into a return: 1.891/5.04 − 1 = 13.52 per cent, against an actual IRR of 13.79.
Worked in full in Alternative Investments by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Fund documents describe a ten-year term with extensions. Allocation papers repeat it. Neither tells the investor how long its capital is invested, which is what links the multiple a manager reports to the rate of return that multiple represents, and what decides how much uncalled and returned cash the investor has to manage around the fund. Duration answers both.
| Year | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Calls | 20 | 25 | 25 | 15 | 10 | ||||||
| Distributions | 5 | 15 | 25 | 35 | 40 | 30 | 20 | 10 |
Total calls 95, total distributions 180, a multiple of 1.89x. The residual value is assumed realised by year 10.
Step 1: the centre of the calls. Weight each year by the amount called in it.
Call centre = Σ(t × callt) ÷ Σ callt = (0 × 20 + 1 × 25 + 2 × 25 + 3 × 15 + 4 × 10) ÷ 95 = 160 ÷ 95 = 1.68
Excel: =SUMPRODUCT(B1:L1, B2:L2)/SUM(B2:L2), with years in row 1 and calls in row 2
Step 2: the centre of the distributions. The same weighting on the cash coming back.
Distribution centre = 1,210 ÷ 180 = 6.72
Step 3: duration.
Duration = 6.72 − 1.68 = 5.04 years
Step 4: the multiple as a rate. If 95 grows to 180 over 5.04 years, the annual rate is the 5.04th root of the multiple.
Approximate IRR = MOIC1/duration − 1 = 1.891/5.04 − 1 = 13.52%
Actual IRR on the same flows: 13.79%, a difference of 0.27 points
The shortcut is not exact because the IRR discounts, so later flows weigh less. Weighting by present value at the IRR instead gives a distribution centre of 6.34, a call centre of 1.49 and a duration of 4.85 years. That version is the textbook Macaulay construction, but it needs the IRR first, which defeats the purpose. The undiscounted version is the one to carry in your head.
A ten-year buyout fund holds the investor's money for about five years, 50 per cent of its legal life. Two consequences follow. A 1.89x multiple is a return in the low teens, not the 6 per cent a reader would get by spreading it over ten years. And because the duration is in the denominator of the exponent, every year it lengthens costs a great deal: at the same 1.89x, a duration of 6.04 years drops the approximate IRR to 11.16 per cent, and the fund would need 2.15x to hold 13.52.
| Strategy | Called | Returned | MOIC | Duration (years) | MOIC1/D − 1 | Actual IRR |
|---|---|---|---|---|---|---|
| Buyout | 95 | 180 | 1.89x | 5.04 | 13.52% | 13.79% |
| Venture | 90 | 220 | 2.44x | 6.36 | 15.08% | 15.23% |
| Secondary | 85 | 125 | 1.47x | 2.93 | 14.05% | 14.68% |
| Private credit | 90 | 117 | 1.30x | 3.63 | 7.50% | 7.63% |
Read the table across. The venture fund returns 2.44x, far more than the secondary fund's 1.47x, yet their IRRs are within a point of each other because the venture money is out for 6.36 years and the secondary money for 2.93. Duration is what makes multiples and IRRs disagree, and it is why an allocator should never compare strategies on one of them alone. The shortcut stays within 0.63 points of the true IRR on all four schedules; it is least precise where distributions start almost immediately, as in the secondary case.
Duration also sizes the liquidity problem. The longer it is, the longer an uncalled commitment sits idle before the calls arrive and the longer returned cash waits for redeployment, which is where the investor's return parts company with the fund's.
Annualising a multiple over the fund's legal term. 1.89x over ten years is 1.890.1 − 1, about 6.6 per cent, less than half the true 13.79. The opposite error is as common in reverse: quoting a manager's IRR and assuming it applied to the whole commitment for the whole term. A 13.79 per cent IRR compounding on 95 for ten years would produce about 346, not 180. The IRR only compounds over the 5.04 years the money is invested, which is why the investor's own return on its whole commitment is usually lower than the fund's.
The book builds the full call and distribution schedule of a fund and the account of the investor who committed to it; the free workbook for this case carries the cash-flow engine, the J-curve and the capital never put to work. The multiples themselves are defined in how to calculate TVPI, DPI and RVPI, and the cost of a later exit is worked in how much a distribution delay cuts fund IRR.
Because the money is neither called on day one nor returned on the last day. In the illustrative buyout fund, calls are spread over five years and centre on year 1.68, and distributions run from year 3 to year 10 and centre on year 6.72. The investor's capital is outstanding for 5.04 years on average, about 50 per cent of the contractual life.
Raise the multiple to the power of one over the fund's duration and subtract one. For the illustrative buyout fund, 1.89 to the power 1/5.04 minus 1 gives 13.52 per cent, within 0.27 points of the true 13.79 per cent IRR. Dividing by the ten-year legal life instead would suggest about 6 per cent, less than half the real figure.
Secondaries and private credit. On illustrative schedules a secondary fund buying seasoned interests has a duration of 2.93 years and a private credit fund 3.63, against 5.04 for buyout and 6.36 for venture. A short duration lets a modest 1.47x multiple produce a 14.68 per cent IRR.
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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