Most PMEs are run with a NAV one quarter older than the index date. What that mismatch does, when it matters, and the two ways to remove it.
It biases the PME by roughly the NAV's share of value times the index move in the lag quarter, with the sign reversed. Pair a 30 September NAV with an index taken to 31 December and a falling quarter makes the fund look better: on an illustrative four-year-old fund the correct Kaplan-Schoar PME is 1.107, but after an 8 per cent index fall the mismatched figure is 1.203. End the index at the NAV date, or roll the NAV forward, and the error disappears.
Worked in full in Private Markets Performance by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Private fund NAVs arrive late. Valuations of unlisted companies take weeks, so an investor closing its books at 31 December usually holds the fund's 30 September NAV. Public indices, by contrast, are available the same evening. The temptation is to put the latest NAV against the latest index level and run the PME. That compares a portfolio valued at one date with a market valued three months later.
| Item | Mature fund | Young fund |
|---|---|---|
| Age at measurement (years) | 10 | 4 |
| Paid in | 90 | 80 |
| Distributed | 135 | 0 |
| Latest NAV, dated 30 September | 45 | 95 |
| TVPI | 2.00x | 1.19x |
| Index return, 1 January to 30 September of the final year | 3% | 3% |
| Index return in the lag quarter | +8% to −15% | +8% to −15% |
The mature fund called 20, 25, 20, 15 and 10 in years 0 to 4 and distributed 15, 25, 30, 35 and 30 in years 5 to 9. The young fund made the same first four calls and has distributed nothing. Annual index total returns before the final year are an illustrative 12, 8, −4, 18, 10, −12, 15, 9 and 6 per cent.
KS PME = (Σ distributions × IT/It + NAV) / Σ calls × IT/It
Mismatched: T is 31 December, IT is the December index level, and the NAV is the September figure. Matched: T is 30 September, the date the NAV describes, and IT is the September index level. In Excel the only change is which index cell the formulas divide into: =B2*IdxDec/C2 against =B2*IdxSep/C2, with the two index levels as named cells.
The mismatch grows the future value of every call and every distribution by the lag quarter's index return, while the NAV stays where it was. That is the same as overstating the NAV against everything else after a falling quarter, and understating it after a rising one. If the market fell, the calls shrink and the NAV does not, so the fund appears to have beaten a market that simply had not been reflected in its valuation yet.
| Lag quarter index return | Mismatched PME | Matched PME | Error |
|---|---|---|---|
| +8% | 1.385 | 1.408 | −1.6% |
| +4% | 1.396 | 1.408 | −0.9% |
| 0% | 1.408 | 1.408 | 0.0% |
| −4% | 1.421 | 1.408 | +0.9% |
| −8% | 1.435 | 1.408 | +1.9% |
| −15% | 1.463 | 1.408 | +3.9% |
With a +8 per cent quarter the mismatched calculation is 214.66 / 155.02; matched it is 202.09 / 143.53. The error is modest because the NAV is only 22.3 per cent of the end value on the matched basis; most of this fund's result is cash already returned, and cash is dated correctly whatever you do.
| Lag quarter index return | FV of calls, mismatched | Mismatched PME | Matched PME | Error |
|---|---|---|---|---|
| +8% | 92.71 | 1.025 | 1.107 | −7.4% |
| 0% | 85.84 | 1.107 | 1.107 | 0.0% |
| −8% | 78.98 | 1.203 | 1.107 | +8.7% |
| −15% | 72.97 | 1.302 | 1.107 | +17.6% |
Here the PME is 95 divided by the future value of the calls, and the lag quarter moves the denominator directly. After a 15 per cent fall, the same fund reports a PME of 1.302 instead of 1.107: almost three times the true outperformance, created by a date. A rising quarter does the opposite and can make a fund that beat the market look as if it barely kept pace.
Falling quarters are precisely when committees scrutinise private equity against listed markets, and precisely when the mismatch flatters it most. A PME produced in a sell-off from a lagged NAV should not be shown without the matched figure beside it.
The same lag affects the IRR, more gently: dating the mature fund's NAV at 30 September gives 11.83 per cent, at 31 December 11.73. For the IRR the issue is the date; for the PME it is the index level paired with that date, and that is where the larger error lives. The interaction between NAV and early-life results is discussed in when a fund's IRR becomes meaningful.
A PME is only as well dated as its NAV. Run it to the NAV date, or roll the NAV forward and say so; never pair a September valuation with a December index. On a young fund the shortcut can turn a PME of 1.107 into 1.302 after one bad quarter. Private Markets Performance works the PME methods on a single fund, and the free workbook for this case includes a PME calculator where the end date of the index is an input you can set to the NAV date; the method itself is in how to calculate the Kaplan-Schoar PME.
Underlying company valuations take weeks to prepare and audit, so a fund's 31 December NAV usually reaches investors in March or later. An investor reporting at 31 December therefore often holds only the 30 September NAV. In the illustrative case that NAV is 45 per 100 committed, 22.3 per cent of the fund's end value, so how it is dated changes the PME.
Either end the whole calculation at the NAV date, discounting flows and index to 30 September, or roll the NAV forward to 31 December with the cash flows of the quarter and the index return. With a beta of 1 both give the same Kaplan-Schoar PME: 1.408 on the mature fund whatever the index did in the lag quarter.
Roughly the NAV's share of the fund's end value times the index move in the lag quarter, with the sign reversed. On a mature fund where NAV is just over a fifth of value, a 15 per cent fall overstates the PME by 3.9 per cent. On a young fund that is almost all NAV, an 8 per cent fall overstates it by 8.7 per cent and a 15 per cent fall by 17.6.
This article is one calculation from Private Markets Performance. 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.
Get the book on Amazon →Free companion files
Also on Amazon UK · Amazon Germany · Amazon France · Amazon Canada
Reading guide: private equity and private markets → · All 1340 articles →
If this book helped, or didn’t, a few lines on Amazon are worth more than they look: they are what the next reader goes on. Write a review. The workbook stays free either way.