How do you calculate the mPME (modified PME) for a private fund?

Cambridge Associates' modified public market equivalent, worked year by year, and why its index replica can never go negative.

Julian R. Sterling · from Private Markets Performance

The mPME (Cambridge Associates' modified public market equivalent) invests every capital call in the index, then sells the same fraction of that index holding as the fund distributes of its own value, and takes the IRR of the resulting cash flows. On an illustrative eight-year fund with a 12.09 per cent IRR, the index replica earns an mPME IRR of 7.55 per cent, an excess return of 4.55 percentage points. Because it scales distributions instead of copying them, the replica's NAV can never go negative.

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

Why a modified PME exists

The Long-Nickels method buys the index with each call and sells exactly the fund's distribution in cash. When the fund outperforms, the replica is asked to pay out more than it holds, its NAV turns negative and the comparison IRR loses its meaning. PME+ fixes this with a single scaling factor applied to every distribution. The mPME, developed by Cambridge Associates, fixes it period by period: each distribution is converted into a share of the fund's value, and the replica sells that same share of itself. The result is an IRR you can set beside the fund's IRR, which is why it appears in so many LP benchmarking packs alongside the Kaplan-Schoar ratio.

The fund and the index

Illustrative fund per 100 of commitment, year-end flows, with a total return index. The same fund as in the Kaplan-Schoar worked example, with interim NAVs added.
Year	Calls	Distributions	Fund NAV after distribution	Index level
0	30	0	30	100.0
1	25	0	58	112.0
2	20	0	80	103.0
3	15	5	100	121.6
4	10	15	108	133.7
5	0	30	95	141.8
6	0	35	80	163.0
7	0	30	60	156.5
8	0	20	40	170.6
Total	100	135

DPI is 1.35x, TVPI 1.75x and the fund IRR 12.09 per cent. The index compounds at 6.90 per cent a year. The mPME needs one input the Kaplan-Schoar PME does not: the fund's NAV at every date on which it distributes.

The calculation, step by step

Distribution weight: w_t = D_t ÷ (D_t + NAV_t), with NAV_t after the distribution

Replica before distribution: P_t = NAV^PME_t−1 × I_t ÷ I_t−1 + C_t

mPME distribution: D^PME_t = w_t × P_t; replica NAV: NAV^PME_t = P_t − D^PME_t

mPME IRR = IRR of −C_t + D^PME_t, plus NAV^PME at the last date

In Excel, row by row: weight =IF(C5=0,0,C5/(C5+D5)), replica before distribution =J4*E5/E4+B5, mPME distribution =F5*G5, then =IRR() on the column of calls, mPME distributions and the closing replica NAV

Step 1: build the replica through the calling years. No distributions, so the replica is simply the calls compounded at the index: 30.00 at year 0, 58.60 at year 1 (30 × 1.12 + 25) and 73.91 at year 2 (58.60 × 0.92 + 20).

Step 2: weight each distribution. In year 3 the fund pays 5 and keeps 100, so it has distributed 5 ÷ 105 = 4.76 per cent of its value. The replica, grown to 87.22 and topped up by the call of 15 to 102.22, pays out 4.76 per cent of itself: 4.87.

Step 3: repeat to the end. The weights rise as the fund harvests: 12.20 per cent in year 4, 24.00 in year 5, 30.43 in year 6 and 33.33 in years 7 and 8.

The index replica, per 100 of commitment.
Year	Replica before distribution	Weight	mPME distribution	Replica NAV
3	102.22	4.76%	4.87	97.35
4	117.08	12.20%	14.28	102.81
5	108.97	24.00%	26.15	82.82
6	95.24	30.43%	28.99	66.26
7	63.61	33.33%	21.20	42.40
8	46.22	33.33%	15.41	30.81

Step 4: take the IRR. Calls of 100, mPME distributions of 110.90 and a closing replica NAV of 30.81 give an IRR of 7.55 per cent. The replica's multiple is 1.42x against the fund's 1.75x.

Reading the result

The fund beat the index by 4.55 percentage points a year, or 455 basis points, on cash flows with the same timing and the same pattern of harvesting. That is the number to quote as the excess return. The Kaplan-Schoar PME on the same fund is 1.227: the two tests agree on the sign, and they answer different questions, one a wealth ratio over the whole life, the other an annual rate. Note that the replica ends with 30.81 against the fund's 40: it has paid out proportionally, not in matching cash, so its NAV tracks the fund's shape rather than its level.

What if: the market and the fund change

mPME against Long-Nickels on the same calls. Index variants shift every annual return by 5 points.
Case	Fund IRR	mPME IRR	Excess, points	Long-Nickels replica NAV	mPME replica NAV
Base	12.09%	7.55%	4.55	4.60	30.81
Index 5 points stronger	12.09%	12.53%	-0.44	43.87	41.74
Index 5 points weaker	12.09%	2.56%	9.54	-22.85	22.50
Outperforming fund, 230 distributed	23.28%	7.76%	15.52	-103.57	10.59

Two things show. In the weak market and for the outperforming fund, the Long-Nickels replica ends deeply negative, so its IRR compares the fund with a short position in the index. The mPME replica stays positive in every case, at 22.50 and 10.59. And in a strong market the fund that looked good on its own IRR trails the index by 0.44 points: the mPME turns a 12.09 per cent fund into an underperformer without touching its cash flows.

The common mistakes

Dividing by the NAV after the distribution alone. Using D ÷ NAV with the post-distribution NAV overweights every payout: here it lifts the mPME IRR to 7.74 per cent and cuts the excess to 4.36 points. The denominator is what the fund was worth just before it paid, D + NAV after.
Comparing the fund IRR with the index's annual return. 12.09 less 6.90 gives 5.19 points, which ignores that the fund's money was invested at different times from a buy-and-hold index position. The mPME exists to correct exactly that.
Using a price index. Dividends are part of what the LP gave up. Use a total return index, and see which index a PME should use.

Takeaway

The mPME asks what the index would have earned if it had been called and harvested in the same proportions as the fund. On this fund the answer is 7.55 per cent, 455 basis points below the fund's 12.09. It needs interim NAVs, but in return it never breaks the way Long-Nickels does. The book sets all four public market equivalents on one set of cash flows, and the free PME calculator for the book runs Kaplan-Schoar, Long-Nickels, PME+ and Direct Alpha on a fund of your own. For the alternatives, see how PME+ scales distributions and the Long-Nickels PME.

Questions readers ask

What is the difference between the mPME and PME+?

Both scale the fund's distributions so the index replica does not go negative. PME+ applies one factor to every distribution, solved so the replica ends at the fund's NAV. The mPME sets a separate weight at each date, D / (D + NAV), so the replica sells the same share of itself as the fund did. On the illustrative fund the mPME replica ends at 30.81 rather than the fund's 40, and its IRR is 7.55 per cent.

Can the mPME replica NAV go negative?

No. Each distribution is a fraction between zero and one of what the replica holds, so it can never pay out more than it owns. Long-Nickels can: for an illustrative outperforming fund that distributes 230 per 100 called, the Long-Nickels replica ends at -103.57, while the mPME replica ends at 10.59.

How do you express the mPME result?

As an excess return: fund IRR minus mPME IRR, in percentage points or basis points. On the worked fund that is 12.09 less 7.55 per cent, 455 basis points a year. Quote it next to a Kaplan-Schoar PME, 1.227 here, so the reader sees both an annual rate and a whole-life wealth ratio.

Read the whole case

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.

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Also on this site

How do you calculate the Kaplan-Schoar PME?Grow distributions, NAV and calls at the index total return, then divide. An illustrative fund with a 12.09% IRR returns 191.57 for 156.18: a PME of 1.227.
How do you calculate Direct Alpha for a private equity fund?Compound each cash flow to the end date at the index total return, then take the IRR. An illustrative fund earns 4.83% a year of Direct Alpha, not 4.61 points.
How do you calculate PME+ for a private equity fund?Scale distributions by lambda so the index portfolio ends at the fund's NAV, then take the IRR. Here lambda is 0.7739 and PME+ 7.05% against 11.07%.
How do you calculate a Dimson beta for private equity returns?Regress fund returns on current and lagged index returns and sum the slopes. Here a 0.59 ordinary beta becomes 1.18, and alpha falls from 12.6% to 6.7%.
How does a lagged NAV distort a private equity PME?Pairing a September NAV with a December index flatters the PME after a falling quarter: an 8 per cent fall turns a young fund's 1.107 into 1.203.
How do exchange rates change a private equity fund's IRR?Convert each flow at its own date's rate: a euro fund earning 14.57% returns 12.71% to a dollar investor after a 10% fall in the euro, not the 13.07% shortcut.

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