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How do you calculate the Kaplan-Schoar PME?

The Kaplan-Schoar public market equivalent worked on an eight-year fund, with the Excel formula, the sensitivity to the index, and the price index trap.

Julian R. Sterling · from Private Markets Performance

Grow every distribution and the final NAV to the measurement date at the public index's total return, grow every capital call the same way, and divide the first sum by the second. On an illustrative eight-year fund with a 12.09 per cent IRR and a 1.75x TVPI, the future value of what it returned is 191.57 against 156.18 for what it called: a Kaplan-Schoar PME of 1.227. The fund returned 22.7 per cent more than the same cash invested in the index would have.

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

A fund's IRR on its own says nothing about whether private equity was worth the illiquidity. The Kaplan-Schoar public market equivalent answers that question with a single ratio: above 1.0 the fund beat the index on the same cash flow timing, below 1.0 it did not. It is the standard first test in a limited partner's benchmarking pack, and it takes one column of index levels to compute.

The fund and the index

Illustrative fund cash flows, per 100 of commitment, and a total return index. Flows assumed at year end.

Year	Calls	Distributions	Index return	Index level	Growth factor to year 8
0	30	0		100.0	1.706
1	25	0	12%	112.0	1.523
2	20	0	−8%	103.0	1.656
3	15	5	18%	121.6	1.403
4	10	15	10%	133.7	1.276
5	0	30	6%	141.8	1.203
6	0	35	15%	163.0	1.046
7	0	30	−4%	156.5	1.090
8	0	20	9%	170.6	1.000
Total	100	135

The fund also holds a NAV of 40.0 at year 8. Its DPI is 1.35x, its TVPI 1.75x and its IRR 12.09 per cent. The index compounds at 6.90 per cent a year over the eight years.

The calculation, step by step

The growth factor is the only new column. It converts every flow into money at the measurement date, as if each call had been taken out of the index and each distribution put back into it. Once everything is in the same date's money, the ratio needs no discount rate and no IRR, which is why early distributions cannot inflate it the way they inflate an IRR.

Reading the result

A KS-PME of 1.227 means that for every unit of index-equivalent value the calls would have produced, the fund produced 1.227. In money, the fund created 35.40 more than an index investment with the same timing, measured at year 8. It is a multiple, not a rate: it does not say how fast the outperformance accrued, and a 1.227 earned over four years is a far better result than the same figure over twelve.

The NAV is 20.9 per cent of the numerator, so the result still depends on an unrealised mark. If the 40.0 NAV were marked down 20 per cent, to 32.0, the PME would be 1.175, not 1.227. Report the share of the PME that is realised alongside the number.

What if the index had done better

KS-PME with every annual index return shifted by the same amount.

Shift in index return	Index CAGR	KS-PME
−4 points	2.89%	1.479
−2 points	4.90%	1.345
None	6.90%	1.227
+2 points	8.91%	1.121
+4 points	10.92%	1.025

The fund stops beating the index at a shift of 4.58 points, an index CAGR of 11.49 per cent, below its own 12.09 per cent IRR. The path matters as well as the average: an index compounding smoothly at 6.90 per cent gives a PME of 1.261, not 1.227, because the real index rose fastest in the years when the fund's calls were still invested in it. An index growing at a constant rate equal to the fund's IRR gives exactly 1.000, by construction. Comparing the IRR with the index CAGR is therefore not a substitute for the PME.

The common mistake

Using a price index instead of a total return index. Private equity distributions are cash returned to the investor, so the public alternative has to include its dividends too. With a dividend yield of 2 per cent left out, the index ends at 146.6 instead of 170.6 and the PME comes out at 1.345, overstating the fund by 0.119. Check the index ticker before checking anything else: a price index is the default series in most data terminals.

Match the timing. Annual buckets are used here for readability. On real data use the actual flow dates and daily or monthly index levels; a call booked at year end that was drawn in January is grown at the wrong factor.

Takeaway

Future value of distributions plus NAV, over future value of calls, both at the index's total return: 1.227 here. Read it with its realised share and its period, and always against a total return series. The free PME calculator for this book computes Kaplan-Schoar alongside Long-Nickels, PME+ and Direct Alpha on one set of flows, the PME calculator template does the same for your own fund, and a companion article on Direct Alpha turns the ratio into an annual rate.

Questions readers ask

What is a good Kaplan-Schoar PME?

Anything above 1.0 means the fund beat the index on the same cash flow timing; the size that counts as good depends on the period. An illustrative fund at 1.227 over eight years produced 35.40 more than the index per 100 committed. Read the PME together with its realised share, since an unrealised NAV of 40.0 here is 20.9 per cent of the numerator.

Why is my PME below 1 when the fund IRR beats the index return?

Because the index CAGR ignores the fund's timing. The PME grows each call at the index return earned while it was invested. In this example the fund's IRR is 12.09 per cent, yet it stops beating the index at an index CAGR of 11.49 per cent, because the index path, not just its average, decides the result.

Should PME use a price index or a total return index?

A total return index, because fund distributions are cash returned and the public alternative must include its dividends. Leaving out a 2 per cent dividend yield here lowers the index's end level from 170.6 to 146.6 and inflates the PME from 1.227 to 1.345.

Also on this site

• 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.
• 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 2 per cent management fee cost over a fund's life?Five years at 2 per cent on commitments, then 1.5 per cent on invested capital: $69.1m on a $500m fund, 13.8 per cent of commitments, not 20.
• Why a quarter-end close needs two routes to the same NAVA close that agrees with itself only one way has not been checked. Bridging a draft $125m to a corrected NAV of $128.5m, two ways.
• How much does a cheaper fund administrator actually save?An administrator 80,000 cheaper on the invoice is 17,488 cheaper to run once rework, reissues and data work are priced, and takes 10.7 years to repay the move.
• What a clawback actually collateralisesA 24 million clawback recovers 13.20 net of tax, of which 7.20 is escrowed. The rule is e ≥ 1 − t, and every euro won on the tax clause lands uncollateralised.

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