How do you calculate the Long-Nickels PME?

The index comparison method worked year by year, with the Excel formula, and the case where it breaks: a fund good enough to drive the index account below zero.

Julian R. Sterling · from Private Markets Performance

Put every capital call into the public index on the day the fund calls it, take out every distribution on the day the fund pays it, and let the balance grow with the index. The balance left at the end replaces the fund's NAV, and the IRR of the fund's flows with that terminal value is the Long-Nickels PME. On an illustrative fund the fund IRR is 12.01 per cent and the Long-Nickels IRR 6.00 per cent: the fund beat the index by 6.01 points.

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

Long-Nickels, also called the index comparison method, was the first public market equivalent and is still the one many LPs mean when they ask how a fund did against public markets. Its appeal is that it answers in the same unit as the fund's own return: a rate. Its weakness is built into the same mechanism, and the second half of this page shows it.

The assumptions

An illustrative fund, annual flows in millions, with a total return index. The fund's NAV at the end of year 6 is 40.0.
Year	Index	Index return	Calls	Distributions
0	100		30.0	0.0
1	108	8.0%	25.0	0.0
2	104	−3.7%	20.0	0.0
3	115	10.6%	15.0	10.0
4	125	8.7%	0.0	30.0
5	131	4.8%	0.0	35.0
6	140	6.9%	0.0	25.0
Total			90.0	100.0

TVPI is 1.56 and DPI 1.11. The index returned 40.0 per cent over the six years, 5.77 per cent a year. The fund's own IRR, on its calls, distributions and the 40.0 NAV, is 12.01 per cent.

The calculation, step by step

PME NAV_t = PME NAV_t−1 × (Index_t ÷ Index_t−1) + Call_t − Distribution_t

Then LN IRR = IRR(−calls + distributions, with PME NAV_T in place of the fund NAV). In Excel, with the index in B, calls in C, distributions in D and the PME NAV in E: =E2*B3/B2+C3-D3 filled down, then =IRR(F2:F8) on a column that is =D-C each year plus the last E in the final row.

The index account, year by year.
Year	Grows by	Plus call	Less distribution	PME NAV
0		30.0	0.0	30.00
1	8.0%	25.0	0.0	57.40
2	−3.7%	20.0	0.0	75.27
3	10.6%	15.0	10.0	88.24
4	8.7%	0.0	30.0	65.91
5	4.8%	0.0	35.0	34.07
6	6.9%	0.0	25.0	11.41

The index investor who mirrored every flow is left with 11.41 at the end of year 6, against the fund's 40.0 of NAV. Replace the 40.0 with 11.41 in the fund's cash flow series and the IRR falls from 12.01 to 6.00 per cent. That is the return the same pattern of money would have earned in the index. The spread, 6.01 points, is the Long-Nickels measure of outperformance.

Why 6.00 and not 5.77? The index's own annualised return ignores timing. The Long-Nickels rate is dollar weighted: it carries the fund's own pattern of calls and distributions, so the years in which more money was in the index count more. Comparing a fund IRR with the index's time-weighted return is the error the PME was invented to avoid.

Where it breaks: a fund that is too good

Keep the same calls and index, but let the fund distribute 155.0 and hold 25.0 of NAV at the end: TVPI 2.00 and a fund IRR of 20.77 per cent. The index account cannot keep up with the withdrawals.

The stronger fund's index account.
Year	Distribution	PME NAV
3	20.0	78.24
4	45.0	40.04
5	50.0	−8.04
6	40.0	−48.59

By year 5 the account is overdrawn, and it ends at minus 48.59. The index investor would have had to short the index to pay out what the fund paid. An IRR still computes, 5.90 per cent, but it is the return on a position that includes a short, and the comparison is no longer like for like. PME+ repairs it by scaling every distribution by one factor so the account ends exactly at the fund's NAV: the factor is 0.562 and the PME+ IRR 6.00 per cent, against the fund's 20.77, a spread of 14.76 points. On the first fund, where nothing went negative, PME+ gives 6.03 per cent, within three basis points of Long-Nickels.

What if: the index ends higher or lower

First fund, only the year-6 index level changed.
Final index level	PME NAV at end	LN IRR	Spread to 12.01%
120	6.21	4.70%	7.31
140	11.41	6.00%	6.01
160	16.61	7.23%	4.79

The terminal PME NAV is small by year 6, so a 40-point swing in the final index level moves the Long-Nickels rate by about 2.5 points. Late in a fund's life the measure leans heavily on index moves in the years the money was invested, which is what it should do.

The common mistakes

Using a price index. The fund's distributions include income, so the index must include reinvested dividends. A price index flatters the fund by the dividend yield.
Reporting the LN IRR without the fund IRR beside it. The number means nothing alone; the spread is the result.
Ignoring a negative PME NAV. Check the last column before quoting the rate. If it goes below zero at any point, report PME+, Kaplan-Schoar or Direct Alpha instead and say why.
Mixing dates. Use the index level on the actual flow dates, or quarter ends consistently. Annual rows are for illustration.

Takeaway

Mirror the fund's flows in the index, use the index account as the terminal value, and compare IRRs: 12.01 against 6.00 here. Then look at the account's path, because a fund strong enough to overdraw it needs PME+. The free PME calculator for this book computes Long-Nickels, PME+, Kaplan-Schoar and Direct Alpha on one set of flows, and the Kaplan-Schoar article gives the ratio version of the same comparison.

Questions readers ask

What is the difference between Long-Nickels and Kaplan-Schoar PME?

Long-Nickels returns a rate: the IRR of the fund's flows with an index-replicated terminal value, compared with the fund's own IRR. Kaplan-Schoar returns a ratio: compounded distributions plus NAV over compounded calls. On the illustrative fund Long-Nickels gives 6.00 per cent against a 12.01 per cent fund IRR, and Kaplan-Schoar gives 1.239. Both say the fund beat the index; they answer in different units.

Why can the Long-Nickels PME NAV go negative?

Because the method withdraws from the index account exactly what the fund distributed. If the fund returns cash much faster than the index grows, the account is emptied and then overdrawn, meaning the index investor would have to short the index. In the illustrative strong fund the account ends at minus 48.59 after 155.0 of distributions on 90.0 of calls.

How does PME+ fix the Long-Nickels problem?

PME+ scales every distribution by a single factor, lambda, chosen so that the index account ends exactly at the fund's NAV. For the illustrative strong fund lambda is 0.562 and the PME+ IRR 6.00 per cent, against a fund IRR of 20.77 per cent. The terminal value can no longer be negative, at the cost of the replicated distributions no longer matching the fund's.

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.
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 big should an evergreen fund's liquidity sleeve be?Four quarters at a 5 per cent cap, net of distributions and a 2 per cent floor, need a 16.9 per cent sleeve, not 20. It costs 127 basis points a year.
How much IRR does one more turn of entry multiple cost in an LBO?Paying 10.0x, not 9.0x, for 50.0 of EBITDA with debt unchanged takes the IRR from 22.1 to 16.1 per cent: 6.0 points for one turn, not the 4.1 a resized table shows.
How far can NAV fall before a NAV facility breaches its LTV covenant?Test adjusted NAV, not reported. A $150m loan on a $900m portfolio breaches a 25 per cent LTV covenant after a 20.8 per cent fall, not the 33.3 headline.

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