Public Market Equivalent: Comparing a Private Fund to an Index

A public market equivalent asks what the same cash, on the same dates, would have done in an index instead. Every drawdown and distribution of Nilgiri Growth Partners Fund II, invented, is carried forward to its record date at an invented index's own return, the unsold value is added unchanged, and one total divided by the other. Nilgiri Growth Partners Fund II's own 8.50 years against that invented index give 1.05.

Start with a household rather than a fund. The awkward thing about this measure is not the arithmetic, and it shows faster on a street than on a spreadsheet. A household puts money into a cousin's printing business. Rs 2,00,000 when it opened, another Rs 1,50,000 eighteen months later when a machine broke, another Rs 50,000 the year after. Some cash came back: Rs 1,00,000 once, Rs 3,00,000 later. Today the cousin says the household's remaining share is worth about Rs 4,00,000, and nobody has offered to buy it. One question matters to the household. Did that go well?

The question cannot be answered. Not for want of arithmetic, but because there is nothing on the other side of the comparison. Totalling what went out and what came back gives a multiple, and the multiple will be a true number that compares the printing business to nothing at all. A multiple records what happened; it does not record what else could have happened to the very same rupees on the very same days. The moment the words instead of are used, a second thing has been asked for to compare against, and two decisions have quietly been made: which second thing, and over what stretch of time.

What question does a public market equivalent actually ask?

Exactly that one, made precise. A public market equivalentA ratio comparing a fund's cash flows against the same flows put into an index. takes every rupee a fund actually called and every rupee it actually paid back, keeps each one on the date it really moved, and asks what those same movements would have come to inside an index instead. Not an average. Not a typical year. The same cash, on the same dates.

The dates matter because of who controls them. A private fund does not receive an investor's money on the day the investor decides; it calls the money when it has somewhere to put it, and it returns the money when it has sold something. The timing belongs to the manager. So a comparison that ignores timing is comparing a set of dated, chosen movements against an undated average, and it has stopped being a comparison somewhere in the middle. The public market equivalent exists to put the fund's own timing into the other side of the comparison rather than leaving it out.

Two consequences follow immediately, and both are worth holding before any number arrives. The first is that the answer is a ratio, not a rate. The answer comes out as one total divided by another, so it has no years in it and no per cent sign. The second is that the index chosen and the date stopped at are decisions somebody made rather than facts anybody discovered, so the answer is only ever as meaningful as those two decisions. The second point is the one that gets dropped when the number is written into a note.

Which index is this, and why does it not exist?

Because a real one would put a real market's real history behind an invented fund's invented numbers, and the two do not belong in the same sentence. Everything from here uses the reference broad equity indexAn invented series. It is not any real index., an invented series whose levels are set by this record and by nothing else.

The rule is simple. The index stands at 1,000.00 on the day Nilgiri Growth Partners Fund II, invented, held its final close, the day that fund's own clock starts. The index then has one locked level at each of that fund's year ends. Ten numbers are the whole of the index, and every factor computed later comes out of them.

Look at Year 3 before moving on. Year 3 does more work later than any other row. The index fell that year, from 1,150.00 to 1,060.00. In an index that only ever rises, every early flow would carry a big factor and every late one a small factor, and nothing would be learned except that time passed. Such an index would hide the whole mechanism. The fall in Year 3 is what makes the picture honest, and it is the reason two calls made a year apart can carry very different factors in the wrong order.

Whose method is this, and what are its four steps?

The method belongs to Steven Kaplan and Antoinette Schoar, who set it out in Private Equity Performance: Returns, Persistence and Capital Flows, in the Journal of Finance in 2005. Knowing whose the method is also says what it was built to do: compare a fund whose flows are dated and chosen against an alternative that has to be given the very same dates.

The whole thing is four steps, and every one of them is arithmetic on figures the fund already publishes. There is no model in it, no forecast in it and no opinion in it. Once the index and the measurement date are fixed, the four steps run themselves.

How does one cash flow get carried forward to the record date?

By one multiplication. Everything that follows is that same multiplication repeated twenty one times and then added up, so slow down here. The method takes a single flow, finds the index level on the day that flow moved, and divides the index level at the measurement dateThe single date every flow is carried forward to. by that level. Multiply. That is all.

The number that results is called the carry-forward factorThe measurement date level divided by the level on the flow's own date., and it answers a small, concrete question: if I had bought index units with this rupee amount on this day, how many times over would those units be worth by the day I am measuring at? Work it on a real flow from this record. Drawdown 2 of Nilgiri Growth Partners Fund II, invented, was Rs 55,00,00,000 called at that fund's Year 1 Q3 to pay for holding 1. The index stood at 1,060.00 that quarter. The record date level is 1,760.00. So the factor is 1,760.00 divided by 1,060.00, being 1.6604, and the Rs 55,00,00,000 carries forward to Rs 91,32,00,000.

Read that result carefully. Mishearing it is easy. The result does not say the fund made Rs 91,32,00,000 on holding 1, and it does not say the index made anything for anybody. The claim is narrower. Had that particular Rs 55,00,00,000 gone into the invented index on that particular day instead of into that company, it would be sitting at Rs 91,32,00,000 by the record date. The factor is a counterfactual about one payment, and the method builds its whole answer out of twenty one of them.

Why does an early call carry a far larger factor than a late one?

Because the factor is a fraction whose top never moves and whose bottom does. The top is always 1,760.00, the record date level. The bottom is whatever the index stood at on the flow's own date. A call made when the index was near 1,000 divides by a small number and gets carried a long way; a call made when the index was already near 1,760 divides by almost the same number and barely moves at all.

The two ends of this fund's own record show it plainly. Drawdown 1 of Nilgiri Growth Partners Fund II, invented, was Rs 13,10,00,000 called at that fund's Year 1 Q1 when the index stood at 1,020.00, so its factor is 1.7255. Drawdown 17 was Rs 2,20,00,000 called at that fund's Year 9 Q1 when the index stood at 1,740.00, so its factor is 1.0115. The same invented index and the same measurement date give one flow a factor almost three quarters again as large as itself and the other a factor that adds barely one per cent.

Now the part that a straight line would have hidden. The index did not rise neatly with time, so the factors do not fall neatly with time. Drawdown 8, called at this fund's Year 3 Q3 when the index had fallen to 1,082.50, carries a factor of 1.6259. Drawdown 6, called a full year earlier at Year 2 Q4 when the index stood at 1,150.00, carries only 1.5304. The later call carries the bigger factor, and it does so for the only reason that ever matters here: the index was lower on its date. Time is not what the factor measures. The index level on the day is.

What are the two totals, and what does dividing them give?

Done twenty one times, the multiplication leaves two piles. One pile is everything the fund took in, carried forward. The other is everything the fund gave back, carried forward, with the value of what it still holds added on top. Here they are, with three of the twenty one shown in full so that the working is visible rather than taken on trust.

Divide. For Nilgiri Growth Partners Fund II, invented, over its own 8.50 years against that invented index, Rs 7,71,39,00,000 over Rs 7,35,21,00,000 is 1.0492, written 1.05. For Nilgiri Growth Partners Fund II, invented, over its own 8.50 years to its record date, measured against the invented reference broad equity index, the public market equivalent is 1.05. That sentence is long on purpose. Every one of its clauses is load bearing, and the number is unreadable without all of them.

One arithmetic housekeeping note, for the careful reader who tries to add the column up. Each individual flow above is rounded to the nearest lakh. Each total is the exact sum, rounded the same way. The seventeen rounded drawdowns added by hand land Rs 1,00,000 below the Rs 7,35,21,00,000 total. The gap is rounding and nothing else.

What happens to the Rs 2,82,00,00,000 nobody has bought?

The unsold value goes into the numerator exactly as it stands, and that is the softest part of the whole measure. Nilgiri Growth Partners Fund II, invented, still holds five of its nine companies at its record date. The residual valueThe carrying value of what the fund still holds, added to the numerator as it stands. of those five is Rs 2,82,00,00,000. Nobody has paid that. The figure is a carrying value, and how a carrying value is struck, and by whom, is covered separately.

Notice why it is added unchanged rather than carried forward. Carrying a flow forward moves it from its own date to the measurement date. The unsold value is already sitting at the measurement date; there is nowhere to carry it to. So the method takes it as it is, and every judgement inside that carrying value walks straight into the answer without being multiplied by anything.

Now weigh it. The numerator is Rs 4,89,39,00,000 of carried-forward distributions plus Rs 2,82,00,00,000 of residual value, being Rs 7,71,39,00,000. So 36.6 per cent of the numerator of this fund's public market equivalent is a carrying value that nobody has bought. The denominator is made entirely of cash that genuinely moved. The two halves of the ratio are not the same kind of thing, and a reader who does not know that has not been told the most important thing about the number.

Why is the index taken at 1,760.00 on the record date?

Because the record date does not fall on a year end, and the method needs a level for it anyway. Nilgiri Growth Partners Fund II, invented, is measured at the end of its Year 9 Q2, being 8.50 years after its final close and halfway through its Year 9. The index has a locked level at that fund's Year 8 year end, 1,720.00, and another at its Year 9 year end, 1,800.00. The index has no locked level in between.

So the method uses interpolationTaking a level inside a year as a straight line between the two year ends.: a level inside a year is taken as a straight line between the two year ends. Half a year in, halfway between. 1,720.00 plus half of the 80.00 point move is 1,760.00, and that is the number sitting on top of every one of the twenty one factors worked here. The same rule produced 1,060.00 for the Year 1 Q3 call and 1,555.00 for the Year 7 Q3 distribution, so the rule is not a special step for the record date; it is how every date inside a year gets a level.

The straight-line convention is worth stating precisely, both for what it is and for what it is not. Applying one stated rule the same way everywhere is the best thing a convention can do. A straight line between two year ends is a rule and not an observation, so 1,760.00 is not a claim about where the index actually stood that day. And it is a choice with consequences: had this fund been measured a quarter earlier, the top of every factor would have been 1,740.00 instead, and every carried-forward amount worked here would change.

Do the fund's 8.3 per cent and the index's 6.9 per cent answer the same question?

No, and this is the single most common way the measure gets misused. Two rates are available for Nilgiri Growth Partners Fund II, invented, over its own 8.50 years to its record date. Its net internal rate of returnThe fund's own dated return after fees. A different question from this ratio. is 8.3 per cent a year, after its own fees and expenses. The invented reference broad equity index stood at 1,000.00 at that fund's final close and is taken at 1,760.00 at its record date, a return of 6.9 per cent a year over the same 8.50 years. Both figures are true. Neither may be subtracted from the other.

Here is why the subtraction is meaningless. The 8.3 per cent is a rate computed on a set of dated flows that somebody chose. The 6.9 per cent is a rate computed on two levels and a length of time, with nobody's dates in it at all. When the money goes in changes what a series of levels does to it. The same rupees put into that index on those dates do not produce 6.9 per cent. The whole reason the public market equivalent exists is that the index's own annual return is the wrong thing to compare a dated set of flows against, and taking the difference between the two rates quietly does exactly that.

The 1.05 that Nilgiri Growth Partners Fund II, invented, produces over its own 8.50 years against that invented index is a third object again, and it is the one the method actually produces. The 1.05 is not a rate and it is not a difference between rates. The ratio is what the fund's flows came to, divided by what those same flows would have come to in that index, both measured at one date. Three numbers, three questions, and none of them is scored against the others.

What does this invented fund's public market equivalent not say?

What has to be true about an index before any of this is worth doing?

Four things, and none of them is about whether the index is a good one. The four are about whether the arithmetic can even be performed honestly.

The index has to have a level on every date a flow moved, or a stated rule for producing one. The straight line inside a year is such a rule. The index has to be in the same currency as the flows. Multiplying rupees by a factor built from a series denominated in something else silently mixes two things. The index has to cover the whole period, with no gap where a level had to be filled in from somewhere else. And it has to be chosen before the answer is seen. Somebody choosing after the result is known already knows which choice produces which answer, so an index picked then is not a comparison at all.

The fourth requirement is the only one about conduct rather than arithmetic, and it is the one that cannot be checked by looking at the working. A note that records which comparison was used is a note that can be read; a note that records only the answer has thrown away the one piece of evidence that would show whether the comparison was fixed in advance.

What would have to be true before a number like this meant more than one fund?

The distance between one fund's ratio and anything wider is much larger than it looks. Four things would have to change, and changing any one of them changes the answer.

Not one of those four is satisfied by anything here, and what has been computed therefore supports no conclusion wider than the fund it is about. That is not a hedge and it is not modesty. The scope of the computation is one invented fund, one invented index, one measurement date, one number. How a fund is set beside the other funds raised around the same time, and what a quartile needs behind it before it means anything, is covered separately and is a different measurement with different requirements.

What does somebody reading a fund's performance report actually do with a ratio like this?

Four things, and every one of them is a question about the working rather than about the number. Far more people read a private fund's performance report than ever compute one, and the reading is where the mistakes happen.

The first thing is to find out what the comparison was and when it was picked. A performance report that names the index it used, and says the same index has been used every quarter, can be read. One that names only the result cannot, and the person reading has learned something about the report rather than about the fund. The second is to separate the parts of the numerator. Rs 4,89,39,00,000 of the top of this fund's ratio is cash that genuinely moved and Rs 2,82,00,00,000 is a carrying value, so the reader who knows the split knows how much of the answer would survive if every mark turned out to be optimistic and how much would survive if every mark turned out to be cautious.

The third is to check the date and hold it constant. A fund that has sold most of what it bought and a fund that has sold hardly any of it are being measured on numerators made of different stuff. A ratio at one fund's Year 9 Q2 and a ratio at some other fund's Year 6 Q3 are not on the same footing. Comparing two of these ratios is a much harder thing than computing either of them, and most of the difficulty lives in the parts of each numerator that nobody has sold.

The fourth is to notice how much the ratio is silent about: everything except the comparison it was built to make. The ratio says nothing about how the fund is run, nothing about what it holds now, nothing about what its remaining six quarters contain and nothing about any other fund anywhere. A household deciding whether the cousin's printing business went well faces exactly the same limitation: putting a second number beside the first says what the alternative would have done to the very same rupees, and that is genuinely useful, and it is also all it says.