A fund's internal rate of return cannot be compared with an index return, and the reason is not a convention. The fund controlled the timing of every cash flow and the index did not, so the two numbers were computed over different capital at different times.
The public market equivalent removes that objection by asking a counterfactual with no timing freedom in it: what if every rupee the fund called had instead been invested in a public index on the same day, and every rupee the fund distributed had instead been withdrawn from that index on the same day?
The counterfactual contains no skill at all, which is exactly what makes it a benchmark.
How is the Kaplan-Schoar PME calculated and read?
The Kaplan-Schoar ratio implements it in one line. Compound every cash flow forward to a common date using the index's own total return, then divide:
KS-PME = Σ distributions × (I_T ÷ I_t) ÷ [ Σ calls × (I_T ÷ I_t) ]
with any residual net asset value added to the numerator as though it were distributed on the final date. Above 1.00, the fund beat the index on the fund's own schedule. Below 1.00, it did not. The ratio is a wealth multiple, not a rate, and that is its point: it is denominated in the same units as a total-value-to-paid-in multiple and can sit next to one in the same table.
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Three properties are worth holding.
The ratio is timing-aware without being timing-flattered. A fund that called capital just before a market fall and distributed just after a rise gets no credit for the market's move, because the index counterfactual received the identical timing.
The ratio is only as good as the index substitution, and the substitution is a choice. A large-buyout fund benchmarked against a broad index and against a small-cap index will report materially different public market equivalents, and neither is wrong; the choice must be stated, defended and held constant across a comparison set. Leverage is the harder half of the same problem, since a buyout fund's portfolio runs at four to six times EBITDA and an index does not, so a like-for-like comparison arguably needs a levered index. The honest position is to report the unlevered comparison and say what leverage would do to it.
The ratio inherits the net asset value problem. For a fully realised fund it does not, because the residual is zero and every input is cash. For a live fund the numerator contains the general partner's own mark, which means an interim public market equivalent is an opinion wearing an arithmetic costume, exactly as an interim total-value-to-paid-in multiple is.
What are direct alpha and PME+?
Two companions are worth naming. Direct alpha takes the same index-adjusted cash flows and computes their internal rate of return, converting the wealth ratio into an annualised excess return, which is the form most investment committees can act on. PME+ and modified PME rescale distributions so the synthetic index position never goes short. That problem arises in strongly performing funds, where naive index-tracking would require selling more index units than were ever bought. A public market equivalent computed on a fund whose distributions dwarf its calls should always name which variant produced it.