A policy benchmark of public equities plus a premium, applied to one fund's cash flows two ways: the shortcut most reports use and the cash-flow-matched test.
To test a fund against a policy benchmark such as "public equities plus 3 per cent", build a benchmark index that compounds at (1 + index return) × 1.03 each year and run a public market equivalent on the fund's own cash flows. On an illustrative fund with an 8.76 per cent IRR, the shortcut of comparing it with the benchmark's ten-year CAGR, 8.84 per cent, says the fund failed by 0.08 points. The cash-flow-matched test says it passed: a Kaplan-Schoar PME of 1.040 and Direct Alpha of 0.59 per cent, with a break-even premium of 3.61 per cent.
Worked in full in Private Markets Performance by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Many pension and endowment policies set private equity's benchmark as a listed index plus a premium for illiquidity, illustratively 2 to 4 per cent. The premium is the easy part. The hard part is that a fund's IRR and an index CAGR measure different things: one weights each year by the capital the fund had at work, the other weights every year equally. Comparing them directly can pass a fund that failed, or fail one that passed, depending on when the market moved.
| Year | Fund net cash flow | Index return in the year to t |
|---|---|---|
| 0 | −25 | |
| 1 | −25 | 18% |
| 2 | −20 | 15% |
| 3 | −15 | 12% |
| 4 | −10 | 10% |
| 5 | 10 | −5% |
| 6 | 20 | 8% |
| 7 | 30 | 2% |
| 8 | 35 | −10% |
| 9 | 30 | 6% |
| 10 | NAV 38 | 4% |
The fund called 95, distributed 125 and holds a NAV of 38 at year 10: TVPI 1.72x, DPI 1.32x, IRR 8.76 per cent. The index returned 5.67 per cent a year over the decade, with its best years at the start, while the fund was still drawing capital.
Benchmark CAGR = (1.0567 × 1.03) − 1 = 8.84 per cent, or 8.67 if 3 points are simply added to the index CAGR. The fund's 8.76 per cent misses the compounded version by 0.08 points and clears the added one by 0.09: on a shortcut this marginal, the verdict depends on a convention nobody wrote down. Most quarterly reports stop here, and the fund is recorded as below benchmark.
Benchmark levelt = levelt−1 × (1 + index returnt) × (1 + premium)
In Excel, with index returns in B3:B12 and the level starting at 1 in C2: =C2*(1+B3)*(1+3%), copied down. The level is all a PME needs.
KS PME = Σ distributions × LT/Lt + NAV, divided by Σ calls × LT/Lt
Against index plus 3 per cent: 179.05 / 172.19 = 1.040. Every call is grown at what the benchmark would have earned on it from the day it was drawn, and every distribution likewise, so the comparison uses the fund's own timing. The same flows give a Direct Alpha of 0.59 per cent and a Long-Nickels benchmark IRR of 8.14 per cent.
| Benchmark | KS PME | Direct Alpha | Benchmark IRR on the fund's flows | Fund IRR minus it |
|---|---|---|---|---|
| Index | 1.266 | 3.61% | 5.11% | 3.65 |
| Index plus 3% | 1.040 | 0.59% | 8.14% | 0.62 |
The fund passes. The shortcut failed it because the benchmark's CAGR includes the index's 18 and 15 per cent in years one and two, when the fund had drawn only half its capital, and gives the falls of years five and eight no more weight than the rises. The money the fund actually had at work earned more than the benchmark would have on the same dates.
The direction can just as easily run the other way. A fund that draws most of its capital before a strong market will look better on the shortcut than on the PME. The shortcut is not conservative; it is simply measuring a different portfolio.
| Premium | Benchmark CAGR | KS PME | Benchmark IRR on the fund's flows | Fund IRR minus it |
|---|---|---|---|---|
| 0% | 5.67% | 1.266 | 5.11% | 3.65 |
| 2% | 7.78% | 1.110 | 7.13% | 1.63 |
| 3% | 8.84% | 1.040 | 8.14% | 0.62 |
| 4% | 9.90% | 0.975 | 9.16% | −0.40 |
| 5% | 10.95% | 0.915 | 10.18% | −1.42 |
The premium at which the PME equals exactly 1.000 is 3.61 per cent, the same figure as the fund's Direct Alpha against the plain index. That is not a coincidence: Direct Alpha is the compounded premium over the index that the fund earned on its own cash flows, which is why it is the cleanest single number to put beside a policy benchmark. The method is set out in how to calculate Direct Alpha.
A policy benchmark of index plus a premium is a PME problem, not an IRR comparison: grow the index at the premium, discount the fund's own flows with it, and read the ratio. This fund fails the shortcut by 0.08 points and passes the real test with a PME of 1.040. Private Markets Performance treats the public market equivalents as one family, and the free workbook for this case includes a PME calculator that runs the test against a policy hurdle for a fund of your own; the Kaplan-Schoar step is worked separately in how to calculate the Kaplan-Schoar PME.
Policy documents rarely say, and the difference is real. Adding 3 points to each year's index return gives a ten-year benchmark of 8.68 per cent here; compounding (1 + index) x 1.03 gives 8.84 per cent. On the cash flows the PME is 1.049 additive and 1.040 compounded. Write the convention into the policy and use it every quarter.
Because the index CAGR covers the whole period equally while the fund's money was invested unevenly. Here the index rose 18 and 15 per cent in the first two years, when little capital was drawn. The point-to-point benchmark of 8.84 per cent beats the fund's 8.76; the cash-flow-matched benchmark IRR is 8.14 per cent, and the fund beats it by 0.62 points.
Solve for the premium that sets the Kaplan-Schoar PME to 1.000. For this illustrative fund it is 3.61 per cent a year, which equals its Direct Alpha against the plain index. At a 4 per cent premium the PME is 0.975 and the fund fails; at 3 per cent it passes with 1.040.
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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