A year of shared deals between a flagship and a newer fund: the aggregate test that passes, the deal-by-deal test that does not, and the gain that moved.
Test allocations deal by deal, not only in aggregate. A newer fund can receive exactly its pro rata share of capital over a year and still take more than its share of the best deals. In an illustrative year of twelve shared deals, five of the newer fund's six overweight positions sit among the six best marks: a pattern that arises by chance only 37 times in 924, or 4.0 per cent, and one that moved 12.62 million of gain away from the flagship's investors.
Worked in full in The Private Fund Compliance Officer by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Allocation of investment opportunities between funds managed by the same adviser is one of the first conflicts an examiner looks at. Most firms have a policy: pro rata to available capital, or to target size, with documented exceptions. The usual test checks that, over the period, each fund received its key share of the capital deployed. That test compares totals, and a total says nothing about which deals made it up. A fund can be overweight in the winners and underweight in the losers and still land on its share to the decimal.
A firm runs a flagship with 800 million of available capital and a newer fund with 300 million. The policy is pro rata to available capital, so the newer fund's key is 300 / 1,100 = 27.27 per cent. Over the year they share twelve deals of 60 million each. On six deals the newer fund took 36 per cent; on the other six, 18.55 per cent. All figures are illustrative, in millions.
| Deal | Multiple | Newer fund | Newer fund amount | Gain to newer fund |
|---|---|---|---|---|
| A | 1.85x | Overweight | 21.60 | 18.36 |
| B | 1.62x | Overweight | 21.60 | 13.39 |
| C | 1.48x | Overweight | 21.60 | 10.37 |
| D | 1.40x | Underweight | 11.13 | 4.45 |
| E | 1.33x | Overweight | 21.60 | 7.13 |
| F | 1.27x | Overweight | 21.60 | 5.83 |
| G | 1.21x | Underweight | 11.13 | 2.34 |
| H | 1.12x | Overweight | 21.60 | 2.59 |
| I | 1.05x | Underweight | 11.13 | 0.56 |
| J | 0.98x | Underweight | 11.13 | −0.22 |
| K | 0.90x | Underweight | 11.13 | −1.11 |
| L | 0.72x | Underweight | 11.13 | −3.12 |
| Total | 196.36 | 60.57 |
The aggregate test passes: 196.36 of 720 is 27.3 per cent, exactly the key. The table, sorted by outcome, tells a different story.
Rank the deals by mark and split them into the top half and the bottom half. The newer fund was overweight in six deals; five of them, A, B, C, E and F, sit in the top six. The question is how often that happens if the six overweight deals had been chosen with no knowledge of how the deals would perform.
Ways to choose 6 overweight deals out of 12: C(12, 6) = 924
Ways with exactly 5 in the top six: C(6, 5) × C(6, 1) = 36; with all 6: 1
P(5 or more of 6 in the top six) = 37 / 924 = 4.0%
Excel: =1-HYPGEOM.DIST(4,6,6,12,TRUE)
This is the hypergeometric distribution, the same arithmetic as drawing cards without replacement. It needs no assumption about the size of the returns, only their order. A stricter version uses the ranks themselves: the overweight deals have a rank sum of 25 against a minimum possible of 21, and only 12 of the 924 combinations do as well or better, 1.30 per cent.
The newer fund earned 60.57 million of gain on its 196.36 million. Had it taken exactly 27.27 per cent of every deal, it would have earned 47.95 million. The difference, 12.62 million, came out of the flagship's investors and into the newer fund's track record, where it will appear in the fundraising materials for its successor. The newer fund's multiple is 1.308x against 1.244x on a strict pro rata split; the flagship's is 1.220x against 1.244x.
| Overweight deals in the top six | Combinations | Probability |
|---|---|---|
| 3 or more | 662 | 71.65% |
| 4 or more | 262 | 28.35% |
| 5 or more | 37 | 4.00% |
| All 6 | 1 | 0.11% |
Four of six would arise by chance more than a quarter of the time and proves nothing. Five of six is unusual. The same proportion sustained over two years, ten of twelve overweight deals in the top twelve of 24, has a probability of 0.17 per cent. Patterns that persist become very hard to explain as luck, which is why the test should run on a rolling period as well as each year.
A low probability is a reason to ask, not a finding. A legitimate explanation may exist for every overweight deal: the newer fund's strategy, a concentration limit in the flagship, a co-investor's ticket. The compliance work is to obtain that explanation deal by deal, check it against the written policy, and record it before an examiner asks.
The mistake is running only the aggregate test because it is the one the policy literally describes. A policy that says "pro rata to available capital" is breached deal by deal, not in total, and the deal-by-deal deviations are where the value moves. The second mistake is ranking on cost rather than on outcome: the test only has power once marks exist, so it belongs in the annual review, with the allocation decisions documented at the time they were made. Sample selection for the underlying expense and allocation records follows the logic in how many expense allocations to test.
A version of this allocation test, on its own figures, sits beside the fees, expenses and testing model in the free workbook for this case.
No. An aggregate check confirms that each fund received its share of capital deployed over the period, not that it received its share of the good deals. In the worked case the newer fund took exactly 27.3 per cent of 720 million, yet its overweight positions sat in the best deals and it earned 60.57 million of gain against 47.95 million on a strict pro rata split.
Treat the deals as a fixed set ranked by outcome and ask how many ways the overweight deals could have been chosen. With 12 deals and 6 overweight there are 924 combinations; 37 of them put five or six overweight deals among the top six. The probability is 37 / 924, or 4.0 per cent. Excel's HYPGEOM.DIST gives the same result.
No. It shows that the pattern is unlikely to be chance and needs an explanation, which may be legitimate: a deal's size, the newer fund's strategy or a concentration limit in the flagship. The compliance step is to obtain and document that explanation for each overweight deal, and to escalate if the policy cannot account for it.
The flagship and the newer fund come from chapter 7 of The Private Fund Compliance Officer; the companion files work a version of this test on their own figures. 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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