A denominator breach is three movements, not one: the public fall, the lag in private marks, and the net cash flows that keep arriving.
Recompute the private share with each side moved by its own return: private × (1 + rprivate) ÷ (private × (1 + rprivate) + public × (1 + rpublic)). A 15 per cent allocation on a 2,000 plan becomes 18.45 per cent after a 22 per cent public fall with private marks unchanged, and 17.84 per cent once they are marked down 4 per cent. A year of net capital calls then takes it to 19.12 per cent, even after a full markdown.
Worked in full in The Private Markets Limited Partner by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The denominator effect is usually described as a single event: public markets fall, the private book does not, and the allocation jumps over its ceiling. The arithmetic shows three separate movements, with different signs and different durations. One is real, one is a reporting lag that reverses on its own, and one is cash, which is the part that keeps a programme overweight after the marks have caught up.
| Input | Value |
|---|---|
| Total plan | 2,000 |
| Private equity NAV (15 per cent) | 300 |
| Public portfolio | 1,700 |
| Policy band | 12% to 18% |
| Public market return over the shock | −22% |
| Private markdown in the next reported quarter | −4% |
| Private markdown once valuations catch up | −12% |
| Capital calls over the following year | 60 |
| Distributions over the following year | 20 |
Share = P(1 + rp) ÷ [P(1 + rp) + Q(1 + rq)]
Public: 1,700 × (1 − 22%) = 1,326, a loss of 374. Private unchanged at 300. Share = 300 ÷ 1,626 = 18.45%, above the ceiling.
In Excel, with private in B2, public in B3 and the two returns in B4 and B5: =B2*(1+B4)/(B2*(1+B4)+B3*(1+B5)).
In currency, the private book now sits 56.1 above its 15 per cent target on the shrunken plan, but only 7.3 above the 18 per cent ceiling. That distinction matters for the response: a breach of 7.3 on a plan of 1,626 is a rounding error against a single year of capital calls, and it is the calls, not the marks, that decide where the share goes next.
Private valuations arrive a quarter late and move less than the market at first. With the next quarter's NAV down 4 per cent, the private book is 288 and the plan 1,614. Share: 17.84%, back inside the band. When the marks catch up fully, at −12 per cent, the private book is 264 and the share 16.60 per cent.
So 1.24 points of the reported overweight, the gap between 17.84 and 16.60, is an artefact of timing. It reverses without anyone doing anything. Selling private interests at a discount to cure it is selling to fix a number that was going to fix itself.
Here is the part that persists. In a falling market, exits slow and distributions dry up, while managers keep calling for deals and follow-ons already committed. With 60 called and 20 distributed, 40 moves from the public book into the private one.
Private: 264 + 40 = 304. Public: 1,326 − 40 = 1,286. Share = 304 ÷ 1,590 = 19.12%.
The cash flows add 2.52 points, more than double the lag effect, and they do not reverse when valuations settle.
| Stage | Private | Plan total | Private share |
|---|---|---|---|
| Public fall, private unchanged | 300 | 1,626 | 18.45% |
| First lagged mark, −4% | 288 | 1,614 | 17.84% |
| Full mark, −12% | 264 | 1,590 | 16.60% |
| Plus a year of net calls of 40 | 304 | 1,590 | 19.12% |
| Public return | Private flat | Private −5% | Private −10% |
|---|---|---|---|
| −10% | 16.39% | 15.70% | 15.00% |
| −20% | 18.07% | 17.33% | 16.56% |
| −30% | 20.13% | 19.32% | 18.49% |
| −40% | 22.73% | 21.84% | 20.93% |
The trigger level: with private marks flat, the plan breaches an 18 per cent ceiling once public markets fall 19.61 per cent. With a 4 per cent private markdown alongside, the trigger moves to a 22.82 per cent fall. Solve it directly: public fall = (P ÷ ceiling − P) ÷ Q − 1.
The common mistake is to read the first number, 18.45 per cent, as the problem and the full markdown as the cure. It is the other way round. The day-one overweight is partly a reporting lag, and the markdown takes care of it. What the markdown does not touch is the commitment pipeline: calls from vintages committed in better years keep arriving whatever the marks say, and they arrive while distributions have stopped. A plan that only looks at the reported share will relax as marks fall and then find itself above the ceiling a year later, at 19.12 per cent, with nothing left to blame on valuations. The second mistake is the reflex the other way, skipping vintages altogether, which leaves a hole in the programme years after public markets have recovered.
Split any denominator breach into three parts: the public move, the lag in private marks, and the net cash flows over the next year or two. Only the last is controllable, through the next commitment budgets, and it is usually the largest. The recovery paths under different budget responses are worked in the free workbook and cases for this book. How much unfunded commitment a plan can carry into such a stress is in what overcommitment ratio a programme can afford.
Solve public fall = (P / ceiling minus P) / Q minus 1. With 300 private and 1,700 public, an 18 per cent ceiling is breached after a 19.61 per cent public fall if private marks stay flat, and after a 22.82 per cent fall if private marks drop 4 per cent alongside.
Only partly. In the worked case the gap between the first lagged mark and the full markdown is 1.24 points, which reverses on its own. A year of net capital calls of 40 adds 2.52 points that do not, taking the share to 19.12 per cent against an 18 per cent ceiling.
Usually not on the first reading. Part of the overweight is a valuation lag that corrects as marks fall. The persistent part comes from capital calls outpacing distributions, and the controllable lever is the size of the next commitment budgets, not a forced secondary sale at a discount.
Chapter 5 of The Private Markets Limited Partner works a denominator shock; the companion files take it through the recovery. 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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