Fifty-nine. At ninety-five per cent confidence, establishing that no more than five per cent of expense allocations are wrong takes 59 items, selected at random. If all 59 are clean, that is precisely what has been established and it can be said in those words. Ruling out a one per cent error rate at the same confidence takes 299 items. Twenty items, all clean, establish only that the error rate is probably below fourteen per cent.
The formula, and what a sample size actually claims
Chapter 13 says to test. It does not say how much, and “periodically” is neither an answer that can be defended to an examiner nor one a resourcing committee can act on. Audit practice supplies an exact one:
n = ln(1 − confidence) divided by ln(1 − error rate)
The formula converts a claim into the number of items that supports it. To be 95 per cent confident that no more than five per cent of expense allocations are wrong, test 59 items. If all 59 are clean, that is what has been established, and it can be stated in exactly those words. To rule out a one per cent error rate at the same confidence takes 299 items.
Attribute sampling at ninety-five per cent confidence.
What a clean sample establishes
Items to test
Error rate below twenty-six per cent
ten
Error rate below fourteen per cent
twenty
Error rate below five per cent
59
Error rate below one per cent
299
Run the other way it becomes uncomfortable. Testing twenty items and finding nothing — which is what a great many programmes actually do — establishes only that the error rate is probably below fourteen per cent. Ten items rules out nothing below twenty-six per cent. A small clean sample feels like assurance and is very nearly none.
What the defensible number costs
The cost is smaller than the argument about it. At half an hour an item, 59 allocations is just under thirty hours, or about four working days a year, for the highest-scrutiny area in the entire programme. The gap between the informal twenty and the defensible 59 is roughly two and a half days of one person's year.
Two honest limits attach to the method. It is attribute sampling: it tests whether items are right or wrong, not how wrong, so a programme should also test by value, because one large mis-allocation matters more than several small ones. And it assumes a genuinely random sample. Testing the items that are easiest to pull, or the ones the finance team suggests, tells the tester about those items and nothing whatever about the population.
Why expenses are where those days belong
Fees and expenses are the most heavily scrutinised area in private markets compliance, and the reason is arithmetic rather than fashion. Take an illustrative fund of 500 million charging a two per cent fee, with four million a year of fund-borne expenses of which 1.2 million is genuinely ambiguous. Every dollar shifted to the fund is a dollar the firm keeps.
An illustrative fund of 500 million, and the grey zone inside its expenses.
Item
Amount
Fund-borne expenses, a year
four million
Of which genuinely ambiguous
1.2 million
A quarter resolved in the firm's favour, a year
300,000
Over the fund's life
three million
Now express that three million the way an investor would recognise it. It is the equivalent of charging a management fee of 2.06 per cent rather than 2.00 — an increase of six basis points that no investor agreed to and no document discloses.
That translation changes what the conversation is about. A list of forty small judgement calls, each defensible on its own, is almost impossible to raise in a partners' meeting without sounding pedantic. Six undisclosed basis points on the fee is a sentence that ends the discussion. Same facts, and only one of the two framings will be acted on. It is also why the written expense allocation policy is worth the trouble of drafting: it is the control on a sum of money of the same order as a fee negotiation, and a firm without one has left part of its fee schedule open.
What to do with this
Three habits follow, and each converts a sentence of policy into something actionable.
State the testing as a claim rather than a frequency. Not “expenses are tested periodically” but “fifty-nine allocations were tested, selected at random, and on that basis the error rate is below five per cent at ninety-five per cent confidence”. The first sentence invites the next question. The second answers it.
Express the grey zone as basis points on the fee, once a year. It takes an afternoon, it produces a number the partnership will engage with, and it is the most reliable way to get an expense allocation policy written and kept current.
Resource the sample before the plan is set. Four working days a year is a number a resourcing committee can approve or refuse; “periodically” is a number it can neither approve nor refuse, which is why it is usually neither.
The claim, not the calendar, is what an examiner is asking for. A programme that can name its sample size, its confidence and its error rate has answered the question. A programme that can only name a frequency has not yet been asked the hard one.
The workbooks behind this article
Every figure above is a live formula in the free companion files for
The Private Fund Compliance Officer. Each workbook ends with a Checks sheet
setting the printed figure beside the computed one. No account and no email address.
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