Starting with a single number
How large a discount. How much premium. Readers are long used to seeing these numbers in a circular, and long used to taking them as fact. A percentage printed in a report, with decimal places and a source, looks unassailable.
But a number is only the answer to a question. Ask the wrong question and the answer, however precise, answers the wrong thing.
In last quarter's study, my team and I ran into a question that had been overlooked in the least conspicuous of places. This percentage, which question is it actually answering?
A new model, and the whole thing run again
It began with a change. Large language models move quickly. ChatGPT 6.0 Sol was superseded by version 6.1 within a week of release. The previous quarter's circulars had originally been read by two local LLMs. I replaced both with another, which raised a question we could actually test. Same circulars, same procedure, only the model changed. Would the answers come out the same?
The first test was blind. Ninety-seven circulars from last quarter went to eight AI agents as readers, twelve or thirteen each, an extraction guide in hand and no sight of the existing answers. The result: all ninety-seven classifications correct, and all twenty adopted figures correct. Nothing read twice, nothing missed. The answers could be found from zero.
The second test was stricter. The entire procedure was run again from the beginning, and the objective output came back identical. The same ninety-seven circulars fell into the same categories. Twenty-two documents carried a business valuation report. Twenty adopted figures, fourteen discounts and six premiums, matched to the last one.
The procedure looked right, and the numbers looked right. I say often that no one should take an AI conclusion on trust.
The disagreement was not in the numbers but in the reading
Yet on the rerun, thirty judgement flags came out differently.
A flag is a judgement the procedure makes about a document, for instance whether a discount should be expected on this transaction, or whether this valuation carries a premium. Same documents, same figures, two models reading the meaning differently.
Thirty cells is not many. I did not sweep them away as noise, because they carried three features. They all fell on the same set of documents. They ran almost all in one direction. And they appeared exactly where the procedure has to judge rather than transcribe. Numbers can be transcribed. Judgements cannot. A disagreement in the judging is worth chasing.
Chasing it produced a small sideshow. The scoring programme returned full marks on its first run. Full marks is itself suspicious. Looking into it, the programme was matching results on stock codes. Nine codes recurred last quarter, and two of those codes each filed two circulars on the same day. A stock code is not enough to identify a document. The document itself has to be used.
That episode is everything that follows in miniature. An identifier that looks usable, quietly standing in for something else.
Finding one: the equity field asked the wrong question
Following the thread, I checked the equity field of each of the twenty-two business valuation reports back against the original text. Four had been recorded wrongly.
Those four recorded the equity of the transaction, not the equity of the valuation. How much is acquired, or sold, is not the same as what the valuer valued. In all four, the valuer had valued 100%, while the field carried the transaction's percentage. One recorded 35.64%, one 49%, one 30%, one 60%.
The trap sits in the circular's headline. The headline speaks of the transaction, of the acquisition of a 49% stake, the disposal of a 30% stake, and that is the number a reader meets first. The valuation report, deep in the appendix, says quietly that it values the entire equity of the whole company.
Why does it matter? Because the procedure's expectation of a discount is derived from the equity field. Record less than half and the procedure infers a minority stake, so a discount should be expected. Four errors, four times the same conclusion. Put the equity back to 100% and the answer turns, by itself, into none should be expected.
Had this not been found, those four expectations of a discount would have sat in the data. Someone would later have built on them and arrived at a discount that does not exist in the market. That is how one mis-filled field quietly gives birth to a conclusion.
Finding two: not one DLOC all quarter
The second finding follows straight on from the first.
Of last quarter's twenty adopted figures, fourteen were discounts and six were premiums. Not one was a discount for lack of control (DLOC). And those four cases were precisely the transactions below half. On a first reading, a minority stake ought to carry a DLOC, and not one could be found. It looked like a contradiction.
The sentence that dissolves it is simple. The control adjustment follows the subject of the valuation, not the transaction.
Where the subject is 100%, the entire equity, a valuer does one of two things. Add a control premium, or make no control adjustment at all. A DLOC moves a controlling value down to a minority value, the opposite direction, so applied here it is turned on its head. A DLOC is only sensible where the subject of the valuation is itself a minority stake.
One case in the second quarter of 2026 sets this out most clearly. The report set out the formula, DLOC = 1 − 1 / (1 + control premium), and then adopted the premium rather than the discount. The reason was precisely that its subject was the entire equity, a controlling level. It knew the formula, and it chose the right direction.
Finding three: the same 100% means three different things
The third finding is the most interesting, and the easiest to overlook.
The same words, 100% of the equity, sat at three different levels across those four reports. The trade calls this the level of value. It asks whether the valuation stands at a controlling level, a non-controlling level, or neutral.
The first, on the market approach, took the entire equity as its subject, and the valuer added a control premium of 18.1%.
The second, also on the market approach, declared at the outset that it valued from a non-controlling shareholder's perspective. The level was non-controlling to begin with, so nothing was added and nothing deducted.
The third and the fourth went by the asset-based approach, the reports stating plainly that no premium or discount for control, or for its absence, was considered. Neutral.
The key lies in that last sentence. Two valuers using the market approach saw the same thing, that the traded price of a listed company's shares represents a minority interest. Then they went in opposite directions. One pulled it up to a controlling level, one left it non-controlling. And the asset-based approach is neutral by nature, so the control question usually does not arise.
So a comparison of 100% pro rata is not a like-for-like comparison. Ask the level first, then the method, and only then compare.
This matters most to anyone analysing M&A. Two transactions both say 100%, one explicitly adding a control premium and one quietly not. Compare the prices pro rata and you have treated two different rulers as one.
Finding four: I got one wrong myself
This section is about a mistake of my own.
Reading the 30% acquisition case at first, my judgement was that the buyer had paid a controlling-level price for an interest carrying no control, swallowing a discount it could never reach. It sounded forceful.
After reading the report through, the judgement was wrong. The report says at the outset that its basis of value is non-controlling and non-marketable. In other words, that 100% was already a non-controlling value, and never a controlling one. The buyer paid 30% of it, so what was paid and what was valued stood at the same level. No premium was paid. The report goes further, and notes that the implied price-to-earnings multiple on the transaction was below the average and the median of its peers. The pricing was conservative.
I write the error down, and not to mock myself. This question is too easy to get wrong. That I, who value for a living, got it wrong at the first attempt is exactly why it belongs on the gatekeeper's checklist. A label reading 100% is not enough to compare two transactions. For every one from here, I will ask first, at which level is this valuation speaking?
What this means for the gatekeeper: three questions
Put the three findings together and each gatekeeper who signs a circular gains three questions.
One. Which interest does this valuation value? The subject of the valuation, not the equity of the transaction. Those two numbers are often not the same.
Two. At which level does this price stand? Controlling, non-controlling, or neutral? Different levels mean two percentages cannot be compared directly.
Three. By which method was it derived, and which method was adopted? Where a report runs both the market approach and the asset-based approach, which one it finally adopted, and why the other was not adopted, should both be written down.
The third, put plainly, asks only that a judgement be written out, and here there was a fine demonstration. In one case the market approach produced a price-to-book of 1.44 and a discount of 20.9%, and the report adopted the asset-based approach instead, stating its reason, that the public information on comparable listed companies was relatively insufficient. It did not adopt it, and it could say why not. That single disclosure is where comparison begins.
These three questions need no new legislation. They ask only that the judgements a valuer has in fact already made be written out. On best practice in valuation, though, I cannot help asking. Where a valuation of 100% of the equity computes no controlling premium, and says so clearly in the report, might there be some intent to mislead, or to take a shortcut? I do not wish to speculate or to judge. It is worth thinking through carefully.
A reader outside the valuation profession need not memorise the three. They compress into one. Does this number match the thing it claims to value? That is the sentence a minority shareholder reads a circular with. It is the sentence a board should ask before approving a transaction.
The machine reads everything. The person asks the right question.
Which brings us to a more fundamental question. Where does artificial intelligence stand in all this?
What we found was not the machine missing numbers. Its numbers were all correct, as the blind test and the rerun proved. What we found was something else. A machine reading everything does not mean the question was asked correctly. Asking the question correctly remains the work of a person.
A machine can lay out every number in 4,000 circulars, but it will not of itself question whether a question was the right one. That layer still needs a person. The machine is responsible for reading completely, every one of more than 4,000 circulars read through, every number traced back to its source, the arithmetic re-checked on the value bridge, each quarter's newly published circulars taken on automatically. The person is responsible for judging accurately, whether the question was the right one, whether a level stands, whether a premise is reasonable.
I got one wrong this time, and then corrected it. That is exactly why judgement has to be done in the sunlight. Laid open, it can be verified.
The limitation, as always, stated once more. This data was compiled by artificial intelligence and sample-checked by me and my team, so one hundred per cent accuracy cannot be promised. But every number is traceable and can be re-checked, and the method and the limits are laid out in full.
The instrument keeps running
Last quarter's gains have been written into the instrument's checks. The equity field will from now on record the interest the valuer valued. A DLOC expectation will arise only where the subject of the valuation is itself a minority stake. Two questions remain open. One, extending the comparison of traded price against valuation pro rata across the whole ten-year database, to see how often minority stakes change hands without a discount. Two, making level a formal field, so that every valuation states the level at which it stands.
Gatekeeping, in the end, is one sentence. Every number capable of moving value must first have had the right question asked of it.
Gatekeeping is not about finding the valuer's error. It is about moving the judgements they have in fact already made out of the depths of the report and into the reader's sight.
Numbers get printed in the report. Questions do not. So someone has to ask them.
Next time
Next time I return to the valuation of intellectual property. The Hong Kong Monetary Authority announced on 30 September that the financing sandbox has seven successful cases, two of which I handled. I will share them next time.