Not at ordinary inputs. The protective-put method, the standard evidence-based construction, indicates 22.0 per cent at 45 per cent volatility, two and a half years to liquidity and a 4 per cent risk-free rate. Inverted, it never reaches 30 at that volatility: the put value peaks at 28.6 per cent, at 9.6 years, then declines as discounting the strike overtakes the growth in the option. Reaching 30 requires asserting volatility near 60 per cent in writing.
What the protective-put method indicates
A discount for lack of marketability is legitimate in principle and abused in practice. The standard evidence-based way to size it values the cost of a protective put over the expected holding period — the price of the right to sell at today's value during a period in which the position cannot be sold at all. That construction turns an assertion about illiquidity into an arithmetic with named inputs: volatility, time to liquidity, and a risk-free rate. Each of them can be challenged by a reviewer. A convention cannot.
At 45 per cent volatility, two and a half years to liquidity and a 4 per cent risk-free rate, the construction indicates 22.0 per cent. That is the base case. Moving the inputs across a plausible range does not move the answer very far.
Indicated marketability discount across the plausible input range.
Case
Volatility
Indicated discount
Eighteen months to liquidity
30 per cent
11.4 per cent
Base case, two and a half years
45 per cent
22.0 per cent
Four years to liquidity
60 per cent
34.7 per cent
A real adjustment, and a modest one. Nothing in that range supports the figure most files reach for.
Inverting the method: what would justify the convention
Convention says 30. The useful question is not whether 30 is defensible in the abstract, but which inputs would produce it. Hold the period fixed at two and a half years and volatility has to be 60 per cent. That is a specific assertion about the subject company, and it is the kind of assertion that has to be written down and defended rather than assumed.
Hold volatility at the base case instead, and solve for time, and the result is stranger. There is no holding period whatever that reaches 30 per cent. The put value rises with time, peaks at 28.6 per cent, and declines after that, because discounting the strike eventually overtakes the growth in the option.
Inverting the construction at base-case inputs.
Quantity
Value
Indicated discount, base case
22.0 per cent
Discount the convention asserts
30 per cent
Volatility required to reach it over the base period
60 per cent
Highest value reachable at base-case volatility, any period
28.6 per cent
Holding period at which that peak occurs
9.6 years
A conventional 30 per cent marketability discount is not merely unevidenced at these inputs. It is unreachable by the method that is supposed to evidence it, at any holding period, unless volatility near 60 per cent is asserted in writing. Very few people applying the convention would assert that, which means the convention is doing something other than what its users believe it is doing.
One caution, because a finding of this shape invites over-claiming. The protective-put construction is one method among several, and on some readings it is a lower bound on illiquidity cost: it prices the loss of the ability to sell at today's price, not the loss of optionality over the whole period. The finding is not that 30 per cent is always wrong. It is that this method cannot produce 30 per cent at these inputs, so anyone using 30 per cent is relying on something else and owes the reader a sentence saying what.
The discount that is already in the entry price
The second way a marketability discount goes wrong is quieter. An asset bought below its listed peers already carries a discount, and adding a conventional one on top charges for the same illiquidity twice.
Take an entry multiple of 7.3 times against a listed peer median of 8.9 times on the same date. The entry price already embeds a discount of 18.0 per cent. Add a conventional 20 per cent and the two do not add to 38 — they compound to an effective 34.4 per cent. Supportable is 18.0. The double-count is 16.4 points, very nearly as much again as the discount that was justified.
On an enterprise value of 120 that is 19.7 of equity value removed twice. It is worth stating in money in the memorandum, because 16.4 points reads as a refinement and 19.7 of value does not.
What to write in the memorandum
Compute the discount rather than adopt it. Name the volatility, the time to liquidity and the risk-free rate, and let the reviewer challenge each one.
Where the computation cannot reach the conventional figure, say so in one sentence rather than using the convention quietly. An auditor who finds that sentence will treat the rest of the file differently from one who has to find the gap alone.
Before applying any discount, ask what the entry price already embeds. Where the asset was bought below peers, the honest supportable figure may be the discount that is already there and nothing further.
State the effect in money as well as in points, on the position and at the fund level.
The discipline here is not that marketability discounts are wrong. Sized with evidence they are real and modest, running from 11.4 to 34.7 per cent across the whole range above, and a specialist who sizes one properly will usually find it does less work than expected. It is the plug the discount becomes when it is not computed that does the damage — and the plug is the version that turns up in the files an auditor decides to test.
The workbooks behind this article
Every figure above is a live formula in the free companion files for
The Private Markets Valuation Specialist. 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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