Discount for Lack of Marketability (DLOM): Calculation, Formula

A discount for lack of marketability reduces an equity interest's value to reflect the simple fact that it cannot be sold quickly, cheaply, or at a known price the way a public share can. Every business valuation that touches gift and estate tax, ESOP compliance, 409A option pricing, litigation, or a minority-interest transaction eventually has to answer one question. How large should that discount be, and what supports the number?

This article works through the actual calculation. It covers the formula behind the Chaffe protective put model with real numbers, how the Finnerty and Longstaff models differ and why, and what the Stout DLOM Calculator does under the hood.

What Is a Discount for Lack of Marketability

Lack of marketability is distinct from lack of control. A 100% owner of a private company has full control but still lacks marketability, because there is no active market to sell the interest into on short notice. DLOM applies to both controlling and minority interests; the related discount for lack of control (DLOC) applies only to minority interests and is calculated separately.

DLOM is applied after a base value has already been established — typically from a discounted cash flow model, a market multiple, or a net asset calculation. That base figure represents a marketable value; DLOM brings it down to what the actual, illiquid interest is worth.

Restricted Stock Studies: The Empirical Benchmark

The earliest and still most commonly cited approach compares prices at which restricted shares of otherwise-public companies traded relative to their freely tradable counterparts. Across the major restricted stock studies conducted since the 1970s, average discounts have generally clustered in the 20% to 35% range. Individual transactions vary well outside that band, based on company size, volatility, and the length of the trading restriction.

Restricted stock studies are empirical, not formula-driven — the discount comes from observed transactions rather than a computed option value. A full walkthrough of how this method is applied and documented for DLOM in a 409A valuation, including the auditor-defense standard, is covered in a companion piece on this site.

Option-Pricing Models: Where the Actual Formula Lives

Restricted stock studies answer "what discount did the market apply, on average, in the past." Option-pricing models answer a different and more precise question: given this specific company's volatility and this specific holding period, what does the cost of illiquidity actually work out to, mathematically.

All three models below treat the inability to sell as equivalent to holding an unhedged position for a fixed period — and price that risk the same way an option is priced.

The Chaffe Protective Put Model

David Chaffe's 1993 approach is the most direct. An investor holding restricted stock is economically in the same position as an investor holding freely tradable stock plus a put option struck at today's price. That put would let them "sell" at today's value at the end of the restriction period even if the price fell. The value of that hypothetical put, expressed as a percentage of the stock price, is the DLOM.

Because the put is struck at the current price (at-the-money) and there is no dividend adjustment in the base case, the Black-Scholes put formula collapses to:

DLOM = e^(−rT) × N(−d2) − N(−d1)

where d1 = (r/σ + σ/2)√T and d2 = d1 − σ√T, using the company's estimated volatility (σ), the holding period in years (T), and the risk-free rate (r).

Worked example

How the result moves with the inputs

The pattern is consistent with the logic of the model: higher volatility and longer restriction periods both increase the value of the hypothetical put, and therefore the discount. A short restriction on a low-volatility company can produce a DLOM close to 10%; a long restriction on a highly volatile company can push past 30%.

What the discount is worth in dollars

A percentage only becomes useful once it is applied to an actual interest. Using the base-case 20.3% result on a $10.0M marketable equity value:

For gift and estate tax purposes specifically, that $2.03M gap is the entire point of the exercise — it is the amount removed from the taxable transfer, and it is exactly why the formula behind it needs to hold up to review.

The Finnerty Average-Strike Put Model

John Finnerty's 2012 model changes one assumption. Instead of striking the hypothetical put at today's price, it strikes the put at the average price of the stock over the entire holding period. That average-price structure is calculated the way an Asian option is priced, rather than a standard European option.

That single change matters. Averaging a price path reduces its effective volatility compared to looking at a single terminal price — the same reason an Asian option is worth less than a European option on identical terms. As a direct consequence, the Finnerty model generally produces a lower DLOM than Chaffe's model for the same volatility and holding period, often meaningfully so.

There is no single named commercial tool for this calculation. Searches for a "Finnerty DLOM calculator" typically lead to explanations of the formula rather than a standalone product, and most appraisers implement it directly in Excel or through general-purpose appraisal software.

The Longstaff Upper-Bound Model

Francis Longstaff's 1995 model takes the opposite approach. It assumes the holder of the restricted stock has perfect foresight of the stock's price path, and is prevented from acting on it. That is economically equivalent to pricing a lookback option rather than a standard put. This is explicitly designed as an upper bound, not a point estimate, and its results are typically well above both Chaffe's and Finnerty's for identical inputs.

Longstaff's model is cited more often to bracket the top of a reasonable DLOM range than used as the sole basis for a concluded discount.

How the three compare

The Stout DLOM Calculator

The Stout DLOM Calculator, licensed through Business Valuation Resources, is a regression-based tool built on the Stout Restricted Stock Study — a database tracking thousands of historical restricted stock transactions. Rather than deriving a discount from an option-pricing formula, it estimates one from empirical patterns across that transaction history.

The specific regression coefficients behind the tool's output are proprietary to Stout and not published, so this article describes the mechanism and inputs rather than reproducing figures that are not publicly available. Many appraisers run the Stout tool alongside an option-pricing model and a restricted stock study benchmark, then reconcile all three.

Selecting and Reconciling a DLOM

No single method is treated as automatically correct. Standard practice, consistent with USPAP and the discount ranges applied across a valuation more broadly, is to compute a DLOM through at least two independent methods. The results are then reconciled into one supported conclusion, with any material gap between them explained.

• Empirical anchor. Start with a restricted stock study range appropriate to the company's size and industry.

• Analytical cross-check. Run the Chaffe model (and Finnerty, where a lower-bound view is useful) using the company's actual estimated volatility and expected holding period.

• Reconcile, don't average blindly. If the option-pricing result and the empirical benchmark diverge by more than a few points, the write-up should explain why — a private company with unusually high volatility relative to its restricted-stock-study peer group, for example, should show a higher analytical result, and that divergence is a feature of the analysis, not an error.

The same reconciliation discipline applies across a full valuation, where the Income, Market and Asset approaches reconcile into a single concluded value. The underlying logic is identical: multiple independent methods, an explained weighting, and a documented final number.

Common Modeling Mistakes

• Using public-company volatility without adjustment. A private company's true volatility is rarely identical to its closest public comparable; some practitioners scale a 30%–35% public-comparable volatility up by 5 to 10 points to reflect the additional risk of a thinner, less diversified operation.

• Ignoring dividend yield. A 2% to 3% dividend yield during the restriction period partially compensates the holder, which should reduce the modeled discount — omitting it overstates DLOM.

• Applying a restricted stock average without adjustment. A 25% average from a broad study is a starting point, not an answer — company-specific volatility and holding period should move the figure up or down from that anchor.

• Treating Longstaff's result as a point estimate. Its explicit design as an upper bound makes it a poor standalone conclusion; using it without that context overstates the discount.

• Using a stale risk-free rate. The r input should match the current Treasury yield for a maturity close to the holding period, not a rate carried over from a prior engagement.

Get Defensible DLOM Support Built Into Your Valuation

A DLOM that cites a single average from a restricted stock study rarely survives close scrutiny on its own. AcumenSphere builds DLOM conclusions using multiple independent methods — empirical benchmarks and option-pricing models together — reconciled and documented to hold up through IRS review, audit, or litigation.

If you need defensible DLOM support for a 409A valuation, an estate or gift filing, or a transaction, contact our team to discuss your specific facts.