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Commerce · V.03 · MMXXVI · daylight

La Bourse  /  Volume V  /  Nº V.03  /  Ten concept briefs

TEN CONCEPT BRIEFS · Chapter V.03 — Ownership and the Worker

One page each. A reader who reads only these ten pages has the chapter.

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BRIEF 1 — The Risk Nobody Pays For

The idea. A share in your employer carries two different risks, and the market pays you for only one of them.

The first is the risk you share with everybody — recessions, interest rates, the weather over the whole economy. That is the covariance risk, and holding it is what an investor gets paid for. The second is everything specific to your firm: its customers, its patent, its plant, its chief executive's judgement. That is idiosyncratic risk, and the market's answer to it is blunt. It pays nothing, because anybody can remove it by holding a hundred companies instead of one.

The arithmetic. With a beta of 1, the split is a subtraction:

  total variance of a single stock  σ_c²         0.1600   (σ_c = 40%/yr)
  covariance term   β · σ_m²                     0.0289   (σ_m = 17%/yr)
  ------------------------------------------------------
  idiosyncratic variance  σ_ε²                   0.1311
  idiosyncratic volatility  σ_ε                   36.2%/yr

Worked example. An employee holds $130,000 of her employer's shares. She is carrying 36.2 percentage points of volatility a year for which no part of her expected return is compensation. A stranger holding the same dollar amount in an index fund has the same expected return and about 17 points of volatility. Same money, same expectation, less than half the risk.

Why it matters. This single subtraction is the whole of the concentration argument. Everything else in the chapter — the swap value, the hurdle rate, the ceiling — is arithmetic performed on σ_ε². If the market paid for idiosyncratic risk, employee ownership would carry no financial objection at all.

You already know this because you would not put your whole pension into one share of one company chosen at random, and you have never been able to say exactly why not in a sentence with a number in it. Now you can.

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BRIEF 2 — The Swap Value

The idea. Ask not what the stake is worth on the statement, but how many diversified dollars would make the holder equally well off. That second number is the one that governs her life.

The arithmetic. Under lognormal returns and constant relative risk aversion, the ratio of certainty equivalents has one term:

  R = exp( −γ · w² · σ_ε² · T / 2 )

  value of $1 of employer stock  =  1 − (1 − R) / w

where w is the stake as a share of financial wealth, γ is risk aversion, T is years held.

Worked example. At γ = 2, σ_ε² = 0.1311, over ten years:

A median participant at 63.4 percent concentration holds a $130,330 stake worth about $46,160 in diversified terms.

Checked by a second route. Lisa Meulbroek priced the same question by the capital asset pricing model — an entirely different machine — and found employees give up on average 42 percent of market value over five years. This model at five years gives up 37 percent. Two methods, no shared assumptions, a few points apart.

The caution written into it. Push γ to 3 and the horizon to 15 years and the formula returns a negative value, which is the algebra of a logarithmic certainty equivalent being extrapolated past where it approximates well. Treat anything under about 15 cents as the model shouting rather than measuring.

You already know this because you have watched somebody turn down a job with a large equity component for one with a smaller salary paid in cash, and thought them cautious. They were doing this calculation in their head.

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BRIEF 3 — The Square Rule

The idea. The benefit of an ownership stake grows in proportion to its size. The cost grows in proportion to its size squared. That asymmetry is the most useful fact in the subject.

The arithmetic. Because σ_p² − σ_m² = w² · σ_ε² exactly when beta is 1:

  benefit of the stake   ∝  w        (any return premium, times the holding)
  cost of the stake      ∝  w²       (the risk charge)

Worked example. Take a worker at 20 percent concentration and double her to

1. Her exposure to any performance premium doubles. Her risk charge — the

certainty-equivalent return she gives up each year, γ · w² · σ_ε² / 2 — goes up four times: from 0.52 to 2.10 points a year at γ = 2. Double again to 80 percent and it is 8.39 points, sixteen times the original.

What follows immediately. There is an interior optimum. Not zero — the benefit is real and linear near the origin, so a small stake is unambiguously good. Not everything — the cost overtakes. Somewhere in between there is a best answer, and finding it is Brief 5.

Why it matters. Almost every argument about employee ownership is conducted as though the choice were between some and none. The square rule says the interesting question was always how much, and that a movement which cannot answer it is arguing about the wrong variable.

You already know this because you know that one glass of wine and eight glasses of wine are not the same substance at different volumes, and you have never needed a model to tell you that the harm rose faster than the quantity.

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BRIEF 4 — The Hurdle Rate of Your Own Employer's Stock

The idea. Holding your employer's shares instead of an index is an investment decision, and every investment decision has a hurdle rate. Almost nobody has ever computed this one.

The arithmetic. Setting the linear benefit equal to the quadratic cost:

  λ*(w)  =  γ · w · σ_ε² / 2

That is the annual excess return the employer's shares must earn over a diversified index for the stake to be worth holding at all.

Worked example. At γ = 2 and σ_ε² = 0.1311:

The uncomfortable comparison. The best meta-analytic estimate of employee ownership's effect on firm performance is a correlation of 0.04. The best productivity estimate is a one-time step of 4 to 7 percent. Neither of those converts into eight points of sustained annual excess return over an index. At 63 percent concentration, the arithmetic does not clear.

What this does not say. It does not say the shares are a bad investment. It says a concentrated holding of them is being asked to do something no reasonable expectation of performance can deliver — which is a fact about concentration, not about the company.

You already know this because you would ask what return you were being paid for taking a risk in any other context, and it has simply never occurred to anyone to ask it about the envelope from work.

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BRIEF 5 — The Stake Ceiling

The idea. Invert the hurdle rate and you get the largest defensible stake — a number a board can put in a plan document.

The arithmetic.

  w*  =  2λ / (γ · σ_ε²)

where λ is the excess return you genuinely believe employee ownership produces.

Worked example. At γ = 2 and σ_ε² = 0.1311:

How to use it. The ceiling is stated as a share of the participant's total retirement savings, never as a share of the company — those are different questions and only the first one is about the person. Enforce it by redirecting future contributions, never by forced sale, because a forced sale is a tax event the participant did not choose.

The honest part. Every row of that table depends on a number you cannot observe: how much better your company really does because its people own it. The ceiling's value is not that it settles the argument. It is that it makes the argument explicit — a board that wants a 30 percent concentration must now say out loud that it believes in a four-point annual premium, in minutes that somebody will read in five years.

You already know this because every covenant you have ever signed had a ratio in it, and the ratio was there so that nobody had to relitigate the judgement every quarter.

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BRIEF 6 — The Funding-Source Test

The idea. Two stakes of identical size can be worth wildly different amounts to the same person, and the difference is what they gave up to get it.

The three cases.

• Bought with a diversified dollar — company stock inside a 401(k), an employer match paid in shares, a purchase plan funded from take-home pay. The comparison is one-for-one against an index fund, and the stake is worth 35 to 58 cents on that dollar. This is Enron's structure.
• Bought with a wage — pay concessions in exchange for equity. Worse still, because a wage has no volatility at all. This is United Airlines' structure.
• Given — the employer contributes, the trust borrows against future profit, the founder transfers shares. The alternative was not an index fund; it was an empty account. Thirty-five cents is not zero. This is Publix, Riverford, Aardman, Richer Sounds, and every properly built ESOP or EOT.

Worked example. Our median participant's $130,330 stake is worth about $46,160 of diversified equivalent. If it was given, that is $46,160 she would not otherwise have. If she bought it with $130,330 of index fund, she is $84,170 worse off. Same stake. Opposite sign.

Why it matters. The concentration critique is real and it is devastating — against purchased ownership. Against employer-funded ownership it reduces to a statement about size, which Brief 5 answers. The critique is about the funding source, not about ownership.

You already know this because you would think differently about a lottery ticket you were handed than about one you bought with the rent money, even though the ticket is identical.

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BRIEF 7 — The Diversification Election

The idea. American law already gives ESOP participants a right that is worth tens of thousands of dollars each, and it is the most valuable unexercised right in the field.

The rule. IRC §401(a)(28)(B). A qualified participant — age 55 with ten years of participation — may elect, across a six-year window, to diversify up to 25 percent of the post-1986 account in years one to five, and up to 50 percent cumulative in year six. The plan satisfies it by offering at least three investment alternatives, by distributing the proceeds, or by transferring them to another defined-contribution plan.

Worked example. Our participant, at 63.4 percent concentration for ten years, holds a stake worth 35.4 cents on the dollar.

  no election:        35.4 cents per dollar
  election in full:   67.5 cents per dollar
  ------------------------------------------
  the election is worth 32.1 cents = $41,867

What it costs. Nothing. At a beta of 1 it surrenders no expected return, because the expected return was never the compensation for the risk being removed. It is a free transfer from risk into certainty.

The gap we could not close. Take-up among eligible participants is not published anywhere we could find. That is reported here as a gap rather than filled with a guess — and it is also the most useful research question in the subject.

You already know this because you have an insurance policy with a clause in it that you have never read, and you already suspect that the clause is worth money.

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BRIEF 8 — The Repurchase Obligation

The idea. In a private employee-owned company, every share issued is a share that must one day be bought back. That obligation is certain, large, growing, and usually invisible on the balance sheet.

The rule. IRC §409(h) requires closely held ESOP shares to carry a put option — the participant can require the company to buy them. Without it, a retiring employee's shares would be worth nothing to her, since there is no market.

Worked example, two ways. The NCEO's 2023 survey of 248 ESOP companies found a median of 5 percent of shares repurchased in the most recent year and annual contributions averaging 11.7 percent of payroll. Compute it independently: a company on a 10 percent EBITDA margin at a 5× enterprise multiple, payroll at 30 percent of revenue, has equity worth half a year's revenue. Repurchasing 5 percent of shares costs 2.5 percent of revenue — which is 8.3 percent of payroll.

  observed:  11.7% of payroll        computed:  8.3% of payroll

Two routes, one order of magnitude. Roughly a tenth of payroll, every year, forever.

The trap. It grows with the share price. A plan that succeeds in raising its own valuation has raised its own liability in the same motion — and a demographic wave of retirements does not arrive smoothly.

What to do. A segregated reserve, contributed to annually, sized by an actuarial projection over fifteen years rather than by last year's outflow, and disclosed. An unfunded repurchase obligation is a defined-benefit promise wearing a defined-contribution costume.

You already know this because you have seen a business that was profitable on paper run out of cash, and you know the difference between an expense and a payment.

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BRIEF 9 — Ownership Is Not the Active Ingredient

The idea. The measured effect of employee ownership on performance is small. The measured effect of employee participation in decisions is two to three and a half times larger. The two together are what works.

The evidence. Doucouliagos's 1995 meta-analysis of 43 studies, with both columns printed because secondary citations print one:

Read the third row. A board seat without a share of the result measured negative on both means. A stake without a voice measures small. Neither alone is the mechanism.

The corroboration, from a hostile source. The US General Accounting Office's 1987 study is quoted everywhere as the great null result: no consistent significant improvement in profitability or productivity. But of every factor it examined, only employee participation in decisions showed a statistically significant relationship with productivity — and the average ESOP stake in its sample was 8.5 percent, one twelfth of the company. An 8.5 percent stake is not employee ownership; it is a benefit.

What to build. Decision rights where the work is: standing work groups with real authority over method, scheduling and quality — which is exactly the form the GAO found to matter — alongside the shares.

You already know this because you have been given a bonus tied to a number you could not influence, and you know precisely how much it changed your behaviour.

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BRIEF 10 — Ask Which Measure

The idea. Before you believe any figure about employee ownership, ask what its denominator was. In this field the disagreements between honest measures are larger than the effects being measured.

Worked example, one. From the same 2023 Form 5500 filings:

  NCEO      6,609 plans   15.1m participants   over $2.0tn plan assets
  Rutgers   6,339 ESOPs   11.0m employees      $475bn company stock

Neither is wrong. One counts everyone with a balance, including people who have left, and every asset in the plan; the other counts active employees and employer stock only. The headcounts differ by 27 percent and the asset figures by 4.2× — larger than any effect in the chapter.

Worked example, two. Italian worker buyouts show a three-year survival of 87.16 percent against 48.30 percent for Italian enterprises — a ratio of 1.80×. But the comparison includes firms in their first year, and a buyout is a going concern on the first morning. Correct for first-year mortality of 10, 15 or 20 percent and the ratio falls to 1.62×, 1.53×, 1.44× — and does not disappear.

Worked example, three. In Britain, the stock of employee-owned businesses grew to 2,824 by March 2026, compounding at 28.8 percent a year since

1. In the same period the flow of new transitions fell, from 560 in

2024 to 500 in 2025. Stock up, flow down, both true.

The rule. State your denominator, state what your figure did not look at, and say which measure you used. A number quoted without those things has told you nothing, however many decimal places it carries.

You already know this because you have read two reports about the same business with different revenue figures in them, and the first thing you did was check what each was counting.

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All figures in these briefs are computed in lib/verify/V_03.py and sourced in the chapter's Works Cited. Run python3 lib/verify.py V.03 to reproduce them.