Volatility drag, not expected return, decides whether a founder's family should pay tax to diversify, and it can be computed to the year.
On the typical outcome, yes, and faster than most families expect. A family with $500m, of which $400m sits in one company at a nil tax basis, pays $71.4m of tax to sell $300m of it, and the diversified portfolio repays that tax in about 5.3 years of median growth. On expected values it never repays it at all, and that difference is the whole argument.
Worked in full in The Family Office Professional by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The question arrives in every family office that grew out of a business: the founder's shares are most of the wealth, the gain is almost all of the value, and selling triggers a tax bill that feels like a certain loss traded for an uncertain benefit. The benefit is not uncertain, it is just measured in the wrong unit. It shows up in the median, not the mean, and it can be computed.
| Input | Value |
|---|---|
| Total family wealth | $500m |
| Held in the single company, nil basis | $400m |
| Shares sold | $300m |
| Tax rate on the gain | 23.8% |
| Expected return, single stock and diversified portfolio | 8.0% |
| Volatility, single stock | 35% |
| Volatility, diversified portfolio | 15% |
| Correlation between the two | 0.5 |
Giving the single stock the same 8.0 per cent expected return as the diversified portfolio is deliberate. Company-specific risk is not usually rewarded, so assuming it is would tilt the answer towards selling. Here selling has to win on risk alone.
Selling $300m at a nil basis taxes the whole proceeds: $300m × 23.8% = $71.4m, or 14.28 per cent of the family's wealth. The family is left with $428.6m: $100m in the company and $328.6m diversified. Before the sale the company is 80.0 per cent of wealth; after it, 23.3 per cent.
The volatility of each portfolio follows from the two-asset formula with the 0.5 correlation. Keeping everything gives 29.6 per cent. After the sale it falls to 17.1 per cent.
An investor compounding at an expected return μ with volatility σ does not grow the typical outcome at μ. The median grows at μ less half the variance:
Median growth = μ − σ² ÷ 2
Keep: 8.0% − 29.6%² ÷ 2 = 8.0% − 4.38% = 3.62%
Sell: 8.0% − 17.1%² ÷ 2 = 8.0% − 1.46% = 6.54%
In Excel: =mu-vol^2/2, with vol from =SQRT(w^2*s1^2+(1-w)^2*s2^2+2*w*(1-w)*rho*s1*s2)
The gap is 2.92 percentage points a year. The concentrated family gives up more than half of its expected return to drag, before anything goes wrong with the company.
The diversified family starts $71.4m behind and grows 2.92 points a year faster. The two median paths meet when the faster growth has made up the log of the shortfall:
Payback = ln(wealth before ÷ wealth after) ÷ growth gap
ln(500 ÷ 428.6) = 0.1541, and 0.1541 ÷ 2.92% = 5.3 years
In Excel: =LN(500/428.6)/(g_sell-g_keep)
| Keep | Sell $300m | |
|---|---|---|
| Median wealth at year 10 | 717.7 | 823.9 |
| Mean wealth at year 10 | 1,112.8 | 953.9 |
| Chance of ending below half | 13.0% | 1.4% |
At year ten the selling family's median is $106.2m ahead, and its chance of halving falls from about one in eight to about one in seventy. The keeping family's mean is $158.9m ahead. Both figures are true, and they describe different things: the mean is pulled up by the few paths in which the company does spectacularly, the median is what the family should expect to see.
| Single-stock volatility | Growth gap | Payback, years | Below half, keep | Below half, sell |
|---|---|---|---|---|
| 25% | 1.18 | 13.1 | 3.3% | 0.6% |
| 35% | 2.92 | 5.3 | 13.0% | 1.4% |
| 45% | 5.25 | 2.9 | 25.4% | 2.7% |
| 55% | 8.16 | 1.9 | 37.6% | 4.7% |
Volatility is the input that matters, because drag rises with its square. A steady 25 per cent stock takes thirteen years to repay the tax; a 45 per cent stock repays it in under three. The tax rate matters less than it feels: at 15 per cent the payback is 3.2 years, at 33 per cent it is 7.7.
| Amount sold | Tax, $m | Growth gap | Payback, years | Below half, sell |
|---|---|---|---|---|
| $100m | 23.8 | 1.19 | 4.1 | 8.0% |
| $200m | 47.6 | 2.19 | 4.6 | 3.8% |
| $300m | 71.4 | 2.92 | 5.3 | 1.4% |
| $400m | 95.2 | 3.26 | 6.5 | 0.7% |
The first $100m sold repays fastest; each further tranche buys less drag reduction per dollar of tax. Most of the protection against halving is bought by the first $300m. Selling the last $100m adds 1.2 years of payback to remove the remaining 0.7 points of risk, which is a decision about control and sentiment as much as arithmetic.
The usual comparison runs both portfolios forward at their expected return. Since the expected returns are equal, the family that pays tax is simply $71.4m behind for ever, and the spreadsheet says never sell. That model is not conservative, it is blind: it assumes the volatility of a single stock costs nothing. A family experiences one path, not the average of all paths, and the path it should plan around is the median. Run the comparison on median growth, and add the probability of halving beside it, because that second number is the one a founder recognises.
Two limits. The model rebalances to constant weights and taxes the sale once; a staged sale, an exchange fund or a charitable structure changes the tax line. And it treats the company as an ordinary stock: if the family has an edge in running it, the expected-return assumption should say so explicitly.
Paying tax to diversify is not trading a certain loss for a vague benefit. On these illustrative figures it trades $71.4m today for 2.92 points a year of median growth and a ninefold cut in the chance of halving, and repays itself in about five years. The family office cost model on the free workbooks for the book sits beside this decision, and the threshold at which an office itself pays is worked in a companion article.
Volatility drag is the gap between expected return and the growth of the median outcome, roughly half the variance. A single stock at 35 per cent volatility inside an 80 per cent concentrated portfolio drags 4.38 points a year off an 8.0 per cent expected return; after diversifying, the drag falls to 1.46 points. That 2.92 point difference is what repays the tax.
Divide the log of wealth before over wealth after tax by the gain in median growth. Selling $300m of a $400m nil-basis stake at 23.8 per cent leaves $428.6m of $500m; ln(500/428.6) is 0.1541, and dividing by a 2.92 point growth gap gives 5.3 years. A steadier 25 per cent volatility stock stretches it to 13.1 years.
If both portfolios earn the same 8.0 per cent expected return, the family that pays tax stays behind for ever in expectation: at ten years the mean is $1,112.8m keeping against $953.9m selling. But the mean is lifted by rare spectacular paths. The median, $717.7m against $823.9m, favours selling, and the chance of halving falls from 13.0 to 1.4 per cent.
The free companion files work a version of this, the fortune in one company, as a case set against chapter 8 of The Family Office Professional. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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