Portfolio size does not change a venture fund's expected multiple. It changes the shape around it, and that shape can be computed exactly.
Enough to make the floor safe, not so many that the ceiling disappears, and the trade-off can be computed. With an illustrative seed outcome distribution averaging 2.19x per company, going from 10 to 40 equal cheques lifts the probability of returning at least 1x gross from 62.8 to 86.2 per cent, while the probability of 3x peaks at around 20 companies, 30.9 per cent at 20 (31.1 at 19), and falls to 13.5 per cent with 100.
Worked in full in Venture Capital by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Every company gets the same initial cheque and returns one of six multiples, with the probabilities below. The distribution is illustrative, not a market statistic: it is shaped like a seed portfolio, where most cheques return little and a few return the fund. Outcomes are treated as independent, which flatters diversification, and follow-on reserves are ignored so that portfolio size is the only thing that moves.
| Multiple of the cheque | Probability | Contribution to the mean |
|---|---|---|
| 0.0x | 50% | 0.000 |
| 0.5x | 15% | 0.075 |
| 1.0x | 15% | 0.150 |
| 3.0x | 12% | 0.360 |
| 10.0x | 6% | 0.600 |
| 50.0x | 2% | 1.000 |
| Mean | 100% | 2.185 |
Sixty-five per cent of companies return less than their cheque, and the 2 per cent at 50x supply 45.8 per cent of the expected value. Add the 10x outcomes and 8 per cent of companies supply 73.2 per cent. That is the power law in six rows.
With equal cheques, the fund's gross multiple is the average of the company multiples. Its expected value is 2.185x whatever the number of companies: portfolio size does not change the mean. What it changes is the distribution around the mean, and that can be computed exactly rather than simulated, by convolving the six-row distribution with itself once per company and reading off the probabilities.
Fund gross multiple = (1 / n) × Σ company multiples
P(at least one 50x) = 1 − (1 − 2%)n
One 50x alone returns = 50 / n times the fund
Excel, for the single-outlier probability: =1-(1-p)^n; the full distribution needs a convolution table, one row per company.
| Companies | P(≥ 1x) | P(≥ 2x) | P(≥ 3x) | Median | P(at least one 50x) | One 50x returns |
|---|---|---|---|---|---|---|
| 10 | 62.8% | 31.1% | 20.5% | 1.35x | 18.3% | 5.00x |
| 20 | 74.7% | 39.2% | 30.9% | 1.55x | 33.2% | 2.50x |
| 30 | 81.4% | 48.1% | 23.3% | 1.87x | 45.5% | 1.67x |
| 40 | 86.2% | 52.4% | 21.6% | 2.08x | 55.4% | 1.25x |
| 60 | 92.2% | 52.7% | 18.2% | 2.05x | 70.2% | 0.83x |
| 100 | 97.4% | 56.6% | 13.5% | 2.12x | 86.7% | 0.50x |
Three things happen as the portfolio grows. The floor rises steadily: the chance of losing money falls from 37 per cent at 10 companies to under 3 per cent at 100. The median climbs from 1.35x towards the 2.185x mean, so the typical outcome improves. And the chance of a great fund, 3x or more, peaks at around 20 companies and then falls, because a 3x fund needs more than the average company to be an outlier and a large portfolio averages the outliers away. At 10 companies one 50x is a 5.00x fund on its own; at 100 it is 0.50x.
The 3x column is lumpy because the outcomes are lumpy. At 10 companies a single 50x is enough for 3x, but there is only an 18.3 per cent chance of finding one; at 20 the chance nearly doubles and one 50x plus a modest rest still clears 3x. Beyond 20, one outlier on its own returns less than 2x (1.67x at 30), the rest of the portfolio has to close a wider gap, and the column falls.
The answer depends on whether the target multiple is above or below the mean. If the manager believes its picks average more than 3x, a larger portfolio raises the probability of 3x and the case for concentration disappears. If the honest average is the illustrative 2.185x, then the only route to 3x is variance, and a portfolio of 20 to 30 companies keeps enough of it while already putting the chance of at least 1x gross at 74.7 per cent or more. The same table also tells a manager how to read a reference portfolio: a fund of 40 companies that ends below 1x has not necessarily picked badly, since 13.8 per cent of such funds do so on this distribution with no difference in skill at all. Correlation pushes the other way: companies of one vintage share a funding market, so the real floor sits below the independent figures in the table.
Treating portfolio size as a way to raise the expected return. It cannot: the mean is 2.185x at 10 companies and at 100. What size buys is a different shape, more certainty of a mediocre result in exchange for less chance of an exceptional one. The second mistake is reading the median company and the fund as the same thing. The median company here returns 0.5x or less, while even a ten-company fund has a median of 1.35x; why the typical investment loses money while the fund does not is worked in why the median venture investment returns less than 1x. And these are gross multiples: fees and carried interest come off before the investor sees any of them.
The book's twenty-eight positions, ranked with a tick box on each line so you can see the fund fall as the outliers are removed, are in the free workbooks for this book.
No. With equal cheques the fund's gross multiple is the average of the company multiples, so its expected value is the same at any portfolio size: 2.185x in the worked distribution, at 10 companies and at 100. More companies narrow the spread, raising the chance of at least 1x from 62.8 to 97.4 per cent and lowering the chance of 3x.
Compute 1 minus (1 minus p) to the power n. With a 2 per cent chance of a 50x outcome per company, a 20-company fund has a 33.2 per cent chance of at least one and a 40-company fund 55.4 per cent. But one 50x returns 50 divided by n times the fund: 2.50x at 20 companies, only 1.25x at 40.
Because 3x is above the 2.185x mean of the illustrative distribution, so reaching it needs more than the average number of outliers, and a large portfolio averages outliers away. The probability of 3x is 30.9 per cent at 20 companies, 21.6 at 40 and 13.5 at 100. A manager whose picks truly average above 3x would see the opposite.
The power law, with the book's twenty-eight positions ranked by proceeds, is worked in the Chapters 4 to 8 workbook of Venture Capital. 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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