Correlation between funds sets a floor under portfolio risk, and the number of funds only decides how fast you approach it.
The dispersion of an equal-weighted portfolio of n funds is σ × √(ρ + (1 − ρ) ÷ n), where σ is the single-fund dispersion and ρ the average correlation between funds. On illustrative inputs, a 0.55x standard deviation of net TVPI and a 0.25 correlation, 7 funds capture 80 per cent of the achievable risk reduction and 15 funds capture 90 per cent. No number of funds takes dispersion below 0.275x.
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The question is usually answered with a rule of thumb, ten to twenty managers, without the arithmetic behind it. The arithmetic is short, and it shows what the rule of thumb hides: the answer depends mostly on the correlation between funds, which a limited partner cannot diversify away, and much less on the count, which it can choose.
| Input | Value |
|---|---|
| Expected net TVPI of a single fund | 1.70x |
| Standard deviation of a single fund's net TVPI | 0.55x |
| Average pairwise correlation between funds | 0.25 |
| Loss threshold tested | 1.0x |
The correlation stands for everything funds share: the vintage year's entry prices, the exit window, the cost of leverage. Funds of different vintages correlate less than funds of the same one, which is part of why pacing across years matters as much as manager count.
σp(n) = σ × √(ρ + (1 − ρ) ÷ n). In Excel, with σ in B1, ρ in B2 and n in B3: =B1*SQRT(B2+(1-B2)/B3).
Floor, as n grows without limit: σ × √ρ = 0.55 × 0.50 = 0.275x.
Achievable reduction = 0.55 − 0.275 = 0.275. Share captured at n = (0.55 − σp(n)) ÷ 0.275.
At n = 10: 0.55 × √(0.25 + 0.75 ÷ 10) = 0.314x, which captures 86.0 per cent of the achievable reduction.
To turn dispersion into something an investment committee recognises, the table also gives the probability that the portfolio returns less than 1.0x and a rough fifth percentile, both on a normal approximation. Fund multiples are skewed to the right, so treat these as orders of magnitude rather than precise odds.
| Funds | Dispersion | Share of reduction captured | P(TVPI below 1.0x) | 5th percentile |
|---|---|---|---|---|
| 1 | 0.550x | 0.0% | 10.2% | 0.80x |
| 3 | 0.389x | 58.6% | 3.6% | 1.06x |
| 5 | 0.348x | 73.5% | 2.2% | 1.13x |
| 10 | 0.314x | 86.0% | 1.3% | 1.18x |
| 15 | 0.301x | 90.5% | 1.0% | 1.20x |
| 20 | 0.295x | 92.8% | 0.9% | 1.21x |
| 30 | 0.288x | 95.1% | 0.8% | 1.23x |
The first few funds do almost all the work. Going from one fund to five cuts the probability of losing money from 10.2 to 2.2 per cent. Going from ten to thirty moves the fifth percentile only from 1.18x to 1.23x, while tripling the number of relationships to monitor, side letters to track and re-up decisions to make. Somewhere around 7 to 15 funds the marginal manager stops buying risk reduction and starts buying administration and, often, a drift towards the average.
The same arithmetic implies that fund-of-funds and large programmes in one strategy should end up with similar outcomes to one another. Past a few dozen funds, every programme in a given strategy converges on the floor, and the only remaining differences are fees, vintage mix and the handful of managers each one overweights.
| Correlation | Dispersion, 10 funds | Floor | Funds for 90 per cent | P(below 1.0x) |
|---|---|---|---|---|
| 0.00 | 0.174x | 0.000x | 100 | 0.0% |
| 0.10 | 0.240x | 0.174x | 19 | 0.2% |
| 0.25 | 0.314x | 0.275x | 15 | 1.3% |
| 0.40 | 0.373x | 0.348x | 13 | 3.0% |
| 0.60 | 0.440x | 0.426x | 12 | 5.6% |
The higher the correlation, the fewer funds it takes to reach the floor, and the higher the floor is. A programme concentrated in one strategy and two or three vintages behaves like the bottom rows: twelve funds get it nearly all the diversification there is, and the residual risk is still more than three quarters of a single fund's. The lever that moves the floor is not more managers but less correlation: other vintages, other strategies, other regions.
Commitment size is the other half. The formula assumes equal weights. A portfolio of fifteen funds in which three take half the capital behaves like a much smaller one. Count effective funds as one divided by the sum of squared weights before reading the table.
The common mistake is to assume fund outcomes are independent and divide the single-fund dispersion by the square root of n. For ten funds that gives 0.174x instead of 0.314x, and a probability of losing money that rounds to zero instead of about 1.3 per cent. It also implies that a hundred funds would remove almost all risk, which is the arithmetic behind over-diversified programmes that end up owning the market at private equity fees. The correct formula never lets dispersion fall below σ × √ρ.
Estimate the single-fund dispersion and the correlation for your strategy, compute the floor, and choose the smallest number of funds that gets you most of the way to it, here 7 for 80 per cent and 15 for 90. Spend the rest of the effort on lowering the correlation through vintage and strategy, and on picking the managers. The companion files in the free workbooks for this book cover manager selection and portfolio construction for a whole programme. On why portfolio returns cannot be built by averaging fund figures, see why fund IRRs cannot be averaged.
On illustrative inputs it gets most of the way. With a single-fund TVPI dispersion of 0.55x and a 0.25 correlation, ten funds bring portfolio dispersion to 0.314x, 86.0 per cent of the achievable reduction, and the probability of a portfolio below 1.0x to about 1.3 per cent. Going to 20 funds only reaches 0.295x.
Because funds share common drivers: vintage conditions, exit markets, credit availability. That shared part is the correlation, and it cannot be diversified by adding managers. At a 0.25 correlation the floor is half the single-fund dispersion, 0.275x against 0.55x, however many funds are held.
Yes, by a wide margin. Assuming zero correlation, ten funds would have a dispersion of 0.174x, against 0.314x at a 0.25 correlation. The independent case implies almost no chance of losing money, while the correlated case still gives about 1.3 per cent.
This article is one calculation from The Private Markets Limited Partner. 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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