How many holdings does it take before the benefit runs out?
Every investor eventually asks for a number. The honest answer has two parts: there is a shape to the curve, and the number itself matters far less than what is in the basket.
The diminishing-returns curve
Using the formula from the last lesson — holdings each at 35% volatility, average pairwise correlation 0.2 — watch what happens as names are added:
- 1 holding: 35.0%
- 5 holdings: 21.0%
- 10 holdings: 18.5%
- 20 holdings: 17.1%
- 30 holdings: 16.7%
- 100 holdings: 16.0%
- every holding available: 15.7% — the floor
The first nine additions removed 16.5 percentage points of risk. Holdings 11 through 30 removed 1.8 more. Holdings 31 through 100 removed 0.7. The curve collapses fast, then flattens onto a floor it never crosses.
Two things the curve tells you
One: most of the benefit arrives early. Classic studies from the late 1960s onward put the "most of the way there" point somewhere in the region of 20 to 30 holdings, and later research argues for considerably more. Every version agrees on the shape: steep, then flat.
Two: there is a floor. No number of holdings takes this portfolio below 15.7%, because that is what ρ = 0.2 implies. The floor is set by correlation, not by count. Unit 4 gives that floor its proper name.
Why the number is the least useful part
Two portfolios of thirty holdings each: one holds thirty companies from a single industry in a single country; the other spans industries, sizes, countries and asset types. Same count, utterly different floors. Anyone answering "how many?" without asking "how different?" is answering the easy question.
There is also a practical ceiling in the other direction. Past some point each additional name is a rounding error in the portfolio and a real cost in attention, fees or paperwork. The curve is flat there — you would be paying for a benefit that has already been collected.
Try it now
- Count your watchlist, then count how many distinct industries it covers. Which number is smaller — and by how much?
- The two charts below cover the same year: a broad index, then one of its own constituents. Compare the size of the swings on each. That gap is the curve above — the single name sits at its left end, the index near the floor.
- State the takeaway in one sentence without using a number: the benefit fades with each addition and stops at a floor set by how alike the holdings are.