Index Concentration Calculator

The number of holdings is the statistic index funds are sold on and the least informative one available. A fund can hold well over a thousand companies and still have a quarter of its value in ten of them, because a market-weighted index holds each company in proportion to what it is worth, and company values are nothing like evenly distributed. The result is a fund that is genuinely diversified across the top of its range and holds a very long tail of positions too small to matter. This page turns the top ten weights that every factsheet publishes into the measures that answer the question people are actually asking. It reports what sits in the largest one, three, five and ten positions, converts the whole distribution into an effective number of holdings using a Herfindahl index, which is the standard measure of concentration, and compares the largest position against what it would be if every holding were weighted equally. It then tests the scenario that concentration exposes you to, which is a fall confined to the largest names while the rest of the index does nothing. None of this is an argument against index funds. A market-weighted index reflects what the market is worth, which is the point of it, and concentration rises and falls with markets rather than being a defect. It is an argument for knowing the number rather than assuming that a large holdings count has dealt with single-company risk on your behalf.

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The Holdings Count Is The Wrong Number

A fund holding 1,400 companies sounds diversified beyond argument. On the worked example it behaves like about 107 equally weighted positions.

The reason is arithmetic rather than anything a fund has done wrong. A market-weighted index holds each company in proportion to its value, and company values follow a very steep distribution, so the top of the list dominates and the bottom contributes almost nothing.

The last 1,390 holdings average 0.0530% each, or $26.51 of a $50,000.00 investment. They are real positions and individually they change nothing.

Worked Example: 1,400 Holdings, $50,000

The largest ten weights run from 5.20% down to 1.10%, totalling 26.30% of the fund, or $13,150.00.

The largest single holding is 5.20%, which is $2,600.00 and 72.8x the 0.0714% it would carry if every holding were weighted equally.

The Herfindahl index across the whole distribution gives an effective count of 107 holdings.

Effective Holdings Is The Measure To Use

The Herfindahl index adds up the square of every weight. Squaring is what makes it useful: it punishes large positions heavily and lets small ones fade to nothing, which is exactly how concentration risk behaves.

Inverting it gives the number of equal positions that would produce the same concentration, which converts an abstract statistic into a count you can reason about.

It is worth applying to any fund you hold, including a New Zealand one, where the effect is usually more pronounced because the market has fewer large companies to spread across.

The Scenario Concentration Creates

A market-wide fall affects a concentrated fund and a spread one similarly. The scenario that separates them is a fall confined to the largest names.

On the worked example a 20% fall in the top ten alone moves the fund 5.26% and costs $2,630.00, with every other company in the index flat. A 50% fall in those ten costs $6,575.00.

That is the risk a holdings count is silently assumed to have removed, and at these weights it has not.

What Is Not In This Calculation

Two things make real concentration worse than the figure here.

The tail is not even. The calculation spreads the weight you do not enter evenly across the remaining holdings. Real tails taper, so genuine concentration is somewhat higher and the effective holdings number is an upper bound.

The largest holdings overlap. The top ten of a broad index are frequently in the same country and often the same sector, so they do not behave independently. Our sector exposure calculator shows that dimension, and our fund overlap calculator shows it across multiple funds.

What To Do About It

Usually nothing, and knowing the number is still worth the five minutes.

Accept it deliberately. A market-weighted index reflects what the market is worth. Concentration rises and falls with markets, and holding the market as it is remains a defensible position.

Add a different exposure. A fund weighted towards smaller companies, or a different region, dilutes the largest names without abandoning indexing. Check first that it is not duplicating what you hold.

Consider equal weighting. It addresses concentration directly, at the cost of higher turnover, usually a higher fee, and a permanent tilt towards smaller companies. It is a different investment rather than a fixed version of the same one, and our fund fee drag calculator prices the fee side of that swap.

Related NZ Portfolio Calculators

• One Fund vs Multi-Fund Calculator: whether to hold one fund or several.
• Fund Overlap Calculator: concentration created across several funds.
• Sector Exposure Calculator: the same question by sector.
• Home Bias Calculator: concentration by country rather than company.
• Fund Fee Drag Calculator: what a fee difference costs over time.