Effective Holdings: How Many Positions Your Portfolio Actually Behaves Like

There is nothing proprietary here and that is deliberate. The underlying measure is the Herfindahl-Hirschman Index, the sum of squared shares, which US antitrust regulators use to measure how concentrated a market is. Its reciprocal is the standard way to express an effective number of participants, and applying it to portfolio weights is a well-established construction.

• Convert each position to a share of the portfolio's total value.
• Square each share.
• Add the squares together. That sum is the HHI, between zero and one.
• Divide one by the HHI. That is your Effective Holdings.

The squaring is what makes it work. A 40% position contributes 0.16 to the sum while a 4% position contributes 0.0016, a hundred times less. So the number reflects what actually drives your portfolio rather than what fills up the list, which is exactly the difference between it and a position count.

We publish this rather than keeping it in a black box because a concentration figure you cannot reproduce is not much use. You can check ours with a spreadsheet.

Every figure in this table is computed by the same function the product runs, so it cannot drift away from what you would see in your own account.

• Ten positions, evenly weighted. The only shape where the number you own and the number you behave like are the same.
• Ten positions, one at 40%. A single large winner left to run. Still ten tickers, and no longer a ten-position portfolio.
• Twenty-five positions, one at 55%. The shape a long-held employer stock or an early bet usually produces.
• Four positions, evenly weighted. Deliberately concentrated, and the number simply says so without objecting.

The third row is the one people recognise. Twenty-five positions sounds diversified, and it is, right up until one of them is more than half the money. At that point the other twenty-four are, collectively, a minority shareholder in your own portfolio.

Worth doing once on your own numbers, because a measure you have computed yourself is one you will trust and argue with rather than accept. Take a five-position portfolio worth $100,000.

• Position A, $50,000. Share 0.50. Squared, 0.2500.
• Position B, $20,000. Share 0.20. Squared, 0.0400.
• Position C, $15,000. Share 0.15. Squared, 0.0225.
• Position D, $10,000. Share 0.10. Squared, 0.0100.
• Position E, $5,000. Share 0.05. Squared, 0.0025.

The squares add to 0.3250. One divided by 0.3250 is about 3.1. So a five-position portfolio behaves like roughly three, because half the money sits in one place. Notice how little the smallest position contributes: 0.0025 out of 0.3250, under one percent of the result, which is a fair reflection of how little it will change what happens to the account.

Now change one thing. Trim A from $50,000 to $30,000 and put the released $20,000 into D and E, so the five sit at $30,000, $20,000, $15,000, $20,000 and $15,000. The squares now add to 0.2150, and Effective Holdings rises to about 4.7 out of 5. Same five companies, same $100,000, and a portfolio that behaves quite differently. That sensitivity to the whole distribution, rather than to the count or to the largest name alone, is the point of the measure.

Being clear about the edge of a measure is part of publishing it. Effective Holdings will tell you the shape of your portfolio and it will not tell you any of the following.

• Whether your concentration is well placed. Two portfolios with identical numbers can hold entirely different things. The measure is blind to quality, valuation and business risk, and it should be: the moment a concentration figure starts grading holdings it becomes an opinion wearing a number.
• What will happen next. It is computed entirely from today's weights and contains no forecast. A concentrated portfolio can outperform for years, which is precisely why concentration persists.
• Whether you should sell anything. That depends on your tax position, your horizon, your income, and why you own what you own, none of which this sees. Walnut is an informational tool and not a registered investment adviser, so it describes and stops there.
• How your accounts interact. If you hold the same company in a taxable account and a retirement account, the concentration is real and the measure computed on one account alone will understate it. Read it across everything you can connect.

A useful measure is one that is honest about its edges. This one is a floor on concentration computed from current weights, and every sentence on this page is written to keep it that.

Nobody sets out to concentrate. In practice a low Effective Holdings almost always arrives by one of four routes, and recognising which one you are in matters more than the number itself.

• A winner left to run. The most common and the most benign-looking. You bought a reasonable position, it did well, and you never trimmed because trimming a winner feels like a mistake. Nothing went wrong at any single moment, and the portfolio quietly became a bet on one company. This is the route where the number is most useful, because there was never a day on which anyone decided.
• Employer stock. Grants vest, you hold them, and the position compounds alongside your salary. The concentration here is worse than the number shows, because your income and your portfolio depend on the same company, which no measure of the portfolio alone can see.
• A conviction position. Someone decided, deliberately, to put a lot into one name. A low number here is not a discovery, it is a description, and there is nothing to fix. Walnut says what is true and does not argue.
• A fund doing more work than you think. One broad ETF at 70% of the account gives a low Effective Holdings even though the fund itself holds hundreds of companies. The number is technically correct and the intuition it creates is misleading, which is why it should be read next to the holdings rather than on its own.

The first two are the ones worth catching early, because they are the two nobody chose.

There are three common alternatives and each answers a narrower question. None is wrong; they are just answering less.

• Position count. Easy and misleading. It treats a 0.5% holding and a 40% holding as equal, which is exactly the arithmetic that makes people feel diversified when they are not.
• Largest position as a percentage. Genuinely useful and the most common single check. It catches one dominant name and misses three medium ones. A portfolio with three positions at 20% each has a reassuring 20% top weight and behaves like far fewer than its position count suggests.
• Sector or geography weights. Answers a different and important question, which is what kind of thing you own rather than how much it is spread. It is the right complement to this measure, not a substitute, and it partly covers the correlation blind spot described below.

Effective Holdings sits between them: one number, sensitive to the whole distribution rather than to its largest member, and directly comparable to the count you already know. That last part is what makes it land. Being told your top position is 38% is information. Being told you own 30 positions and behave like 5 is the same information in a form that means something immediately.

Nothing, necessarily. It is a description, and plenty of people look at it, recognise the shape, and carry on deliberately. If you do want to act, the number suggests where to look rather than what to do.

• Check whether the gap surprised you. If it did, that is the finding. A portfolio you believed was spread across thirty names and is really driven by five was not built on purpose, and the useful next step is deciding whether you would build it that way today.
• Look at what the largest position actually is. Concentration in a broad index fund and concentration in one company are the same arithmetic and very different situations.
• Check the correlation the number cannot see. If the top five holdings are all in one industry, your real concentration is higher than the figure, and no amount of position-counting will show it.
• Remember the tax side exists. Trimming a long-held winner in a taxable account is a taxable event, so the cost of reducing concentration is not zero and is specific to your basis and bracket. This is a question for you or a professional, not for a measure.

Because a concentration number you cannot reproduce is not evidence, it is a claim. Anyone can take the weights from their own brokerage statement, square them in a spreadsheet, add them up and divide one by the total, and get the same figure Walnut shows. If the numbers disagree, ours is wrong and we would like to know.

There is a second reason, which is that the measure is not ours. The Herfindahl-Hirschman Index has been used to assess market concentration for decades and its reciprocal is a standard way to express an effective count. Presenting a recognised measure as a proprietary score would be dressing up something borrowed, and it would also be worse: a published method can be checked, argued with and trusted, and a black box can only be believed. What Walnut adds is not the formula, it is running it on the account you actually hold, which is the part most tools cannot do.

Two limitations, stated up front, because a measure that oversells itself is worse than no measure.

• It does not know about correlation. Two different tickers that move together count as two separate holdings. A portfolio of eight semiconductor companies can show a perfectly healthy Effective Holdings while behaving like a single bet on one industry. Read the number alongside what the holdings actually are, not instead of it.
• It does not look inside your funds. An ETF counts as one position at its own weight. If two funds you own hold many of the same underlying companies, your real concentration is higher than this number says. Fund overlap is a separate question and worth asking separately.

Both limitations point the same way: Effective Holdings is a floor on how concentrated you are. Your true concentration is never lower than it says, and can be meaningfully higher.

There is no correct value and Walnut does not grade it. A four-position portfolio held on purpose has a low number and there is nothing wrong with that; the number simply says what is true. Anyone selling you a concentration score with a pass mark on it is adding an opinion to an arithmetic result.

The signal worth attention is the gap between what you own and what you behave like. Owning thirty positions and behaving like five is not automatically a problem, but it is almost always a surprise, and the surprise is the useful part. Most people discover it after a position has quietly grown for a few years rather than because they decided to concentrate.

Because the number scales with how many positions you hold, it does not compare cleanly between portfolios of different sizes. For that, use the ratio of effective to actual, which runs from just above zero to one, where one means every position carries equal weight.

It needs your actual holdings and their actual weights, which is a higher bar than it sounds. A stock scorer rates a security in isolation and has no idea what else you own. A general assistant like ChatGPT or Claude has no connection to your account, so it can only work from a list you paste in, which goes stale the moment anything moves. A robo-advisor knows the portfolio it manages and not the accounts it does not.

Walnut computes it from the brokerage account you connect, read-only by default, which is why the number describes what you own rather than what you told it you own. If you want the wider context, AI portfolio analyzers covers the category, and AI investing without automatic trading covers how a tool can read your account without being able to act on it.

The Herfindahl-Hirschman Index was developed independently by two economists in the mid-twentieth century as a way to describe how concentrated an industry is, and it became the standard tool competition regulators use when deciding whether a market has too few meaningful participants. The insight that makes it useful is the squaring: it deliberately weights large shares more than proportionally, because a market with one dominant firm and nine small ones does not behave like a market with ten similar firms, even though both contain ten.

The same reasoning applies exactly to a portfolio, which is a set of shares summing to one, and the reciprocal form has been used for decades in other fields to express an effective count. Ecologists use it to describe how many species a habitat effectively contains when a few dominate. Statisticians use it to describe an effective sample size when observations are unevenly weighted. Portfolio weights are the same mathematical object.

What is new here is not the measure but the data. Running it requires knowing every position and its current value, which is why the number tends to appear inside institutional tools and not in front of individual investors. Connecting the account you already hold is what makes it available to you, and publishing the method is what makes it worth having.