# Portfolio concentration

Portfolio concentration is the extent to which a portfolio’s value depends on a small number of holdings or on shared exposures such as a sector or country.

## What it means

A portfolio can hold several stocks yet still depend heavily on one stock, sector or country. Portfolio concentration describes how unevenly its value is distributed across holdings or shared exposures. A large position is an obvious source of concentration; several smaller stocks in the same sector can create a less obvious one.

Concentration is not automatically good or bad. It identifies where a portfolio is most exposed, but a concentration measure alone does not describe the probability or size of a loss. The answer also depends on what is being measured: individual stocks, sectors, countries and currencies can each tell a different story.

## How it is calculated

Start with each holding’s weight, then examine the largest weight and the Herfindahl-Hirschman index (HHI):

- `w_i = V_i / V_total`: `w_i` is holding `i`’s weight, `V_i` is its market value in US$, and `V_total` is the total market value of holdings in US$. Weights are unitless; `i` identifies a holding.
- `largest weight = max(w_i)`: the greatest individual holding weight, usually shown as a percentage.
- `HHI = sum(w_i^2)`: add the squared weights of all holdings, using decimal weights that sum to 1. HHI is unitless and ranges from `1/N` for `N` equally weighted holdings to 1 for a portfolio entirely in one holding. Here, `N` is the number of holdings.

A higher HHI means greater concentration *by holding weight*. To examine sectors or countries, first add the weights belonging to each group, then square and sum those group weights. Group-level HHI answers a different question from stock-level HHI. If weights include short positions or borrowing, the simple interpretation and range above may not apply without a clearly defined convention.

## Worked example

Suppose a hypothetical, long-only stock portfolio is worth US$10,000. It holds Stock A worth US$5,000, Stock B worth US$3,000, and Stocks C and D worth US$1,000 each.

1. Divide each value by US$10,000. The weights are 50%, 30%, 10% and 10%, or 0.50, 0.30, 0.10 and 0.10 as decimals.
2. The largest holding weight is 50%.
3. Square each decimal weight and add: `HHI = 0.50^2 + 0.30^2 + 0.10^2 + 0.10^2 = 0.36`.
4. For comparison, four equally weighted stocks would have `HHI = 4 × 0.25^2 = 0.25`. The hypothetical portfolio is more concentrated by stock weight.

Now suppose A and B are in the same sector. That sector represents 80% of the portfolio even though no single stock exceeds 50%. This illustrates why a holding-level calculation does not replace a sector-exposure check.

## Why it matters before you trade

A proposed order changes portfolio weights. Even a modest purchase can raise the largest weight or increase an existing sector or country exposure; selling one holding can also increase the *percentage* weight of the holdings left behind. Calculating weights for the proposed portfolio, rather than only the current one, makes that change visible before an order is placed.

Concentration and liquidity are separate questions. A portfolio can be concentrated in readily traded stocks, diversified across hard-to-trade stocks, or both. Neither HHI nor the largest weight measures trading costs, correlations or how holdings might respond to the same event. These checks complement one another rather than producing a single complete measure of risk.

## How PreTrAIde uses it

In PreTrAIde, a user builds a stock basket with a side, quantity and execution conditions for each line. Its pre-trade analysis includes an HHI concentration index and portfolio breakdowns by country, sector, region, currency and market capitalization. It returns a GO, NO-GO or MODIFY verdict for the basket and each line, with reasoning, a risk assessment and a suggested execution strategy. Those verdicts support decisions; they are not recommendations.

PreTrAIde also offers a free portfolio concentration checker on pretraide.com that shows HHI and the largest weight, without sign-up.

## Common mistakes

- **Counting stocks instead of weighing them.** Ten holdings do not imply low concentration if one accounts for most of the value.
- **Reading stock HHI as sector diversification.** Several holdings may share the same sector, country or currency exposure.
- **Using percentage figures directly in the decimal formula.** Enter 50% as 0.50; otherwise the HHI scale changes.
- **Treating concentration as a loss forecast.** It shows the distribution of exposure, not what prices will do.
- **Ignoring the proposed trade.** Current weights may differ substantially from the weights after an order is filled.

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Source: https://pretraide.com/glossary/portfolio-concentration