# Effective number of stocks

Effective number of stocks is the number of equally weighted holdings that would have the same weight-based concentration as a stock portfolio, calculated as one divided by the sum of squared holding weights.

## What it means

A list of ten stocks does not necessarily spread a portfolio's money evenly across ten companies. If one holding accounts for most of its value, the portfolio is more concentrated than the stock count suggests. The effective number of stocks expresses that weight-based concentration as an equivalent number of equally weighted holdings.

For a fully invested, long-only stock portfolio, the measure ranges from 1 to the actual number of stocks. It equals the actual count when every holding has the same weight. Unequal weights lower it. This is a measure of **position-weight concentration**, not a count of independent sources of risk.

## How it is calculated

`Effective number of stocks = 1 / HHI = 1 / Σ(wᵢ²)`

- `wᵢ` is stock `i`'s share of the total stock portfolio value, expressed as a decimal; 25% becomes 0.25.
- `Σ` means add the squared weights for all individual stock holdings.
- `HHI` is the Herfindahl-Hirschman concentration index when calculated using decimal weights.

The weights must sum to 1. This version of HHI runs from `1 / N` to 1 for `N` long-only stocks with positive weights. If HHI is reported on a 0–10,000 scale using percentage weights, convert it to the decimal-weight scale first: `effective number = 10,000 / HHI`. The result is a unitless equivalent count and need not be a whole number.

Specify what counts as a holding. Combining two positions in the same company or treating an ETF as a single line rather than looking through to its constituent stocks changes the calculation's meaning. Cash, borrowing and short positions require an explicitly defined weighting convention; the simple range above assumes fully invested, long-only stock weights.

## Worked example

Suppose a hypothetical US$10,000 portfolio contains four stocks:

| Stock | Value | Weight | Squared weight |
| --- | ---: | ---: | ---: |
| A | US$5,000 | 0.50 | 0.2500 |
| B | US$3,000 | 0.30 | 0.0900 |
| C | US$1,000 | 0.10 | 0.0100 |
| D | US$1,000 | 0.10 | 0.0100 |

1. Divide each stock's value by US$10,000 to get its weight. The four weights sum to 1.
2. Square each weight and add the results: `0.2500 + 0.0900 + 0.0100 + 0.0100 = 0.36`.
3. Take the reciprocal: `1 / 0.36 ≈ 2.78`.

Although the portfolio holds four stocks, its weight-based concentration is equivalent to about **2.78 equally weighted stocks**. Four holdings at 25% each would instead have `HHI = 4 × 0.25² = 0.25` and an effective number of `1 / 0.25 = 4`.

## Why it matters before you trade

A proposed trade can change concentration even when the number of tickers stays the same. Increasing the weight of an already large holding generally raises HHI and lowers the effective number; shifting weight toward a smaller holding can have the opposite effect. Calculating weights for both the current portfolio and the proposed portfolio makes that change visible before an order is placed.

The measure does **not** account for correlations, sectors, countries, volatility or the ability to trade a position without substantial cost. Two portfolios can have the same effective number but very different exposures and risks. It is one concentration check, not a verdict on whether a trade is suitable.

## How PreTrAIde uses it

PreTrAIde calculates the Herfindahl-Hirschman concentration index and portfolio breakdowns as part of its pre-trade analysis of a proposed stock basket. Its free portfolio concentration checker reports HHI and the largest weight. Because effective number of stocks is the reciprocal of decimal-weight HHI, you can derive it from HHI using the formula above; PreTrAIde's product facts do not say it reports the effective number directly.

PreTrAIde returns a GO, NO-GO or MODIFY verdict with reasoning for the basket and each line. Those verdicts are decision support, not investment recommendations. Users place any trades themselves through their own broker.

## Common mistakes

- **Using the ticker count as the answer:** Unequal position sizes reduce the effective number below the actual count.
- **Mixing HHI scales:** Dividing 1 by an HHI stated on the 0–10,000 scale gives the wrong result.
- **Treating it as correlation-adjusted diversification:** Squared weights alone say nothing about whether holdings move together.
- **Comparing mismatched portfolios:** Decide consistently whether cash, ETFs and multiple lines in the same company are included.

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Source: https://pretraide.com/glossary/effective-number-of-stocks