Portfolio Diversification Score
Estimate how diversified your portfolio is using a simple concentration index. Enter your holdings and weights to calculate a diversification score between 0 and 1 and see which positions dominate your risk.
Diversification score formulas
The portfolio diversification score in this tool is built on a simple concentration index similar to the Herfindahl-Hirschman Index (HHI). It uses squared portfolio weights to measure how much of your portfolio is concentrated in a few holdings and then converts that concentration into a score between 0 and 1, where higher values indicate more diversification.
1. Normalized weights
Total weight = Σ wᵢ
Normalized weightᵢ = wᵢ ÷ Total weight
If your weights do not sum exactly to 100%, the calculator normalizes them so that the total equals 1 (or 100%). This allows you to enter either percentages or dollar amounts and still get a consistent concentration measure.
2. Concentration index (HHI-style)
Concentration index = Σ (Normalized weightᵢ)²
Each holding’s normalized weight is squared and summed. Larger positions contribute disproportionately more to the index because their squared weights are much larger than those of small positions. A portfolio with one holding at 100% will have a concentration index of 1. A portfolio with many small holdings will have a lower index.
3. Diversification score
Diversification score = 1 − Concentration index
This simple transformation converts concentration into a diversification score. If your portfolio is fully concentrated in a single holding, the concentration index is 1 and the diversification score is 0. As you spread your portfolio across more holdings with smaller weights, the concentration index falls and the diversification score rises toward 1.
You can think of the diversification score as a quick proxy for how evenly your portfolio is spread across holdings. It does not capture correlations or asset class differences, but it does highlight whether your risk is dominated by a few large positions or more evenly distributed.
Understanding portfolio diversification and concentration
Diversification is one of the most fundamental ideas in investing. Instead of placing all your money in a single asset, you spread it across multiple holdings so that no single position can completely determine your outcome. In practice, however, many portfolios are less diversified than they appear. A handful of large positions can dominate risk even when there are many smaller holdings.
Why concentration matters
Concentration is the flip side of diversification. When a portfolio is highly concentrated, a small number of holdings account for most of the total weight. If one of those holdings experiences a large loss, the impact on the overall portfolio can be severe. Concentration can be intentional—for example, a focused stock-picking strategy—but it can also creep in over time as winners grow and losers shrink.
By measuring concentration, you gain a clearer view of how your portfolio is actually structured. A portfolio with ten holdings might sound diversified, but if two of them account for 70% of the total weight, the portfolio is effectively dominated by those positions. The diversification score in this tool helps you quantify that reality.
How this calculator models diversification
When you enter your holdings and weights, the calculator first normalizes the weights so they sum to 100%. This step ensures that the concentration index is meaningful even if you entered approximate percentages or dollar amounts. It then squares each normalized weight and sums the squared values to produce a concentration index.
Squaring the weights is important because it magnifies the impact of large positions. A holding with a 40% weight contributes 0.16 (0.4²) to the index, while a holding with a 10% weight contributes only 0.01 (0.1²). This makes the index sensitive to concentration in a way that simple counts of holdings are not.
The diversification score is calculated as 1 minus the concentration index. If your portfolio is fully concentrated in a single holding, the index is 1 and the score is 0. If your portfolio is evenly spread across many holdings, the index falls and the score rises. For example, a portfolio with four holdings at 25% each has a concentration index of 0.25 (4 × 0.25²) and a diversification score of 0.75.
Worked example
Consider a portfolio with four holdings:
- Holding 1: 40%
- Holding 2: 25%
- Holding 3: 20%
- Holding 4: 15%
The normalized weights are already percentages that sum to 100%. The squared weights are 0.16, 0.0625, 0.04, and 0.0225. Summing these gives a concentration index of 0.285. The diversification score is 1 − 0.285 = 0.715. If you add more holdings with smaller weights, the concentration index will fall and the diversification score will rise.
Practical tips for using the score
- Use the score to compare different portfolio configurations, such as before and after rebalancing.
- Pay attention to holdings with large squared weights—they are the main drivers of concentration.
- Remember that diversification is not just about the number of holdings; it’s about how much weight each one carries.
- Combine this score with other metrics, such as asset class breakdowns and sector exposures, for a fuller picture.
- Use the CSV export to extend the analysis, add more holdings, or track changes over time.
Ultimately, the portfolio diversification score is a quick, intuitive way to see whether your portfolio is dominated by a few large positions or more evenly spread across many holdings. It won’t replace full risk modeling, but it can highlight concentration issues that deserve a closer look.
Frequently Asked Questions
Do my weights need to sum to 100%?
No. The calculator will normalize your weights so they sum to 100%. However, starting with weights that roughly add up to 100% makes the results easier to interpret and compare.
Can I enter dollar amounts instead of percentages?
Yes. If you enter dollar amounts, the calculator will treat them as weights and normalize them to 100%. The breakdown will show normalized percentages and squared weights based on those amounts.
How many holdings should I include?
This tool supports up to eight holdings for a quick analysis. If you have more positions, you can group smaller holdings together or export the CSV and extend the model in a spreadsheet.
Does a higher diversification score always mean lower risk?
Not necessarily. The score measures concentration of weights, not volatility or correlations. A highly diversified portfolio can still be risky if all holdings are volatile or highly correlated. Use the score as one input among many.
Can this tool replace a full risk analysis?
No. It is a simplified measure focused on concentration. For a full risk analysis, you would need to consider correlations, factor exposures, historical volatility, and your personal goals and constraints.
Is this financial advice?
No. This tool is for education and planning. It can help you see concentration patterns in your portfolio, but it is not personalized financial advice. Consider speaking with a qualified advisor before making major changes.
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