How to use the portfolio diversification calculator
The calculator has two tools.
Your holdings measures the concentration of an actual portfolio:
- List each position and its market value. Use the current values from your brokerage statement, not what you paid. The example has eight fictional holdings worth $80,000 in total; replace them with your own and add rows as needed.
- Optionally enter an average volatility and an average correlation. These turn the concentration figures into an estimate of portfolio volatility. Leave them empty if you only want the weights and the index.
How many holdings? answers a general question: for a given volatility and correlation, how much does each extra equal-sized position reduce risk, and where does the benefit stop?
The formulas
HHI = Σ wi2
Effective number of holdings = 1 ÷ HHIThe Herfindahl-Hirschman index (HHI) runs from 1/N for N equal positions to 1 for a single holding. Multiplied by 10,000 it gives the 0–10,000 scale used in antitrust work.
To link concentration with risk, the calculator assumes every holding has the same volatility σ and every pair has the same correlation ρ. Under that assumption the portfolio’s variance depends only on the HHI:
Floor with unlimited holdings = σ × √ρFor N equal weights, HHI = 1/N, so volatility = σ × √(1/N + ρ × (1 − 1/N)). The remaining diversifiable share is (σp2 − ρσ2) ÷ σp2.
A worked example
The example portfolio holds 8 positions worth $80,000.00. The largest, Company A, is 30.0% of the money, the top three are 63.7% and the top five 84.4%.
Squaring and adding the weights gives an HHI of 0.1785 (1,785 points), so the effective number of holdings is 5.6. The portfolio is as concentrated as 5.6 equal positions, not eight.
With 30% volatility per holding and an average correlation of 0.3, the estimated portfolio volatility is 19.6%. The floor for that correlation is 16.4%, and 29.4% of the portfolio’s remaining variance could still be removed with more, smaller positions. Holding the same eight names in equal amounts would give 18.7%.
Equal weights are the benchmark: the same eight holdings at $10,000 each would have an HHI of 0.1250 and an effective number of exactly 8.
Why position size matters as much as the count
Counting holdings overstates diversification whenever the weights are uneven. The HHI squares each weight, so a 30% position contributes 0.09 to the index while a 2.5% position contributes about 0.0006. The table under the results shows each holding’s share of the HHI: in the example, Company A alone causes about half of the concentration.
That is why a portfolio of 40 stocks with one large legacy position can be less diversified than 12 stocks held in equal amounts. Common causes are company stock from an employer, a position that grew after a big run, or an inheritance that was never rebalanced.
How many holdings is enough?
Each new equal-sized holding removes a smaller slice of risk than the one before, and correlation sets the floor. With 30% volatility per holding and a correlation of 0.3:
| Holdings | Portfolio volatility |
|---|---|
| 1 | 30.0% |
| 10 | 18.2% |
| 20 | 17.36% |
| 30 | 17.1% |
| 100 | 16.6% |
| Unlimited | 16.43% |
Going from one to ten holdings removes most of the risk that can be removed. Going from 30 to 100 barely moves the number. One fact holds whatever the correlation: N equal holdings always remove a share of 1 − 1/N of the diversifiable variance, so ten names remove 90% of it and twenty remove 95%.
Correlation changes where the floor sits and how many names it takes to get close. At a correlation of 0.1 the floor is 9.49% and you need 43 holdings to get within 10% of it. At 0.6 the floor is 23.24% and 4 holdings already get you there, because most of the risk is shared and cannot be diversified away within that group. Correlations between stocks tend to rise in sharp market sell-offs, which is when diversification across stocks helps least.
How to read the results
- Effective number below 5: a few positions drive the outcome. A large fall in the biggest holding would show up clearly in the total.
- 5 to 20: typical of a hand-picked stock portfolio. Check the largest position and the top-three share.
- Above 20: the position sizes are well spread. Risk now depends mainly on what the holdings have in common, such as sector, country or style, which this index does not see.
What this calculator does not include
- Real correlations differ by pair. The risk estimate uses one average correlation and one volatility for every holding. A full calculation needs the correlation matrix; our portfolio volatility calculator uses it.
- Look-through for funds. A fund counts as one holding even if it owns hundreds of stocks, and two funds that own the same companies are treated as unrelated.
- Sector and factor concentration. Ten technology stocks can score well on the HHI and still move together.
- Other asset classes. Bonds, cash and real estate change portfolio risk in ways a stock-by-stock count does not capture.