Diversification Risk Calculator
See how spreading money across more stocks reduces portfolio volatility, and how correlation sets the floor diversification cannot cross.
How it works
Portfolio variance = σ² × [ 1 ÷ N + (1 − 1 ÷ N) × ρ ] · Portfolio volatility = √variance · Floor = σ × √ρ
For an equally weighted portfolio of stocks that share the same volatility and average correlation, this formula shows exactly how risk falls as you add names. The first term shrinks toward zero as the number of stocks grows, wiping out the stock-specific (diversifiable) risk. What remains is the correlation-driven market risk — the square-root-of-rho floor that no amount of diversification can remove. It explains why the benefit of adding stocks fades quickly after the first twenty or thirty.
Worked example
Twenty stocks, each with 35% volatility and 20% average correlation. Variance = 35² × [1/20 + (19/20) × 0.20] = 1,225 × 0.24 = 294, so portfolio volatility = √294 ≈ 17.1% — down from 35% for a single stock, but above the ~15.7% undiversifiable floor.
Frequently asked questions
Why does diversification stop helping?
Adding stocks removes company-specific risk, but the shared market risk captured by correlation stays. Once the diversifiable part is nearly gone — usually after 20 to 30 stocks — extra names barely move portfolio volatility.
What is the undiversifiable floor?
It is the volatility a portfolio approaches as the number of holdings grows very large, equal to the single-stock volatility times the square root of the average correlation. Correlation, not count, sets how low you can go.
Is this a precise risk model?
It is a simplified equal-weight model assuming identical volatilities and one average correlation. Real portfolios have varying weights, volatilities and correlations, but the model captures the core intuition well.
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Educational estimate, not investment advice. Past returns do not predict future results.