How to calculate the diversification ratio
Diversification ratio = Σ(wᵢ × σᵢ) ÷ σ_portfolio
With a constant correlation ρ:
σ_p² = Σᵢ Σⱼ wᵢ wⱼ σᵢ σⱼ ρᵢⱼ (ρᵢᵢ = 1)
Worked example
- Weights 40/30/30 with volatilities 10%, 15% and 20%.
- Weighted volatility = 0.4 × 10 + 0.3 × 15 + 0.3 × 20 = 14.5%.
- If the portfolio's actual volatility is 12%: DR = 14.5 ÷ 12 = 1.21.
- A portfolio with weighted volatility 16.4% and actual volatility 10% scores 1.64 — much better diversified.
How to interpret the diversification ratio
A ratio of 1.0 means the holdings move in lockstep and diversification removes nothing. The higher the ratio, the more the assets offset each other. Don't know the portfolio volatility? Estimate it from an average correlation, or measure correlations directly with the correlation calculator.
Limitations and common mistakes
- Weights are normalised automatically if they don't add up to 100%.
- Use volatilities measured over the same period and frequency.