Portfolio Diversification Ratio Calculator
A portfolio diversification ratio calculator divides the entered long-only portfolio’s weighted standalone volatility by its covariance-aware portfolio volatility. The ratio describes the supplied weights and risk assumptions; it is not a diversification grade, suitability test or instruction to change an allocation.
Enter one aligned portfolio risk set
Provide 2 to 8 matching names, positive weights, same-period volatilities and a complete valid correlation matrix.
Enter 2 to 8 labels in one consistent order.
Enter matching positive weights that sum to exactly 100%.
Enter matching positive standard deviations in one return period.
Enter one row per asset. Values must be symmetric, use 1 on the diagonal and form a positive-semidefinite matrix.
Entered diversification ratio
Entered Portfolio Risk Decomposition 1.0.0.
| Asset | Weight | Volatility | Covariance with portfolio | Marginal contribution | Component contribution | Contribution share |
|---|
How the diversification ratio is calculated
Portfolio volatility = √(w′Σw)
Diversification ratio = Σ(wiσi) ÷ √(w′Σw)
Version 1.0.0 first calculates the weighted sum of individual asset volatilities while ignoring cross-asset covariance. It then calculates the actual portfolio volatility under the full entered correlation matrix. Dividing the first value by the second produces the diversification ratio introduced for long-only portfolios.
For valid long-only inputs, the weighted standalone volatility is greater than or equal to portfolio volatility, so the ratio is at least one within numerical tolerance. A value of one can occur for a single effective risk direction, including perfectly correlated assets. A larger value indicates more volatility reduction under the entered assumptions, not automatically a better portfolio.
The denominator uses exactly the same covariance engine as the Portfolio Volatility Calculator. This prevents different routes from silently applying different periods, matrix rules or rounding. Results remain unrounded inside the engine and are rounded only for display.
Worked example from the audited fixture
The audited fixture enters weights of 60% and 40%, same-period volatilities of 10% and 20%, and zero correlation between EUR/USD and GBP/USD.
- Weighted standalone volatility is 0.6 × 10% + 0.4 × 20% = 14%. The covariance calculation produces portfolio variance of 100 percentage-points squared and portfolio volatility of 10%.
- The diversification ratio is 14% ÷ 10% = 1.4. That value belongs only to the entered assumptions; changing either correlation, either volatility or either weight changes the ratio.
Reproduce it: select “Load audited example” above to use the immutable Batch 35 values. The engine retains full precision and rounds only the visible display.
How to interpret the result
- A ratio of 1.4 means weighted standalone volatility is 1.4 times the portfolio volatility after the entered correlations are applied.
- Do not interpret 1.4 as 40% less risk without defining the comparison carefully. The denominator is 28.57% below the 14% numerator, while the ratio itself is 40% above one; these are different statements.
- The ratio is sensitive to estimated correlations. Assets that appeared weakly correlated in one sample can move together in another sample, particularly during changing market regimes.
- Use the visible numerator, denominator and matrix audit table to understand the arithmetic. A bare ratio without its period and inputs is not comparable evidence.
Assumptions and limits
- The model accepts only long-only positive weights summing to 100% and performs no leverage or short-position treatment.
- It measures diversification through volatility only; tail dependence, liquidity, gap risk, concentration by currency and nonlinear exposures remain outside the model.
- The page does not estimate a number of independent bets or an effective asset count.
- No optimisation is run and no maximum-diversification, minimum-variance or risk-parity portfolio is produced.
- No quality label, future stability claim, safe threshold, signal or recommendation is generated.
Portfolio volatility vs diversification ratio vs risk contribution
These views share one entered covariance set but should not be substituted for one another. Volatility calculates the total dispersion, the diversification ratio compares two volatility constructions, and risk contribution attributes the total by asset. Portfolio heat remains a separate monetary stop-risk workflow.
| Measure | Evidence entered | Question answered | Main boundary |
|---|---|---|---|
| Portfolio volatility | Weights, volatilities, correlations | Total covariance-aware standard deviation | Not cash loss or maximum loss. |
| Diversification ratio | Same entered covariance set | Standalone volatility divided by portfolio volatility | Not a quality grade or asset count. |
| Risk contribution | Same entered covariance set | Additive volatility attribution by asset | Not optimisation or a rebalance instruction. |
| Portfolio heat | Entered account-currency stop-risk amounts | Correlation-adjusted open-trade risk amount | A different input and risk unit. |
Frequently asked questions
- It is weighted standalone asset volatility divided by covariance-aware portfolio volatility for the entered long-only portfolio.
- Each entered volatility is multiplied by its decimal portfolio weight and those weighted values are added without cross-asset covariance.
- For a valid long-only covariance set, portfolio volatility cannot exceed the weighted sum of individual volatilities within numerical tolerance.
- No. It describes volatility reduction under the entered assumptions and does not assess returns, suitability, tail risk, liquidity or future stability.
- No. Version 1.0.0 does not convert the ratio into an independent-bet count or effective asset count.
- No. It evaluates the entered weights only and performs no optimisation, risk-parity calculation or rebalancing.
- Estimated volatilities and correlations can change with the sample window, observation alignment and market regime even when capital weights remain fixed.
- Every volatility must use the same return frequency and convention, and every correlation must describe aligned observations from that same context.
Sources and methodology
- Choueifaty, Froidure and Reynier — Properties of the Most Diversified Portfolio — Primary paper defining the long-only diversification ratio as weighted average volatility divided by portfolio volatility.
- MathWorks — Mean-variance portfolio analysis — Official documentation for covariance-based portfolio standard deviation.
The implementation contract also fixes input bounds, matrix tolerances, additive reconciliation and permanent exclusions so later page changes cannot silently alter the arithmetic.
Inspect the ratio components
Verify the instrument records behind your assumptions
Before comparing any covariance result with your account, confirm that symbols, contract specifications, statement currency and return observations refer to the intended broker entity and account. This browser calculator does not retrieve broker history or certify that differently sourced volatility and correlation estimates are aligned.
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