Portfolio Risk Contribution Calculator
A portfolio risk contribution calculator decomposes covariance-aware volatility into additive component contributions for each entered asset. It shows marginal contribution and percentage share under the supplied long-only assumptions; it does not optimise weights, create a risk budget or recommend a rebalance.
Enter the portfolio to decompose
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.
Additive volatility contributions
Entered Portfolio Risk Decomposition 1.0.0.
| Asset | Weight | Volatility | Covariance with portfolio | Marginal contribution | Component contribution | Contribution share |
|---|
How portfolio risk contribution is calculated
Component contributioni = wi × Marginal contributioni
Σ Component contributions = Portfolio volatility
Version 1.0.0 multiplies the covariance matrix by the decimal weight vector. Dividing each resulting covariance-with-portfolio value by total portfolio volatility gives that asset’s marginal contribution: the local sensitivity of portfolio volatility to its weight under the entered covariance matrix.
Multiplying marginal contribution by the asset weight gives component contribution. Because volatility is homogeneous in weights, these components add back to total portfolio volatility. The calculator verifies that reconciliation before releasing a result and displays each component both in volatility percentage points and as a share of total volatility.
Contribution share is not the same as capital weight. A smaller position can contribute more volatility when its individual volatility and covariance with the portfolio are larger. Conversely, a negative entered covariance can produce a negative component, reducing the total under the supplied matrix.
Worked example from the audited fixture
The audited two-asset fixture uses weights of 60% and 40%, volatilities of 10% and 20%, and zero correlation. Total portfolio volatility is 10%.
- Covariance times weight is [60, 160]. Dividing by 10% portfolio volatility gives marginal contributions of 6% and 16%; multiplying by weights gives component contributions of 3.6% and 6.4%.
- The components add to 10%. Their shares are 36% and 64%, so GBP/USD is the larger positive contributor in this entered example even though its capital weight is smaller.
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
- Component contribution answers how much each entered asset adds to the portfolio’s current volatility decomposition. The sum, including any negative components, equals total portfolio volatility.
- Marginal contribution is a local mathematical sensitivity, not the result of removing the position. Changing a weight also changes the portfolio and may require renormalising all other weights.
- A negative component identifies an offset under the entered covariance matrix. It does not establish stable hedge effectiveness, executable protection or positive performance during stress.
- Use contribution share to compare the entered components, while keeping the volatility-unit contribution visible so the percentage does not become detached from the total risk measure.
Assumptions and limits
- The model is a static long-only decomposition and does not calculate new risk-parity or equal-risk-contribution weights.
- Inputs are not estimated or validated against market history; period, return basis, window and timestamp consistency remain the user’s responsibility.
- Linear covariance does not capture optionality, leverage tiers, stop execution, margin liquidation, jumps, liquidity or tail dependence.
- Risk contribution can change materially when correlations or volatilities change, even if capital weights stay fixed.
- No concentration grade, safe risk budget, rebalance instruction, forecast, 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 attributes covariance-aware portfolio volatility across entered assets so that the component contributions add back to total volatility.
- The asset row of covariance times weights is divided by total portfolio volatility under the entered covariance matrix.
- The asset marginal contribution is multiplied by its decimal capital weight and reported in volatility percentage points.
- An asset with higher volatility or covariance with the portfolio can contribute more volatility than its capital weight alone suggests.
- Yes. Negative entered covariance with the portfolio can create a negative component, but that does not prove stable or executable hedge protection.
- Yes. Version 1.0.0 verifies the Euler additive reconciliation before it releases the calculated result.
- No. It decomposes the entered portfolio and never solves for equal-risk, minimum-variance or recommended weights.
- No. It is the largest positive volatility component under the entered assumptions, not a loss forecast, quality grade, signal or recommendation.
Sources and methodology
- MathWorks — Portfolio risk contribution — Official documentation for individual asset contribution to overall portfolio volatility.
- Choueifaty, Froidure and Reynier — Diversification properties — Primary discussion connecting long-only covariance, volatility and diversification.
The implementation contract also fixes input bounds, matrix tolerances, additive reconciliation and permanent exclusions so later page changes cannot silently alter the arithmetic.
Compare portfolio risk views
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.
XM
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