Portfolio Volatility Calculator
A portfolio volatility calculator combines entered long-only weights, same-period asset volatilities and correlations into one covariance-aware standard deviation. It describes the assumptions you supply; it does not retrieve returns, predict future account loss or decide whether the portfolio is safe.
Enter one aligned risk assumption set
Use 2 to 8 assets. Names, weights and volatilities must have the same item count, and the correlation matrix must have one complete row per asset.
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.
Covariance-aware portfolio volatility
Entered Portfolio Risk Decomposition 1.0.0.
| Asset | Weight | Volatility | Covariance with portfolio | Marginal contribution | Component contribution | Contribution share |
|---|
How portfolio volatility is calculated
Portfolio variance = w′Σw
Portfolio volatility = √(w′Σw)
Version 1.0.0 converts the entered percentage weights to decimals and builds every covariance cell from the two asset volatilities and their entered correlation. It then multiplies the covariance matrix by the weight vector, takes the weight-vector dot product and reports the positive square root as portfolio volatility.
The calculation keeps the entered volatility period unchanged. Daily inputs create a daily portfolio volatility; weekly inputs create a weekly result. It performs no square-root-of-time scaling because serial dependence and the intended horizon are not established by the fields on this page.
The matrix must be symmetric, have ones on its diagonal and be positive semidefinite. This matters because several individually plausible pairwise correlations can still be impossible when considered together. Invalid joint assumptions are rejected instead of producing an apparently precise portfolio statistic.
Worked example from the audited fixture
The audited fixture uses EUR/USD at a 60% weight and 10% volatility plus GBP/USD at a 40% weight and 20% volatility. Their entered correlation is zero.
- The covariance matrix is [[100, 0], [0, 400]]. Multiplying by weights [0.6, 0.4] gives [60, 160], and the final weighted dot product is 100 percentage-points squared.
- The square root of 100 is 10%, so the entered portfolio volatility is 10%. Weighted standalone volatility is separately 14%; that difference reflects the entered zero correlation, not a forecast of future diversification.
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
- Read the result in the same period and return units as the volatility inputs. If the inputs are monthly percentage-return standard deviations, the output is a monthly percentage-return standard deviation.
- Portfolio volatility can be below the weighted average of individual volatilities because covariance terms recognize that the entered assets need not move together. This is a mathematical result under the entered matrix, not proof that the relationship will persist.
- Compare changes only when weights, estimation window, return convention, instrument basis and period remain consistent. Otherwise the apparent difference may be caused by incompatible inputs.
- Volatility measures dispersion around an average. It does not directly describe gaps, liquidation, nonlinear payoffs, spread expansion, tail severity or the largest possible account loss.
Assumptions and limits
- The tool does not fetch prices, calculate returns or estimate volatilities and correlations.
- Long-only positive weights are required and must sum to exactly 100%; leverage and short positions are outside version 1.0.0.
- Historical estimates can be unstable, selected from different windows or changed by missing observations and return alignment.
- The model assumes the entered covariance representation is the intended one and cannot verify its economic relevance.
- No expected return, VaR, drawdown, cash risk, margin, safe level, quality grade, allocation change 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 the standard deviation implied by the entered long-only weights, same-period volatilities and correlation matrix.
- Version 1.0.0 builds the covariance matrix, calculates weights transposed times covariance times weights, then takes the positive square root.
- The result keeps the period of the entered volatilities; daily inputs produce a daily volatility and monthly inputs produce a monthly volatility.
- Individually plausible pairwise correlations can be jointly impossible, so the model rejects a matrix that cannot represent a valid covariance structure.
- No. Version 1.0.0 requires 2 to 8 strictly positive long-only weights that sum to exactly 100%.
- No. Volatility uses return dispersion and correlation, while portfolio heat uses entered account-currency stop-risk amounts for open trades.
- No. Standard deviation does not cap future losses or model every gap, liquidity, nonlinear-payoff or tail event.
- No. It estimates no inputs and creates no risk grade, safe level, allocation change, forecast, signal or recommendation.
Sources and methodology
- MathWorks — Mean-variance portfolio analysis — Official documentation describing portfolio risk as return standard deviation using the mean and covariance of asset returns.
- MathWorks — Portfolio risk contribution — Official covariance-based portfolio-volatility and contribution documentation used to cross-check the shared engine.
The implementation contract also fixes input bounds, matrix tolerances, additive reconciliation and permanent exclusions so later page changes cannot silently alter the arithmetic.
Continue the covariance review
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
Review the available instrument specifications and history records for the account used.
Check XM termsFXOpen
Verify instrument, statement and account specifications before entering estimates.
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