Risk Parity Allocator
Calculate equal risk contribution weights from annualized volatility and pairwise correlation, with portfolio volatility and diversification results.
Enter annualized volatility from 0.0001% through 1000% for every asset to calculate the allocation.
Earlier editorial review
- Reviewed
- 2026-09-22
- Methodology
- 1.1
Sources
How it works
Enter at least two assets, each with a positive annualized volatility in percent. Enter a correlation for every pair, from negative one to positive one. Newly added pairs start at zero and can be edited in the matrix. The calculator builds a covariance matrix and checks that the supplied correlations form a mathematically possible matrix.
The solver starts with candidate weights inversely proportional to volatility, then iteratively adjusts them toward equal variance contribution and normalizes their sum to 100%. Results show the candidate risk parity weights, equal capital weights, each asset contribution share, both portfolio volatility values, the diversification ratio, and the iteration status.
The reported contribution percentages are calculated from the final candidate allocation before rounding. Negative contributions can occur when correlations are negative. A zero variance portfolio has undefined contribution shares. The solver may stop at the iteration limit or earlier when a nonpositive contribution prevents a usable update. In either case, the status remains not converged unless the target tolerance was met.
Use the output to inspect how stated assumptions affect weights. Volatility and correlation estimates can change with the sample period. Review other risks and trading constraints separately before using an allocation outside this illustration.
Step by step
- Enter asset names and annualized volatility
- Enter or review every pairwise correlation
- Compare weights, risk contributions, and volatility
Worked example
Enter two uncorrelated assets with annualized volatility of 20% and 10%. The calculated weights are 33.33% and 66.67%. Each asset contributes 50% of modeled portfolio variance. Portfolio volatility is 9.43%, compared with 11.18% for equal capital weights of 50% each.
The weighted average of the two asset volatilities is 13.33%, so the diversification ratio is 1.414. This ratio compares that weighted average with portfolio volatility. The figures illustrate the formula and are not a forecast or a recommended allocation.
When to use this calculator
Use this calculator to compare capital weights with equal modeled variance contributions when volatility and correlation assumptions are available for each asset. It is useful for exploring how those inputs change an allocation.
Use a different model when you need expected returns, drawdown scenarios, leverage, trading costs, or account constraints. This calculator does not forecast performance or assess personal suitability.
Common input mistakes
Do not mix daily volatility for one asset with annualized volatility for another. Do not enter covariance values in the correlation matrix. Correlations have no units and must use the same return frequency, currency basis, and observation period.
Do not treat the displayed weights as a return or loss forecast. Review negative risk contributions, concentration, leverage, liquidity, and turnover separately. A mathematically valid correlation matrix does not make estimated inputs certain.
Risk contribution formula
wᵢ = portfolio weight for asset i, with Σwᵢ = 1
σᵢ = annualized volatility for asset i, entered as a percent and converted to a decimal
ρᵢⱼ = correlation for assets i and j
Cᵢⱼ = ρᵢⱼ × σᵢ × σⱼ
Portfolio variance: σ²ₚ = wᵀCw
Variance contribution: RCᵢ = wᵢ × (Cw)ᵢ
Contribution share: RC%ᵢ = RCᵢ / σ²ₚ
Target share: RC%ᵢ = 1 / n for each of n assets
The solver adjusts weights and normalizes them after each step.
The calculation uses annualized volatility and one static correlation matrix. The matrix is checked on correlation scale so the positive semidefinite test is not weakened by small volatility inputs. Convergence uses the largest difference between an asset contribution share and 1 divided by the number of assets, with tolerance 0.00000001 and a 200 iteration cap.
Limitations and assumptions
This is a long only calculation based on one static covariance matrix. It does not include expected returns, leverage, financing, transaction costs, taxes, liquidity, turnover limits, drawdowns, or stress scenarios. The input estimates can be uncertain and may change across periods. Correlation validation checks mathematical consistency, not whether estimates are reliable. The 20 asset limit keeps the pairwise matrix calculation bounded. Results are not forecasts or personal allocation recommendations.
Key terms
- Risk parity
- An allocation method that targets the same share of modeled portfolio variance from each asset.
- Correlation matrix
- The pairwise correlation values used to form a covariance matrix.
- Risk contribution share
- An asset variance contribution divided by total portfolio variance.
Compare related methods
Risk parity assigns capital so each asset has a similar share of modeled portfolio variance. Equal weight assigns capital evenly, while an expected return optimizer solves a different objective. Compare these methods using the same asset definitions and assumptions.
Use Portfolio Rebalancer to turn a chosen allocation into trade amounts, ETF Overlap Detector to review repeated holdings, Maximum Drawdown to inspect historical loss paths, and Portfolio Beta to compare sensitivity to an equity benchmark.
FAQ
What does risk parity mean?
Risk parity is an allocation method that targets equal contributions to modeled portfolio risk. It does not mean equal amounts of capital. With lower volatility, an asset can receive a larger capital weight while contributing the same share of variance as a more volatile asset.
What inputs does the calculator need?
Enter a positive annualized volatility in percent for each asset and one correlation for every pair. Correlations must be between negative one and positive one. Use values measured over a consistent return frequency and historical period. The tool accepts up to 20 assets.
How is each risk contribution calculated?
For weight wᵢ and covariance matrix C, the variance contribution is wᵢ times (Cw)ᵢ. The share of total variance divides this contribution by wᵀCw. The solver targets an equal share for each asset. If total portfolio variance is zero, contribution shares are undefined.
Why might my inputs be rejected?
The calculator requires a complete set of pairwise correlations. It rejects values outside the permitted range and correlation matrices that are not positive semidefinite. Volatility must be finite and from 0.0001% through 1000%. A valid matrix can still be difficult for the iterative solver.
What does the convergence status mean?
The result is marked converged only when every modeled risk contribution share is within 0.000001 percentage points of its equal target. The solver can stop after 200 iterations or earlier if a contribution becomes nonpositive and the update is no longer usable. If it does not converge, the displayed candidate weights and contribution shares remain estimates, not a solved equal risk allocation.
Related tools
Portfolio Rebalancer converts a selected allocation into trade amounts. ETF Overlap Detector identifies repeated holdings, while Maximum Drawdown and Portfolio Beta answer separate questions about historical losses and benchmark sensitivity.