Equal risk contribution portfolio
Risk Parity Calculator
Calculate long-only risk-parity weights for two or three assets from their volatilities and correlations. Compare equal risk contribution with inverse-volatility and equal-weight allocations.
Risk parity and equal risk contribution formulas
Risk parity chooses weights so that each asset contributes the same amount to total portfolio volatility. Unlike equal weighting, it accounts for both each asset’s volatility and its correlations with the other assets.
Portfolio variance: σₚ² = wᵀΣw
Marginal contribution: MCRᵢ = (Σw)ᵢ ÷ σₚ
Component contribution: RCᵢ = wᵢ × MCRᵢ
Equal risk contribution condition: RCᵢ ÷ σₚ = 1 ÷ N
The calculator solves the positive long-only equal-risk system, normalizes weights to 100%, and then independently reports marginal, component and percentage risk contributions. It also compares the result with inverse-volatility weights and a simple equal-weight portfolio.
Verified three-asset example
For annual volatilities of 15%, 20% and 10%, correlations of 0.30, 0.20 and 0.10, and a US$100,000 portfolio, the verified equal-risk weights are 29.1437%, 22.9662% and 47.8901%. That allocates US$29,143.68, US$22,966.20 and US$47,890.12, produces 9.3789% portfolio volatility and gives each asset 33.3333% of total risk before display rounding.
How to use the calculator
- Select two or three assets.
- Enter volatilities measured from compatible return periods.
- Enter pairwise correlations from the same observations.
- Review risk-parity weights, monetary allocations and the risk contribution table.
- Compare the ERC result with inverse-volatility and equal-weight portfolios.
Risk parity versus inverse volatility
Inverse-volatility weights ignore correlations. For two assets they match equal-risk weights, but for three assets correlations can change the allocation materially. Equal risk contribution uses the full covariance matrix; it does not optimize expected return or guarantee the lowest possible volatility.
Limits and assumptions
- The model supports two or three long-only assets and does not allow short positions, leverage or custom risk budgets.
- Volatility must be greater than 0% and no more than 1,000%. Correlations must be from −1 through 1, and the full matrix must be positive definite.
- Inputs accept up to six decimal places. Portfolio value must be greater than zero and no more than 1,000,000,000,000,000.
- Historical estimates can change abruptly. Risk parity can concentrate capital in low-volatility assets and may require leverage in institutional implementations; this calculator does not model borrowing.
- Taxes, fees, rebalancing costs, liquidity, estimation error, non-normal returns and future correlation changes are excluded.
Risk warning: Equal risk contribution does not mean equal dollar loss in every market scenario. Correlations can rise during stress, and a portfolio can lose money even when its historical risk contributions are balanced.
Related calculators
Use the Portfolio Variance Calculator to evaluate weights you already have, the Efficient Frontier Calculator to optimize expected return and variance, the Sharpe Ratio Calculator for risk-adjusted return, and the Portfolio Rebalancing Calculator to turn target weights into trades.