Risk Parity Calculator

How risk contributions are calculated

For weights w and covariance matrix Σ, portfolio variance is V = wᵀΣw and volatility is √V. The contribution of asset i to volatility is RCᵢ = wᵢ(Σw)ᵢ / √V. Its percentage share is 100 × wᵢ(Σw)ᵢ / V. These contributions sum to portfolio volatility; their percentage shares sum to 100%.

This calculator uses Σᵢᵢ = σᵢ² and Σᵢⱼ = ρσᵢσⱼ for distinct assets. With the same ρ for every pair, wᵢ = (1/σᵢ) / Σⱼ(1/σⱼ) makes every wᵢσᵢ equal. Therefore inverse volatility and equal risk contribution weights coincide for all accepted correlations. Equal capital weighting assigns 1/n to each asset and is a separate comparison. The underlying definition follows Maillard, Roncalli and Teiletche's equal risk contribution paper and Robeco's analysis of uniform correlations. The calculations below are independently reproducible examples.

Worked example: equal capital versus equal risk

Assume annual volatility of 18% for Stocks and 6% for Bonds, with ρ = 0.2. These are illustrative inputs, not historical estimates. In decimal return units, the covariance matrix has diagonal entries 0.0324 and 0.0036 and off-diagonal entries 0.00216.

Inverse volatilities are 1/18 and 1/6, so normalized weights are 0.25 and 0.75. Variance is 0.25² × 0.18² + 0.75² × 0.06² + 2 × 0.25 × 0.75 × 0.2 × 0.18 × 0.06 = 0.00486. Its square root is 0.0697137. Each volatility contribution is 3.4857 percentage points. Equal capital weights instead produce variance 0.01008 and volatility 10.0399%.

Input quality and invalid correlations

Estimate volatilities from returns using the same dates, sampling frequency, currency and annualization convention. A common annualization is daily standard deviation times the square root of the assumed observations per year; state that assumption. Mixing option-implied volatility with unrelated historical correlations produces a different model, not a consistent historical covariance estimate.

For n assets, the constant correlation matrix has eigenvalues 1 − ρ and 1 + (n − 1)ρ. Positive definiteness requires −1/(n − 1) < ρ < 1. For three assets, ρ = −0.6 is invalid, even though it is between −1 and 1. The lower endpoint can make this model's risk parity variance zero, so percentage risk contributions become undefined. This tool excludes singular endpoints and eigenvalues below 10⁻¹⁰ rather than inventing a risk allocation. Blank, zero, negative or non-finite volatilities also produce an error. One asset has 100% weight and risk share.

Negative contributions in the equal-weight comparison are possible: an asset can offset some of the other assets' modeled risk. Its share is not clamped to zero. Positive weights alone do not guarantee positive contributions for arbitrary correlations and unequal exposures.

Full covariance input is not implemented

This version accepts one common correlation, not a matrix of pairwise values. If your asset pairs have different correlations, use a model that accepts the full covariance matrix. The weights here should not be described as equal risk contributions under that different matrix.

A single average correlation can conceal differences between asset pairs. Changing this field is a sensitivity exercise; it does not fit the covariance matrix to observations. The calculator has no return forecast, short positions, custom risk budgets, leverage target or historical rebalancing engine.

Rebalancing research with TradingView exports

1. Choose an estimation window and rebalance schedule before testing. Calculate target weights using only observations available at each decision time.
2. Apply target weights to subsequent returns and let weights drift between rebalances. Include transaction costs, slippage and any financing costs.
3. Compare equal capital and risk parity over the same period. Check realized volatility, drawdowns, turnover and capital concentration; equal estimated risk does not guarantee equal realized losses.

TradingView exports each Strategy Report tab separately: a List of Trades export contains trades, while a Performance Summary export contains summary metrics. A trade list is not a synchronized return history for several assets. Portfolio covariance research needs returns aligned to common timestamps, including valuation changes while positions remain open. See TradingView's export documentation.

Pineify's Backtest Deep Report analyzes imported trade records and includes profit factor, drawdown and trade statistics. This page calculates risk parity independently; it is not a built-in covariance optimizer in that report. The Pine Script AI Coding Agent can help draft and revise a script for a specified rule. You still need to check the code, data and execution assumptions. Neither workflow here automatically rebalances a live portfolio.

Method and product scope checked October 21, 2026. This tool is for research and education, not investment advice. Estimated volatility does not measure every source of investment risk.

Frequently asked questions