Portfolio Risk Parity Calculator
Enter three current weights, annual volatilities, and pairwise correlations to see where portfolio risk is concentrated. The calculator also solves long-only equal-risk weights and translates them into target allocations and rebalance trades.
Current portfolio volatility9.9%
- Largest current risk contributor
- Asset 1 (73.00% of volatility)
- Diversification ratio
- 1.18
- Equal-risk target weights
- Asset 1 17.70%, Asset 2 28.04%, Asset 3 54.26%
- Risk-parity portfolio volatility
- 6.3%
- Maximum risk-budget error
- 0%
Current risk contribution and equal-risk rebalance
| Asset | Current weight | Annual volatility | Current contribution | Current risk share | Equal-risk weight | Target allocation | Rebalance trade |
|---|---|---|---|---|---|---|---|
| Asset 1 | 50% | 15% | 7.23% | 73% | 17.7% | $17,697.24 | -$32,302.76 |
| Asset 2 | 30% | 10% | 2.31% | 23.32% | 28.04% | $28,040.05 | -$1,959.95 |
| Asset 3 | 20% | 6% | 0.36% | 3.67% | 54.26% | $54,262.71 | $34,262.71 |
Risk contributions are component contributions to annualized portfolio volatility; a negative value can occur when covariance provides a hedge.
Target weights are long-only, fully invested, and solved before display rounding. Rebalance trades exclude taxes, transaction costs, and trading constraints.
How to use this calculator
- Enter the total value of the three-asset portfolio; it is used only for allocation and trade amounts.
- Enter the three current weights, which must add to 100%.
- Use annualized volatilities measured with the same return frequency and lookback period.
- Enter the three pairwise correlations, then compare current risk shares with the equal-risk target and trades.
How portfolio risk contribution is calculated
A weight is not the same thing as a risk contribution. A small holding can account for much of a portfolio's volatility when it is volatile or tends to move with the rest of the portfolio. This calculator combines the three entered annual volatilities and correlations into a covariance matrix, then attributes the volatility of the current allocation.
Let w be the vector of decimal portfolio weights, s_i the annual volatility of asset i, and rho_ij the correlation between assets i and j. The covariance entries are Sigma_ii = s_i^2 and Sigma_ij = rho_ij * s_i * s_j. Current portfolio volatility is:
sigma_p = sqrt(w^T * Sigma * w)
The marginal contribution of asset i is (Sigma * w)_i / sigma_p. Its component contribution is w_i * (Sigma * w)_i / sigma_p, and its risk share is that contribution divided by sigma_p. The three component contributions add to portfolio volatility, while the risk shares add to 100% before display rounding.
How the equal-risk target is solved
Equal risk contribution, often called risk parity, asks each asset to contribute one-third of total portfolio variance and volatility. The calculator solves the positive vector x that minimizes 0.5 * x^T * Sigma * x - sum(ln(x_i)), using cyclic coordinate updates, then normalizes it as w_i* = x_i / sum(x_j). At the solution, w_i* * (Sigma * w*)_i is the same for every asset.
The diversification ratio is sum(w_i * s_i) / sigma_p. It compares the current weighted average standalone volatility with portfolio volatility. A value above one reflects the diversification effect of correlations below perfect positive correlation; it is not a forecast of return or protection against loss.
What moves the result and what it leaves out
Volatility estimates and correlations move both the diagnosis and the equal-risk weights. Lower correlations usually reduce portfolio volatility, but negative correlations can also make a current component contribution negative. The calculator rejects correlation combinations that do not form a positive-definite covariance matrix because they do not provide a unique interior equal-risk solution.
This is a covariance model, not a forecast. It does not estimate expected returns, tail dependence, changing regimes, liquidity, leverage, tax lots, transaction costs, account restrictions, or the timing of rebalances. Dollar trades assume all entered value belongs to these three assets and can be traded in fractional amounts.
Worked example
Suppose a $100,000 portfolio is 50% in Asset 1, 30% in Asset 2, and 20% in Asset 3. Their annual volatilities are 15%, 10%, and 6%, with correlations of 60% between Assets 1 and 2, 20% between Assets 1 and 3, and 10% between Assets 2 and 3.
The covariance calculation gives current portfolio volatility of 9.90%. Asset 1 contributes about 7.23 percentage points of volatility, or about 73.0% of total risk; the smaller positions contribute the rest. The solved equal-risk portfolio is about 17.7% in Asset 1, 28.0% in Asset 2, and 54.3% in Asset 3, with volatility of about 6.30%. The table converts those target weights into dollars and shows the amount to buy or sell for each asset.
Common questions
What is portfolio risk contribution?
Portfolio risk contribution is the portion of total portfolio volatility attributed to one holding after its covariance with every other holding is considered. It is not the same as allocation weight. The component contributions add to total portfolio volatility, and their shares add to 100%.
Why can a small holding contribute most of the risk?
A holding can have a large risk contribution when its standalone volatility is high or when it tends to move in the same direction as the other holdings. Correlation matters because it determines how much a holding adds to the portfolio rather than how risky it is by itself.
How is risk parity different from equal weighting?
Equal weighting gives each asset the same dollar weight. Risk parity gives each asset the same contribution to portfolio risk, so lower-volatility or diversifying assets can receive larger weights. The two are only the same under special combinations of volatility and correlation.
Can an asset have a negative risk contribution?
Yes. A holding with sufficiently negative covariance against the rest of the portfolio can reduce total volatility, producing a negative current component contribution. That result describes the entered covariance estimates; it does not mean the asset cannot lose money.
How often should risk-parity weights be recalculated?
Recalculation frequency depends on the strategy, trading costs, tax considerations, and how quickly the volatility and correlation estimates change. Many investors set a regular review schedule and rebalance only when weights drift past practical thresholds. This calculator does not recommend a schedule.