How to use the minimum variance and risk parity weights calculator
- List each asset on its own line with its annual volatility in percent, for example "Stocks, 18".
- Choose one correlation for all pairs, or switch to a full matrix and enter one row per line.
- Read the three sets of weights: minimum variance with short positions allowed, long-only minimum variance and risk parity.
- Check the risk table to confirm that under risk parity each asset adds the same share of the portfolio variance.
Formula
Covariance(i, j) = volatility i x volatility j x correlation(i, j)
Minimum variance weights = inverse covariance x 1 / (1 x inverse covariance x 1)
Long only: the lowest variance with every weight at least 0 and the weights adding to 1
Risk parity: weights where weight i x (covariance x weights)i is the same for every asset
The long-only answer is found by checking every mix of assets that could be held and keeping the one with the lowest variance. Asset limits are 2 to 10.
Three assets with 10%, 20% and 30% volatility
With a correlation of 0.3 between every pair, the unconstrained minimum variance weights are 89.79%, 10.69% and -0.48%. The last asset is a small short position, and the portfolio volatility is 9.786%.
The long-only solution drops it: 89.47%, 10.53% and 0.00%, with volatility 9.787%. Risk parity gives 54.55%, 27.27% and 18.18%, which is the inverse of the volatilities because the correlation is equal, and its volatility is 11.950%.
Three different goals
Minimum variance finds the mix with the lowest volatility whatever the returns. It leans heavily on the least volatile asset and on assets that are weakly correlated with it. It can use short positions, which a long-only investor cannot, so the long-only column gives the best mix without them.
Risk parity aims for equal risk instead. It holds more of the calm assets and less of the volatile ones so that each contributes the same share of the variance. It does not minimize risk, and its volatility is usually higher than the minimum.
Limits of a weights calculator
The result depends only on the volatilities and correlations you type. Estimates from history are noisy, and a small change in a correlation can move the weights a lot, especially with many assets. There are no expected returns here, so the mix says nothing about reward.
Taxes, trading costs and limits on position size are also left out. Use this to understand how the risk of a mix depends on its parts, not as advice to buy or sell.
Assumptions and limits
- The covariance matrix must be positive definite. The page reports when your correlations cannot all hold at once.
- Volatilities are annual percentages above 0.
- Weights are fully invested and add to 100%.
- The assets and figures are examples. Nothing is uploaded.
Frequently asked questions
Why is one weight negative?
The unconstrained solution is allowed to short an asset. If that is not possible for you, use the long-only column.
Why do risk parity weights equal the inverse volatilities here?
When every pair has the same correlation, equal risk contributions are reached by weights proportional to one over the volatility.
How many assets can I use?
From 2 to 10. The long-only search checks every subset, which stays quick at that size.
What does it mean when my correlations are rejected?
Some sets of correlations cannot occur together. For example, three assets cannot all have a correlation of -0.9 with each other.