This is the mathematical foundation of diversification: combining two assets that don’t move in lockstep produces a portfolio with less risk than a simple weighted average of the two assets’ individual risks.
How it works
Each asset’s variance is weighted by the square of its portfolio weight, then a covariance term (correlation times both standard deviations, weighted by both portfolio weights) is added — the classic Markowitz two-asset variance formula.
What this does not include
This does not include portfolios of more than two assets, which require a full covariance matrix rather than this simplified two-asset formula, or the efficient frontier optimization that finds the ideal weighting to minimize risk for a given return.
How to use this calculator
- Enter the weight and standard deviation of each asset, plus the correlation between them.
Frequently asked questions
Why does a lower correlation reduce portfolio risk?
When two assets don’t move together, one’s decline is often at least partly offset by the other’s stability or gain, smoothing out the combined portfolio’s swings compared to either asset alone.
What happens if correlation is exactly 1.0?
Diversification benefit disappears entirely — the portfolio’s risk becomes exactly the simple weighted average of the two assets’ individual risks, since they always move together.
Can portfolio variance ever be lower than either individual asset’s variance?
Yes — with a low enough (especially negative) correlation, the combined portfolio can actually have less risk than either asset held alone.
