Two-Asset Portfolio Volatility Calculator
Combine two assets’ weights, volatilities and correlation into the portfolio’s true volatility — and see the diversification benefit in numbers.
How it works
σₚ = √( wA²σA² + wB²σB² + 2·wA·wB·σA·σB·ρ ) · Diversification benefit = weighted-average σ − σₚ
A two-asset portfolio’s volatility is not the simple weighted average of the two volatilities — the correlation term pulls it down whenever the assets are less than perfectly correlated. That reduction is the diversification benefit: the same expected return with a smoother ride. The lower (or more negative) the correlation, the bigger the gap between the naive average and the true portfolio volatility.
Worked example
Hold 60% in Asset A at 15% volatility and 40% in Asset B at 8%, with a 0.2 correlation. The variance is 0.36×225 + 0.16×64 + 2×0.6×0.4×15×8×0.2 = 81 + 10.24 + 11.52 = 102.76, so portfolio volatility is about 10.14%. The weighted average would be 12.2%, so diversification shaves off roughly 2.06 points.
Frequently asked questions
Why is portfolio volatility lower than the average?
Because the two assets rarely move in perfect sync. When one dips while the other holds up, their swings partly cancel, so the combined volatility falls below the weighted average — the mathematical core of diversification.
What if the correlation is 1?
At a correlation of +1 the assets move in lockstep and the cross term is at its maximum, so portfolio volatility equals the weighted average exactly — there is no diversification benefit at all.
Can adding a volatile asset lower portfolio risk?
Yes. If a volatile asset has low or negative correlation with the rest, a modest allocation can reduce overall portfolio volatility, because its independent swings offset the others rather than adding to them.
Related calculators
Educational estimate, not investment advice. Trading involves risk of loss.