Two-Asset Min-Variance Weight Calculator
From two assets' volatility and correlation, solve analytically for the weight of A that minimizes portfolio volatility and that minimum itself.
Results
Fill in the inputs and click Calculate.
- Optimal A Weight
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- Optimal B Weight
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- Min Portfolio Vol
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Risk disclaimer
Volatility and correlation are inputs or estimates; results are pure quadratic math, not executable advice.
Why is there an optimal weight?
Diversification makes portfolio volatility vary with the weights, and a minimum exists (the vertex of a quadratic).
Unconstrained results can go negative or above 100%, meaning shorting one side or leveraging the mix.
How to use
- Enter both assets' annualized volatility %.
- Enter the correlation (-1 to 1, default 0).
- Click Calculate for the weight and volatility at the minimum.
Formula
- Optimal A weight = (σB² − ρ·σA·σB) ÷ (σA² + σB² − 2ρ·σA·σB)
- B weight = 1 − A weight
- Min volatility = √(portfolio variance at that weight)
Example
σA 20%, σB 10%, ρ=0 → optimal A weight 0% (all in B), min volatility 10%.
With ρ=−0.5 the optimal A is ≈28.6% and the minimum drops sharply.
FAQ
Why can weights be below 0 or above 100?
The analytic solution does not ban shorting; add your own constraints if you want weights within 0–100%.
Relation to the two-asset volatility tool?
That computes volatility for given weights; this page finds the minimizing weights — complements it.