Portfolio variance calculator

Find the risk of a two-asset portfolio from its weights, volatilities and correlation.

Enter your portfolio

Example values shown. Results update as you type.

Asset A weight

Asset B weight: 50%.

Correlation

From −1 to +1.

Asset A volatility

Standard deviation of returns.

Asset B volatility

Use the same period as asset A.

Portfolio volatility

Standard deviation of combined returns.

11.18%

Variance (decimal returns): 0.0125
Diversification benefit: 3.82 pp

How this is calculated

Variance = wA² × σA² + wB² × σB² + 2 × wA × wB × σA × σB × correlation. Volatility is the square root of variance.

Asset A weight: 50%. Asset B weight: 50%.

Portfolio variance: 0.0125. Its square root gives 11.18% volatility.

Weights total 100% and short positions are excluded. Use volatilities measured over the same period. Diversification benefit is the weighted-average volatility minus portfolio volatility, in percentage points. The variance identity does not require normally distributed returns; the inputs still have to describe the same return distribution.

Reference: CISI · Portfolio construction theory

How to use this calculator

Enter the share held in asset A. Asset B automatically receives the remaining weight, so the two weights total 100%.
Enter each asset’s return volatility and their correlation. Both volatilities must use the same time period.
Read portfolio volatility and variance. Change the correlation to see how it affects diversification.

Example: two equally weighted assets

Use Reset example to reproduce these inputs.

Asset A / asset B weights: 50% / 50%
Asset A / asset B volatility: 20% / 10%
Correlation: 0

Portfolio volatility: 11.18%

With decimal returns, variance is 0.5² × 0.2² + 0.5² × 0.1² = 0.0125. Its square root is about 0.1118, or 11.18% volatility. The weighted-average volatility is 15%, so the diversification benefit is about 3.82 percentage points.

Frequently asked questions

What does a portfolio variance of 0.0125 mean?

Variance uses squared decimal-return units. Take its square root to get standard deviation: √0.0125 is about 0.1118, or 11.18%. If you entered annual volatilities, that is annual portfolio volatility; if you entered monthly volatilities, it is monthly volatility.

Can I mix daily and annual volatilities?

Use the same period for both assets, with a correlation estimated from compatible return observations. Mixing daily and annual inputs produces a number without a consistent risk interpretation. Converting between periods requires assumptions about how returns behave over time.

How does correlation change portfolio risk?

For the example weights and volatilities, correlation +1 gives 15% portfolio volatility, correlation 0 gives about 11.18%, and correlation −1 gives 5%. Lower correlation reduces the covariance contribution while the weights and individual volatilities stay fixed.

Can I enter short positions or more than two assets?

This calculator supports two assets with nonnegative weights totaling 100%. Short positions, leverage and larger portfolios need a more general set of weights and covariances. The displayed result describes the inputs you provide; it does not estimate volatilities or correlations from market data.

Want to understand the calculation?

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