How this calculation works
Portfolio volatility depends on how asset returns move together, not just the average of individual volatilities. Covariance combines each standard deviation with the corresponding pairwise correlation. This page computes portfolio variance and attributes total standard deviation to its assets under entered weights. It keeps risk contributions separate from capital weights because they generally are not the same.
Variance = w transpose Σ w; component volatility i = wi(Σw)i / portfolio SDA worked example
Two equally weighted assets with twenty-percent annualized volatility and zero correlation have variance 0.5²×0.2² twice, or 0.02. Portfolio volatility is about 14.1421 percent. The weighted standalone volatility is twenty percent, illustrating the distinction between averaging volatilities and combining covariance. Perfect positive correlation removes that particular diversification reduction.
Good to know
All volatilities and correlations are entered, not estimated from prices. Their uncertainty, nonstationarity, leverage, liquidity and tail dependence are outside the calculation. No expected return, value-at-risk estimate or recommended allocation is produced. Historical covariance, when used as an input, does not guarantee future diversification.
Reference: MIT — portfolio covariance and diversification (opens in a new tab) ↗
What this calculation answers
Portfolio volatility depends on how asset returns move together, not just the average of individual volatilities. Covariance combines each standard deviation with the corresponding pairwise correlation.
This page computes portfolio variance and attributes total standard deviation to its assets under entered weights. It keeps risk contributions separate from capital weights because they generally are not the same.
The Portfolio rebalance trades with cash contribution calculator creates exact value trades toward entered weights. Risk contributions can differ from those capital weights even after a rebalance.
Use the right input conventions
Weights must be nonnegative and sum to one hundred percent. Volatilities must describe the same annualized return convention and horizon. Correlation rows and columns follow the asset order exactly.
A correlation matrix needs symmetry, ones on the diagonal and positive semidefiniteness. Pairwise values between minus one and one alone are not enough to form a valid multivariate correlation structure.
Interpret the result
Component standard-deviation contributions sum to portfolio standard deviation when it is nonzero. A contribution may be negative when an asset offsets other risk, even with positive capital weights.
A zero-variance singular hedge is permitted mathematically and reports zero component volatility contributions. It does not establish that a real hedge is stable, affordable or free of other risks.
Work through the example
Two equally weighted assets with twenty-percent annualized volatility and zero correlation have variance 0.5²×0.2² twice, or 0.02. Portfolio volatility is about 14.1421 percent.
The weighted standalone volatility is twenty percent, illustrating the distinction between averaging volatilities and combining covariance. Perfect positive correlation removes that particular diversification reduction.
Where the model stops
All volatilities and correlations are entered, not estimated from prices. Their uncertainty, nonstationarity, leverage, liquidity and tail dependence are outside the calculation.
No expected return, value-at-risk estimate or recommended allocation is produced. Historical covariance, when used as an input, does not guarantee future diversification.
A few questions, answered
Why check the complete matrix rather than just each correlation?
Pairwise plausible correlations can still be mutually inconsistent and imply negative variance for some combination.
What changes in the comparison?
Make the two assets perfectly positively correlated and inspect the lost volatility reduction.