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Portfolio variance and volatility unit labels

Variance and covariance use squared-return units; standard deviation returns to the original return scale.

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Compare two representations

Decimal-return variance 0.01288 is 128.8 percentage points squared. Its square root is decimal standard deviation 0.113490..., or approximately 11.349%. Multiplying variance by 100 instead of 10,000 gives the wrong squared-unit conversion.

Add compatible quantities

Variance components must use the same squared-return basis. A 20% standard deviation cannot be added directly to decimal variance 0.0036. Square, weight and convert according to the stated formula before aggregating.

Original unit labels
QuantityDecimal unitsPercentage representation
Variance0.01288128.8 percentage points²
Standard deviation0.113490...11.3490%
Covariance0.00660 percentage points²

Keep volatility contributions labeled

Weighted volatility contributions are in the return scale, often shown as percentage points. Variance contributions use squared units. The same word contribution does not make them interchangeable.

Use an inverse conversion

Divide the squared-unit result by 10,000 and take the square root to reproduce the decimal standard deviation. This check helps identify a unit error before a result is interpreted as risk.

Further references