Syntax
COVARIANCE.S(array1, array2)
| Parameter | Description |
|---|---|
| array1 | Parameter of the COVARIANCE.S function. |
| array2 | Parameter of the COVARIANCE.S function. |
Examples
Sample asset covariance
Formula
=COVARIANCE.S(B2:B100, C2:C100)
Returns the sample covariance of two assets' returns from 99 sampled trading days.
Survey data
Formula
=COVARIANCE.S(D2:D500, E2:E500)
Measures the covariance between two survey questions across 499 respondents (a sample of the population).
Compared to population covariance
Formula
=COVARIANCE.S(A2:A20, B2:B20) > COVARIANCE.P(A2:A20, B2:B20)
Returns TRUE — sample covariance (dividing by 19) is always larger in absolute value than population covariance (dividing by 20) for the same data.
Common Errors
#N/A
The two arrays have different lengths.
#DIV/0!
Fewer than 2 data pairs. Sample covariance requires at least 2 paired observations.
Tips
Default choice for most analyses
Unless you have complete population data, COVARIANCE.S is the statistically correct choice. Most business data is sampled.
Difference from COVARIANCE.P
COVARIANCE.S divides by n-1, COVARIANCE.P by n. For large samples (n > 30), the difference becomes negligible.
Building a covariance matrix
For portfolio analysis with multiple assets, compute COVARIANCE.S for each pair to build a covariance matrix. This matrix is the core input for mean-variance optimization.
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