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On the percentage-number scale, covariance is −18 and the standard deviations are 6 and 5. The denominator is 6×5 = 30, so correlation is −18/30 = −0.6. The covariance magnitude 18 is below its maximum possible magnitude of 30 under the stated standard deviations.
Recalculate on a decimal-return scale
| Scale | Covariance | Standard deviations | Correlation |
|---|---|---|---|
| Percentage-number | −18 | 6 and 5 | −18/(6×5) = −0.6 |
| Decimal-return | −0.0018 | 0.06 and 0.05 | −0.0018/(0.06×0.05) = −0.6 |
Identify the missing factor
Dividing −18 by only 5 gives −3.6; dividing by only 6 gives −3. Neither is a standardized correlation. Dividing by 6 + 5 gives approximately −1.6364, also outside the correlation range. The denominator needs the product of both standard deviations.
Interpret the sign without claiming a fixed slope
The negative sign indicates negative linear co-movement under this model or dataset. Correlation −0.6 does not mean one asset falls exactly 0.6% whenever the other rises 1%. A regression slope depends on scale and a specified model.