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Square the return-scale conversion
A return written as 6% can be represented numerically as 6 in percentage-number units or as 0.06 in decimal-return units. The factor between the representations is 100. Since variance squares deviations, its conversion factor is 100².
Convert a complete set of moments
| Statistic | Percentage-number representation | Decimal-return representation |
|---|---|---|
| Mean | 6.2 | 0.062 |
| Variance | 33.96 | 0.003396 |
| Standard deviation | Approximately 5.8275 | Approximately 0.058275 |
Do not attach a percentage sign to variance directly
A variance of 49 in squared percentage-point units has standard deviation 7%. A decimal-return variance of 0.0049 has standard deviation 0.07, again 7%. Reporting the variance itself as 49% would confuse a squared-unit quantity with an ordinary return-scale quantity.
Keep covariance and standard deviations on the same basis
When calculating correlation from covariance, its numerator and denominator must use matching scales. Converting the standard deviations to decimals without also converting covariance creates a factor-of-10,000 error.