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Identify the stated quantity
A fictional continuously compounded return is 0.10 over one period. It means the logarithm of the growth factor is 0.10. It does not directly mean wealth increased by 10%.
Exponentiate to recover wealth
The growth factor is exp(0.10) ≈ 1.10517092. From initial 100, ending wealth is approximately 110.517092. Simple return is 10.517092%.
| Measure | Value |
|---|---|
| Log return | 0.10 |
| Growth factor | 1.10517092 |
| Simple return | 10.517092% |
Check the other direction
A simple return of 10% has factor 1.10 and log return ln(1.10) ≈ 0.095310. The log value is close for small rates but is not identical. Approximation should be labeled rather than presented as an exact conversion.
Keep complete losses outside finite logs
At a simple return of −100%, terminal wealth is zero. There is no finite real logarithm of zero. Do not replace the undefined log with zero, which would instead describe unchanged wealth.