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Read the supplied duration
The fictional observation covers one equal quarter, treated as one fourth of a year. Starting index 100 ends at 102. The observed change is 2%, and the historical record contains only that one quarter.
Apply the rate conversion
An annual-equivalent factor is 1.02⁴ = 1.08243216, giving 8.243216%. Multiplying the quarterly percentage by four gives 8%, a simple annualization rather than the geometric conversion.
| Measure | Value | Meaning |
|---|---|---|
| Observed quarterly return | 2% | Change actually supplied |
| Simple annualized rate | 8% | Four times the quarterly percentage |
| Geometric annual equivalent | 8.243216% | Compound rate conversion |
Avoid inventing three later observations
The power of four is a convention-matched conversion. It does not show that three future quarters actually earned 2% or will do so. A chart extending observed wealth to later quarters would need an explicit scenario label.
Use another exponent for another horizon
For a three-year cumulative factor, the annual exponent is one third. For a month treated as one twelfth of a year, it is twelve. Retain the stated time convention instead of inferring duration from the number of rows.