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Find which operation is intended
A 2% quarterly rate can be described as 8% under simple annual scaling or 8.243216% under geometric annual equivalence. The same input therefore supports different outputs with different labels. Neither is four observed future quarters.
Retain compounding when required
The geometric expression is (1.02)^4−1. The simple expression is 4×0.02. Calling the second expression an exact compound annual rate drops the interaction of successive growth.
| Method | Expression | Rate |
|---|---|---|
| Simple | 4 × 2% | 8% |
| Geometric | 1.02⁴ − 1 | 8.243216% |
Read the horizon before the exponent
A two-year cumulative return is not multiplied by two to become annual. Its growth factor is raised to one half. For uneven dates, explicitly supply the elapsed-year convention rather than using the number of observations as the horizon.
Keep the measure beside the number
Label observed holding-period return, simple annualized rate or geometric annual equivalent. This lets a reader compare like with like and prevents an arithmetic conversion from being mistaken for a prediction.