CFA Level I · CFA Level I Exam · Returns of Financial Assets and Instruments
An analyst has a monthly return of 1.5% and wants to state the annualized return with compounding. Which approach is most appropriate?
The most appropriate approach is to raise one plus the monthly return to the power of 12 and subtract 1. This compounds twelve monthly periods into one year. Simple multiplication ignores compounding, and the 1/12 exponent converts an annual return into a monthly one.
- AMultiply 1.5% by 12
- BRaise (1 + 0.015) to the power of 12 and subtract 1Correct
- CRaise (1 + 0.015) to the power of 1/12 and subtract 1
Explanation
Compounding 12 monthly periods gives (1.015)^12 − 1, about 19.56%. Multiplying by 12 gives 18%, which ignores compounding. Raising to 1/12 would convert an annual return to a monthly one, the wrong direction.
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