CFA Level I · CFA Level I Exam · Types of Financial Returns
An analyst converts a holding period return of 10.00% into a continuously compounded return. The continuously compounded return is closest to:
The continuously compounded return equals the natural log of one plus the holding period return. ln(1.10) is 0.0953, so the answer is 9.53%. It is below 10% because continuous compounding reaches the same growth with a smaller rate.
- A9.53%Correct
- B10.00%
- C10.52%
Explanation
The continuously compounded return is ln(1 + 0.10) = ln(1.10) = 0.09531, or 9.53%. The 10.52% figure comes from e^0.10 - 1, which wrongly treats the discrete return as if it were the continuous rate. The continuous return is always lower than the discrete return for a positive return.
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