CFA Level I · CFA Level I Exam · Types of Financial Returns
An investment rises from 80 to 100 in one year and the next year falls to 90. Compared with the discrete two-year holding period return, the two-year continuously compounded return is most likely:
The continuously compounded return is the natural log of ending over beginning value: ln(90/80) = 11.78%. The discrete return is 12.50%. For a positive return the log return is always smaller than the discrete return, so the continuous figure is lower.
- Aequal to 12.50%
- Blower, at about 11.78%Correct
- Chigher, at about 13.35%
Explanation
The two-year holding period return is 90/80 - 1 = 12.50%. The continuous return is ln(90/80) = ln(1.125) = 0.1178, or 11.78%, which is lower. Adding the yearly logs gives ln(1.25) + ln(0.90) = 0.2231 - 0.1054 = 0.1178, confirming the result. The 13.35% option is not supported by any valid computation.
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