CFA Level I · CFA Level I Exam · Types of Financial Returns
A portfolio's value falls from 200 to 150 in the first year and then recovers to 200 in the second year. The two-year continuously compounded return and the second-year continuously compounded return are, respectively, closest to:
Log returns are additive and symmetric: the first year is ln(0.75) = -28.77% and the second is +28.77%, so the two-year log return is 0.00% since the value returned to 200. The 33.33% figure is the simple second-year return, not the log return.
- A0.00% and 28.77%Correct
- B0.00% and 33.33%
- C6.25% and 28.77%
Explanation
Year 1 log return = ln(150/200) = -28.77%. Year 2 log return = ln(200/150) = +28.77%. The two-year log return is the sum, 0.00%, because the price ends where it began. The 33.33% option is the simple return in year 2, not the log return.
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