Financial Risk Manager Part 1
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A simple return for an investment in a particular holding period is 15%. What is the equivalent continuously compounded return over the same holding period?
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NNikitesh
A
0.1256
B
0.1578
C
0.1398
D
0.1278
Explanation:
The relationship between simple return (R_t) and continuously compounded return (r_t) is given by:
1 + R_t = e^{r_t}
1 + R_t = e^{r_t}
Solving for r_t:
r_t = ln(1 + R_t)
r_t = ln(1 + R_t)
Given R_t = 15% = 0.15:
r_t = ln(1 + 0.15) = ln(1.15) = 0.1398 = 13.98%
r_t = ln(1 + 0.15) = ln(1.15) = 0.1398 = 13.98%
Therefore, the equivalent continuously compounded return is 0.1398 or 13.98%.
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