多期的continuously compounded怎么求？答案对应哪个公式？

An analyst gathers the following one-period continuously compounded returns.

r_0,1 4.2%

r_1,2 3.0%

r_2,3 –1.0%

The continuously compounded return from time t = 0 to time t = 3 is closest to:

1. 6.07%.
2. 6.20%.
3. 6.25%.

Solution

B is correct because "the continuously compounded return to time T is the sum of the one-period continuously compounded returns: r_0,T = r_T−1,T + r_T−2,T−1 + . . . + r_0,1."

In this case, r_0,3 = r_2,3 + r_1,2 + r_0,1 = –1.0% + 3.0% + 4.2% = 6.20%.