No.PZ2022071202000017 (选择题)

问题如下：

Question

A portfolio provides the following returns over a five-year period.

The compound rate of return of the portfolio across the five-year period is closest to:

选项：

A.0.02%. B.1.00%. C.-9.31%.

解释：

Solution

A is correct. The geometric mean return is the correct approach to calculate portfolio average returns across a period of time:$R_G={\left[\prod _{t=1}^T\left(1+R_t\right)\right]}^{1/T}?1$ where

R_G = the geometric mean return

T = 5 and is the length of the period

t = the index of time (i.e., t = 1 for Year 1, t = 2 for Year 2, …)

R_t = the return during period t

In this problem, the geometric mean return is:

R_G = [(1 + 0.10) × (1 - 0.25) × (1 + 0.08) × (1 + 0.05) × (1 + 0.07)]^1/5 - 1

= (1.10 × 0.75 × 1.08 × 1.05 × 1.07)^1/5 -1

= 0.02%.

B is incorrect. It is the arithmetic average: (0.10 - 0.25 + 0.08 + 0.05 + 0.07)/5 = 1.00%.

C is incorrect. It is the geometric mean of the given values (i.e., does not add 1 to each return): (0.10 × -0.25 × 0.08 × 0.05 × 0.07)^1/5 = -9.31%: it also ignores the negative sign inside the brackets, but applies it to the answer.