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Lydia · 2020年04月30日

问一道题：NO.PZ2015121810000013

问题如下：

Which of the following pairs of weights would be used to achieve the highest Sharpe ratio and optimal amount of active risk through combining the Indigo Fund and benchmark portfolio, respectively?

选项：

A.

1.014 on Indigo and –0.014 on the benchmark

B.

1.450 on Indigo and –0.450 on the benchmark

C.

1.500 on Indigo and –0.500 on the benchmark

解释：

A is correct.

The optimal amount of active risk is:

{$table2}

The weight on the active portfolio (Indigo) would be 8.11%/8.0% = 1.014 and the weight on the benchmark portfolio would be 1 – 1.014 = – 0.014.

考点：Optimal amount of active risk

解析：Optimal amount of active risk

$\sigma_A=\frac{IR}{SR_B/\sigma_B}=\frac{0.15}{0.333/18\%}=8.11\%$

Indigo Fund现在的active risk是8%，为了使active risk达到最优水平，就将Indigo Fund与benchmark再做组合，形成active risk最优的combined fund。

假设Indigo Fund的权重为c, 那么

$\sigma_A=c\sigma_A^{fund},\;8.11\%=c8\%,\;c=1.014$

因此，benchmark的权重为1-1.014=-0.014

助教让我说明问题. 我来给你写上

1. 原版书公式

2. 品职讲义的公式

3. 这道原版书课后题的原版书解析.

4. 品职题库里面的答案中文解析.

请问助教看出问题了吗? 从讲义到原版书, 后面都是✖️σB, 只有在这个解析里面写成了分母➗σB. 我知道✖️一个数等于➗这个数的倒数, 但是为什么不按着标准的公式写答案解析一定要做一个更复杂更不直观的变形呢??

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星星_品职助教 · 2020年04月30日

同学你好，问题收到，已按原版书修改

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