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徐威廉 · 2020年07月28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:

\sigma_A=\frac{IR}{SR_B}\sigma_B=\frac{0.15}{0.333}\times18\%=8.11\%

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

$\sigma_A=\frac{IR}{SR_B}\sigma_B=\frac{0.15}{0.333}\times18\%=8.11\%$

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

本题已知两个条件1.highest shap ratio和 2.optimal active risk，解析答案按照已知条件2 optimal active risk公式求出了新的σ，我按照已知条件1.最高shap ratio得到的σ确是20.54%，为什么？

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丹丹_品职答疑助手 · 2020年07月29日

嗨，努力学习的PZer你好：

同學，本题是先求出optimal active risk，然后根据比率求的权重。一旦权重改变，其information ratio也会变，请知悉

-------------------------------
加油吧，让我们一起遇见更好的自己！

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