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little_back · 2020年05月17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

请问老师，题目中由于是在benchmark (SP500)和active portfolio (Indigo Fund之)间配置，是不是可以理解组合的IR就和active portfolio的IR相等？

由于组合的SP²=IC²+active portfolio的SP²，因此组合的SP根本不变？不存在最大的SP一说，本题目只是为了求一个optimal 的risk，是这样吗？

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丹丹_品职答疑助手 · 2020年05月18日

嗨，从没放弃的小努力你好：

同学你好，我们认为sharp ratio 和information ratio 是不变的。因为我们可以通过调整cash的比例找到适合每个投资者的最大的sharp ratio，在本题中我们认为sharp ratio for benmark 是0.3333。根据公式σA=SRBIRσB。求得最优σA。从而求得权重。请知悉。

-------------------------------
虽然现在很辛苦，但努力过的感觉真的很好，加油！

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