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Feeling · 2020年02月09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.

We can demonstrate that these weights achieve the maximum Sharpe ratio (of 0.365). Note that 8.11% is the optimal level of active risk, and that Indigo has an expected active return of 1.014(1.2%) = 1.217% over the benchmark (and a total excess return of 6.0% + 1.217% = 7.217%. The portfolio total risk is

$STD{(R_P)}^2=STD{(R_B)}^2+STD{(R_A)}^2=18.0^2+8.111^2=389.788$

Taking the square root, $STD(R_P)$ = 19.743, and the optimal Sharpe ratio is indeed 7.217/19.743 = 0.365.

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

请问老师，题干说想要得到最高SR和optimal acitve risk。

是可以得到optimal active risk，可是就算改变avive risk不改变IR，因此还是无法达到最高的SR呀。

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星星_品职助教 · 2020年02月10日

同学你好，

这道题主要还是针对于optimal acitve risk的。可以理解为，在达到optimal acitve risk的时候，这个时候的SR就是最大的SR

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wenxing · 2020年03月04日

σ A = I R S R B / σ B = 0.15 0.333 / 18 % = 8.11 % σA=SRB/σBIR=0.333/18%0.15=8.11% 这里按照课本公式不应该是除以delta B的，应是乘以啊？

星星_品职助教 · 2020年03月05日

同学你好，如果有自己的问题可以单独提问

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