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木木RJ · 2021年09月01日

为什么14.4%能得出p=1?

  1. CFA I
  2. Portfolio

NO.PZ2015121801000044

问题如下：

A portfolio manager creates the following portfolio:

If the standard deviation of the portfolio is 14.40%, the covariance between the two securities is equal to:

选项：

A.

0.0006.

B.

0.0240.

C.

1.0000.

解释：

B   is correct.

A portfolio standard deviation of 14.40% is the weighted average, which is possible only if the correlation between the securities is equal to 1.0. If the correlation coefficient is equal to 1.0,then the covariance must equal 0.0240, calculated as:

Cov( R 1 , R 2 )= ρ 12 σ 1 σ 2  =(1.0)(20%)(12%)=2.40%=0.0240.

老师，14.4%推出p=1,这个点还不是很懂？请解惑，谢谢！

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1 个答案

Kiko_品职助教 · 2021年09月01日

嗨，从没放弃的小努力你好：


同学你好，这道题用了比较巧妙的算法，因为通过计算刚好发现给出的组合方差14.40%正好和单个资产乘以相应权重之和相等，从而得出了ρ=1（因为只有ρ=1时这两者才相等），然后直接就可以算cov了。我直接从ρ=1推，这样看更直观，如下图：

（当然这道题完全可以就直接带入组合方差那个公式算，这里只是提供了更快的计算方法）

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NO.PZ2015121801000044 问题如下 A portfolio manager creates the following portfolio:If the stanrviation of the portfolio is 14.40%, the covarianbetween the two securities is equto: A.0.0006. B.0.0240. C.1.0000. is correct.A portfolio stanrviation of 14.40% is the weighteaverage, whiis possible only if the correlation between the securities is equto 1.0. If the correlation coefficient is equto 1.0,then the covarianmust equ0.0240, calculateas: Cov( R 1 , R 2 )= ρ 12 σ 1 σ 2 =(1.0)(20%)(12%)=2.40%=0.0240. 14%^2= 30%^2✖️20%^2+70%^2✖️12%^2+2✖️30%✖️70%✖️covcov算出来=0.1014请问是哪里算错了

2023-12-06 11:34 1 · 回答

NO.PZ2015121801000044 问题如下 A portfolio manager creates the following portfolio:If the stanrviation of the portfolio is 14.40%, the covarianbetween the two securities is equto: A.0.0006. B.0.0240. C.1.0000. is correct.A portfolio stanrviation of 14.40% is the weighteaverage, whiis possible only if the correlation between the securities is equto 1.0. If the correlation coefficient is equto 1.0,then the covarianmust equ0.0240, calculateas: Cov( R 1 , R 2 )= ρ 12 σ 1 σ 2 =(1.0)(20%)(12%)=2.40%=0.0240. 我用了，(w+σ)^2+(w+σ)^2+2w1w2σ1σ2 cov这个公式反推不出来，算出来的结果是0.9901

2022-12-28 12:24 2 · 回答

https://class.pzacamy.com/qa/45937 我看的这里的图，助教的图显示不出来 我想问下“是通过给出的组合方差14.40%正好和单个资产的平方和的形式相等，从而得出了ρ=1” 14.4%等于资产2的方差12%的平方，但是公式 rp^2=(w1*r1)^+(w2*r2)^2+w1*w2*+2*w1*w2*r1*r2*p 我不知道怎么和这个复杂的式子就联系上了呢？ r2^2=0.12^2=14.4% 而rp^2= 14.4%^2=0.020736，完全没关系啊

2020-10-21 16:36 2 · 回答

0.0240. 1.0000. B   is correct. A portfolio stanrviation of 14.40% is the weighteaverage, whiis possible only if the correlation between the securities is equto 1.0. If the correlation coefficient is equto 1.0,then the covarianmust equ0.0240, calculateas: Cov( R 1 , R 2 )= ρ 12 σ 1 σ 2  =(1.0)(20%)(12%)=2.40%=0.0240. 老师，正常是不是要用组合标准差公式到算出相关系数？即，已知组合标准差是14.4%，两个组合的权重和分别的标准差。求相关系数？

2020-06-13 12:04 1 · 回答