问一道题：NO.PZ2018070201000061 [ CFA I ]

问题如下：

Laurel, an manager from an investment company, recently constructs the following portfolio, assuming that the correlation of the two securities is -0.8, what is the expected standard deviation if the two assets are equal-weighted:

选项：

4.82%.

5.22%.

5.68%.

解释：

A is correct.

Each stock contains the same weight in the equal-weighted portfolio, so $ω_{1} = ω_{2} = 0.5$

$σ_{p o r t} = \sqrt{{ω_{1}}^{2} {σ_{1}}^{2} + {ω_{2}}^{2} {σ_{2}}^{2} + 2 \cdot ω_{1} ω_{2} \cdot ρ \cdot σ_{1} σ_{2}} = \sqrt{(0.5)^{2} (16 %)^{2} + (0.5)^{2} (12 %)^{2} - 2 \times 0.5 \times 0.5 \times 0.8 \times 16 % \times 12 %} = 4.82 %$

为什么不能用equally-weighted portfolio 的公式？

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1 个答案

星星_品职助教 · 2020年10月15日

同学你好，

可以把你理解的用equally-weighted portfolio 的公式计算的流程列一下，便于分析

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NO.PZ2018070201000061 5.22%. 5.68%. A is correct. Eastocontains the same weight in the equal-weighteportfolio, so ω1=ω2=0.5 lσp=w12σ12+w22σ22+2w1w2σ1σ2∗ρ=0.52(0.16)2+0.52(0.12)2−2×0.5×0.5×0.16×0.12×0.8=4.82%{l}\sigma_p=\sqrt{w_1^2\sigma_1^2+w_2^2\sigma_2^2+2w_1w_2\sigma_1\sigma_2\ast\rho}=\\\sqrt{0.5^2(0.16)^2+0.5^2(0.12)^2-2\times0.5\times0.5\times0.16\times0.12\times0.8}=4.82\%lσp=w12σ12+w22σ22+2w1w2σ1σ2∗ρ =0.52(0.16)2+0.52(0.12)2−2×0.5×0.5×0.16×0.12×0.8 =4.82% 老师，您好，这道题为什么不能求A的方差，即16%*16%=2.56%，B的方差，即12%*12%=1.44%，然后取平均，即(2.56%+1.44%)/2=2%然后用1/2*2%+（2-1）/2*2%*（-0.8)=0.002，得出标准差为4.47%?

2022-08-20 00:02 6 · 回答

NO.PZ2018070201000061 请问题目给的Annureturn有什么用处吗？

2021-11-19 20:23 1 · 回答

老师好，请问用“portfolio of equally weighterisky assets”的方法来求得portfolio的variance是1/2*(16%+12%)/2-1/2*0.8*16%*12%=0.06232, 得S0.24，为什么用这个方法不对呢？

2020-08-23 20:35 2 · 回答

5.22%. 5.68%. A is correct. Eastocontains the same weight in the equal-weighteportfolio, so ω1=ω2=0.5 σport=ω12σ12+ω22σ22+2·ω1ω2·ρ·σ1σ2=(0.5)2(16%)2+(0.5)2(12%)2-2×0.5×0.5×0.8×16%×12%=4.82% 请问，直接用equweighte公式做，这个算前半部分对吗？

2020-05-24 22:46 1 · 回答

问一道题：NO.PZ2018070201000061 [ CFA I ]

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