方差的平方=（资产1方差平方+资产2方差平方）/2

NO.PZ2015121801000062

问题如下：

A portfolio manager creates the following portfolio:

If the two securities are uncorrelated, the expected standard deviation of an equal-weighted portfolio is closest to:

选项：

14.00%.

14.14%.

20.00%.

解释：

B is correct.

${l}{\sigma _{port}} = \sqrt {w_1^2\sigma _1^2 + w_2^2\sigma _2^2 + 2{w_1}{w_2}{\rho _{1,2}}{\sigma _1}{\sigma _2}} \\ = \sqrt {{{(0.5)}^2}{{(20\% )}^2} + {{(0.5)}^2}{{(20\% )}^2} + 2(0.5)(0.5)(0.00)(20\% )(20\% )} \\ = {(1.0000\% + 1.0000\% + 0.0000\% )^{0.5}} = {(2.0000\% )^{0.5}} = 14.14\%$

这道题可以用之前讲的多个资产，求方差的公式么？

那个的假设也是没个资产的权重都是一样，刚好和这道题相同

方差的平方=（资产1方差平方+资产2方差平方）/2

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已采纳答案

Kiko_品职助教 · 2023年11月22日

嗨，从没放弃的小努力你好：

你说的这是什么公式啊？是这个吗？这个公式我们一般用于定性判断多一些，像这种计算题，我们还是按照最原始的计算公式来算。

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

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NO.PZ2015121801000062问题如下A portfolio manager creates the following portfolio:If the two securities are uncorrelate the expectestanrviation of equal-weighteportfolio is closest to:A.14.00%.B.14.14%.C.20.00%.is correct.lσport=w12σ12+w22σ22+2w1w2ρ1,2σ1σ2=(0.5)2(20%)2+(0.5)2(20%)2+2(0.5)(0.5)(0.00)(20%)(20%)=(1.0000%+1.0000%+0.0000%)0.5=(2.0000%)0.5=14.14%{l}{\sigma _{port}} = \sqrt {w_1^2\sigma _1^2 + w_2^2\sigma _2^2 + 2{w_1}{w_2}{\rho _{1,2}}{\sigma _1}{\sigma _2}} \\ = \sqrt {{{(0.5)}^2}{{(20\% )}^2} + {{(0.5)}^2}{{(20\% )}^2} + 2(0.5)(0.5)(0.00)(20\% )(20\% )} \\ = {(1.0000\% + 1.0000\% + 0.0000\% )^{0.5}} = {(2.0000\% )^{0.5}} = 14.14\% lσport=w12σ12+w22σ22+2w1w2ρ1,2σ1σ2=(0.5)2(20%)2+(0.5)2(20%)2+2(0.5)(0.5)(0.00)(20%)(20%)=(1.0000%+1.0000%+0.0000%)0.5=(2.0000%)0.5=14.14%想象成了完全相同的两个资产，他们也不相关，应该没有分散效应啊，为啥不能直接理解成组合标准差保持一样

2023-09-22 17:23 1 · 回答

NO.PZ2015121801000062问题如下 A portfolio manager creates the following portfolio:If the two securities are uncorrelate the expectestanrviation of equal-weighteportfolio is closest to:A.14.00%.B.14.14%.C.20.00%.is correct.lσport=w12σ12+w22σ22+2w1w2ρ1,2σ1σ2=(0.5)2(20%)2+(0.5)2(20%)2+2(0.5)(0.5)(0.00)(20%)(20%)=(1.0000%+1.0000%+0.0000%)0.5=(2.0000%)0.5=14.14%{l}{\sigma _{port}} = \sqrt {w_1^2\sigma _1^2 + w_2^2\sigma _2^2 + 2{w_1}{w_2}{\rho _{1,2}}{\sigma _1}{\sigma _2}} \\ = \sqrt {{{(0.5)}^2}{{(20\% )}^2} + {{(0.5)}^2}{{(20\% )}^2} + 2(0.5)(0.5)(0.00)(20\% )(20\% )} \\ = {(1.0000\% + 1.0000\% + 0.0000\% )^{0.5}} = {(2.0000\% )^{0.5}} = 14.14\% lσport=w12σ12+w22σ22+2w1w2ρ1,2σ1σ2=(0.5)2(20%)2+(0.5)2(20%)2+2(0.5)(0.5)(0.00)(20%)(20%)=(1.0000%+1.0000%+0.0000%)0.5=(2.0000%)0.5=14.14%为何不能用50%*16%+50%*12%算出A，错在哪里？uncorrelate定说明相关系数＝0嘛？

2023-03-20 16:36 1 · 回答

NO.PZ2015121801000062 A portfolio manager creates the following portfolio: If the two securities are uncorrelate the expectestanrviation of equal-weighteportfolio is closest to: A 14.00%. B 14.14%. C 20.00%.

2022-01-08 16:04 1 · 回答

NO.PZ2015121801000062 14.14%. 20.00%. B is correct. lσport=w12σ12+w22σ22+2w1w2ρ1,2σ1σ2=(0.5)2(20%)2+(0.5)2(20%)2+2(0.5)(0.5)(0.00)(20%)(20%)=(1.0000%+1.0000%+0.0000%)0.5=(2.0000%)0.5=14.14%{l}{\sigma _{port}} = \sqrt {w_1^2\sigma _1^2 + w_2^2\sigma _2^2 + 2{w_1}{w_2}{\rho _{1,2}}{\sigma _1}{\sigma _2}} \\ = \sqrt {{{(0.5)}^2}{{(20\% )}^2} + {{(0.5)}^2}{{(20\% )}^2} + 2(0.5)(0.5)(0.00)(20\% )(20\% )} \\ = {(1.0000\% + 1.0000\% + 0.0000\% )^{0.5}} = {(2.0000\% )^{0.5}} = 14.14\% lσport=w12σ12+w22σ22+2w1w2ρ1,2σ1σ2 =(0.5)2(20%)2+(0.5)2(20%)2+2(0.5)(0.5)(0.00)(20%)(20%) =(1.0000%+1.0000%+0.0000%)0.5=(2.0000%)0.5=14.14%是用不到的么迷惑我们的么

2021-06-10 22:53 2 · 回答

方差的平方=（资产1方差平方+资产2方差平方）/2

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