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投資組合優(yōu)化,,,多資產(chǎn),,,,,

輸入,,,,,,,,

,,預(yù)期收益率,標(biāo)準(zhǔn)差,1+E（r）,百分百,,,

無風(fēng)險(xiǎn)利率（r）,,4.0%,0.0%,104.0%,,,,

風(fēng)險(xiǎn)資產(chǎn)1,,8.0%,20.0%,108.0%,100.0%,,,

風(fēng)險(xiǎn)資產(chǎn)2,,9.0%,20.0%,109.0%,100.0%,,,

風(fēng)險(xiǎn)資產(chǎn)3,,10.0%,20.0%,110.0%,100.0%,,,

風(fēng)險(xiǎn)資產(chǎn)4,,11.0%,20.0%,111.0%,100.0%,,,

風(fēng)險(xiǎn)資產(chǎn)5,,12.0%,20.0%,112.0%,100.0%,,,

,,,,,,,,,

,,,相關(guān)系數(shù),,,,,

,1,2,3,4,5,,,

1,1.0,0.0,0.0,0.0,0.0,,,

2,0.0,1.0,0.0,0.0,0.0,,,

3,0.0,0.0,1.0,0.0,0.0,,,

4,0.0,0.0,0.0,1.0,0.0,,,

5,0.0,0.0,0.0,0.0,1.0,,,

,,,,,,,,,

,,,標(biāo)準(zhǔn)差,,,,,

,1,2,3,4,5,,,

,20.0%,20.0%,20.0%,20.0%,20.0%,,,

,,,,,,,,,

,,,方差與協(xié)方差,,,,,

,1,2,3,4,5,,,

1,4.00%,0.00%,0.00%,0.00%,0.00%,,,

2,0.00%,4.00%,0.00%,0.00%,0.00%,,,

3,0.00%,0.00%,4.00%,0.00%,0.00%,,,

4,0.00%,0.00%,0.00%,4.00%,0.00%,,,

5,0.00%,0.00%,0.00%,0.00%,4.00%,,,

,,,,,,,,,

輸出,,,,,,,,

,A,125,,,,,,

,B,137.5,,,,,,

,C.,151.275,,,,,,

,Delta,3.125,,,,,,

,Gamma,0.133333333,,最小方差,有效集直線單個(gè)資產(chǎn),,,

,,,,邊界預(yù)期,預(yù)期,預(yù)期,,切點(diǎn)處組合

,,指數(shù),標(biāo)準(zhǔn)差,收益率,收益率,收益率,,的最優(yōu)權(quán)重

風(fēng)險(xiǎn)資產(chǎn)1,,,20.0%,,,8.0%,,13.3%

風(fēng)險(xiǎn)資產(chǎn)2,,,20.0%,,,9.0%,,16.7%

風(fēng)險(xiǎn)資產(chǎn)3,,,20.0%,,,10.0%,,20.0%

風(fēng)險(xiǎn)資產(chǎn)4,,,20.0%,,,11.0%,,23.3%

風(fēng)險(xiǎn)資產(chǎn)5,,,20.0%,,,12.0%,,26.7%

最小方差組合邊界,,0,25.00%,6.3%,,,,

最小方差組合邊界,,1,22.84%,6.7%,,,,

最小方差組合邊界,,2,20.71%,7.0%,,,,

最小方差組合邊界,,3,18.63%,7.4%,,,,

最小方差組合邊界,,4,16.62%,7.8%,,,,

最小方差組合邊界,,5,14.71%,8.2%,,,,

最小方差組合邊界,,6,12.93%,8.5%,,,,

最小方差組合邊界,,7,11.36%,8.9%,,,,

最小方差組合邊界,,8,10.09%,9.3%,,,,

最小方差組合邊界,,9,9.24%,9.6%,,,,

最小方差組合邊界,,10,8.94%,10.0%,,,,

最小方差組合邊界,,11,9.24%,10.4%,,,,

最小方差組合邊界,,12,10.09%,10.7%,,,,

最小方差組合邊界,,13,11.36%,11.1%,,,,

最小方差組合邊界,,14,12.93%,11.5%,,,,

最小方差組合邊界,,15,14.71%,11.8%,,,,

最小方差組合邊界,,16,16.62%,12.2%,,,,

最小方差組合邊界,,17,18.63%,12.6%,,,,

最小方差組合邊界,,18,20.71%,13.0%,,,,

最小方差組合邊界,,19,22.84%,13.3%,,,,

最小方差組合邊界,,20,25.00%,13.7%,,,,

最優(yōu)風(fēng)險(xiǎn)組合,,,9.2%,,10.3%,,,

有效集直線,,0.0%,0.0%,,4.0%,,,

有效集直線,,100.0%,9.2%,,10.3%,,,

有效集直線,,200.0%,18.4%,,16.7%,,,

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