为什么单一Portfolio的return计算不用时间加权分子的Cash flow，但是求composite的时候，分子需要？

NO.PZ2022010601000004 问题如下 A Singapore equity composite contains three portfolios whose cash flow weighting factors are follows.A Calculate the returns of Portfolio Portfolio anPortfolio for the month of July using Mofieetz formula.B Calculate the July composite return asset-weighting the inviportfolio returns using beginning-of-periovalues.C Calculate the July composite return asset-weighting the inviportfolio returns using a methothreflects both beginning-of-periovalues anexterncash flows. A Portfolio returns:rA=91−80−980+（0.516×9）=284.64=0.0236=2.36%r_A=\frac{91-80-9}{80+（0.516\times9）}=\frac2{84.64}=0.0236=2.36\%rA​=80+（0.516×9）91−80−9​=84.642​=0.0236=2.36%rB=105−130−（−20）130+（−20×0.677）=−5116.46=−0.0429=−4.29%r_B=\frac{105-130-（-20）}{130+（-20\times0.677）}=\frac{-5}{116.46}=-0.0429=-4.29\%rB​=130+（−20×0.677）105−130−（−20）​=116.46−5​=−0.0429=−4.29%rB=135−115−15115+（15×0.323）=5119.85=0.0417=4.17%r_B=\frac{135-115-15}{115+（15\times0.323）}=\frac5{119.85}=0.0417=4.17\%rB​=115+（15×0.323）135−115−15​=119.855​=0.0417=4.17% B To calculate the composite return baseon beginning assets, f首先确定每个投资组合所代表的期初综合资产的百分比； 然后确定当月的加权平均回报: Beginning composite assets =80 +130 + 115= 325Portfolio A = 80÷325= 0.246 = 24.6%Portfolio B = 130÷325= 0.4 = 40%Portfolio C = 115÷325 = 0.354 = 35.4%rComp=（0.0236×0.246）+（−0.0429×0.4）+（0.0417×0.354）=0.00581−0.01716+0.01476=0.00341=0.34%r_{Comp}=（0.0236\times0.246）+（-0.0429\times0.4）+（0.0417\times0.354）=0.00581-0.01716+0.01476=0.00341=0.34\%rComp​=（0.0236×0.246）+（−0.0429×0.4）+（0.0417×0.354）=0.00581−0.01716+0.01476=0.00341=0.34%C To calculate the composite return baseon beginning assets plus cash flows, 首先使用修正迪茨公式的分母来确定每个投资组合所代表的期初资产加上加权现金流量的百分比，然后计算加权平均回报 Beginning composite assets + Weightecash flows = [80 + (9 × 0.516)] + [130 + (−20 × 0.677) ] + [115+ (15 × 0.323)] = 84.64 + 116.46+ 119.85= 320.95Portfolio A = 84.64÷320.95 = 0.264 = 26.4%Portfolio B = 116.46÷320.95 = 0.363 = 36.3% Portfolio C = 119.85÷320.95 = 0.373 = 37.3%rComp=（0.0236×0.264）+（−0.0429×0.363）+（0.0417×0.373）=0.0062−0.0156+0.0156=0.00613=0.62%r_{Comp}=（0.0236\times0.264）+（-0.0429\times0.363）+（0.0417\times0.373）=0.0062-0.0156+0.0156=0.00613=0.62\%rComp​=（0.0236×0.264）+（−0.0429×0.363）+（0.0417×0.373）=0.0062−0.0156+0.0156=0.00613=0.62%The Aggregate Return metho是将期初资产和期内外部现金流相加，将整个组合视为一个单一的投资组合，然后直接使用修正迪茨公式计算回报。.rComp=331−325−（−20+9+15）325+[(−20)×0.677+9×0.516+15×0.323]=2320.95=0.0062=0.62%r_{Comp}=\frac{331-325-（-20+9+15）}{325+\lbrack(-20)\times0.677+9\times0.516+15\times0.323\rbrack}=\frac2{320.95}=0.0062=0.62\%rComp​=325+[(−20)×0.677+9×0.516+15×0.323]331−325−（−20+9+15）​=320.952​=0.0062=0.62% 是不是计算beginning-of-periovalues要先算出来修正etz公式的结果？都是这个顺序是吗？

NO.PZ2022010601000004 问题如下 A Singapore equity composite contains three portfolios whose cash flow weighting factors are follows.A Calculate the returns of Portfolio Portfolio anPortfolio for the month of July using Mofieetz formula.B Calculate the July composite return asset-weighting the inviportfolio returns using beginning-of-periovalues.C Calculate the July composite return asset-weighting the inviportfolio returns using a methothreflects both beginning-of-periovalues anexterncash flows. A Portfolio returns:rA=91−80−980+（0.516×9）=284.64=0.0236=2.36%r_A=\frac{91-80-9}{80+（0.516\times9）}=\frac2{84.64}=0.0236=2.36\%rA​=80+（0.516×9）91−80−9​=84.642​=0.0236=2.36%rB=105−130−（−20）130+（−20×0.677）=−5116.46=−0.0429=−4.29%r_B=\frac{105-130-（-20）}{130+（-20\times0.677）}=\frac{-5}{116.46}=-0.0429=-4.29\%rB​=130+（−20×0.677）105−130−（−20）​=116.46−5​=−0.0429=−4.29%rB=135−115−15115+（15×0.323）=5119.85=0.0417=4.17%r_B=\frac{135-115-15}{115+（15\times0.323）}=\frac5{119.85}=0.0417=4.17\%rB​=115+（15×0.323）135−115−15​=119.855​=0.0417=4.17% B To calculate the composite return baseon beginning assets, f首先确定每个投资组合所代表的期初综合资产的百分比； 然后确定当月的加权平均回报: Beginning composite assets =80 +130 + 115= 325Portfolio A = 80÷325= 0.246 = 24.6%Portfolio B = 130÷325= 0.4 = 40%Portfolio C = 115÷325 = 0.354 = 35.4%rComp=（0.0236×0.246）+（−0.0429×0.4）+（0.0417×0.354）=0.00581−0.01716+0.01476=0.00341=0.34%r_{Comp}=（0.0236\times0.246）+（-0.0429\times0.4）+（0.0417\times0.354）=0.00581-0.01716+0.01476=0.00341=0.34\%rComp​=（0.0236×0.246）+（−0.0429×0.4）+（0.0417×0.354）=0.00581−0.01716+0.01476=0.00341=0.34%C To calculate the composite return baseon beginning assets plus cash flows, 首先使用修正迪茨公式的分母来确定每个投资组合所代表的期初资产加上加权现金流量的百分比，然后计算加权平均回报 Beginning composite assets + Weightecash flows = [80 + (9 × 0.516)] + [130 + (−20 × 0.677) ] + [115+ (15 × 0.323)] = 84.64 + 116.46+ 119.85= 320.95Portfolio A = 84.64÷320.95 = 0.264 = 26.4%Portfolio B = 116.46÷320.95 = 0.363 = 36.3% Portfolio C = 119.85÷320.95 = 0.373 = 37.3%rComp=（0.0236×0.264）+（−0.0429×0.363）+（0.0417×0.373）=0.0062−0.0156+0.0156=0.00613=0.62%r_{Comp}=（0.0236\times0.264）+（-0.0429\times0.363）+（0.0417\times0.373）=0.0062-0.0156+0.0156=0.00613=0.62\%rComp​=（0.0236×0.264）+（−0.0429×0.363）+（0.0417×0.373）=0.0062−0.0156+0.0156=0.00613=0.62%The Aggregate Return metho是将期初资产和期内外部现金流相加，将整个组合视为一个单一的投资组合，然后直接使用修正迪茨公式计算回报。.rComp=331−325−（−20+9+15）325+[(−20)×0.677+9×0.516+15×0.323]=2320.95=0.0062=0.62%r_{Comp}=\frac{331-325-（-20+9+15）}{325+\lbrack(-20)\times0.677+9\times0.516+15\times0.323\rbrack}=\frac2{320.95}=0.0062=0.62\%rComp​=325+[(−20)×0.677+9×0.516+15×0.323]331−325−（−20+9+15）​=320.952​=0.0062=0.62% 老师，为什么在Mofieetz算return方法中间Cash inflow(+)要在分子减掉，但是在算“beginning plus weighteCF\"的时候，现金流入（+）就变成在分子加上了？

NO.PZ2022010601000004问题如下 A Singapore equity composite contains three portfolios whose cash flow weighting factors are follows.A Calculate the returns of Portfolio Portfolio anPortfolio for the month of July using Mofieetz formula.B Calculate the July composite return asset-weighting the inviportfolio returns using beginning-of-periovalues.C Calculate the July composite return asset-weighting the inviportfolio returns using a methothreflects both beginning-of-periovalues anexterncash flows. A Portfolio returns:rA=91−80−980+（0.516×9）=284.64=0.0236=2.36%r_A=\frac{91-80-9}{80+（0.516\times9）}=\frac2{84.64}=0.0236=2.36\%rA​=80+（0.516×9）91−80−9​=84.642​=0.0236=2.36%rB=105−130−（−20）130+（−20×0.677）=−5116.46=−0.0429=−4.29%r_B=\frac{105-130-（-20）}{130+（-20\times0.677）}=\frac{-5}{116.46}=-0.0429=-4.29\%rB​=130+（−20×0.677）105−130−（−20）​=116.46−5​=−0.0429=−4.29%rB=135−115−15115+（15×0.323）=5119.85=0.0417=4.17%r_B=\frac{135-115-15}{115+（15\times0.323）}=\frac5{119.85}=0.0417=4.17\%rB​=115+（15×0.323）135−115−15​=119.855​=0.0417=4.17% B To calculate the composite return baseon beginning assets, f首先确定每个投资组合所代表的期初综合资产的百分比； 然后确定当月的加权平均回报: Beginning composite assets =80 +130 + 115= 325Portfolio A = 80÷325= 0.246 = 24.6%Portfolio B = 130÷325= 0.4 = 40%Portfolio C = 115÷325 = 0.354 = 35.4%rComp=（0.0236×0.246）+（−0.0429×0.4）+（0.0417×0.354）=0.00581−0.01716+0.01476=0.00341=0.34%r_{Comp}=（0.0236\times0.246）+（-0.0429\times0.4）+（0.0417\times0.354）=0.00581-0.01716+0.01476=0.00341=0.34\%rComp​=（0.0236×0.246）+（−0.0429×0.4）+（0.0417×0.354）=0.00581−0.01716+0.01476=0.00341=0.34%C To calculate the composite return baseon beginning assets plus cash flows, 首先使用修正迪茨公式的分母来确定每个投资组合所代表的期初资产加上加权现金流量的百分比，然后计算加权平均回报 Beginning composite assets + Weightecash flows = [80 + (9 × 0.516)] + [130 + (−20 × 0.677) ] + [115+ (15 × 0.323)] = 84.64 + 116.46+ 119.85= 320.95Portfolio A = 84.64÷320.95 = 0.264 = 26.4%Portfolio B = 116.46÷320.95 = 0.363 = 36.3% Portfolio C = 119.85÷320.95 = 0.373 = 37.3%rComp=（0.0236×0.264）+（−0.0429×0.363）+（0.0417×0.373）=0.0062−0.0156+0.0156=0.00613=0.62%r_{Comp}=（0.0236\times0.264）+（-0.0429\times0.363）+（0.0417\times0.373）=0.0062-0.0156+0.0156=0.00613=0.62\%rComp​=（0.0236×0.264）+（−0.0429×0.363）+（0.0417×0.373）=0.0062−0.0156+0.0156=0.00613=0.62%The Aggregate Return metho是将期初资产和期内外部现金流相加，将整个组合视为一个单一的投资组合，然后直接使用修正迪茨公式计算回报。.rComp=331−325−（−20+9+15）325+[(−20)×0.677+9×0.516+15×0.323]=2320.95=0.0062=0.62%r_{Comp}=\frac{331-325-（-20+9+15）}{325+\lbrack(-20)\times0.677+9\times0.516+15\times0.323\rbrack}=\frac2{320.95}=0.0062=0.62\%rComp​=325+[(−20)×0.677+9×0.516+15×0.323]331−325−（−20+9+15）​=320.952​=0.0062=0.62% 现金流流出20，按照资金存在的时间算权重，期初的投资应该是130-20*0.323，为什么是按照资金流出后的时间算权重？

NO.PZ2022010601000004 问题如下 A Singapore equity composite contains three portfolios whose cash flow weighting factors are follows.A Calculate the returns of Portfolio Portfolio anPortfolio for the month of July using Mofieetz formula.B Calculate the July composite return asset-weighting the inviportfolio returns using beginning-of-periovalues.C Calculate the July composite return asset-weighting the inviportfolio returns using a methothreflects both beginning-of-periovalues anexterncash flows. A Portfolio returns:rA=91−80−980+（0.516×9）=284.64=0.0236=2.36%r_A=\frac{91-80-9}{80+（0.516\times9）}=\frac2{84.64}=0.0236=2.36\%rA​=80+（0.516×9）91−80−9​=84.642​=0.0236=2.36%rB=105−130−（−20）130+（−20×0.677）=−5116.46=−0.0429=−4.29%r_B=\frac{105-130-（-20）}{130+（-20\times0.677）}=\frac{-5}{116.46}=-0.0429=-4.29\%rB​=130+（−20×0.677）105−130−（−20）​=116.46−5​=−0.0429=−4.29%rB=135−115−15115+（15×0.323）=5119.85=0.0417=4.17%r_B=\frac{135-115-15}{115+（15\times0.323）}=\frac5{119.85}=0.0417=4.17\%rB​=115+（15×0.323）135−115−15​=119.855​=0.0417=4.17% B To calculate the composite return baseon beginning assets, f首先确定每个投资组合所代表的期初综合资产的百分比； 然后确定当月的加权平均回报: Beginning composite assets =80 +130 + 115= 325Portfolio A = 80÷325= 0.246 = 24.6%Portfolio B = 130÷325= 0.4 = 40%Portfolio C = 115÷325 = 0.354 = 35.4%rComp=（0.0236×0.246）+（−0.0429×0.4）+（0.0417×0.354）=0.00581−0.01716+0.01476=0.00341=0.34%r_{Comp}=（0.0236\times0.246）+（-0.0429\times0.4）+（0.0417\times0.354）=0.00581-0.01716+0.01476=0.00341=0.34\%rComp​=（0.0236×0.246）+（−0.0429×0.4）+（0.0417×0.354）=0.00581−0.01716+0.01476=0.00341=0.34%C To calculate the composite return baseon beginning assets plus cash flows, 首先使用修正迪茨公式的分母来确定每个投资组合所代表的期初资产加上加权现金流量的百分比，然后计算加权平均回报 Beginning composite assets + Weightecash flows = [80 + (9 × 0.516)] + [130 + (−20 × 0.677) ] + [115+ (15 × 0.323)] = 84.64 + 116.46+ 119.85= 320.95Portfolio A = 84.64÷320.95 = 0.264 = 26.4%Portfolio B = 116.46÷320.95 = 0.363 = 36.3% Portfolio C = 119.85÷320.95 = 0.373 = 37.3%rComp=（0.0236×0.264）+（−0.0429×0.363）+（0.0417×0.373）=0.0062−0.0156+0.0156=0.00613=0.62%r_{Comp}=（0.0236\times0.264）+（-0.0429\times0.363）+（0.0417\times0.373）=0.0062-0.0156+0.0156=0.00613=0.62\%rComp​=（0.0236×0.264）+（−0.0429×0.363）+（0.0417×0.373）=0.0062−0.0156+0.0156=0.00613=0.62%The Aggregate Return metho是将期初资产和期内外部现金流相加，将整个组合视为一个单一的投资组合，然后直接使用修正迪茨公式计算回报。.rComp=331−325−（−20+9+15）325+[(−20)×0.677+9×0.516+15×0.323]=2320.95=0.0062=0.62%r_{Comp}=\frac{331-325-（-20+9+15）}{325+\lbrack(-20)\times0.677+9\times0.516+15\times0.323\rbrack}=\frac2{320.95}=0.0062=0.62\%rComp​=325+[(−20)×0.677+9×0.516+15×0.323]331−325−（−20+9+15）​=320.952​=0.0062=0.62% C问题的表述，我看基础班讲义P41说的第二种方法的表述一样，using a methothrefleboth beginning of periovalues anexterncash flow