composite return和portfolio return

NO.PZ2022010501000005 问题如下 A Europeequity composite contains three portfolios whose cash flow weighting factors are follows.A Calculate the returns of Portfolio Portfolio anPortfolio C for the month of August using Mofieetz formula.B Calculate the August composite return asset-weighting the inviportfolio returns using beginning-of- periovalues.C Calculate the August composite return asset- weighting the inviportfolio returns using a methothreflects both beginning-of-periovalues anexterncash flows. A Portfolio returns:rA=85.3−74.9−7.574.9+（7.5×0.613）=2.979.5=0.0365=3.65%r_A=\frac{85.3-74.9-7.5}{74.9+（7.5\times0.613）}=\frac{2.9}{79.5}=0.0365=3.65\%rA​=74.9+（7.5×0.613）85.3−74.9−7.5​=79.52.9​=0.0365=3.65%rB=109.8−127.6−(−15)−(−5)127.6+（−15×0.742）+(−5×0.387）=2.2114.535=0.0192=1.92%r_B=\frac{109.8-127.6-(-15)-(-5)}{127.6+（-15\times0.742）+(-5\times0.387）}=\frac{2.2}{114.535}=0.0192=1.92\%rB​=127.6+（−15×0.742）+(−5×0.387）109.8−127.6−(−15)−(−5)​=114.5352.2​=0.0192=1.92%rC=128.4−110.4−15110.4+（15×0.387）=3116.205=0.0258=2.58%r_C=\frac{128.4-110.4-15}{110.4+（15\times0.387）}=\frac3{116.205}=0.0258=2.58\%rC​=110.4+（15×0.387）128.4−110.4−15​=116.2053​=0.0258=2.58% B To calculate the composite return baseon beginning assets, first termine the percentage of beginning composite assets representeeaportfolio; then termine the weighteaverage return for the month: Beginning composite assets = 74.9 + 127.6 + 110.4 = 312.9Portfolio A = 74.9/312.9 = 0.239 = 23.9%Portfolio B = 127.6/312.9 = 0.408 = 40.8%Portfolio C = 110.4/312.9 = 0.353 = 35.3%rComp=  (0.0365  ×  0.239)  +  (0.0192  ×  0.408)  +  (0.0258  ×  0.353)=  0.0257  =  2.57%r_{Comp}=\;(0.0365\;\times\;0.239)\;+\;(0.0192\;\times\;0.408)\;+\;(0.0258\;\times\;0.353)=\;0.0257\;=\;2.57\%rComp​=(0.0365×0.239)+(0.0192×0.408)+(0.0258×0.353)=0.0257=2.57%C To calculate the composite return baseon beginning assets plus cash flows, first use the nominator of the Mofieetz formula to termine the percentage of totbeginning assets plus weightecash flows representeeaportfolio, anthen calculate the weighteaverage return: Beginning composite assets + Weightecash flows = [74.9 + (7.5 × 0.613)] + [127.6 + (−15 × 0.742) + (−5 × 0.387)] + [110.4 + (15 × 0.387)] = 79.5 + 114.535 + 116.205 = 310.24Portfolio A = 79.5/310.24 = 0.256 = 25.6%Portfolio B = 114.535/310.24 = 0.369 = 36.9% Portfolio C = 116.205/310.24 = 0.375 = 37.5%rComp  =  (0.0365  ×  0.256)  +  (0.0192  ×  0.369)  +  (0.0258  ×  0.375)    =  0.0261  =  2.61%r_{Comp}\;=\;(0.0365\;\times\;0.256)\;+\;(0.0192\;\times\;0.369)\;+\;(0.0258\;\times\;0.375)\;\;=\;0.0261\;=\;2.61\%rComp​=(0.0365×0.256)+(0.0192×0.369)+(0.0258×0.375)=0.0261=2.61%The Aggregate Return methois calculatesumming beginning assets anintrperioexterncash flows, treating the entire composite though it were a single portfolio anthen computing the return rectly with the Mofieetz formula.rComp  =  323.5−312.9−(−15+7.5+10)312.9+[(−15)×0.742+7.5×0.613+10×0.387]=  0.0261  =  2.61%r_{Comp}\;=\;\frac{323.5-312.9-(-15+7.5+10)}{312.9+\lbrack(-15)\times0.742+7.5\times0.613+10\times0.387\rbrack}=\;0.0261\;=\;2.61\%rComp​=312.9+[(−15)×0.742+7.5×0.613+10×0.387]323.5−312.9−(−15+7.5+10)​=0.0261=2.61% 最后computing the return rectly with the Mofieetz formula这地方，是缺了“-5”这个现金流吧。

题干错误 没有给出这三个月组合的return，没办法计算。只能找到权重。其次这个问题计算composite return的第一项没有这种说法，这个是计算组合收益的

NO.PZ2022010501000005 问题如下 A Europeequity composite contains three portfolios whose cash flow weighting factors are follows.A Calculate the returns of Portfolio Portfolio anPortfolio C for the month of August using Mofieetz formula.B Calculate the August composite return asset-weighting the inviportfolio returns using beginning-of- periovalues.C Calculate the August composite return asset- weighting the inviportfolio returns using a methothreflects both beginning-of-periovalues anexterncash flows. A Portfolio returns:rA=85.3−74.9−7.574.9+（7.5×0.613）=2.979.5=0.0365=3.65%r_A=\frac{85.3-74.9-7.5}{74.9+（7.5\times0.613）}=\frac{2.9}{79.5}=0.0365=3.65\%rA​=74.9+（7.5×0.613）85.3−74.9−7.5​=79.52.9​=0.0365=3.65%rB=109.8−127.6−(−15)−(−5)127.6+（−15×0.742）+(−5×0.387）=2.2114.535=0.0192=1.92%r_B=\frac{109.8-127.6-(-15)-(-5)}{127.6+（-15\times0.742）+(-5\times0.387）}=\frac{2.2}{114.535}=0.0192=1.92\%rB​=127.6+（−15×0.742）+(−5×0.387）109.8−127.6−(−15)−(−5)​=114.5352.2​=0.0192=1.92%rC=128.4−110.4−15110.4+（15×0.387）=3116.205=0.0258=2.58%r_C=\frac{128.4-110.4-15}{110.4+（15\times0.387）}=\frac3{116.205}=0.0258=2.58\%rC​=110.4+（15×0.387）128.4−110.4−15​=116.2053​=0.0258=2.58% B To calculate the composite return baseon beginning assets, first termine the percentage of beginning composite assets representeeaportfolio; then termine the weighteaverage return for the month: Beginning composite assets = 74.9 + 127.6 + 110.4 = 312.9Portfolio A = 74.9/312.9 = 0.239 = 23.9%Portfolio B = 127.6/312.9 = 0.408 = 40.8%Portfolio C = 110.4/312.9 = 0.353 = 35.3%rComp=  (0.0365  ×  0.239)  +  (0.0192  ×  0.408)  +  (0.0258  ×  0.353)=  0.0257  =  2.57%r_{Comp}=\;(0.0365\;\times\;0.239)\;+\;(0.0192\;\times\;0.408)\;+\;(0.0258\;\times\;0.353)=\;0.0257\;=\;2.57\%rComp​=(0.0365×0.239)+(0.0192×0.408)+(0.0258×0.353)=0.0257=2.57%C To calculate the composite return baseon beginning assets plus cash flows, first use the nominator of the Mofieetz formula to termine the percentage of totbeginning assets plus weightecash flows representeeaportfolio, anthen calculate the weighteaverage return: Beginning composite assets + Weightecash flows = [74.9 + (7.5 × 0.613)] + [127.6 + (−15 × 0.742) + (−5 × 0.387)] + [110.4 + (15 × 0.387)] = 79.5 + 114.535 + 116.205 = 310.24Portfolio A = 79.5/310.24 = 0.256 = 25.6%Portfolio B = 114.535/310.24 = 0.369 = 36.9% Portfolio C = 116.205/310.24 = 0.375 = 37.5%rComp  =  (0.0365  ×  0.256)  +  (0.0192  ×  0.369)  +  (0.0258  ×  0.375)    =  0.0261  =  2.61%r_{Comp}\;=\;(0.0365\;\times\;0.256)\;+\;(0.0192\;\times\;0.369)\;+\;(0.0258\;\times\;0.375)\;\;=\;0.0261\;=\;2.61\%rComp​=(0.0365×0.256)+(0.0192×0.369)+(0.0258×0.375)=0.0261=2.61%The Aggregate Return methois calculatesumming beginning assets anintrperioexterncash flows, treating the entire composite though it were a single portfolio anthen computing the return rectly with the Mofieetz formula.rComp  =  323.5−312.9−(−15+7.5+10)312.9+[(−15)×0.742+7.5×0.613+10×0.387]=  0.0261  =  2.61%r_{Comp}\;=\;\frac{323.5-312.9-(-15+7.5+10)}{312.9+\lbrack(-15)\times0.742+7.5\times0.613+10\times0.387\rbrack}=\;0.0261\;=\;2.61\%rComp​=312.9+[(−15)×0.742+7.5×0.613+10×0.387]323.5−312.9−(−15+7.5+10)​=0.0261=2.61% 请问这题，在计算B,C的时候，为什么可以直接带入A的结果？A用的是mofieetz methoportfolio return。B和C不是应该用TWR 算portfolio return么？谢谢

NO.PZ2022010501000005 问题如下 A Europeequity composite contains three portfolios whose cash flow weighting factors are follows.A Calculate the returns of Portfolio Portfolio anPortfolio C for the month of August using Mofieetz formula.B Calculate the August composite return asset-weighting the inviportfolio returns using beginning-of- periovalues.C Calculate the August composite return asset- weighting the inviportfolio returns using a methothreflects both beginning-of-periovalues anexterncash flows. A Portfolio returns:rA=85.3−74.9−7.574.9+（7.5×0.613）=2.979.5=0.0365=3.65%r_A=\frac{85.3-74.9-7.5}{74.9+（7.5\times0.613）}=\frac{2.9}{79.5}=0.0365=3.65\%rA​=74.9+（7.5×0.613）85.3−74.9−7.5​=79.52.9​=0.0365=3.65%rB=109.8−127.6−(−15)−(−5)127.6+（−15×0.742）+(−5×0.387）=2.2114.535=0.0192=1.92%r_B=\frac{109.8-127.6-(-15)-(-5)}{127.6+（-15\times0.742）+(-5\times0.387）}=\frac{2.2}{114.535}=0.0192=1.92\%rB​=127.6+（−15×0.742）+(−5×0.387）109.8−127.6−(−15)−(−5)​=114.5352.2​=0.0192=1.92%rC=128.4−110.4−15110.4+（15×0.387）=3116.205=0.0258=2.58%r_C=\frac{128.4-110.4-15}{110.4+（15\times0.387）}=\frac3{116.205}=0.0258=2.58\%rC​=110.4+（15×0.387）128.4−110.4−15​=116.2053​=0.0258=2.58% B To calculate the composite return baseon beginning assets, first termine the percentage of beginning composite assets representeeaportfolio; then termine the weighteaverage return for the month: Beginning composite assets = 74.9 + 127.6 + 110.4 = 312.9Portfolio A = 74.9/312.9 = 0.239 = 23.9%Portfolio B = 127.6/312.9 = 0.408 = 40.8%Portfolio C = 110.4/312.9 = 0.353 = 35.3%rComp=  (0.0365  ×  0.239)  +  (0.0192  ×  0.408)  +  (0.0258  ×  0.353)=  0.0257  =  2.57%r_{Comp}=\;(0.0365\;\times\;0.239)\;+\;(0.0192\;\times\;0.408)\;+\;(0.0258\;\times\;0.353)=\;0.0257\;=\;2.57\%rComp​=(0.0365×0.239)+(0.0192×0.408)+(0.0258×0.353)=0.0257=2.57%C To calculate the composite return baseon beginning assets plus cash flows, first use the nominator of the Mofieetz formula to termine the percentage of totbeginning assets plus weightecash flows representeeaportfolio, anthen calculate the weighteaverage return: Beginning composite assets + Weightecash flows = [74.9 + (7.5 × 0.613)] + [127.6 + (−15 × 0.742) + (−5 × 0.387)] + [110.4 + (15 × 0.387)] = 79.5 + 114.535 + 116.205 = 310.24Portfolio A = 79.5/310.24 = 0.256 = 25.6%Portfolio B = 114.535/310.24 = 0.369 = 36.9% Portfolio C = 116.205/310.24 = 0.375 = 37.5%rComp  =  (0.0365  ×  0.256)  +  (0.0192  ×  0.369)  +  (0.0258  ×  0.375)    =  0.0261  =  2.61%r_{Comp}\;=\;(0.0365\;\times\;0.256)\;+\;(0.0192\;\times\;0.369)\;+\;(0.0258\;\times\;0.375)\;\;=\;0.0261\;=\;2.61\%rComp​=(0.0365×0.256)+(0.0192×0.369)+(0.0258×0.375)=0.0261=2.61%The Aggregate Return methois calculatesumming beginning assets anintrperioexterncash flows, treating the entire composite though it were a single portfolio anthen computing the return rectly with the Mofieetz formula.rComp  =  323.5−312.9−(−15+7.5+10)312.9+[(−15)×0.742+7.5×0.613+10×0.387]=  0.0261  =  2.61%r_{Comp}\;=\;\frac{323.5-312.9-(-15+7.5+10)}{312.9+\lbrack(-15)\times0.742+7.5\times0.613+10\times0.387\rbrack}=\;0.0261\;=\;2.61\%rComp​=312.9+[(−15)×0.742+7.5×0.613+10×0.387]323.5−312.9−(−15+7.5+10)​=0.0261=2.61% 对于B和C问，讲义中是基于TWR来算这些回报率的，但是这里用的是mofieetz的方法，考试时，应该基于什么回报率哦？