BC两问默认使用modified dietz

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% A.the returns of Portfolio A for the month of August using Mofieetz formula.(85.3-7.5-74.9)/(74.9+0.613*7.5)= 3.65%the returns of Portfolio Portfolio anPortfolio C for the month of August using Mofieetz formula.(109.8-127.6+15+ 5 ) / (127.6-15 *0.742 - 5 * 0.387)= 1.92%the returns of Portfolio Portfolio anPortfolio C for the month of August using Mofieetz formula.(128.4-110.4-15)/ （110.4 + 15* 0.387）=2.58%74.9+127.6+110.4=312.974.9/312.9 * 3.65% + 127.6/312.9 * 1.92%+ 110.4/312.9 * 2.58% = 2.57%C.74.9+0.613*7.5=79.50 127.6-15 * 0.742- 5 * 0.387 = 114.54110.4+15* 0.387= 116.21116.21 + 114.54+ 79.5= 310.2579.5/ 310.25 * 3.65% + 114.54/ 312.18 * 1.92% + 116.21/310.25 * 2.57% = 2.61%

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% 在算composite的 asset weighting return时，对于所用到的composite中包含的portfolio的return，其计算方法有要求吗，还是说不管用TWR还是用MWR还是mofieetz都可以？就类似这题的B和C，直接用了A算出来的mofieetz的return，这有什么讲究吗？

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