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hyi725 · 2023年08月12日

为什么Ra Rb分母一个用期初一个用期末？

  1. CFA III
  2. GIPS

NO.PZ2022010501000005

问题如下：

A European equity composite contains three portfolios whose cash flow weighting factors are as follows.


A Calculate the returns of Portfolio A, Portfolio B, and Portfolio C for the month of August using Modified Dietz formula.

B Calculate the August composite return by asset-weighting the individual portfolio returns using beginning-of- period values.

C Calculate the August composite return by asset- weighting the individual portfolio returns using a method that reflects both beginning-of-period values and external cash flows.

选项：

解释：

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\%

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\%

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\%

B To calculate the composite return based on beginning assets, first determine the percentage of beginning composite assets represented by each portfolio; then determine the weighted-average return for the month:

Beginning composite assets = 74.9 + 127.6 + 110.4 = 312.9

Portfolio 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\%


C To calculate the composite return based on beginning assets plus cash flows, first use the denominator of the Modified Dietz formula to determine the percentage of total beginning assets plus weighted cash flows represented by each portfolio, and then calculate the weighted-average return:

Beginning composite assets + Weighted cash 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 = 310.24

Portfolio 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\%


The Aggregate Return method is calculated by summing beginning assets and intra- period external cash flows, treating the entire composite as though it were a single portfolio and then computing the return directly with the Modified Dietz 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\%

第一问

rB

分母127.6+（−15×0.742）+(−5×0.387）


可Ra和Rc分母都是用的期末值 为什么呢

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1 个答案

伯恩_品职助教 · 2023年08月13日

嗨，努力学习的PZer你好：


实在抱歉同学，我看了好半天，实在是没get到你说的期初和期末是指什么？

----------------------------------------------
就算太阳没有迎着我们而来，我们正在朝着它而去，加油！

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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

2024-10-16 10:33 1 · 回答

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

2024-10-15 07:06 2 · 回答

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？

2024-07-26 21:11 1 · 回答

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% 老师，第三问，答案是不是写错了？我算是3.48%。有一笔正负号答案好像写错了。

2024-06-29 21:31 1 · 回答

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% 如题。

2024-05-18 15:00 2 · 回答