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mousesky · 2024年05月16日

为什么问题B和C里的rate of return都可以直接用问题A里的值呢？

  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\%

问题A里算出来的三个portfolio的return，不都是用modified Dietz method算出来的么？为什么默认这个值就可以用作beginning-of-values method和beginning-of-period values plus external cash flows的分子呢？


我能理解B和C是在计算分母加权平均时与A不同，但从逻辑上来说，分子也应该用相应的算法呀（比如答案里问题C的第二种解法，就和分母的逻辑是一致的），虽然从计算结果来看，问题C的两种算法恰好算出来的结果差异不大


我知道从现有已知条件来看，只有通过问题A这么一种rate of return可得，但万一考试的时候有别的return rate呢？或者有别的条件让你另算问题B的rate of return，算出来呢？问题C的两种算法算出来的rate of return不一样，我觉得只有第二种，严格按照beginning-of-period values plus external cash flows方法计算才是对的


另外从书上例题来看，两个portfolio的monthly return已经是给定的了（虽然我也没弄明白这两个return是怎么算出来的），直接代入计算即可，我觉得在这里没法作为参考




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mousesky · 2024年05月16日

问题C的两种算法，我用代数公式推导了一遍，两种算法的结果一定是一样的，所以问题C的疑问，助教老师可以忽略我 就是问题B，为什么分子也可以直接用问题A中算出的rate of return?

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伯恩_品职助教 · 2024年05月17日

嗨，从没放弃的小努力你好：


最后，我的疑问在于分子return，现在问题B和问题C所采用的分子，都是基于问题A，根据modified Dietz method算出来的。如果，问题B的分子，不用问题A的modified Dietz method，而是也使用beginning-of-period values method计算（如果题干中给了相应的条件，比如用money-weighted），是不是更合理？——可以的。

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

伯恩_品职助教 · 2024年05月17日

嗨，努力学习的PZer你好：


A算的是各个portfolio的return，B是计算的composite的return，composite是包含portfolio的，这个应该知道的对吧？然后portfolio A的收益3.65%，看它在composite里的的占比，计算出portfolio A给composite贡献的收益，portfolio A B C这样全部计算完，就把composite的return计算出来了

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努力的时光都是限量版，加油！

mousesky · 2024年05月17日

我重新表述一下我的问题： 首先，要计算rate of return，就要分别计算分子return和分母total assest value; 其次，计算分母total asset value，就是算三个portfolios asset的加权平均。问题B和问题C分别用的是根据beginning-of-period value和beginning-of-period values plus external cash flows的方法，这个没有问题

mousesky · 2024年05月17日

最后，我的疑问在于分子return，现在问题B和问题C所采用的分子，都是基于问题A，根据modified Dietz method算出来的。如果，问题B的分子，不用问题A的modified Dietz method，而是也使用beginning-of-period values method计算（如果题干中给了相应的条件，比如用money-weighted），是不是更合理？

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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

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% 题目里只说了考虑期初和期间现金流，externcash flow和aggregate return metho符合要求，题目表达的意思是想让用哪种算呢

2024-05-06 00:46 1 · 回答