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圣灵霜子 · 2020年10月11日

问一道题:NO.PZ2016031101000007 [ CFA III ]

问题如下:

A European equity composite contains three portfolios. For convenience, the cash flow weighting factors are presented below.

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

解释:

A.

Portfolio returns:

lrA=85.374.97.574.9+(7.5×0.613)=2.979.5=0.0365=3.65%{l}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=109.8127.6(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=128.4110.415110.4+(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 percent 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%

                              lrComp=(0.0365×0.239)+(0.0192×0.408)+(0.0258×0.353)=0.0257=2.57%{l}r_{Comp}=(0.0365\times0.239)+(0.0192\times0.408)+(0.0258\times0.353)\\=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%

lrComp=(0.0365×0.256)+(0.0192×0.369)+(0.0258×0.375)=0.0261=2.61%{l}r_{Comp}=(0.0365\times0.256)+(0.0192\times0.369)+(0.0258\times0.375)\\=0.0261=2.61\%

A mathematically equivalent method consists simply in 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.

lrComp=323.5312.9(15+7.5+10)312.9+[(15)×0.742+7.5×0.613+10×0.387]=0.0261=2.61%{l}r_{Comp}=\frac{323.5-312.9-(-15+7.5+10)}{312.9+\lbrack(-15)\times0.742+7.5\times0.613+10\times0.387]}\\=0.0261=2.61\%

请问考试的时候不会考这三个计算吧?记得和老师上课的时候说过。。。这个是课后题还是品职自己出的题呢?
1 个答案

韩韩_品职助教 · 2020年10月15日

嗨,从没放弃的小努力你好:


同学你好,这个的确是课后题,这两种计算方法我们在课程上面都是讲过的。一般情况下不会在GIPS当中考到这么大的计算的。可以先把精力用在其他科目上。


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努力的时光都是限量版,加油!