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EmilyZhou · 2024年08月02日

老师 ,不明白为什么这样算,可以麻烦帮解释下逻辑吗?

NO.PZ2022061307000045

问题如下:

Question

A price-weighted index series is composed of the following three stocks:


If stock Z completes a three-for-one split at the end of Day 1, the value of the index after the split (at the end of Day 2) is closest to:

选项:

A.31.7. B.32.3. C.29.9.

解释:

Solution

A is correct. The value of the price-weighted index is determined by dividing the sum of the security values by the divisor, which is typically set at inception to equal the initial number of securities in the index. In the case of a stock split, the index provider must adjust the value of the divisor by dividing the sum of the constituent prices after the split by the value of the index before the split. This adjustment results in a new divisor that keeps the index value at the same level as before the split. The new divisor will then be used to calculate the index value after the split.

Index before the split = 10+20+60 3

= 30

New divisor, X: 30 = 10+20+20 X

X = 1.67

Index after the split = 12+19+22 1.67

= 31.7

B is incorrect. It calculates the changes in prices and uses it to derive the new index.

C is incorrect. It uses price after split to calculate the new divisor.

老师 ,不明白为什么这样算,可以麻烦帮解释下逻辑吗?

1 个答案

王园圆_品职助教 · 2024年08月02日

同学你好,你要理解,一个股票如果拆股了,虽然股价立刻下跌,但是本质上这个股票还是原来的股票,那就应该在一个index中享有一样的地位,且这个index也不应该因为这个股票的拆股产生任何实质变化,这就是拆股计算分母的原理

请看以下讲义截图,按照黄色的公式,price weighted index在拆股前value = (10+20+60)/3 = 30

而在拆股后,其本质和拆股前不应该发生任何变化,所以value和拆股前应该完全一致,即30 = (10+20+拆股后股价)/未知的分母——其中拆股后价值 ,本题是 three-for-one split 就是1拆3,所以拆股后价值 = 60/3=20

把20带入上面的粉色公式,就可以求出未知分母应该是多少了

有了这个新的分母,我们就可以用来替代最开始的绿色的那个分母3,然后再利用讲义公式求解股价真实变动后的这个index的value了,也就是(12+19+22)/这个新的分母

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NO.PZ2022061307000045 问题如下 QuestionA price-weighteinx series is composeof the following three stocks:If stoZ completes a three-for-one split the enof y 1, the value of the inx after the split (the enof y 2) is closest to: A.31.7. B.32.3. C.29.9. SolutionA is correct. The value of the price-weighteinx is termineving the sum of the security values the visor, whiis typically set inception to equthe initinumber of securities in the inx. In the case of a stosplit, the inx provir must aust the value of the visor ving the sum of the constituent prices after the split the value of the inx before the split. This austment results in a new visor thkeeps the inx value the same level before the split. The new visor will then useto calculate the inx value after the split.Inx before the split = 10+20+60 3 = 30New visor, X: 30 = 10+20+20 X X = 1.67Inx after the split = 12+19+22 1.67 = 31.7B is incorrect. It calculates the changes in prices anuses it to rive the new inx.C is incorrect. It uses priafter split to calculate the new visor. New visor, X: 30 = 10+20+20/𝑋

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