price-weighted index with splits

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Swissfox

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Hi,
Could someone explain me the logic with the below exercice taken from the CFAI topic test?
A price-weighted index series is composed of the following three stocks:
Price before split (day 1) price after split (day 2)
Stock X 10 12
Stock Y 20 19
Stock Z 60 22
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:A price-weighted index series is composed of the following three stocks:
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 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
New divisor, X: 30
X = 1.67
Index after the split
OK so I have to admit that calculate indexes are not my biggest strength… But I don’t understand the second step… your help would be appreciated
Thanks
 
The idea is that the split shouldn’t change the value of the index. Because the value was 30 before the split, it should remain 30 after the split (before any price changes in the stocks). So you compute the new divisor so that the price remains at 30: the new divisor is 1.6667.
After that, you continue to use that new divisor to compute the index value until the next split/reverse split/stock dividend/change in stocks in the index.
 
Thanks s2000 magician. I have two questions left:
1. how did they compute the 10+20+20?
2. you say that the idea is that a split shouldn’t change the value of a price index. But in the CFA books it’s written that these indexes are affected by splits… it’s a bit confused for me now.
Thanks!
 
  1. If the $60 stock splits 3:1, the new shares will have a price of $20 apiece.
  2. I’ve never seen indices affected by the split per se: it’s affected by price changes before and after the split. If you have a page reference in the curriculum, let me know; I’d like to read it.
 
Is a EOC sufficient?
CFAI, R.46, Q.15
Which of the following index weighting methods requires an adjustment to the divisor after a stock split?

A Price weighting.

B Fundamental weighting.

C Market-capitalization weighting.

A is correct. In the price weighting method, the divisor must be adjusted so the index value immediately after the split is the same as the index value immediately prior to the split.

But now I understand that it’s the divisor that must change, not the index, my bad!
 
and now I also see that it’s the stock Z that is subject to a split, I thought it was the three stocks… anyway, thanks a lot!
 
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