CFA Practice Question
There are 275 practice questions for this study session.
CFA Practice Question
A price-weighted index was constructed two months ago using 2 stocks, A and B, then priced at $10 and $17 respectively. The index is adjusted at stock splits so as not to allow splits to affect its value. Stock B underwent a 3-for-2 split a month ago, when it was trading at $24 and A was trading at $12. Right now, A is trading at $11 and B is trading at $14. The value of the index equals ______.
Explanation: First note that a price-weighted index is derived by summing up the prices of the constituent stocks and then dividing the sum by a divisor. When the index is first constructed with N stocks, the divisor equals N.
Later on, when changes like stock splits or index composition take place, the divisor is adjusted so as to keep the value of the index constant across the change (the Dow Jones Industrial Average is adjusted in this fashion, hence its divisor is no longer 30 but a much lower value, less than 1).
Just before stock B split, the value of the index was (24+12)/2 = 18. After the split, the price of B changed to 24 / 3 * 2 = 16 per share. Hence, the divisor changes from 2 to (16+12)/18 = 1.556. Therefore, the current index value equals (11+14)/1.556 = 16.07.
User Contributed Comments 9
|murli||Denominator is adjusted to (Pre-split adjusted price / Pre-split index) so as to maintain the average.|
|iceluke||think twice --> 36 / 2 = 18; 28 / x = 18; x=1,555
|labsbamb||ok got it.
For price weighed index
index value = sum (pricei)/ divisor
when stocke split ----------> divisor decrease.
|MaiHuong||What's about the now price A of $11 and B of $14?|
|ljamieson||P(0) = [A(0)+B(0)]/D = [10+17]/2 = 13.5
P(1) = [A(1)+B(1)]/D = [12+24]/2 = 18
= [A(1)+B'(1)]/D'= [12+24*(2/3)]/D'
= 28/D' = 18 => D' = 28/18
P(2) = [A(2)+B(2)]/D' = [11+14]/(28/18) = 16.0714
|Kuki||3 for 2 split means you will get 2 shares for every 3 you hold? or is it the other way around?|
|micheleus||3 for 2 split means u will get 3 shares for every 2 you hold|
|bvdlaan||The index is adjusted at stock splits so as to not allow splits to affect its value. ....I fell for it, and gave 12 as an answer|
|jpducros||To complete micheleus answer....if you get 3 shares for every 2 you hold. As the total value of your shares is constant (Stop split is not really a present !), the price of each share has decreased...being multiplied by 2/3.|