The Trio Index is comprised of three stocks, Eins, Zwei, and Tri. Their current
ID: 2621723 • Letter: T
Question
The Trio Index is comprised of three stocks, Eins, Zwei, and Tri.
Their current prices are listed below.
STOCK PRICE AT TIME ( t )
Eins $10
Zwei $20
Tri $40
a. Between now and the next time period, the stock prices of Eins
and Zwei increase 10 percent while Tri increases 20 percent.
What is the percentage change in the price-weighted Trio Index?
b. Suppose instead that the price of Eins increases 20 percent
while Zwei and Tri rise 10 percent. What is the percentage
change in the price-weighted Trio Index? Why does it differ
from the answer to part a?
Explanation / Answer
a)
Initiial index = (10+20+40)/3 = 70/3
New index = (10*1.1+20*1.1+40*1.2)/3 = 27
% change = (27-(70/3))/(70/3) = 15.71%
b)
New index = (10*1.2+20*1.1+40*1.1)/3 = 26
% change = 26-23.3333)/23.3333 = 11.42%
because in Price weighted index, stock with higher price has higher weight in index so change in price of stock with higher weight will have more effect than change in price with lower weight
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