Question

In the list of stocks below, which firm is most likely to have the smallest impact on the behavior of a price-weighted index over the short-term future?

	Time T
Stock	Price	# of shares
A	$30	100
B	$60	150
C	$90	40
D	$100	100

• A. Stock A
• B. Stock B
• C. Stock C
• D. Stock D
• E. Cannot determine

Answer 1

In a price-weighted stock index the index is calculated by doing a simple arithmetic average of prices of all stocks included in the index.

In a price-weighted index, stocks with higher prices have more weight & it doesn't take into regard other factors like company size or a number of outstanding shares. The higher the share price of the stock, the bigger the impact it will have on the index value.

Price-weighted index (PWI) = Summation of individual stock prices / Number of stocks

PWI = (Price of Stock A + Price of Stock +B + Price of Stock C + Price of Stock D) / 4 = (30+60+90+100)/4 = 70

Now weight of indivudual stock in the index = Price of the individual stock / Summation of individual stock prices

Weight of Stock A in Index = 30/280= 10.71%

Weight of Stock B in Index = 60/280 = 21.43%

Weight of Stock C in Index = 90/280 = 32.14%

Weight of Stock D in Index = 100/280 = 35.72%

Here, Stock A has the lowest share price which leads to its lower weightage in PWI. So, Firm A will have the smallest impact on the behaviour of PWI over the short term future.

Option A - Stock A is Correct.