Question

Suppose that a stock index is constructed with three stocks priced at $7, $43, and $56. The number of outstanding shares for each is 500,000 shares, 405,000 shares, and 553,000 shares, respectively. Today the prices for each stock are changed to $14, $44, and $52 and the number of outstanding shares for each are changed to 250,000 shares, 405,000 shares and 553,000 shares today, what is the equal weighted index value today if the index yesterday was 1000?

Answer 1

Here we are asked to find the index value of an equal weighted index thus here the number of shares are not important as it is equal weighted.

An equal weighted stock index is calculated by change in average price of stock with respect to previous day average stock price:

Average price of stocks at Day 1 = 7+43+56/3 = 106/3 = 35.3333333333

Average price of stocks at Day 2 (Today) = 14+44+52/3 = 110/3 = 36.6666666667

% change in Average Stock Price = (36.667/35.333)-1 = 1.0377550732 -1 = 0.037755 = 3.78%

Now the Index would also increase by 3.78% Thus 1000 will become 1000 + (1000*0.0378) = 1000 + 37.8 = 1037.8

Index Value = 1037.8