Question

Assume that you construct a price weighted index of 30 stocks. The sum of the prices of these stocks is $2000. The divisor for this index is 30, and the value of this index is 100. Now assume that one of the 30 stocks, with an average price of $100, has a three-for-one stock split while the value of other stocks remains unchanged.

a) If you make no adjustments to the index, what will be the new value of the index?

b) What does the new divisor have to be to keep the value of the index unchanged at 100

Answer 1

a)

The Sum of all the stocks in the index is 3000, and the index value is 100.

Under no adjustments, the divisor will remain 30 which was the earlier divisor.

When a stock split happens in a ratio of 3:1 the price of that stock gets divided by 3. So now the sum of all the prices of stock will be = 29*100 + 100/3 = 2933.333

With divisor = 30,

Index value = 2933.333/30 = 97.778

b)

New index = Sum of all the stock price post-split/Initial index value = 2933.333/100 = 2.933333

So the new divisor is 2.933333