Question

Consider the three stocks in the following table. Pt represents price at time t, and Qt represents shares outstanding at time t. Stock C splits two-for-one in the last period.

a) Calculate the rate of return on a price-weighted index of the three stocks for the first period (from t=0 to t=1). 

b) What must happen to the divisor for the price-weighted index in year 2? 

c) Calculate the rate of return of the price-weighted index for the second period (from t = 1 to t=2)

Answer 1

Price weighted index has the index value equal to the average of the prices of all the stocks in the index in a given year

	P0	P1	P2
Stock A	90	95	95
Stock B	50	45	45
Stock C	100	110	55
Sum of prices	240	250	195
Value of index	80	83.33333	83.33333

In year 0, the sum of the prices was 90+50+100 = 240 and this when divided by the number of securities i.e. 3 gives the average or the value of the index = 240/3 = 80

In year 1, the sum of the prices was 95+45+110= 250 and this when divided by the number of securities i.e. 3 gives the average or the value of the index = 250/3 = 83.33

So the return from year 0 to year 1 will be = 4.167%

(83.33 - 80) - X 100 80

In year 2 we see that the price of the stock c has fallen to 55 and the quantity has risen to 400. Price has halved and quantity has doubled, so this implies a 1 in to two stock split

Had the split not happened then the price would have been 110 and the sum of the prices would have been 95+45+110 = 250 and the value of the index would be 250/3 = 83.33, however, if the split has taken place, this doesn't imply that the index value has seen a decline which is misleading because index has stayed the same. So the divisor needs to change from 3 to a new value so that the value of the index still remain the same. New sum of the index should also be calculated

So the new divisor can be calculated as follows:

(New sum) diusor == 83.33

(195) divsor -= 83.33

divisor = 2.34

So the new divisor is 2.34 and as the index remained at the same value there is no return in year 2 over year1