Question

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

	P0	Q0	P1	Q1	P2	Q2
A	90	100	95	100	95	100
B	50	200	45	200	45	200
C	100	200	110	200	55	400
Calculate the first-period rates of return on the following indexes of the three stocks: (Do not round intermediate calculations. Round answers to 2 decimal places.) An equally weighted index?

Answer 1

Equally weighted index return is calculated as the average of each stock return for the period.

The divisor (for average) is no of stocks.

But when stock split happens , the divisor changes. ie in this case the divisor changes after period 2,

For period 1, there is no stock split ; hence the equally weighted return is imple average of each stock's returns

Return of A = (P1-P0)/P0 = (95-90)/90 = 5.56%

Return of B = (P1-P0)/P0 = (45-50)/50 = -10%

Return of C = (P1-P0)/P0 = (110-100)/ 100 = 10%

Equally weighted index return = (5.56% + (-10%) + 10% ) / 3

= 1.852%