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.)

a. A market value–weighted index

Rate of return             %

b. An equally weighted index

Rate of return             %

Answer 1

(a) Value of stock V_t = Price * Number of shares = P_t*Q_t

At time t = 0,

V_A0 = 90*100 = 9000
V_B0 = 50*200 = 10000
V_C0 = 100*200 = 20000

At time t = 1,

V_A1 = 95*100 = 9500
V_B1 = 45*200 = 9000
V_C1 = 110*200 = 22000

Returns for Period 1 :

Return_A = (9500 - 9000) / 9000 *100% = 5.56%
Return_B = (9000 - 10000) / 10000 *100% = -10%
Return_C = (22000 - 20000) / 20000 *100% = 10%

Market Valued weight of A = V_A0 / (V_A0 + V_B0 + V_C0) = 9000 / (9000 + 10000 + 20000) = 0.2308
Market Valued weight of B = V_B0 / (V_A0 + V_B0 + V_C0) = 10000 / (9000 + 10000 + 20000) = 0.2564
Market Valued weight of C = V_C0 / (V_A0 + V_B0 + V_C0) = 20000 / (9000 + 10000 + 20000) = 0.5128

Market weighted Returns = 0.2308*5.56 + 0.2564*(-10) + 0.5128*10 = 3.85%

(b) Equally weighted index return = (1/3)*5.56 + (1/3)*(-10) + (1/3)*10 = 1.85%