Question

# Consider the three stocks in the following table. Pt represents price at time t, and Qt...

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.

 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             %

(a) Value of stock Vt = Price * Number of shares = Pt*Qt

At time t = 0,

VA0 = 90*100 = 9000
VB0 = 50*200 = 10000
VC0 = 100*200 = 20000

At time t = 1,

VA1 = 95*100 = 9500
VB1 = 45*200 = 9000
VC1 = 110*200 = 22000

Returns for Period 1 :

ReturnA = (9500 - 9000) / 9000 *100% = 5.56%
ReturnB = (9000 - 10000) / 10000 *100% = -10%
ReturnC = (22000 - 20000) / 20000 *100% = 10%

Market Valued weight of A = VA0 / (VA0 + VB0 + VC0) = 9000 / (9000 + 10000 + 20000) = 0.2308
Market Valued weight of B = VB0 / (VA0 + VB0 + VC0) = 10000 / (9000 + 10000 + 20000) = 0.2564
Market Valued weight of C = VC0 / (VA0 + VB0 + VC0) = 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%