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	87	100	92	100	92	100
B	47	200	42	200	42	200
C	94	200	104	200	52	400

Calculate the first-period rates of return on the following indexes of the three stocks: (Do not round intermediate calculations. Round your answers to 2 decimal places.)

a. A market value–weighted index



b. An equally weighted index

Answer 1

a). Total market value (at t = 0) = ($87 × 100) + ($47 × 200) + ($94 × 200)

= $8,700 + $9,400 + $18,800 = $36,900

Total market value (at t = 1) = ($92 × 100) + ($42 × 200) + ($104 × 200)

= $9,200 + $8,400 + $20,800 = $38,400

Rate of return=(V1 / V0)-1= ($38,400/$36,900) - 1 = 1.0407 - 1 = 0.0407, or 4.07%

b). The return on each stock is as follows:

RA = (V1 / V0) - 1 = ($92/$87) - 1 = 1.0575 - 1 = 0.0575, or 5.75%

RB = (V1 / V0) - 1 = ($42/$47) - 1 = 0.0894 - 1 =-0.1064, or -10.64%

RC = (V1 / V0) - 1 = ($104/94) - 1 = 1.1064 - 1 = 0.1064, or 10.64%

The equally-weighted average is: [5.75% + (-10.64%) + 10.64%] / 3 = 5.75% / 3 = 1.92%