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.
P0 Q0 P1 Q1 P2 Q2
A 99 100 104 100 104 100
B 59 200 54 200 54 200
C 118 20 128 200 64 400
Calculate the first-period rates of return on the following indexes of the three stocks:
a. A market value–weighted index
b. An equally weighted index.

Answer 1

Answer:

a. Rate of return = 94.51%

b. Rate of return = 1.68%

Explanation:

a. A market value–weighted index

Total market value at time 0 = Market value of Stock A at time 0 + Market value of Stock B at time 0 + Market value of Stock C at time 0 = ($99 * 100) + ($59 * 200) + ($118 * 20) = $24,060

Total market value at time 1 = Market value of Stock A at time 1 + Market value of Stock B at time 1 + Market value of Stock C at time 1 = ($104 * 100) + ($54 * 200) + ($128 * 200) = $46,800

Rate of return = (Total market value at time 1 / Total market value at time 0) – 1 = ($46,800 / $24,060) - 1 = 0.9451, or 94.51%

b. An equally weighted index

Return on a Stock for the first period = (P1 / P0) - 1 …………. (1)

Therefore, we have:

Return on Stock A for the first period = ($104 / $99) - 1 = 0.0505, or 5.05%

Return on Stock B for the first period = ($54 / $59) - 1 = - 0.0847, or - 8.47%

Return on Stock C for the first period = ($128 / $118) - 1 = 0.0847, or 8.47%

Therefore, we have:

Return of return = (Return on Stock A for the first period + Return on Stock B for the first period + Return on Stock C for the first period) / 3 = (5.05% - 8.47% + 8.47%) / 3 = 1.68%