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%
