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.
P_{0} | Q_{0} | P_{1} | Q_{1} | P_{2} | Q_{2} | |
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
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%
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