3. Consider the three stocks in the following table. Pt represents price at time
ID: 2730315 • Letter: 3
Question
3. 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
135
140
140
140
140
140
B
125
280
120
280
120
280
C
250
280
260
280
135
560
Calculate the first period rates of return on the following indexes of the three stocks (t = 0 to t = 1)
a. A market value-weighted index. (10 points)
b. An equally weighted index. (10 points
P0
Q0
P1
Q1
P2
Q2
A
135
140
140
140
140
140
B
125
280
120
280
120
280
C
250
280
260
280
135
560
Explanation / Answer
a) Rate of return on market-value weighted index:-
When t = 0, the value of the index is: (135+ 125 + 250 ) /3 = 170
When t = 1, the value of the index is: (140 + 120 + 260) /3 = 173.33
Rate of return = (173.3333/170) – 1
= 1.96 % (approx)
Conclusion:- The rate of return on market value weighted index = 1.96 %.
b) When Stock C splits two for one, then the stock will sell at 260 / 2 = $ 130 at end of year 1 (t = 1) and 250 /2 = $ 125 at the year beginning (t = 0).
When t = 0, the value of the index is: (135+ 125 + 125 ) /3 = 128.33
When t = 1, the value of the index is: (140 + 120 + 130) /3 = 130
Rate of return = (130 /128.33) – 1
= 1.30 % (approx)
Conclusion:- The rate of return on equity weighted index = 1.30 %.
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