Consider the three stocks in the following table. P t represents price at time t
ID: 2382421 • Letter: C
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 spits two-for-one in the last period.
P0
Q0
P1
Q1
P2
Q2
A
90
100
95
100
95
100
B
50
200
45
200
45
200
C
100
200
110
200
55
400
a. Calculate the rate of return on a price-weighted index of the three stocks for the first period (t=0 to t=1).
b. What must happen to the divisor for the price-weighted index in year 2?
c. Calculate the rate of return of the price-weighted index for the second period (t=1 to t=2).
P0
Q0
P1
Q1
P2
Q2
A
90
100
95
100
95
100
B
50
200
45
200
45
200
C
100
200
110
200
55
400
Explanation / Answer
a) Calculate the rate of return on a price-weighted index of the three stocks for the first period (t=0 to t=1)
At t = 0,
Price value of the index = (90 + 50 + 100)/3
Price value of the index = 80
At t = 1,
Price value of the index = (95+45+110)/3
Price value of the index = 83.33
The rate of return = (83.33/80) - 1
The rate of return = 4.16%
(b)What must happen to the divisor for the price-weighted index in year 2?
In the absence of a split, stock C would sell for 110, and the value of the index would be:
(95 + 45 + 110)/3 = 83.33
After the split, stock C sells at 55. Therefore, we need to set the divisor (d) such that:
83.33 = (95 + 45 + 55)/d
d = 195/83.33
d= 2.34
Divisor for the price-weighted index in year 2 = 2.34
(c) Calculate the rate of return of the price-weighted index for the second period (t=1 to t=2).
The rate of return is zero.
Note : The index remains unchanged, as it should, since the return on each stock separately equals zero.