Consider the three stocks in the following table. P t represents price at time t
ID: 1169911 • 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 splits two-for-one in the last period.
P0
Q0
P1
Q1
P2
Q2
A
85
150
90
150
90
150
B
40
600
35
600
35
600
C
70
100
80
100
40
200
Calculate the rate of return on a price-weighted index of the three stocks for the first period (t = 0 to t = 1).
What must happen to the divisor for the price-weighted index in year 2?
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
85
150
90
150
90
150
B
40
600
35
600
35
600
C
70
100
80
100
40
200
Explanation / Answer
a)
at time , t = 0
p0A = 85
p0B = 40
p0C = 70
the index value ( at time t=0) =x = (p0A + p0B + p0C)/3 = (85+40+70)/3 = 65
similarly the index value at t=1 = x1= (90+35+80)/3 = 68.3333
rate of return = (x1-x)/x = (68.3333-65)/65 = 0.0512815 or 5.12815% or 5.13% ( rounding off to 2 decimal places)
b)
in year 2, there is a stock split , but the stock split does not affect the index value
let
price of A at t=2 = p1 = 90
price of B at t=2 = p2 = 35
price of C at t=2 = p3 = 40
the new divisor , d, should be set such that:
(p1+p2+p3)/d = x1
(90+35+40)/d = 68.3333
d = (90+35+40)/68.3333 = 165/68.3333 = 2.41463 or 2.41 ( rounding off to 2 decimal places)
c) since the value of the index during t=2 remains the same , the rate of return for second period = 0