Question

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.

	P0	Q0	P1	Q1	P2	Q2
A	97	100	102	100	102	100
B	57	200	52	200	52	200
C	114	200	124	200	62	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 will be 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).

Answer 1

a)
Value of index (t=0) = (97 + 57 + 114) / 3 = 268 / 3 = 89.33

Value of index (t=1) = (102 + 52 + 124) / 3 = 278 / 3 = 92.67

Rate of return = (Value of index (t=1) - Value of index (t=0)) / Value of index (t=0)
= (92.67 - 89.33) / 89.33
= 3.3333 / 89.3333
= 3.73%

Rate of return = 3.73%

b)
92.67 = (102 + 52 + 62) / Divisor
92.67 = 216 / Divisor

Divisor = 216 / 92.67 = 2.33

Divisor = 2.33

c)
Rate of return = (Value of index (t=2) - Value of index (t=1)) / Value of index (t=1)
= (92.67 - 92.67) / 92.67
= 0.00%

Rate of return = 0.00%