Question

# Consider the three stocks in the following table. Pt represents price at time t, and Qt...

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 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).

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%