Assume there are only three stocks in the market: A, B, and C. At time 0, P(A) =
ID: 2638574 • Letter: A
Question
Assume there are only three stocks in the market: A, B, and C. At time 0, P(A) = $10, P(B) = $20, and P(C) = $10. At time 1, P(A) = $15, P(B) = $30, P(C) = $5. The number of shares outstanding is 1 million for A, 2 million for B, and 2 million for C.
a. What are the individual stock returns for A, B, and C from time 0 to time 1?
b. What is the return on a price weighted index of these three stocks?
c. What is the return on a price weighted index of these three stocks?
d. What is the return on an equal weighted index of these three stocks?
e. Why the three indexes give different returns?
Answer:
a. Ret(A) = (15-10)/10 = 50%, Ret(B) = (30-20)/20 = 50%, Ret(C) = (5-10)/10 = -50%
b. Ret(PW) =
Explanation / Answer
a. Individual Return of A = P1 - P0 / P0
= 15 - 10 / 10 = 50%
For B = 30 - 20 / 20 = 50%
For C = 5 - 10 / 10 = -50%
b, Total Price of Three stocks at P0 = 10 + 20 + 10 = $40
Weight of A = 10 / 40 = 1/4, Weight of B = 20 / 40 = 2/4, Weight of C = 10/40 = 1/4
Return of A according to Price Weighted Index = 1/4 x 50% = 12.50%
Return of B according to Price Weighted Index = 2/4 x 50% = 25%
Return of C according to Price Weighted Index = 1/4 x -50% = -12.50%
Total Return = 12.50 + 25 - 12.50 = 25%
c. return on a price weighted index of these three stocks:
Total Value of A Stock = $10 x 1 million(Outstanding Share) = 10 million
Total Value of B Stock = $20 x 2 million = 40 million
Total value of C Stock = $10 x 2 million = 20 million
Total Value = 70 million
Proportion of A, B and C = A = 10/70 = 1/7, B = 40 / 70 = 4/7, C = 20/70 = 2/7
Return = 1/7 x 50 + 4/7 x 50 - 2/7 x 50
Return = 21.4%
d. If we give equal weight than = A = 1/3, B =1/3, C = 1/3
Return = 1/3 x50 + 1/3 x 50 - 1/3 x 50
Return = 16.67%
e. Three index giving different returns because weights given to 3 Stocks are different.