Question

1. Three stocks have share prices of $12 (A), $75 (B), and $30 (C) with total market values of $400 million, $350 million, and $150 million, respectively. If you were to construct a price-weighted index of the three stocks, what would be the index value? If one year late the stock price of A (+10%), B (+6%) and C (-8%), what would be the new value and return of this index? Show all calculations.

2. Use the information of the problem 1. and calculate the initial and final value, and return for an Equal Weighted Index using this 3 stocks. Show all calculations.

Answer 1

1) Index value = Sum of membes stock price/ No of member stocks

= 12+75+30 / 3

= 117/3

= 39

After one year ,

Price of stock A = 12 x (1+10%)

= 12 x (1+ 0.1)

= 12 x 1.1

= 13.2 $

Price of stock B = 75 x (1+6%)

= 75 x (1+ 0.06)

= 75 x 1.06

= 79.5 $

Price of stock C = 30 x (1+(-8%)

= 30 x (1- 0.08)

= 30 x 0.92

= 27.6 $

Thus value of index after one year = 13.2 + 79.5 + 27.6 / 3

= 120.3 / 3

= 40.10

Thus return over one year = Index value after one year - Index value at begining / Index value at begining

= 40.10 - 39 / 39

= 1.10/39

= 2.82%

2) Equal weighted index value is constructed by investing equal amount in each security

Thus we nedd to find no of shares to be bought for Stock A , Stock B and Stock C

we need to find number which is divisible by 12 , 75 and 30. and that comes to be 300

Thus $300 needs to be invested in each stock to crease equal weighted index

Thus Value of qual weighted index = 300 + 300 + 300 = 900

Equal Weightesd Index is simple avarage of return

Thue Equal weighted Index = Return from stock A + Return from stock B + Return from stock C / 3

= 10% + 6% -8% /3

=8%/3

=2.67%

Thus New Index value = old index value(1+return)

= 900(1+0.0267)

= 900(1.0267)

= 924.03