Question

Calculate three stocks A, B, C with prices $10, $20, and $50 respectively.

a) Calculate a price-weighted index.

b) The next day, prices change to $12, $18, and $55. What is the new value of the index?

c) What is the return on a portfolio that holds the same number of shares of each stock?

d) Calculate the divisor if stock C splits two for one, using initial prices.

Answer 1

Answer-

The three stock prices A, B and C have prices $ 10 , $ 20 and $ 50 respectively.

a) The price-weighted index.

price weighted index = sum of the stock prices / divisor
price weighted index = $ 10 + $ 20 + $ 50 / 3
price weighted index = $ 80 / 3 = 26.67

price weighted index = 26.67

b) the prices of A,B and C change to $ 12, $ 18 and $ 55

price weighted index = $ 12 + $ 18 + $ 55 / 3
price weighted index = $ 85 / 3 = 28.33

Therefore the new price weighted index = 28.33

c) The  return on a portfolio that holds the same number of shares of each stock

Suppose there is only one stock of A,B and C
Then return on the portfolio = ( $ 85 - $ 80 ) / $ 80
Then return on the portfolio = $ 5 / $ 80
Then return on the portfolio = 0.0125
Then return on the portfolio = 1.25 %

d) initial prices are A, B and C have prices $ 10 , $ 20 and $ 50 respectively.

Stock C has split by 2:1

Therefore the value of stock C = $ 50 / 2 = $ 25
The index before stock split = ($ 10 + $ 20 + $ 50) / 3 = 26.67
The index after stock split = ($ 10 + $ 20 + $ 25) / 3 = $ 55 / 3 = 18.33

which means that the index decreased although it should not have since stock C's share price did not go down.

We need to keep 26.67 index as it is.

so we have 55 / X = 26.67
Therefore X = 55 / 26.67 = 2.062

X should be lower than 3. It is = 2.062.
Therefore the divisor is 2.062