What is the return of a market capitalization weighted and evenly weighted index of two stocks with market prices of $30 and $50 that increase to $40 and $60 where the market capitalizations of each is $4 billion and $6 billion respectively at the beginning of the period?
Please show work.
No of shares will be calculated by formula = Market
capitalisation/Price per share
By calculating number of shares, ending Market capitalisation will be calculated by = No of shares* Market price per share
Beg.Price per share Market value No of shares
Stock A 30 4000000000 133333333.3
Stock B 50 6000000000 120000000
Total 80 10000000000
End. Price per share Market value= (no of shares*Price per share) No of shares
Stock A 40 5333333333
Stock B 60 7200000000
Total 100 12533333333
Market weighted return is return calculated on the basis of Market weights.
Formula =(Ending capitalisation-Opening capitalisation)/opening
(12533333333 -10000000000)/ 10000000000
= 0.2533333333 or 25.33%
Equally weighted index return is sum of return of all stocks of index divided by no. of stocks
Return of individual stock formula = (End price - Beginning price)/Beginning price
Return of A = (40-30)/30= 33.33%
Return of B = (60-50)/50= 20.00%
equally weightex return = Total of stock Return/No of stocks
So, Market weighted index Return is 25.33% and equal weighted index return over period is 26.67%