Question

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.

Answer 1

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 capitalisation          
(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          
(33.33333%+20%)/2=   26.67%      

So, Market weighted index Return is 25.33% and equal weighted index return over period is 26.67%