Question

Yesterday Stock A had a price of $50 per share while Stock B had a price of $25 per share. Stock A has 100 shares outstanding while Stock B has 10 shares outstanding. If the prices today of Stock A and B are $55 and $30 respectively, the return of the Equal Weighted Index of these two stocks would be _________%

Answer #1

Weight of each security in equal weighted index = 1/N

Where, N is the number of securities in index

Therefore, weight of each security = 1/2 = 0.5

Initial value of stock A = Initial price of stock A*Number of shares outstanding

= $50*100

= $5000

Ending value of stock A = Ending price of stock A*Number of shares outstanding

= $55*100

= $5500

Return on stock A = (Ending value/Initial value)-1

= ($5500/$5000)-1

= 0.10 or 10%

Initial value of stock B = Initial price of stock B*Number of shares outstanding

= $25*10

= $250

Ending value of stock B = Ending price of stock B*Number of shares outstanding

= $30*10

= $300

Return on stock B = (Ending value/Initial value)-1

= ($300/$250)-1

= 0.20 or 20%

Return of the equal weighted index =Weight of each stock*(Return on stock A + Return of stock B)

= 0.50*(10%+20%)

= 0.50*30%

= 15%

Return of equal weighted index of stock A and B would be 15%.

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