Question

Stock Initial Price Final Price Number of Outstanding Shares Stock 1 $20 $23 5 million Stock 2 $40 $42 4 million Stock 3 $80 $70 2 million Compute the rate of return for each of the following portfolios: (a) Price weighted (b) Value weighted (c) Equal weighted

Answer 1

Particulars	Stock 1	Stock 2	Stock 3
Initial Price	$20	$40	$80
Final Price	$23	$42	$70
Number of Outstanding Shares	5 million	4 million	2 million

a. Price Weighted

Rate of Return = (Sum of Final Share Prices -Sum of Initial Share Prices)/Number of Stocks

Rate of Return = ((23+42+70)- (20+40+80))/(20+40+8) = (135-140)/140 = -3.57%

b. Value weighted

Rate of Return = [Sum of (lnitial Price*Outstanding Shares) for all stock - Sum of (Final Price*Outstanding Shares) for all stock] / Sum of (lnitial Price*Outstanding Shares) for all stock

Sum of (lnitial Price*Outstanding Shares) for all stock = 5*20+4*40+2*80 = $420 million

Sum of (Final Price*Outstanding Shares) for all stock = 5*23+4*42+2*70 = $423 million

Rate of Return = (423-420)/420 = 0.71%

c. Equal Weighted

A’s return is ($23 – $20) / $20 = 15%, B’s return is ($42 – $40) / $40 = 5%, and C’s return is ($70 – $80) / $80 = -12.5%. The average return, therefore, is (15% + 5% – 12.5%)/3 = 2.5%.