Question

7b. Consider three stocks A, B, and C, with closing price at time t being P, and the number of shares time t as Q Stock C splits three-for-one at the beginning of period -2 (before the market opens). 1000 the market opens of shares outstanding at 43 1000 35 56 102 1000 30 5000 67 5000 5000 B 62 C 98 i. What is the return on a price-weighted index of the three stocks for the period r-0 to r-1? 3000 3000 = Inden-Indera Indexo Create the index at r-o and尸1 and compute Return on index = maerden PW, a P PC At the start of the index the divisor d, is typically the number of companies in the index ii. What is the return on an equally-weighted index of the three stocks for the period r-0 to r-1? Compute the return on each stock in the index and take average return ii. What is the return on a value-weighted index of the three stocks for the period r-0 to-1? Create the index at r-0 and 1 and compute return on index Pa (Q) is the price (number of shares outstanding) for stock A at time r; Pao (Q40) are values at -0 MVAt PAtxQAt is the market value of stock A at time t Base is a number, typically 100 or 1,000, to move the index value away from a fraction

Answer 1

Part (i)

Index₀ = (30 + 62 + 98) / 3 = 63.33

Index₁ = (35 + 56 + 102) / 3 = 64.33

hence, return on index = (64.33 - 63.33) / 63.33 = 1.58%

Part (ii)

Return on A = 35/30 - 1 = 16.67%

Return on B = 56 / 62 - 1 = - 9.68%

Return on C = 102 / 98 - 1 = 4.08%

Average of these returns = 3.69%

Part (iii)

	P0	Q0	P0 x Q0	P1	Q1	P1 x Q1
A	30	1,000	30,000	35	1,000	35,000
B	62	5,000	310,000	56	5,000	280,000
C	98	3,000	294,000	102	3,000	306,000
Total			634,000			621,000

Return on value weighted index = 621,000 / 634,000 - 1 = - 2.05%