Consider the three stocks in the following table. Pt represents price at time t,
ID: 2722760 • Letter: C
Question
Consider the three stocks in the following table. Pt represents price at time t, and Qt represents shares outstanding at time t. Stock C splits two-for-one in the last period. P0 Q0 P1 Q1 P2 Q2 A 84 100 89 100 89 100 B 44 200 39 200 39 200 C 88 200 98 200 49 400 a. Calculate the rate of return on a price-weighted index of the three stocks for the first period (t = 0 to t = 1). (Do not round intermediate calculations. Round your answer to 2 decimal places.) Rate of return % b. What will be the divisor for the price-weighted index in year 2? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Explanation / Answer
(a). Rate of return on a price-weighted index of the three stocks for the first period (t = 0 to t = 1) = (i) In $ term it is $3.00 (ii) Rate of return in % = 1.19%
%WQs = Weight of a stock in %, %Rs = Return of a stock in %, %WRs = Weightd return of a stock in %, $WRs = Weightd return of a stock in $
Price weighted Index = (84 x 0.20 ) + (44 x 0.40) + (88 x 0.40) = 69.6
(b) The divisor for the price-weighted index in year 2 would be 500 quantity. At t-2, Stock C Split effect should be adjusted for numerator as Pc = $49 x 20 = $98 & QC = 400/2 = 200.
Stock P0 Q0 % WQ0 P1 Q1 %Rs $WRs %WRs A 84 100 0.20 89 100 5.95 1.00 1.19 B 44 200 0.40 39 200 -11.36 -2.00 -4.55 C 88 200 0.40 98 200 11.36 4.00 4.54 SUM 500 3.00 1.19