Question

Consider the three stocks in the following table. P_t represents price at time t, and Q_t represents shares outstanding at time t. Stock C splits two for one in the last period.

	P0	Q0	P1	Q1	P2	Q2
A	55	65	65	65	65	65
B	45	120	35	120	35	120
C	90	120	95	120	50	240

Calculate the first-period rates of return on the following indexes of the three stocks (t = 0 to t = 1): (Do not round intermediate calculations. Round your answers to 2 decimal places.)

a. A market-value-weighted index.

Rate of return %?

b. An equally weighted index.

Rate of return %?

Answer 1

a)
Market value weighted index (t = 0) = Sum of (P0 * Q0)
= (55 * 65) + (45 * 120) + 90 * 120)
= 19,775

Market value weighted index (t = 1) = Sum of (P1 * Q1)
= (65 * 65) + (35 * 120) + (95 * 120)
= 19,825

Rate of return = (Market value weighted index (t = 1) - Market value weighted index (t = 0)) / Market value weighted index (t = 0)
= (19,825 - 19,775) / 19,775
= 50/ 19,775
= 0.25%

Rate of return = 0.25%

b)
Rate of return on stock A = (P1 - P0) / P0
= (65 - 55) / 55
= 10 / 55
= 18.18%

Rate of return on stock B = (35 - 45) / 45
= -10 / 45
= -22.22%

Rate of return on stock C = (95 - 90) / 90
= 5 / 90
= 5.56%

Rate of return on equally weighted index = (18.18% - 22.22% + 5.56%) / 3
= 1.5152% / 3
= 0.51%

Rate of return on equally weighted index = 0.51%