Question

# Consider the three stocks in the following table. Pt represents price at time t, and Qt...

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 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 %?

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%

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