Consider the three stocks in the following table Pt represen

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

50      

130      

40      

130      

40      

130      

  C

100      

130      

110      

130      

60      

260      

Calculate the first-period and second-period rates of return on the following indexes of the three stocks

1. A market-value-weighted index.

2. An equally weighted index.

	P0	Q0	P1	Q1	P2	Q2
A	55	65	65	65	65	65
B	50	130	40	130	40	130
C	100	130	110	130	60	260

Solution

base period period 1 period 2 market value weight index 55 65 3575 65 65 4225 65 65 4225 50 130 6500 40 130 5200 40 130 5200 100 130 13000 110 130 14300 60 260 15600 23075 23725 25025 base index 100 market weighted index return for period 1 102.8169 0.028169 2.816901 market weighted index return for period 2 105.4795 0.025896 2.589604 equally weighted index return price at period 0 price at period 1 average change price at period 1 price at period 2 average change 55 65 0.181818 65 65 0 50 40 -0.2 40 40 0 100 110 0.1 110 60 -0.45455 average return for period 1 0.081818 index 108.18182 average return for period 1 average return for period 1 -0.45455 index 59.00826 return over period 1 0.0818182 8.181818 return over period 1 return over period 1 -0.45455 -45.4545