Question

Consider the following stock information (price and number of shares outstanding):

	Stock G	Stock A	Stock Q
P0	$70	$85	$105
Q0	200	500	300
P1	$84	$81	$110
Q1	200	500	300
P2	$20	$85	$24
Q2	800	500	1500

1. Based on the information given, for a price-weighted index of the three stocks calculate:

1.1. the rate of return for the first period (t=0 to t=1). Interpret your answer.

1.2. the value of the divisor in the second period (t=1 to t=2). Assume that Stock G had a 4-1 split and stock Q has a 5-1 split, both during this period just before the market opens in t=2. Interpret your answer.

1.3. the rate of return for the second period (t=1 to t=2). Interpret your answer.

2. Based on the information given for the three stocks, calculate the first-period rates of return (from t=0 to t=1) on

2.1. a market-value-weighted index. Interpret your answer.

2.2. an equally-weighted index. Explain any differences with 1.1. and 2.1.

Answer 1

1.1. The price-weighted index at time 0 is (70 + 85 + 105)/3 = 86.67. The price-weighted index at time 1 is
(84 + 81 + 110)/3 = 91.67. The return on the index is 91.67/86.67 - 1 = 5.77%.

1.2. The divisor must change to reflect the stock split. Because nothing else fundamentally changed, the
value of the index should remain 91.67. So the new divisor is (20 + 85 + 24)/91.67 = 1.41. The index
value is (20 + 85 + 24)/1.41 = 91.67.

1.3. The rate of return for the second period is 91.67/91.67 - 1 = 0.00%.

2.1. The total market value at time 0 is $70 × 200 + $85 × 500 + $105 × 300 = $88,000.

The total market value at time 1 is $84 × 200 + $81 × 500 + $110 × 300 = $90,300.

The return is $90,300/$88,000-1 = 2.61%

2.2. The return on Stock A for the first period is $84/$70 - 1 = 20%

The return on Stock B for the first period is $81/$85 - 1 = -4.71%.

The return on Stock C for the first period is $110/$105 - 1 = 4.76%

The return on an equally weighted index of the three stocks is (20% - 4.71% + 4.76%)/3 = 6.68%