Sample Questions Chapter 2

Question 1)

Based on the information given in the above table, for a price-weighted index of the three stocks calculate:

a. the rate of return for the first period (t = 0 to t = 1).

b. the value of the divisor in the second period (t = 2). Assume that Stock A had a 2-1 split during this period.

c. the rate of return for the second period (t = 1 to t = 2).

A) The price-weighted index at time 0 is (70 + 85 + 105)/3 = 86.67.

The price-weighted index at time 1 is (72 + 81 + 98)/3 = 83.67.

The return on the index is 83.67/86.67 - 1 = -3.46%.

B) The divisor must change to reflect the stock split. Because nothing else fundamentally changed, the value of the index should remain 83.67.

So the new divisor is (36 + 81 + 98)/83.67 = 2.57.

The index value is (36 + 81 + 98)/2.57 = 83.67.

C) The rate of return for the second period is 83.67/83.67 - 1 = 0.00%.

Question 2)

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

a. a market-value-weighted index.

b. an equally-weighted index.

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

The total market value at time 1 is ($72 × 200) + ($81 × 500) + ($98 × 300) = $84,300.

The return is $84,300/$88,000 - 1 = -4.20%. (4.20% Loss).

B. The return on Stock A for the first period is $72/$70 - 1 = 2.86%.

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 $98/$105 - 1 = -6.67%.

The return on an equally weighted index of the three stocks is (2.86% - 4.71% - 6.67%)/3 = -2.84%.