12. APT (S8.4) Consider a three-factor APT model. The factors and associated risk premiums are Factor Risk Premium (%)

Change in gross national product (GNP) +5 Change in energy prices −1 Change in long-term interest rates +2 Calculate expected rates of return on the following stocks. The risk-free interest rate is 7%.

a. A stock whose return is uncorrelated with all three factors.

b. A stock with average exposure to each factor (b = 1 for each).

c. A pure-play energy stock with high exposure to the energy factor (b = 2) but zero exposure to the other two factors.

d. An aluminum company stock with average sensitivity to changes in interest rates and GNP, but negative exposure of b = –1.5 to the energy factor. (The aluminum company is energy-intensive and suffers when energy prices rise.)