Question

Consider a three-factor APT model. The factors and associated risk premiums are: Factor Risk Premium (%) Change in gross national product (GNP) +5.7 Change in energy prices 0.3 Change in long-term interest rates +2.7 Calculate expected rates of return on the following stocks. The risk-free interest rate is 5.5%. A stock whose return is uncorrelated with all three factors. (Enter your answer as a percent rounded to 1 decimal place.) A stock with average exposure to each factor (i.e., with b = 1 for each). (Enter your answer as a percent rounded to 1 decimal place.) A pure-play energy stock with high exposure to the energy factor (b = 2.1) but zero exposure to the other two factors. (Enter your answer as a percent rounded to 2 decimal places.) An aluminum company stock with average sensitivity to changes in interest rates and GNP, but negative exposure of b = –1.6 to the energy factor. (The aluminum company is energy-intensive and suffers when energy prices rise.) (Enter your answer as a percent rounded to 2 decimal places.) a. Expected rate of return % b. Expected rate of return % c. Expected rate of return % d. Expected rate of return %

Answer 1

APT implies that

1)

A stock whose return is uncorrelated with all three factors

signifies that the stock is uncorrelated

=0

=0

=0

E(R) = 0.055 + 0*0.057 + 0*0.003 + 0*0.027

E(R) = 5.5%

2) A stock with average exposure to each factor (i.e., with b = 1 for each)

=1

=1

=1

E(R) = 0.055 + 1*0.057 + 1*0.003 + 1*0.027

E(R) =14.2%

3)  A pure-play energy stock with high exposure to the energy factor (b = 2.1) but zero exposure to the other two factors.

=0

=2.1

=0

E(R) = 0.055 + 0*0.057 + (2.1)*(0.003) + 0*0.027

E(R) =0.613%

4) An aluminum company stock with average sensitivity to changes in interest rates and GNP, but negative exposure of b = –1.6 to the energy factor. (The aluminum company is energy-intensive and suffers when energy prices rise.)

=1

= -1.6

=1

E(R) = 0.055 + 1*0.057 + (-1.6)*(0.003) + 1*0.027

E(R) =13.42%