The following question illustrates the APT. Imagine that there are only two pervasive macroeconomic factors. Investments X, Y, and Z have the following sensitivities to these two factors: Investments...

The following question illustrates the APT. Imagine that there are only two pervasive macroeconomic factors. Investments X, Y, and Z have the following sensitivities to these two factors:



                 Investments                       b1                        b2

                        X                                1.75                      0.25

                        Y                                1.00                      2.00

                        Z                                2.00                      1.00



Assume that the expected risk premium is 4% on factor 1 and 8% on factor 2. Treasury bills offer zero risk premium.

a. According to the APT, what is the risk premium on each of the three stocks?

b. Suppose you buy $200 of X and $50 of Y and sell $150 of Z. What is the sensitivity of your portfolio to each of the two factors? What is the expected risk premium?

c. Suppose you buy $80 of X and $60 of Y and sell $40 of Z. What is the sensitivity of your portfolio to each of the two factors? What is the expected risk premium?

d. Finally, suppose you buy $160 of X and $20 of Y and sell $80 of Z. What is your portfolio’s sensitivity now to each of the two factors? And what is the expected risk premium?

e. Suggest two possible ways that you could construct a fund that has a sensitivity of .5 to factor 1 only. (Hint: One portfolio contains an investment in Treasury bills.) Now compare the risk premiums on each of these two investments.