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. According to the APT, what is the risk premium on each of the three stocks? 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. Suppose that the APT did not hold and that X offered a risk premium of 8%, Y offered a premium of 14%, and Z offered a premium of 16%. Devise an investment that has zero sensitivity to each factor and that has a positive risk premium.

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