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: Investment b1 b2 X 1.75 0 Y −1.00 2.00 Z 2.00 1.00 We assume that the expected risk premium is 7.8% on factor 1 and 11.8% on factor 2. Treasury bills obviously offer zero risk premium. According to the APT, what is the risk premium on each of the three stocks? Suppose you buy $500 of X and $125 of Y and sell $375 of Z. What is the sensitivity of your portfolio to each of the two factors? What is the expected risk premium? Suppose you buy $200 of X and $150 of Y and sell $100 of Z. What is the sensitivity of your portfolio to each of the two factors? What is the expected risk premium? Finally, suppose you buy $400 of X and $50 of Y and sell $200 of Z. What is your portfolio's sensitivity now to each of the two factors? And what is the expected risk premium?
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: Investment b1 b2 X 1.75 0 Y −1.00 2.00 Z 2.00 1.00 We assume that the expected risk premium is 7.8% on factor 1 and 11.8% on factor 2. Treasury bills obviously offer zero risk premium. According to the APT, what is the risk premium on each of the three stocks? Suppose you buy $500 of X and $125 of Y and sell $375 of Z. What is the sensitivity of your portfolio to each of the two factors? What is the expected risk premium? Suppose you buy $200 of X and $150 of Y and sell $100 of Z. What is the sensitivity of your portfolio to each of the two factors? What is the expected risk premium? Finally, suppose you buy $400 of X and $50 of Y and sell $200 of Z. What is your portfolio's sensitivity now to each of the two factors? And what is the expected risk premium?
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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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:
| Investment | b1 | b2 |
| X | 1.75 | 0 |
| Y | −1.00 | 2.00 |
| Z | 2.00 | 1.00 |
We assume that the expected risk premium is 7.8% on factor 1 and 11.8% on factor 2. Treasury bills obviously offer zero risk premium.
-
According to the APT, what is the risk premium on each of the three stocks?
-
Suppose you buy $500 of X and $125 of Y and sell $375 of Z. What is the sensitivity of your portfolio to each of the two factors? What is the expected risk premium?
-
Suppose you buy $200 of X and $150 of Y and sell $100 of Z. What is the sensitivity of your portfolio to each of the two factors? What is the expected risk premium?
-
Finally, suppose you buy $400 of X and $50 of Y and sell $200 of Z. What is your portfolio's sensitivity now to each of the two factors? And what is the expected risk premium?
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