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pre-Exam I-solution

# pre-Exam I-solution - University of Southern California...

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University of Southern California Pre-test FBE 441 Time 1 Hr 40 Min. Answer all questions 1. Consider the multifactor APT with two factors. Stock A has an expected return of 17.6%, a beta of 1.45 on factor 1 and a beta of .86 on factor 2. The risk premium on the factor 1 portfolio is 3.2%. The risk-free rate of return is 5%. What is the risk-premium on factor 2 if no arbitrage opportunities exit? A. 9.26% B. 3% C. 4% D. 7.75% E. none of the above 17.6% = 1.45(3.2%) + .86x + 5%; x = 9.26. 2. Consider the one-factor APT. The standard deviation of returns on a well-diversified portfolio is 19%. The standard deviation on the factor portfolio is 12%. The beta of the well-diversified portfolio is approximately __________. (19%) 2 = (12%) 2 b 2 ; b = 1.58. 3. Consider the one-factor APT. The variance of returns on the factor portfolio is 11%. The beta of a well-diversified portfolio on the factor is 1.45. The variance of returns on the well- diversified portfolio is approximately __________. s 2 P = (1.45) 2 (11%) = 23.13%.

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4. Consider a single factor APT. Portfolio A has a beta of 2.0 and an expected return of 22%. Portfolio B has a beta of 1.5 and an expected return of 17%. The risk-free rate of return is 4%. If you wanted to take advantage of an arbitrage opportunity, you should take a short position in portfolio __________ and a long position in portfolio _______. A: 22% = 2.0F + 4%; F = 9%; B: 17% = 1.5F + 4%: F = 8.67%; thus, short B and take a long position in A. 5. Consider the multifactor model APT with three factors. Portfolio A has a beta of 0.8 on factor 1, a beta of 1.1 on factor 2, and a beta of 1.25 on factor 3. The risk premiums on the factor 1, factor 2, and factor 3 are 3%, 5% and 2%, respectively. The risk-free rate of return is 3%. The expected return on portfolio A is __________ if no arbitrage opportunities exist. A. 13.5% B. 13.4% C. 16.5% D. 23.0% E. none of the above 3% + 0.8(3%) + 1.1(5%) + 1.25(2%) = 13.4%. 6. Security A has an expected rate of return of 0.10 and a beta of 1.3. The market expected rate of return is 0.10 and the risk-free rate is 0.04. The alpha of the stock is 10% - [4% +1.3(10% - 4%)] = -1.8%. 7. The risk-free rate is 4 percent. The expected market rate of return is 12 percent. If you expect stock X with a beta of 1.0 to offer a rate of return of 10 percent, you should 10% < 4% + 1.0(12% - 4%) = 12.0%; therefore, stock is overpriced and should be shorted.

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pre-Exam I-solution - University of Southern California...

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