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CH8 - CHAPTER 8 Risk and Return Answers to Practice...

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CHAPTER 8 Risk and Return Answers to Practice Questions 1. a. False – investors demand higher expected rates of return on stocks with more nondiversifiable risk. b. False – a security with a beta of zero will offer the risk-free rate of return. c. False – the beta will be: (1/3) × (0) + (2/3) × (1) = 0.67 d. True. e. True. 2. In the following solution, security one is Coca-Cola and security two is Reebok. Then: r 1 = 0.10 σ 1 = 0.315 r 2 = 0.20 σ 2 = 0.585 Further, we know that for a two-security portfolio: r p = x 1 r 1 + x 2 r 2 σ p 2 = x 1 2 σ 1 2 + 2x 1 x 2 σ 1 σ 2 ρ 12 + x 2 2 σ 2 2 Therefore, we have the following results: x 1 x 2 r p σ p1 when ρ = 0 σ p1 when ρ = 1 σ p1 when ρ = -1 1.0 0.0 0.10 0.315 0.315 0.315 0.9 0.1 0.11 0.289 0.342 0.225 0.8 0.2 0.12 0.278 0.369 0.135 0.7 0.3 0.13 0.282 0.396 0.045 0.6 0.4 0.14 0.301 0.423 0.045 0.5 0.5 0.15 0.332 0.450 0.135 0.4 0.6 0.16 0.373 0.477 0.225 0.3 0.7 0.17 0.420 0.504 0.315 0.2 0.8 0.18 0.472 0.531 0.405 0.1 0.9 0.19 0.527 0.558 0.495 0.0 0.0 0.20 0.585 0.585 0.585 71
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72 Correlation = 0 0.0% 5.0% 10.0% 15.0% 20.0% 25.0% 0.0% 20.0% 40.0% 60.0% 80.0% Standard Deviation Expected Return Correlation = 1 0.0% 5.0% 10.0% 15.0% 20.0% 25.0% 0.0% 20.0% 40.0% 60.0% 80.0% Standard Deviation Expected Return Correlation = -1 0.0% 5.0% 10.0% 15.0% 20.0% 25.0% 0.0% 20.0% 40.0% 60.0% 80.0% Standard Deviation Expected Return
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3. a. Portfolio r σ 1 10.0% 5.1% 2 9.0 4.6 3 11.0 6.4 b. See the figure below. The set of portfolios is represented by the curved line. The five points are the three portfolios from Part (a) plus the two following two portfolios: one consists of 100% invested in X and the other consists of 100% invested in Y. c. See the figure below. The best opportunities lie along the straight line. From the diagram, the optimal portfolio of risky assets is portfolio 1, and so Mr. Harrywitz should invest 50 percent in X and 50 percent in Y.-+ 4. a. Expected return = (0.6 × 15) + (0.4 × 20) = 17% Variance = (0.6) 2 × (20) 2 + (0.4) 2 × (22) 2 + 2(0.6)(0.4)(0.5)(20)(22) = 327 Standard deviation = (327) (1/2) = 18.1% b. Correlation coefficient = 0 Standard deviation = 14.9% Correlation coefficient = -0.5 Standard deviation = 10.8% c. His portfolio is better. The portfolio has a higher expected return and a lower standard deviation. 73 0 0.05 0.1 0.15 0 0.02 0.04 0.06 0.08 0.1 Standard Deviation H H H H H
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5. Internet exercise; answers will vary depending on time period. 6. Internet exercise; answers will vary depending on time period. 7. a. b. Market risk premium = r m - r f = 0.12 - 0.04 = 0.08 = 8.0% c. Use the security market line: r = r f + β (r m - r f ) r = 0.04 + [1.5 × (0.12 - 0.04)] = 0.16 = 16.0% d. For any investment, we can find the opportunity cost of capital using the security market line. With β = 0.8, the opportunity cost of capital is: r = r f + β (r m - r f ) r = 0.04 + [0.8 × (0.12 - 0.04)] = 0.104 = 10.4% The opportunity cost of capital is 10.4 percent and the investment is expected to earn 9.8 percent. Therefore, the investment has a negative NPV.
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