chap08_newsol

Fundamentals of Corporate Finance + Standard & Poor's Educational Version of Market Insight

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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 ExxonMobil and security two is Coca- Cola. Then: r 1 = 0.10 σ 1 = 0.182 r 2 = 0.15 σ 2 = 0.273 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 p when ρ = 0 σ p when ρ = 1 σ p when ρ = -1 1.0 0.0 0.100 0.182 0.182 0.182 0.9 0.1 0.105 0.166 0.191 0.137 0.8 0.2 0.110 0.156 0.200 0.091 0.7 0.3 0.115 0.151 0.209 0.046 0.6 0.4 0.120 0.154 0.218 0.000 0.5 0.5 0.125 0.164 0.228 0.046 0.4 0.6 0.130 0.179 0.237 0.091 0.3 0.7 0.135 0.199 0.246 0.137 0.2 0.8 0.140 0.221 0.255 0.182 0.1 0.9 0.145 0.246 0.264 0.228 0.0 1.0 0.150 0.273 0.273 0.273 60
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Correlation = 0 0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00% 14.00% 16.00% 0.00% 10.00% 20.00% 30.00% Standard Deviation Expected Return Correlation = 1 0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00% 14.00% 16.00% 0.00% 10.00% 20.00% 30.00% Standard Deviation 61
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Correlation = -1 0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00% 14.00% 16.00% 0.00% 10.00% 20.00% 30.00% Standard Deviation Expected Return 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 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. 62
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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) = 327.04 Standard deviation = 327.04 (1/2) = 18.08% b. Correlation coefficient = 0 Standard deviation = 14.88% Correlation coefficient = –0.5 Standard deviation = 10.76% c. His portfolio is better. The portfolio has a higher expected return and a lower standard deviation. 5.
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chap08_newsol - CHAPTER 8 Risk and Return Answers to...

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