Chapter 10 Solutions V2

Chapter 10 Solutions V2 - Chapter 10: Return and Risk: The...

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Chapter 10: Return and Risk: The Capital Asset Pricing Model (CAPM) 10.1 a. Expected Return = (0.1)(-0.045) + (.2)(0.044) + (0.5)(0.12) + (0.2)(0.207) = 0.1057 = 10.57% The expected return on Q-mart’s stock is 10.57%. b. Variance ( σ 2 ) = (0.1)(-0.045 – 0.1057) 2 + (0.2)(0.044 – 0.1057) 2 + (0.5)(0.12 – 0.1057) 2 + (0.2)(0.207 – 0.1057) 2 = 0.005187 Standard Deviation ( σ ) = (0.005187) 1/2 = 0.0720 = 7.20% The standard deviation of Q-mart’s returns is 7.20%. 10.2 a. Expected Return A = (1/3)(0.063) + (1/3)(0.105) + (1/3)(0.156) = 0.1080 = 10.80% The expected return on Stock A is 10.80%. Expected Return B = (1/3)(-0.037) + (1/3)(0.064) + (1/3)(0.253) = 0.933 = 9.33% The expected return on Stock B is 9.33%. b. Variance A ( σ A 2 ) = (1/3)(0.063 – 0.108) 2 + (1/3)(0.105 – 0.108) 2 + (1/3)(0.156 – 0.108) 2 = 0.001446 Standard Deviation A ( σ A ) = (0.001446) 1/2 = 0.0380 = 3.80% The standard deviation of Stock A’s returns is 3.80%. Variance B ( σ B 2 ) = (1/3)(-0.037 – 0.0933) 2 + (1/3)(0.064 – 0.0933) 2 + (1/3)(0.253 – 0.0933) 2 = 0.014447 Standard Deviation B ( σ B ) = (0.014447) 1/2 = 0.1202 = 12.02% The standard deviation of Stock B’s returns is 12.02%. c. Covariance(R A , R B ) = (1/3)(0.063 – 0.108)(-0.037 – 0.0933) + (1/3)(0.105 – 0.108)(0.064 – 0.933) + (1/3)(0.156 – 0.108)(0.253 – 0.0933) = 0.004539 The covariance between the returns of Stock A and Stock B is 0.004539.
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Correlation(R A ,R B ) = Covariance(R A , R B ) / ( σ A * σ B ) = 0.004539 / (0.0380 * 0.1202) = 0.9937 The correlation between the returns on Stock A and Stock B is 0.9937. 10.3 a. Expected Return HB = (0.25)(-0.02) + (0.60)(0.092) + (0.15)(0.154) = 0.0733 = 7.33% The expected return on Highbull’s stock is 7.33%. Expected Return SB = (0.25)(0.05) + (0.60)(0.062) + (0.15)(0.074) = 0.0608 = 6.08% The expected return on Slowbear’s stock is 6.08%. b. Variance A ( σ HB 2 ) = (0.25)(-0.02 – 0.0733) 2 + (0.60)(0.092 – 0.0733) 2 + (0.15)(0.154 – 0.0733) 2 = 0.003363 Standard Deviation A ( σ HB ) = (0.003363) 1/2 = 0.0580 = 5.80% The standard deviation of Highbear’s stock returns is 5.80%. Variance B ( σ SB 2 ) = (0.25)(0.05 – 0.0608) 2 + (0.60)(0.062 – 0.0608) 2 + (0.15)(0.074 – 0.0608) 2 = 0.000056 Standard Deviation B ( σ B ) = (0.000056) 1/2 = 0.0075 = 0.75% The standard deviation of Slowbear’s stock returns is 0.75%. c. Covariance(R HB , R SB ) = (0.25)(-0.02 – 0.0733)(0.05 – 0.0608) + (0.60)(0.092 – 0.0733)(0.062 – (0.0608) + (0.15)(0.154 – 0.0733)(0.074 – 0.0608) = 0.000425 The covariance between the returns on Highbull’s stock and Slowbear’s stock is 0.000425. Correlation(R A ,R B ) = Covariance(R A , R B ) / ( σ A * σ B ) = 0.000425 / (0.0580 * 0.0075) = 0.9770 The correlation between the returns on Highbull’s stock and Slowbear’s stock is 0.9770. 10.4
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Chapter 10 Solutions V2 - Chapter 10: Return and Risk: The...

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