Ross4eChap11sm - Chapter 11 Return and Risk The...

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Chapter 11: Return and Risk: The Capital-Asset-Pricing Model (CAPM) 11.1 a. Expected Return = (0.1)(-0.045) + (.2)(0.046) + (0.5)(0.125) + (0.2)(0.207) = 0.1086 = 10.86% The expected return on Q-mart’s stock is 10.86%. b. Variance ( σ 2 ) = (0.1)(-0.045 – 0.1086) 2 + (0.2)(0.046 – 0.1086) 2 + (0.5)(0.125 – 0.1086) 2 + (0.2)(0.207 – 0.1086) 2 = 0.005214 Standard Deviation ( σ ) = (0.005214) 1/2 = 0.0722 = 7.22% The standard deviation of Q-mart’s returns is 7.22%. 11.2 a. Expected Return = (0.2)(0.05) + (.6)(0.08) + (0.2)(0.15) = 0.088 = 8.8% The expected return on 8.8%. c. Variance ( σ 2 ) = (0.2)(0.05 – 0.088) 2 + (0.6)(0.08 – 0.088) 2 + (0.2)(0.15 – 0.088) 2 = 0.001096 Standard Deviation ( σ ) = (0.001096) 1/2 = 0.03311 = 3.31% The standard deviation of the return is 3.31%. 11.3 a. and b. Economic condition Probability Market return Weighted average Trebli return Weighted average Rapid expansion 0.12 0.0276 0.0144 Moderate expansion 0.40 0.072 0.036 No growth 0.25 0.0375 0.0125 Moderate contraction 0.15 0.0135 0.0015 Serious contraction 0.08 0.0024 -0.0016 Total 1.00 0.153 0.0628 The expected return on the market is 15.3% and on Trembli is 6.28% Answers to End-of-Chapter Problems B-129
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11.4 a. and b. Belinkie Enterprises: P Weighted average (R-E( R))^2 P(R-E( R)^2 Year Probability Return Expected return 1 0.25 0.0400 0.0100 0.00030625 0.000076563 2 0.25 0.0600 0.0150 0.00000625 0.000001563 3 0.25 0.0900 0.0225 0.00105625 0.000264063 4 0.25 0.0400 0.0100 0.00030625 0.000076563 Expected return 0.0575 Variance 0.000418752 The expected return for Belinkie is 5.75% and the variance is 0.00041875 Overlake Company P Weighted average (R-E( R))^2 P(R-E( R)^2 Year Probability Return Expected return 1 0.25 0.0500 0.0125 0.0016000 0.000400000 2 0.25 0.0700 0.0175 0.0004000 0.000100000 3 0.25 0.1000 0.0250 0.0001000 0.000025000 4 0.25 0.1400 0.0350 0.0025000 0.000625000 Expected return 0.0900 Variance 0.001150000 The expected return for Overlake is 9% and the variance is 0.00115. 11.5 The return on the T-Bills is 3.5% in very state, so the expected return is 3.5%. Economic condition Probability Market return Weighted average Recession 0.20 -1.64% Normal 0.60 7.38% Boom 0.20 5.16% Total 1.00 10.9% The expected return on the market is 10.9% and on T-Bills is 3.50%. The market risk premium is the difference of 7.4% ( 10.9% – 3.5%). 11.6 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) Answers to End-of-Chapter Problems B-130
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= 0.0933 = 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 – 0.0933) + (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. 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. 11.7 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)(0.045) + (0.60)(0.057) + (0.15)(0.069) = 0.0558 = 5.58% The expected return on Slowbear’s stock is 5.58%. Answers to End-of-Chapter Problems B-131
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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%.
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