Chapter 8 Homework Problems Solutions

Chapter 8 Homework Problems Solutions -...

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Solutions to End-of-Chapter Problems 8-1 r ˆ = (0.1)(-50%) + (0.2)(-5%) + (0.4)(16%) + (0.2)(25%) + (0.1)(60%) = 11.40%. σ 2  = (-50% – 11.40%) 2 (0.1) + (-5% – 11.40%) 2 (0.2) + (16% – 11.40%) 2 (0.4)     + (25% – 11.40%) 2 (0.2) + (60% – 11.40%) 2 (0.1) σ 2  = 712.44;  σ  = 26.69%. CV =  11.40% 26.69%  = 2.34. 8-2 Investment Beta $35,000 0.8   40,000 1.4 Total $75,000 b p  = ($35,000/$75,000)(0.8) + ($40,000/$75,000)(1.4) = 1.12. 8-3 r RF  = 6%; r M  = 13%; b = 0.7; r = ? r = r RF  + (r M  – r RF )b = 6% + (13% – 6%)0.7 = 10.9%. 8-4 r RF  = 5%; RP M  = 6%; r M  = ? r M  = 5% + (6%)1 = 11%. r when b = 1.2 = ? r = 5% + 6%(1.2) = 12.2%. 8-5 a. r = 11%; r RF  = 7%; RP M  = 4%. r = r RF  + (r M  – r RF )b Chapter 8:  Risk and Rates of Return Answers and Solutions 1
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11% = 7% + 4%b 4% = 4%b b = 1. 2 Answers and Solutions Chapter 8:  Risk and Rates of Return
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r RF  = 7%; RP M  = 6%; b = 1. r = r RF  + (r M  – r RF )b = 7% + (6%)1 = 13%. 8-6 a. = = N 1 i i i r P r ˆ . Y r ˆ = 0.1(-35%) + 0.2(0%) + 0.4(20%) + 0.2(25%) + 0.1(45%) = 14% versus 12% for X. b. σ  =  = - N 1 i i 2 i P ) r ˆ r ( . 2 X σ  = (-10% – 12%) 2 (0.1) + (2% – 12%) 2 (0.2) + (12% – 12%) 2 (0.4)     + (20% – 12%) 2 (0.2) + (38% – 12%) 2 (0.1) = 148.8%. σ X  = 12.20% versus 20.35% for Y. CV X  =  σ X /r ˆ X  = 12.20%/12% = 1.02, while CV Y  = 20.35%/14% = 1.45. If Stock Y is less highly correlated with the market than X, then it might have a lower beta than  Stock X, and hence be less risky in a portfolio sense. 8-7 Portfolio beta =  $4,000,000 $400,000 (1.50) +  $4,000,000 $600,000 (-0.50) +  $4,000,000 $1,000,000 (1.25) +  $4,000,000 $2,000,000 (0.75)   b p = (0.1)(1.5) + (0.15)(-0.50) + (0.25)(1.25) + (0.5)(0.75) = 0.15 – 0.075 + 0.3125 + 0.375 = 0.7625. r p = r RF  + (r M  – r RF )(b p ) = 6% + (14% – 6%)(0.7625) = 12.1%. Alternative solution:  First, calculate the return for each stock using the CAPM equation  [r RF  + (r M  – r RF )b], and then calculate the weighted average of these returns. r
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Chapter 8 Homework Problems Solutions -...

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