3331 ch8 sol

# 3331 ch8 sol - 8-1rˆ =(0.1-50(0.2-5(0.4(16(0.2(25(0.1(60)=...

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Unformatted text preview: 8-1rˆ = (0.1)(-50%) + (0.2)(-5%) + (0.4)(16%) + (0.2)(25%) + (0.1)(60%)= 11.40%.σ2 = (-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)σ2 = 712.44; σ = 26.69%.CV = 11.40%26.69% = 2.34.8-2InvestmentBeta\$35,0000.8 40,0001.4Total\$75,000bp = (\$35,000/\$75,000)(0.8) + (\$40,000/\$75,000)(1.4) = 1.12.8-3rRF = 6%; rM = 13%; b = 0.7; r = ?r = rRF + (rM – rRF)b= 6% + (13% – 6%)0.7= 10.9%.8-4rRF = 5%; RPM = 6%; rM = ?rM = 5% + (6%)1 = 11%.r when b = 1.2 = ?r = 5% + 6%(1.2) = 12.2%.8-5a.r = 11%; rRF = 7%; RPM = 4%.r = rRF + (rM – rRF)b11% = 7% + 4%b4% = 4%bChapter 8: Risk and Rates of ReturnAnswers and Solutions1b = 1.Chapter 8: Risk and Rates of ReturnAnswers and Solutions2b.rRF = 7%; RPM = 6%; b = 1.r = rRF + (rM – rRF)b= 7% + (6%)1= 13%.8-6a.∑==N1iiirPrˆ.Yrˆ= 0.1(-35%) + 0.2(0%) + 0.4(20%) + 0.2(25%) + 0.1(45%)= 14% versus 12% for X.b.σ = ∑=-N1ii2iP)rˆr(.2Xσ = (-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%.σX = 12.20% versus 20.35% for Y.CVX = σX/rˆX = 12.20%/12% = 1.02, whileCVY = 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.8-7Portfolio 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) bp= (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.rp= rRF + (rM – rRF)(bp) = 6% + (14% – 6%)(0.7625) = 12.1%.Alternative solution: First, calculate the return for each stock using the CAPM equation [rRF + (rM – rRF)b], and then calculate the weighted average of these returns.rRF = 6% and (rM – rRF) = 8%.Chapter 8: Risk and Rates of ReturnAnswers and Solutions3StockInvestmentBetar = rRF + (rM – rRF)bWeightA\$ 400,0001.5018%0.10B600,000(0.50)20.15C1,000,0001.25160.25D 2,000,0000.7512 .50 Total\$4,000,0001 .00 rp = 18%(0.10) + 2%(0.15) + 16%(0.25) + 12%(0.50) = 12.1%.8-8In equilibrium:rJ = Jrˆ = 12.5%.rJ= rRF + (rM – rRF)b12.5% = 4.5% + (10.5% – 4.5%)bb = 1.33....
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3331 ch8 sol - 8-1rˆ =(0.1-50(0.2-5(0.4(16(0.2(25(0.1(60)=...

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