16 5 9 Portfolio beta 4000000 400000 150 4000000 600000 050 4000000 1000000 125

16 5 9 portfolio beta 4000000 400000 150 4000000

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1.16. 5-9 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. k p = k RF + (k M - k RF )(b p ) = 6% + (14% - 6%)(0.7625) = 12.1%. Alternative solution: First, calculate the return for each stock using the CAPM equation [k RF + (k M - k RF )b], and then calculate the weighted average of these returns. k RF = 6% and (k M - k RF ) = 8%.
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Stock Investment Beta k = k RF + (k M - k RF )b Weight A $ 400,000 1.50 18% 0.10 B 600,000 (0.50) 2 0.15 C 1,000,000 1.25 16 0.25 D 2,000,000 0.75 12 0.50 Total $4,000,000 1.00 k p = 18%(0.10) + 2%(0.15) + 16%(0.25) + 12%(0.50) = 12.1%. 5-10 We know that b R = 1.50, b S = 0.75, k M = 13%, k RF = 7%. k i = k RF + (k M - k RF )b i = 7% + (13% - 7%)b i . k R = 7% + 6%(1.50) = 16.0% k S = 7% + 6%(0.75) = 11.5 4.5% 5-11 X k ˆ = 10%; b X = 0.9; X = 35%. Y k ˆ = 12.5%; b Y = 1.2; Y = 25%. k RF = 6%; RP M = 5%. a. CV X = 35%/10% = 3.5. CV Y = 25%/12.5% = 2.0. b. For diversified investors the relevant risk is measured by beta. Therefore, the stock with the higher beta is more risky. Stock Y has the higher beta so it is more risky than Stock X. c. k X = 6% + 5%(0.9) k X = 10.5%. k Y = 6% + 5%(1.2) k Y = 12%. d. k X = 10.5%; X k ˆ = 10%. k Y = 12%; Y k ˆ = 12.5%. Stock Y would be most attractive to a diversified investor since its expected return of 12.5% is greater than its required return of 12%. e. b p = ($7,500/$10,000)0.9 + ($2,500/$10,000)1.2 = 0.6750 + 0.30 = 0.9750. k p = 6% + 5%(0.975) k p = 10.875%. f. If RP M increases from 5% to 6%, the stock with the highest beta will have the largest increase in its required return. Therefore, Stock Y will have the greatest increase. Check: k X = 6% + 6%(0.9) = 11.4%. Increase 10.5% to 11.4%. k Y = 6% + 6%(1.2)
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= 13.2%. Increase 12% to 13.2%. 5-12 k RF = k* + IP = 2.5% + 3.5% = 6%. k s = 6% + (6.5%)1.7 = 17.05%. 5-13 Using Stock X (or any stock): 9% = k RF + (k M k RF )b X 9% = 5.5% + (k M k RF )0.8 (k M k RF ) = 4.375%. 5-14 In equilibrium: k J = J k ˆ = 12.5%. k J = k RF + (k M - k RF )b 12.5% = 4.5% + (10.5% - 4.5%)b b = 1.33. 5-15 b HRI = 1.8; b LRI = 0.6. No changes occur. k RF = 6%. Decreases by 1.5% to 4.5%.
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