And cv a cv b 6 5 according to the security market

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and CV A > CV B . 6-5 According to the Security Market Line (SML) equation, an increase in beta will increase a company’s expected return by an amount equal to the market risk premium times the change in beta. For example, assume that the risk-free rate is 6 percent, and the market risk premium is 5 percent. If the company’s beta doubles from 0.8 to 1.6 its expected return increases from 10 percent to 14 percent. Therefore, in general, a company’s expected return will not double when its beta doubles. SOLUTIONS TO END-OF-CHAPTER PROBLEMS 6-1 Investment Beta \$20,000 0.7 35,000 1.3 Total \$55,000 (\$20,000/\$55,000)(0.7) + (\$35,000/\$55,000)(1.3) = 1.08. 6-2 r RF = 4%; r M = 12%; b = 0.8; r s = ? r s = r RF + (r M - r RF )b = 4% + (12% - 4%)0.8 = 10.4%. 28
6-9 Old portfolio beta = 5,000 7 \$ 00 0 , 70 \$ (b) + 5,000 7 \$ 00 0 , 5 \$ (0.8) 1.2 = 0.9333b + 0.0533 1.1467 = 0.9333b 1.229 = b. New portfolio beta = 0.9333(1.229) + 0.0667(1.6) = 1.25. Alternative Solutions: 1. Old portfolio beta = 1.2 = (0.0667)b 1 + (0.0667)b 2 +...+ (0.0667)b 20 1.2 = ( b i )(0.0667) b i = 1.2/0.0667 = 18.0. New portfolio beta = (18.0 - 0.8 + 1.6)(0.0667) = 1.253 = 1.25. 2. b i excluding the stock with the beta equal to 0.8 is 18.0 - 0.8 = 17.2, so the beta of the portfolio excluding this stock is b = 17.2/14 = 1.2286. The beta of the new portfolio is: 1.2286(0.9333) + 1.6(0.0667) = 1.1575 = 1.253. 29
6-10 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) = 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 compute the return for each stock using the CAPM equation [r RF + (r M - r RF )b], and then compute the weighted average of these returns. r RF = 6% and r M - r RF = 8%. Stock Investment Beta r = r RF + (r M - r 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 r p = 18%(0.10) + 2%(0.15) + 16%(0.25) + 12%(0.50) = 12.1%. 6-13 The answers to a, b, and c are given below: ¯ A ¯ B Portfolio 2009 (20.00%) (5.00%) (12.50%) 30
2010 42.00 15.00 28.50 2011 20.00 (13.00) 3.50 2012 (8.00) 50.00 21.00 2013 25.00 12.00 18.50 Mean 11.80 11.80 11.80 Std Dev 25.28 24.32 16.34 d. A risk-averse investor would choose the portfolio over either Stock A or Stock B alone, since the portfolio offers the same expected return but with less risk. This result occurs because returns on A and B are not perfectly positively correlated (ρ AB = -0.13). Chapter 25 Portfolio Theory and Asset Pricing Models ANSWERS TO END-OF-CHAPTER QUESTIONS 25-1 a. A portfolio is made up of a group of individual assets held in combination. An asset that would be relatively risky if held in isolation may have little, or even no risk if held in a well-diversified portfolio. The feasible, or attainable, set represents all portfolios that can be constructed from a given set of stocks. This set is only efficient for part of its combinations. An efficient portfolio is that portfolio which provides the highest expected return for any degree of risk. Alternatively, the efficient portfolio is that which provides the lowest degree of risk for any expected return. The efficient frontier is the set of efficient portfolios out of the full set of potential portfolios. On a graph, the efficient frontier constitutes the boundary line of the set of potential portfolios. 31
b. An indifference curve is the risk/return trade-off function for a particular investor and reflects that investor's attitude toward risk. The indifference curve specifies an investor's required rate of return for a given level of risk. The greater the slope of the indifference curve, the greater is the investor's risk aversion. The optimal portfolio for an investor is the point at which the efficient set of portfolios--the
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