Workshop 3 - INVESTMENTS WORKSHOP 2 DR BEN TIMS CHAPTER 8 9...

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INVESTMENTS: WORKSHOP 2 DR. BEN TIMS
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CHAPTER 8: 9 R A = 2 . 4 % + 0 . 85 R M + e A with R 2 = 0 . 17 R B = - 2 . 4 % + 1 . 3 R M + e B with R 2 = 0 . 11 σ M = 25 % Question: what are σ A and σ B ? R 2 = Explained variance Totalvariance = σ 2 ( β A R M ) σ 2 A σ 2 A = σ 2 ( β A R M ) R 2 A = ( 0 . 85 * 0 . 25 ) 2 0 . 17 = 0 . 265625 σ ( R A ) = p ( 0 . 265625 ) = 0 . 515388 Similarly σ ( R B ) = 0 . 979912 % Dr. Ben Tims (RSM) Investments: Workshop 2 September 23, 2015 2 / 26
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CHAPTER 8: 10 Total risk = Systematic risk + firm-specific risk σ 2 = β 2 σ 2 M + σ 2 ( e ) σ 2 ( e A ) = σ 2 A - β 2 A σ 2 M = 0 . 265625 - 0 . 85 2 * 0 . 25 2 = 0 . 220469 Similarly σ 2 ( e B ) = 0 . 854602 Dr. Ben Tims (RSM) Investments: Workshop 2 September 23, 2015 3 / 26
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CHAPTER 8: 11 Cov ( R A , R B ) = Cov ( 2 . 4 % + 0 . 85 R M + e A , - 2 . 4 % + 1 . 3 R M + e B ) Note that Cov ( X + Y , Z ) = Cov ( X , Z ) + Cov ( Y , Z ) Furthermore, note that constant (= α ) is uncorrelated with other factors market return is uncorrelated with residuals (systematic vs firm-specific risk) residuals of A and B are assumed to be uncorrelated as risk is firm-specific Dr. Ben Tims (RSM) Investments: Workshop 2 September 23, 2015 4 / 26
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CHAPTER 8: 11 Cov ( 2 . 4 %+ 0 . 85 R M + e A , - 2 . 4 %+ 1 . 3 R M + e B ) = = Cov ( 0 . 85 R M , 1 . 3 R M ) = = 0 . 85 * 1 . 3 * 0 . 25 2 (= β A β B σ 2 M ) = = 0 . 0690625 Correlation ( R A , R B ) = Cov ( R A , R B ) σ A σ B = = 0 . 0690625 0 . 5154 * 0 . 9799 = 0 . 136746 Dr. Ben Tims (RSM) Investments: Workshop 2 September 23, 2015 5 / 26
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CHAPTER 8: 12 Several ways to calculate Cov ( R A , R M ) Method 1: note that β A = Cov ( R A , R M ) σ 2 M Cov ( R A , R M ) = β A σ 2 M = 0 . 85 * 0 . 25 2 = 0 . 053125 Method 2: for simple regressions R 2 = Correlation ( R A , R M ) 2 = = Cov ( R A , R M ) 2 σ 2 A σ 2 M Cov ( R A , R M ) = p ( R 2 ) σ A σ B = 0 . 053126216 Dr. Ben Tims (RSM) Investments: Workshop 2 September 23, 2015 6 / 26
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CHAPTER 8: 12 Method 3: Cov ( R i , R j ) = β i β j σ 2 M Cov ( R A , R M ) = β A β M σ 2 M = 0 . 85 * 1 * 0 . 25 2 = 0 . 053125 Similarly, Cov ( R A , R M ) = 0 . 08125 Dr. Ben Tims (RSM) Investments: Workshop 2 September 23, 2015 7 / 26
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