solution to hw3.pdf - Solutions of HW3 1 A 1 = market β 12...

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Solutions of HW3 1 A 1 = market β % 12 % 3 2 . 0 % 18 3 . 0 % 12 5 . 0 ) ( = × + × + × = dell R E 0027 . 0 %) 12 % 3 ( 2 . 0 %) 12 % 18 ( 3 . 0 %) 12 % 12 ( 5 . 0 ) ( 2 2 2 = × + × + × = dell R Var % 4 . 14 % 4 2 . 0 % 12 3 . 0 % 20 5 . 0 ) ( = × + × + × = market R E 003904 . 0 %) 4 . 14 % 4 ( 2 . 0 %) 4 . 14 % 12 ( 3 . 0 %) 4 . 14 % 20 ( 5 . 0 ) ( 2 2 2 = × + × + × = market R Var 00144 . 0 %) 4 . 14 % 4 ( %) 12 % 3 ( 2 . 0 %) 4 . 14 % 12 ( %) 12 % 18 ( 3 . 0 %) 4 . 14 % 20 ( %) 12 % 12 ( 5 . 0 ) , ( = × × + × × + × × = market dell R R Cov 368852 . 0 003904 . 0 00144 . 0 ) ( ) , ( = = = market market dell dell R Var R R Cov β B Using CAPM, %) 5 % 4 . 14 ( % 5 %) 5 ) ( ( % 5 ) ( × + = × + = i M i i R E R E β β % 4672 . 8 %) 5 % 4 . 14 ( 368852 . 0 % 5 ) ( = × + = dell R E So Dell’s stock, from the perpetuity formula, equals 10 . 118 % 4672 . 8 10 ) ( = = dell R E Div 2 A The risk of current portfolio is 10 percent. The standard deviation of Treasury bill is 0. 0 = f σ , So, 375 . 0 625 . 0 % 16 % 10 = = × = + = f i i f f i i p x x x x x σ σ σ % 11 375 . 0 % 6 625 . 0 % 14 ) ( = × + × = + = f f i i p x r x r E r Therefore, he can improve his expected rate of return without changing the risk of his portfolio. B % 5 . 11 5 . 0 % 9 5 . 0 % 14 ) ( ) ( = × + × = + = b b i i p x r E x r E r 1
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