HW3_solutions

HW3_solutions - 1 MS&E 242 Investment Science HW #3...

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Unformatted text preview: 1 MS&E 242 Investment Science HW #3 Solutions Prof. James Primbs November 12, 2006 Problem 6.2 Let a and b be the outcomes of two die rolls. Then Z = a b . By independence, we have E[ a ]= (1+2+3+4+5+6)/6 = 3.5 E[ a 2 ]=(1+4+9+16+25+36)/6 = 91/6 E[Z] = E[ a ]E[ b ] = 12.25 Var[Z] = E[ a 2 ]E[ b 2 ] (E[ a ]E[ b ]) 2 = 79.97 Problem 6.3 To find the minimum variance point, we solve ( 29 ( 29 2 2 , 2 2 1 1 2 min B B A A - +- + First order conditions are ( 29 ( 29 1 2 2 1 2 2 2 , 2 =--- + B B A A a) Using 2 2 ) 15 (. = A , 2 2 ) 30 (. = B and 0045 . , = = B A B A , solving we have we have 23 / 19 = and 23 / 4 ) 1 ( =- . b) Plugging in give a minimum standard deviation of approximately 13.7%. c) Expected return of this portfolio is % 4 . 11 ) 1 ( =- + B A r r . Problem 6.4 The total variance of the portfolio is 12 2 2 2 2 1 2 2 ) 1 ( 2 ) 1 ( w w w w P- +- + = ....
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This note was uploaded on 11/15/2008 for the course MS&E 242 taught by Professor Primbs during the Fall '06 term at Stanford.

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HW3_solutions - 1 MS&E 242 Investment Science HW #3...

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