ps4 - ECO 362 October 18, 2007 PROBLEM SET 4 FINANCIAL...

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ECO 362 October 18, 2007 PROBLEM SET 4 FINANCIAL INVESTMENTS Professor: Burt Malkiel Exercise 1 (a) Let X and Y information about the random variables X and Y : E [ X ]= μ X =0 . 10 , V [ X ]= σ 2 X =(0 . 15) 2 ,and E [ Y ]= μ Y =0 . 21 , V [ Y ]= σ 2 Y =(0 . 25) 2 . Recall from last week: the expected return ( E [ Z ] where Z = wX +(1 w ) Y )ofaport fo l iomadeup of w (1 w ) in Microsoft is given by the linear combination of the expected returns of E [ Z ]= X +(1 w ) μ Y . Hence, substituting μ X , μ Y ,and w =1 / 2 ,weget E [ Z ]= 1 2 0 . 10 + 1 2 0 . 21 = 0 . 155 . (b) Recall from last week, the variance of a portfolio made up of w (1 w ) in Microsoft, V [ Z ] ,isg ivenby V [ Z ]= w 2 σ 2 X +(1 w ) 2 σ 2 Y +2 w (1 w ) ρσ X σ Y . Hence, substituting σ X =0 . 15 , σ Y =0 . 25 , ρ =0 . 5 and w =1 / 2 ,weget V [ Z ]= μ 1 2 2 (0 . 15) 2 + μ 1 2 2
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ps4 - ECO 362 October 18, 2007 PROBLEM SET 4 FINANCIAL...

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