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Unformatted text preview: ACTSC 372 Assignment 1 Solutions 1 Shape of the efficient set [8 points] In the case of N = 2 assets: (a) Prove that when = 1 the relationship between R and R is linear. Solution: Let w be the weight in asset 1. Then R = w 1 +(1 w ) 2 and 2 R = w 2 2 1 +(1 w ) 2 2 2 + 2 w (1 w ) 1 2 . So when = 1 we have R = w ( 1 2 ) + 2 and R =  w ( 1 2 ) + 2  . Wlog assume 1 2 . Then R = w ( 1 2 ) + 2 and so w = R 2 1 2 which means R = 2 + R 2 1 2 ( 1 2 ) = R 1 2 1 2 + 2 2 1 2 1 2 , which shows that R is a linear function of R . (b) Prove that when = 1, it is possible to find weights w 1 and w 2 such that R = 0. Give an expression for the weights w 1 and w 2 satisfying this property. Solution: In this case R =  w ( 1 + 2 ) 2  . So by taking w = 2 / ( 1 + 2 ) we get R = 0. This means w 1 = 2 / ( 1 + 2 ) and w 2 = 1 / ( 1 + 2 ). 2 Estimating risk and return [12 points] Use the two files TSX20002010.xls and MSFT.xls for this problem....
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 Spring '09
 MARYHARDY

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