sol1 - ACTSC 372 Assignment 1 Solutions 1- Shape of the...

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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 TSX2000-2010.xls and MSFT.xls for this problem....
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sol1 - ACTSC 372 Assignment 1 Solutions 1- Shape of the...

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