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

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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 ρ = 1 the relationship between μ R and σ R is linear. Solution: Let w be the weight in asset 1. Then μ R = wμ 1 +(1- w ) μ 2 and σ 2 R = w 2 σ 2 1 +(1- w ) 2 σ 2 2 + 2 w (1- w ) σ 1 σ 2 ρ . So when ρ = 1 we have μ R = w ( μ 1- μ 2 ) + μ 2 and σ R = | w ( σ 1- σ 2 ) + σ 2 | . Wlog assume σ 1 ≥ σ 2 . Then σ R = w ( σ 1- σ 2 ) + σ 2 and so w = σ R- σ 2 σ 1- σ 2 which means μ R = μ 2 + σ R- σ 2 σ 1- σ 2 ( μ 1- μ 2 ) = σ R μ 1- μ 2 σ 1- σ 2 + μ 2- σ 2 μ 1- μ 2 σ 1- σ 2 , which shows that μ R is a linear function of σ R . (b) Prove that when ρ =- 1, it is possible to find weights w 1 and w 2 such that σ R = 0. Give an expression for the weights w 1 and w 2 satisfying this property. Solution: In this case σ R = | w ( σ 1 + σ 2 )- σ 2 | . So by taking w = σ 2 / ( σ 1 + σ 2 ) we get σ R = 0. This means w 1 = σ 2 / ( σ 1 + σ 2 ) and w 2 = σ 1 / ( σ 1 + σ 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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This note was uploaded on 11/16/2011 for the course ACTSC 372 taught by Professor Maryhardy during the Spring '09 term at Waterloo.

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

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