mid-sol - INVESTMENT ANALYSIS 70-492 Fall 2009 Suggested...

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INVESTMENT ANALYSIS 70-492 Fall 2009 Suggested Solution to Midterm Exam Professor Anisha Ghosh 1. CAPM (a) Let ω 1 denote the proportion of wealth invested in asset A and ω 2 the proportion in asset B. The tangency portfolio solves the following problem: max ω 1 2 E ( r T ) - r f σ T where E ( r T ) = ω 1 E ( r A ) + ω 2 E ( r B ) σ T = q ω 2 1 σ 2 A + ω 2 2 σ 2 B + 2 ω 1 ω 2 ρ AB σ A σ B ω 1 + ω 2 = 1 This gives the following equations with 2 unknowns z 1 and z 2 : ± z 1 z 2 ² = ± σ 2 A ρ AB σ A σ B ρ AB σ A σ B σ 2 B ²± E ( r A ) - r f E ( r B ) - r f ² The composition of the tangency portfolio is obtained as ω * 1 = z 1 z 1 + z 2 ω * 2 = z 2 z 1 + z 2 For the given problem, we have ω * 1 = 0 . 605 * 2 = 0 . 395. (b) Plugging the composition obtained in part (a) yields E ( r T ) = 0 . 605 × 0 . 02 + 0 . 395 × 0 . 09 = 0 . 048 . σ T = p (0 . 605) 2 × (0 . 02) 2 + (0 . 395) 2 × (0 . 07 2 ) = 0 . 030 (c) If the CAPM is true, the market portfolio is the tangency portfolio and, hence, has the highest
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mid-sol - INVESTMENT ANALYSIS 70-492 Fall 2009 Suggested...

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