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Chapter6

# Chapter6 - Investment Science Chapter 6 Solutions to...

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Investment Science Chapter 6 Solutions to Suggested Problems Dr. James A. Tzitzouris 6.1 The money invested is X 0 . The money received at the end of a year is X 0 - X 1 + X 0 . Hence, R = 2 X 0 - X 1 X 0 . 6.3 For solution method, see solution to Problem 6.4 in this solution set. (a) α = 19 / 23 (b) The minimum standard deviation is approximately 13 . 7%. (c) The expected return of this portfolio is approximately 11 . 4%. 6.4 Let α and β equal the percent of investment in stock 1 and stock 2, respectively. The problem is: min α,β α 2 σ 2 1 + 2 αβσ 12 + β 2 σ 2 2 s.t. α + β = 1 . 1

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Setting up the Lagrangian, L , we have: L = α 2 σ 2 1 + 2 αβσ 12 + β 2 σ 2 2 - λ ( α + β - 1) . The first order necessary conditions are: 0 = ∂L ∂α = 2 ασ 2 1 + 2 βσ 12 - λ, 0 = ∂L ∂β = 2 βσ 2 2 + 2 ασ 12 - λ, 1 = α + β, which imply α = σ 2 2 - σ 12 σ 2 1 + σ 2 2 - 2 σ 12 . The mean rate of return is simply αm 1 + βm 2 . 6.5 (a) The expected rate of return equals (0 . 5)(3)(10 6 ) + (0 . 5) u 10 6 + 0 . 5 u .
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