STAT244.Lecture.04 2

STAT244.Lecture.04 2 - Portfolio Theory R is N 1 returns on...

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Portfolio Theory I R is N × 1 returns on risky assets; E ( R ) = μ ; Var ( R ) = Ω. I Minimize w 0 Ω w =risk, s . t . , w 0 μ = μ p , w 0 1 = 1. I Objective Function: L ( w , δ 1 , δ 2 ) = w 0 Ω w + δ 1 ( μ p - w 0 μ ) + δ 2 (1 - w 0 1). I Let A = 1 0 Ω - 1 μ, B = μ 0 Ω - 1 μ and C = 1 0 Ω - 1 1. Then w p = g + μ p h where g = B D Ω - 1 1 - A D Ω - 1 μ ; h = C D Ω - 1 μ - A D Ω - 1 1. I Obtain w p and σ μ p = p w 0 p Ω w p ; plot ( w p , σ μ p ) to get the efficient frontier. I At the minimum,
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