Markowitz

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Unformatted text preview: (1 − x1 )σ2 = µP · σ1 −σ2 µ1 − µ2 + µ1 σ2 −µ2 σ1 µ1 − µ2 ⇒ linear in the (σP , µP )-plane ρ = −1, ⇒ σP = |x1 σ1 − (1 − x1 )σ2 | ￿ 2 2 −1 < ρ < 1, σP = x2 σ1 + (1 − x1 )2 σ2 + 2x1 (1 − x1 ) · ρσ1 σ2 1 K.S. Tan/Actsc 372 F11 Modern Portfolio Theory & CAPM – p. 14 Investment Opportunity Set or Feasible Set (Region) Feasible Set: 2 The possible (µP , σP ) or (µP , σP ) pairs of all portfolios that can be constructed from a given set of assets Describe the feasible set for a portfolio of two assets? see Figure 11.4 What if there are three assets? What if there are N assets? see Figure 11.6 K.S. Tan/Actsc 372 F11 Modern Portfolio Theory & CAPM – p. 15 General Case: N Risky Assets the economy has N risky assets with return r.v. R1 , . . . , RN . assume their first and second moments exist; i.e. µT = (µ1 , . . . , µN ), with µi = E[Ri ], i = 1, . . . , N, Σ = (σij )i,j =1,...,N , with σij = Cov(Ri , Rj ), i, j = 1, . . . , N. 2 note: σii = Cov(Ri , Ri ) = Var(Ri ) = σi A portfolio is constructed with portfolio weights xT = (x1 , . . . , xN ), where xi denot...
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This note was uploaded on 01/04/2012 for the course ACTSC 372 taught by Professor Maryhardy during the Fall '09 term at Waterloo.

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