markowitz

# 12 minimum risk portfolio contd 1 8 1 12 2 14

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Unformatted text preview: ) · ρσ1 σ2 1 2 ∂σP x1 2 2 = 2x1 σ1 − 2(1 − x1 )σ2 + (2 − 4x1 ) · ρσ1 σ2 = 0 ⇒ x1 = xMIN = 1 2 σ2 − ρσ1 σ2 σ 2 − Cov(R1 , R2 ) = 2 22 2 2 σ1 + σ2 − 2ρσ1 σ2 σ1 + σ2 − 2Cov(R1 , R2 ) xMIN = 1 − xMIN 2 1 ρ = −1 ⇒ xMIN = 1 2 σ2 + σ1 σ2 σ2 σ1 = , xMIN = 2 2 (σ1 + σ2 ) σ1 + σ2 σ1 + σ2 What is so special about this case? K.S. Tan/Actsc 372 F11 Modern Portfolio Theory & CAPM – p. 12 Minimum Risk Portfolio (cont’d) µ1 = 8%, σ1 = 12%, µ2 = 14%, σ2 = 20% ρ xMIN 1 xMIN 2 -1.0 -0.3 0.0 0.3 0.625 0.686 0.735 0.820 0.375 10.25 0.00 0.314 9.88 8.73 0.265 9.59 10.29 0.180 9.08 11.45 µP σP K.S. Tan/Actsc 372 F11 Modern Portfolio Theory & CAPM – p. 13 Risk vs Return For a given x1 , we have E(RP ) = µP = x1 µ1 + (1 − x1 )µ2 ⇒ x1 = µP − µ2 , µ1 − µ2 µ1 ￿= µ2 2 2 2 Var(RP ) = σP = x2 σ1 + (1 − x1 )2 σ2 + 2x1 (1 − x1 )ρσ1 σ2 1 interested in the relationship between µP and σP i.e. risk and reward tradeoff ρ = 1 ⇒ σP = x1 σ1 +...
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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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