9 the impact of correlations on portfolio risk let f

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: .66 12.92 14.46 16.18 18.04 20.00 12.00 11.56 11.45 11.70 12.26 13.11 14.20 15.47 16.88 18.40 20.00 12.00 12.80 13.60 14.40 15.20 16.00 16.80 17.60 18.40 19.20 20.00 Modern Portfolio Theory & CAPM – p. 9 The Impact of Correlations on Portfolio Risk Let f (ρ) = ￿ 2 2 x2 σ1 + x2 σ2 + 2x1 x2 · ρσ1 σ2 1 2 Perfect positively correlated ρ = 1: ￿ 2 2 σP = f (1) = x2 σ1 + x2 σ2 + 2x1 x2 · σ1 σ2 1 2 = |x1 σ1 + x2 σ2 | = x1 σ1 + x2 σ2 = σ2 + x1 (σ1 − σ2 ) 0 ≤ x1 , x2 ≤ 1 Perfect negatively correlated ρ = −1: σP = f (−1) = |x1 σ1 − x2 σ2 | = |x1 (σ1 + σ2 ) − σ2 | For fixed 0 ≤ x1 , x2 ≤ 1 and −1 < ρ < 1, f (−1) ≤ f (ρ) ≤ f (1) K.S. Tan/Actsc 372 F11 Modern Portfolio Theory & CAPM – p. 10 Impact of Weights on Portfolio Risk What is the shape of the portfolio risk against weight ? K.S. Tan/Actsc 372 F11 Modern Portfolio Theory & CAPM – p. 11 Minimum Risk Portfolio 2 2 2 σP = x2 σ1 + (1 − x1 )2 σ2 + 2x1 (1 − x1...
View Full Document

Ask a homework question - tutors are online