markowitz

# 9 the impact of correlations on portfolio risk let f

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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 &amp; 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 &lt; ρ &lt; 1, f (−1) ≤ f (ρ) ≤ f (1) K.S. Tan/Actsc 372 F11 Modern Portfolio Theory &amp; 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 &amp; CAPM – p. 11 Minimum Risk Portfolio 2 2 2 σP = x2 σ1 + (1 − x1 )2 σ2 + 2x1 (1 − x1...
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