Optimal+Risky+Portfolios

# Optimal+Risky+Portfolios - Optimal Risky Portfolios Reading...

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Optimal Risky Portfolios Reading: Chapter 7

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2 Construction of the Risky Portfolio How do we construct an active risky portfolio and control its risk? How do we achieve the maximal level of diversification ? Co-movements between risky asset returns! Covariance and Correlation
3 A Two-Security Portfolio: Return r p = w 1 r 1 + w 2 r 2 w 1 = Proportion of funds in Security 1 w 2 = Proportion of funds in Security 2 r 1 = Expected Return on Security 1 r 2 = Expected Return on Security 2 We need to have w 1 + w 2 = 1

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4 A Two-Security Portfolio: Risk σ p 2 = w 1 2 σ 1 2 + w 2 2 σ 2 2 + 2w 1 w 2 Cov(r 1, r 2 ) σ 1 2 = Variance of Security 1 σ 2 2 = Variance of Security 2 Cov(r 1, r 2 ) = Covariance of returns for Security 1 and Security 2
5 Covariance ρ 1,2 = Correlation coefficient of returns Cov(r 1 r 2 ) = ρ 1,2 σ 1 σ 2 σ 1 = standard deviation of returns for Security 1 σ 2 = standard deviation of returns for Security 2

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6 Correlation coefficient Range of values for ρ
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Optimal+Risky+Portfolios - Optimal Risky Portfolios Reading...

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