CalculatingPortfolioVariance

# CalculatingPortfolioVariance - 2 = x 1 2 σ 1 2 x 2 2 σ 2...

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An Alternative Method of Calculating Portfolio Variance Probability Hi Tech Collections .1 -.22 .28 .2 -.02 .147 .4 .2 0 .2 .35 -.1 .1 .5 -.2 Expected return ( ˆ k ) .174 .017 σ .2 .134 Covariance 12 = Correlation Coefficient 12 x Standard deviation 1 x Standard Deviation 2 σ 12 = Σ Probability x [(k 1i - ˆ k 1i )( k 2i - ˆ k 2i )] Covariance between Hi Tech and Collections Covariance 12 ( σ 12 ) = [.1x(-.22-.174)(.28-.017)] +[.2x(-.02-.174)(.147-.017)] + [.4x(.2-.174)(0-.017)] + [.2x(.35-.174)(.1-.017)] + [.1x(.5-.174)(.2-.017)] = -.0267 Correlation ( ρ 12 ) = σ 12 / σ 1 σ 2 = -.0267/(.2)(.134) = -.996 Portfolio Variance σ p 2 = x 1 2 σ 1 2 + x 2 2 σ 2 2 + 2x 1 x 2 σ 12 OR σ p 2 = x 1 2 σ 1 2 + x 2 2 σ 2 2 ρ 12 σ 1 σ 2 For Hi Tech and Collections: σ HT = .2 σ COL = .134 ρ 12 = -.996 So, using σ p

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Unformatted text preview: 2 = x 1 2 σ 1 2 + x 2 2 σ 2 2 + 2x 1 x 2 σ 12 σ p 2 = (.5)2(.2)2 + (.5)2(.134)2 + 2(.5)(.5)(-.0267) = .0011 Or, using σ p 2 = x 1 2 σ 1 2 + x 2 2 σ 2 2 ρ 12 σ 1 σ 2 σ p 2 = (.5)2(.2)2 + (.5)2(.134)2 + 2(.5)(.5)(-.996)(.2)(.134) = .0011 σ p = 2 σ = .0011 = .033 or 3.3% This is close to zero risk because the correlation coefficient is close to –1, very unusual and not found in the real world) Note how portfolio risk changes if the correlation coefficient changes: For Hi Tech and Collections Correlation Coefficient +1 +.5-.5-1 Standard Deviation 16.7% 14.6% 12% 8.8%...
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CalculatingPortfolioVariance - 2 = x 1 2 σ 1 2 x 2 2 σ 2...

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