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Module3_PortMgmt_Lecture

# Module3_PortMgmt_Lecture - Course Outline I Measuring...

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Course Outline: I Measuring Risk-Two Asset

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Portfolio Variance = I) In general the weight in A that brings the risk to zero is II) In general the weight in A that brings the risk to zero is III) In general the weight in A that brings the risk to zero is IV) Minimum Variance Portfolio if correlation > -1 and less than 1 V) Riskless asset Case Portfolio Mean Ep = X A * E A + X B * E B If ρ = -1 then If ρ = 1 then If ρ = 0 then If -1< ρ < 1 or <> 0 then B A B A X σ + = B A B A A B A B X ρσ 2 2 2 2 - + - = Commonly Known as the Markowitz Equation The expected return of Portfolio (Ep) is weighted average of expected return of Stock A and expected return of Stock B. Variance of Portfolio is "NOT" weighted average of the variance of Stock A and the variance of Stock B ====> See Markowtiz Equation Below ρ 2 2 2 2 2 2 B B A A B B A A P X X X X + + = 2 2 2 2 2 2 B B A A B B A A P X X X X - + = B A B A A B A A B B A A B B A A p X x x x x x x + = = - - = - - = 0 ) 1 ( 0 ) ( 2 2 Commonly Known as the Markowitz Equation A B B A X - = Commonly Known as the Markowitz Equation 2 2 2 B A B A X + = A p F A F p F A A F F A A p A A p A A p F F a A F F A A p R E R E R E R X E X E X x Therefore x x x x ) ( 07 . 0 15 . 0 26 . 0 . , . 0 then riskless, is F If 2 2 2 2 F 2 2 2 2 2 - + = = = = + = = = = + + =
Computation of Portfolio Variance Using Excel vs. Markowitz Equation Stock A Stock B Portfolio Mean Ep = XA * EA + XB * EB Portfolio Variance <> XA * VarA + XB * VarB Mean 14.91% 6.89% 9.29% Stock Weight Return Stock Weight Var Variance 6.90% 1.60% 2.10% A 30.00% 14.91% 4.47% A 30.00% 6.90% 2.07% std 26.27% 12.67% B 70.00% 6.89% 4.82% B 70.00% 1.60% 1.12% Mean Portfolio A-B: 9.29% Variance Portfolio A-B: 3.19% 0.50 Weights= 30.00% 70.00% Portfolio Variance = Year A B Stock Weight Std ρ 1 7.34% 7.68% 7.58% A 30.00% 26.27% 0.62% 7.88% 0.50 2 31.08% -7.82% 3.85% B 70.00% 12.67% 0.79% 8.87% 0.50 3 -7.11% 14.68% 8.14% Variance Portfolio A-B: 2.10% 4 -15.83% 5.14% -1.15% 5 -6.98% 6.05% 2.14% 6 30.64% 28.59% 29.20% 7 5.70% -11.31% -6.21% 8 31.40% 31.29% 31.32% 9 14.10% 12.78% 13.18% 10 -24.96% 16.12% 3.79% 11 33.79% 13.04% 19.27% 12 -25.13% 7.35% -2.39% 13 49.19% 16.30% 26.17% 14 31.82% 23.19% 25.78% 15 31.63% 25.57% 27.39% 16 59.72% 19.32% 31.44% 17 -3.64% 5.95% 3.07% 18 -5.81% 4.02% 1.07% 19 41.08% 22.24% 27.89% 20 11.07% 6.57% 7.92% 21 37.35% 10.71% 18.71% 22 32.43% 29.25% 30.21% 23 43.77% 7.46% 18.35% 24 13.14% 10.81% 11.51% 25 55.63% 8.92% 22.93% 26 42.15% 20.91% 27.28% 27 -33.90% -8.95% -16.44% 28 -43.69% -23.62% -29.64% 29 11.43% 2.55% 5.21% 30 40.26% 11.86% 20.38% 31 -22.21% -0.95% -7.33% 32 11.17% 1.99% 4.74% 33 4.42% -7.12% -3.66% 34 56.71% 8.87% 23.22% 35 76.75% 26.62% 41.66% 36 22.70% 6.25% 11.18% 37 -1.38% 8.79% 5.74% 38 17.82% 0.14% 5.45% 39 -44.29% -25.69% -31.27% 40 -9.87% -26.90% -21.79% 41 15.85% -8.01% -0.85% 42 60.31% 3.78% 20.74% 43 7.80% 20.88% 16.96%

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Module3_PortMgmt_Lecture - Course Outline I Measuring...

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