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Lecture 14 Portfolio Theory - MIT OpenCourseWare

Portfolio TheoryPortfolio TheoryMIT KempthorneFall 2013 MIT TheoryLecture 14: 1 Portfolio TheoryMarkowitz Mean-Variance OptimizationMean-Variance Optimization with Risk-Free AssetVon Neumann-Morgenstern Utility TheoryPortfolio Optimization ConstraintsEstimating Return Expectations and CovarianceAlternative Risk MeasuresOutline1 Portfolio TheoryMarkowitz Mean-Variance OptimizationMean-Variance Optimization with Risk-Free AssetVon Neumann-Morgenstern Utility TheoryPortfolio Optimization ConstraintsEstimating Return Expectations and CovarianceAlternative Risk MeasuresMIT Theory2 Portfolio TheoryMarkowitz Mean-Variance OptimizationMean-Variance Optimization with Risk-Free AssetVon Neumann-Morgenstern Utility TheoryPortfolio Optimization ConstraintsEstimating Return Expectations and CovarianceAlternative Risk MeasuresMarkowitz Mean-Variance Analysis (MVA)Single-Period Analyisismrisky assets:i= 1,2,..,mSingle-Period Returns:m variate random vectorR= [R1,R2.]

Problem I: Risk Minimization: For a given choice of target mean return 0;choose the portfolio w to Minimize: 1. w. 2 0. w Subject to: w. 0 = 0. w. 0. 1. m = 1 Solution: Apply the method of Lagrange multipliers to the convex optimization (minimization) problem subject to linear constraints: MIT 18.S096 Portfolio Theory

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