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Unformatted text preview: Overview MeanVariance Preferences Portfolio Choice Eco331: MeanVariance Analysis Marciano Siniscalchi November 2 Overview MeanVariance Preferences Portfolio Choice Overview When Mean and Variance are All That Matters The portfolio problem in the MeanVariance Setting Twoasset problem and MutualFund Theorem Overview MeanVariance Preferences Portfolio Choice Mean Good, Variance Bad Recall Var [ X ] = n i =1 p i ( x i E [ X ]) 2 = E [ X 2 ] ( E [ X ]) 2 ; also StDev [ X ] = p Var [ X ]. Natural measure of dispersion, or risk . Formally: recall ( W , ) 1 2 A ( W ) Var (small ). Now define W = W + , so E [ W ] = W , Var h W i = Var : then C [ W ] E [ W ] 1 2 A ( W ) Var [ W ] . Risk aversion implies A ( W ) 0, so variance is bad . But this is only an approximation for small risks ! Overview MeanVariance Preferences Portfolio Choice Mean and Variance are not always enough For general preferences and general risks, EU looks beyond means and variances. X with p.d. (100 , 9 32 ; 200 , 14 32 ; 300 , 9 32 ) Y with p.d. (50 , 1 8 ; 200 , 3 4 ; 350 , 1 8 ) E [ X ] = E [ Y ] = 200 and Var [ X ] = Var [ Y ] = 5625 However, with utility u ( x ) = x , X Y : E [ u ( X )] = 9 32 100 + 14 32 200 + 9 32 300 = 13 . 871; E [ u ( Y )] = 1 8 50 + 3 4 200 + 1 8 350 = 13 . 829 ....
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This note was uploaded on 11/17/2009 for the course ECONOMICS 331 taught by Professor Marciano during the Spring '09 term at Northwestern.
 Spring '09
 Marciano
 Economics

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