KIC000019 - 16 14 12 10 8 6 4 2 o l-__-.... w.--__--l- __ o...

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Two Asset Portfolio: Risk The standard deviation is not a linear combination of the individual asset standard deviations. Instead, it is the square root of variance given by: a/ =w 2 a/ +(I-w)2aB2 +2w(I-w)a A ·a B · PAB The standard deviation of the 500/0150% portfolio is: [ (05)'(6.68%)2 +(05)'(8.67%)2 ]"2 Up ~ + 2'(05)'(05)'(6.68%).(8.67%).(02592) ~612% The portfolio risk is lower than either individual asset's because of diversification. Diversification Suppose security A has expected return ECR A ) = 16% and standard deviation c A = 30%, Security B has expected return ECRa) = 10% and standard deviation aa = 16%. Consider the expected return and standard deviation of a portfolio of securities A and B when ·the correlation between them is + I, when the correlation is 0, and when the correlation is -1. Case 2: Zero correlation between securities, i.e., PAR = O. Min Variance Portfolio (14.12,11.33) Asset A (30,16)
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Unformatted text preview: 16 14 12 10 8 6 4 2 o l-__-.... w.--__--l- __ o Expec:ted Return E(RJ Asset B (16,10) 9 16 23 30 37 StdDevcr, IBM and John Deere Portfolios 1.00% uO"!. ...... 0.70-4 SOIRM. SIOOODE o.w;. '.J4J% 0.2,,'" 0.10% ..,..I---+-----+--.,~~ ........... OJI[-_+--_-~ S.80% 5.50% ,.00-.4 6.50"'.4 7.00% 7.50"4 1.W4 8.5r'1e '.00-'" SId.Dn'. Case 1: Perfect positive correlation between securities, i.e., PAB = + 1 16 / Asset A Expected (30,16) Return 14 E(R.l 12 / Portfolio 10 AssetB (23,13) 8 (16,10) 6 4 2 9 16 23 30 37 StdDev cr, Case 3: Perfect negative correlation between securities, i.e., PAB = -1 Zero Variance Portfolio Asset A (30,16) Expected Return 16 14 12 10 8 6 4 2 0.l-------I--- . ......--4.------. o 9 AssetB (16,10) 16 23 30 37 StdDevcr, 34...
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