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Unformatted text preview: Diversification leads to smaller variance! The diversification works even better if one could pick two stocks for which the returns X and Y had negative covariance . In this case the risk is Var( X + Y ) = Var X + Var Y + 2Cov( X,Y ) < Var X + Var Y. A general rule for the variance of a sum : if X 1 ,...,X n are random variables then Var n X i =1 X i = n X i =1 Var X i +2 n X i =1 n X j = i +1 Cov( X i ,X j ) . If X 1 ,...,X n are independent, then Var n X i =1 X i = n X i =1 Var X i . Variance of a linear combination of random variables If X 1 ,...,X n are random variables and a 1 ,...,a n are numbers then Var n X i =1 a i X i = n X i =1 a 2 i Var X i + 2 n X i =1 n X j = i +1 a i a j Cov( X i ,X j ) . If X 1 ,...,X n are independent, then Var n X i =1 a i X i = n X i =1 a 2 i Var X i . Correlation The correlation or the correlation coefficient between random variables X and Y is X,Y = Cov( X,Y ) Var X Var Y = Cov(...
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This note was uploaded on 12/03/2010 for the course OR&IE 3500 taught by Professor Samorodnitsky during the Fall '10 term at Cornell University (Engineering School).
 Fall '10
 SAMORODNITSKY

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