NotesSep27 - Diversification leads to smaller variance! The...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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(...
View Full Document

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).

Page1 / 10

NotesSep27 - Diversification leads to smaller variance! The...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online