Markowitz Result for VarianceofReturn on PortfolionnZZpw,w,o,0jVariance of Portfolio Return =i=l j=lw, is weight of ith asset in portfolioo: is variance of return on ith assetin portfolioPi, is correlatio n between returns of ithand jth assetsRiskManagementandFinancialInstitutions3e,Chapter15,CopyrightJohnC.Hull201211
Markowitz Result for Variance of Return on Portfolio Risk Management and Financial Institutions 3e, Chapter 15, Copyright © John C. Hull 2012 11 and th assets is correlatio n between returns of th in portfolio is variance of return on th asset is weight of th asset in portfolio Variance of Portfolio Return i j 2 i 1 1 j i i w i w w i n i n j i j i j i j r s = r s s = =
Corresponding Result forVarianceofPortfolioValue△P=Zα,Ax;i=1o=ZZp,α,α,0,0ji=l j=lA92α,o?+2Zp,α,α,0,0j=i=1i<j, is the daily volatility of the ith asset (i.e., SD of daily returns)p is the SD of the change in the portfolio value per dayα, =w, P is amount invested in ith asset12RiskManagementandFinancialInstitutions3e,Chapter15,CopyrightJohnC.Hull2012
Risk Management and Financial Institutions 3e, Chapter 15, Copyright © John C. Hull 2012 Corresponding Result for Variance of Portfolio Value = = = = s = s + r s s s = r s s = n i i j i j i j P i i i j n i n j P i j i j i j n i i i P x 1 2 2 2 1 1 2 1 2 12 si is the daily volatility of the ith asset (i.e., SD of daily returns) sP is the SD of the change in the portfolio value per day i =wi P is amount invested in ith asset
Covariance Matrix (var; =cov(page328)var,COV12COV13COV21var2COV23COVCOV31COV32var3COVCOVCOVCOVvarnn2n3YRiskManagementandFinancialInstitutions3e,Chapter15,CopyrightJohnC.Hull201213
Covariance Matrix (vari = covii) (page 328) Risk Management and Financial Institutions 3e, Chapter 15, Copyright © John C. Hull 2012 13 = n n n n n n n C cov cov cov var cov cov var cov cov var cov cov var cov cov cov 1 2 3 3 1 3 2 3 3 2 1 2 2 3 2 1 1 2 1 3 1