Given that the variance for portfolio of three assets is o wigi wo (1 Wi wa) o3 2 (WW2012 wi (1 wi W2) 013 W2 (1 Wi W2) 023) where o var (ri) is the variance of asset i, Oij cov (ri, rj) is the covariance of asset i and j and wi is the weight of asset i Prove that weights of the global minimum risk portfolio are given by o012 o ( 03 013) (012 013) 023 023 203012 012 03 (o3 2013) 2012013 013 o (oz oz 2023) 2 (012 013) 023 o23 o012 o ( 03 023) ( 012 013 023) 013 203012 012 o (oz 2013) 2012013 013 oi (oz oz 2023) 2 (012 013) 023 o23 and w3 1 Wi W W2 W2 Given that the variance for portfolio of three assets is o wigi wo (1 Wi wa) o3 2 (WW2012 wi (1 wi W2) 013 W2 (1 Wi W2) 023) where o var (ri) is the variance of asset i, Oij cov (ri, rj) is the covariance of asset i and j and wi is the weight of asset i Prove that weights of the global minimum risk portfolio are given by o012 o ( 03 013) (012 013) 023 023 203012 012 03 (o3 2013) 2012013 013 o (oz oz 2023) 2 (012 013) 023 o23 o012 o ( 03 023) ( 012 013 023) 013 203012 012 o (oz 2013) 2012013 013 oi (oz oz 2023) 2 (012 013) 023 o23 and w3 1 Wi W W2 W2

Question

Given that the variance for portfolio of three assets is o    wigi wo (1 Wi wa)  o3 2 (WW2012   wi (1 wi W2) 013   W2 (1 Wi W2) 023) where o   var (ri) is the variance of asset i, Oij   cov (ri, rj) is the covariance of asset i and j and wi is the weight of asset i  Prove that weights of the global minimum risk portfolio are given by o012   o ( 03  013) (012  013) 023   023 203012   012   03 (o3 2013) 2012013  013  o  (oz   oz 2023) 2 (012  013) 023   o23 o012   o ( 03   023)  ( 012  013   023) 013 203012   012   o (oz   2013)   2012013  013   oi (oz   oz 2023)   2 (012  013) 023   o23 and w3   1 Wi W   W2 W2 Given that the variance for portfolio of three assets is o    wigi wo (1 Wi wa)  o3 2 (WW2012   wi (1 wi W2) 013   W2 (1 Wi W2) 023) where o   var (ri) is the variance of asset i, Oij   cov (ri, rj) is the covariance of asset i and j and wi is the weight of asset i  Prove that weights of the global minimum risk portfolio are given by o012   o ( 03  013) (012  013) 023   023 203012   012   03 (o3 2013) 2012013  013  o  (oz   oz 2023) 2 (012  013) 023   o23 o012   o ( 03   023)  ( 012  013   023) 013 203012   012   o (oz   2013)   2012013  013   oi (oz   oz 2023)   2 (012  013) 023   o23 and w3   1 Wi W   W2 W2

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Question

Given that the variance for portfolio of three assets is o* = wigi+wo+(1 Wi wa)? o3+2 (WW2012 + wi (1 wi W2) 013 + W2

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