6 Optimal risk sharing

O n the other hand, the condi t ional variances formula (1.4.38) gives

V a r ( X ) = E ( V a r ( X | 0)) + V a r ( E ( X | 0))

= E [ ( r A 2 ) - V a r ( X , | 0)] + V a r [ ( f A ) ' M 0 ) ]

Substi tuting these i n (6.5.23) gives (6.5.24).