Active portfolio management @ bec dom s

10. Combining Active Portfolio with Market Portfolio ( passive portfolio) A . M p CML New CAL Return Risk r A =a A + r f +b A (r m -r f )

11. Given: r p = wr A + (1-w)r m The optimal weight in the active portfolio is: w = w 0 /[1+(1-b A )w 0 ] The slope of the CAL (called the Sharpe index) for the optimal portfolio ( consisting of active and passive portfolio ) turns out to include two components, which are: [(r m -r f )/s m ] 2 + [a A /s 2 (e A )] 2 a A /s 2 (e A ) (r m -r f )/s 2 m where w 0 =

12. The optimal weights in the active portfolio for each individual security will be: a k /s 2 (e k ) a 1 /s 2 (e 1 )+...+a n /s 2 (e n ) w k =

14. Composition of active portfolio: a A = w 1 a 1 +w 2 a 2 +w 3 a 3 =1.1477(7%)-1.6212(5%)+1.4735(3%) =20.56% b A = w 1 b 1 +w 2 b 2 +w 3 b 3 = 1.1477(1.6)-1.6212(1)+1.4735(0.5) = 0.9519 s(e A ) = [w 2 1 s 2 1 +w 2 2 s 2 2 +w 2 3 s 2 3 ] 0.5 = [1.1477 2 (0.45 2 )+1.6212 2 (0.32 2 ) +1.4735 2 (0.26 2 )] 0.5 = 0.8262 Composition of the optimal portfolio : w 0 = (0.2056/0.8262 2 ) / (0.08/0.2 2) = 0.1506 w = w 0 /[1+(1-b A ) w 0 ] = 0.1495

15. Composition of the optimal portfolio: Stock Final Position w (w k ) 1 0.1495(1.1477)=0.1716 2 0.1495(-1.6212)=-0.2424 3 0.1495(1.1435)=0.2202 Active portfolio 0.1495 Passive portfolio 0.8505 1.0