2 Assets
Returns:  10 16
Var - Cov Matrix 16 6
6 36
A= mu1 mu2
Target Return: 11 1 1
Solves Equality
AT mu1 1
mu2 1
Min: z1 + z2
ST
Z x1 x2 u1 u2 v1 v2 h1 h2 RHS
Row zero 1 1000 1000 0
n -equations -16 -6 -10 -1 1 = 0
-6 -36 -16 -1 1 = 0
2-Equations 10 16 1 = 11
1 1 1 = 1
New Row Zero 1 -11000 -17000 0 0 0 0 0 0 = -12000
Z x1 x2 u1 u2 v1 v2 h1 h2 RHS
Tableau 1 Row zero 1 -11000 -17000 0 0 0 0 0 0 = -12000 Ratio
x2 in; h1 out v1 0 -16 -6 -10 -1 1 0 0 0 = 0
ignore neg coeff v2 0 -6 -36 -16 -1 0 1 0 0 = 0
h1 (x2) 0 10 16 0 0 0 0 1 0 = 11 0.6875
h2 0 1 1 0 0 0 0 0 1 = 1 1
Tableau 2 Row zero 1 -375 0 0 0 0 0 1063 0 -312.5
x1 in; h2 out v1 0 -12.25 0 -10 -1 1 0 0.38 0 4.125
ignore neg coeff v2 0 16.5 0 -16 -1 0 1 2.25 0 24.75 1.5
x2 0 0.625 1 0 0 0 0 0.06 0 0.6875 1.1
h2 (x1) 0 0.375 0 0 0 0 0 -0.1 1 0.3125 0.833333
Tableau 3 Enter u1out v1 Row zero 1 0 0 0 0 0 0 1000 1000 0
Remove complementary Slackness v1 (u1) 0 0 0 -10 -1 1 0 -1.7 32.7   14.333
v2 0 0 0 -16 -1 0 1 5 -44 11
x2 0 0 1 0 0 0 0 0.17 -1.7 0.1667
x1 0 1 0 0 0 0 0 -0.2 2.67 0.8333
Tableau 4 Enter u2; out v2 Row zero 1 0 0 0 0 0 0 1000 1000 0
Remove complementary Slackness u1 0 0 0 1 0.1 -0.1 0 0.17 -3.3 -1.433
v2 (u2) 0 0 0 0 0.6 -1.6 1 7.67 -96   -11.93
x2 0 0 1 0 0 0 0 0.17 -1.7 0.1667
x1 0 1 0 0 0 0 0 -0.2 2.67 0.8333
Tableau 5 Row zero 1 0 0 0 0 0 0 1000 1000 0
u1 0 0 0 1 0 0.17 -0.2 -1.1 12.8 0.5556
u2 0 0 0 0 1 -2.7 1.67 12.8 -160 -19.89
x2 0 0 1 0 0 0 0 0.17 -1.7 0.1667
x1 0 1 0 0 0 0 0 -0.2 2.67 0.8333
DONE!
x1 0.833333
x2 0.166667