* MEAN-VARIANCE Markowitzuv model (bez prodeju na kratko)


Set a mnozina aktiv /A1, A2, A3/;
* set a mnozina aktiv /1*1000/;
Set b(a) (pod)mnozina aktiv /A1, A2, A3/;

Set j /1*2/;


* -----------------------------------------;

Scalars r0 minimalni vynos / .1 /
r1 minimalni vynos / .25 /;

Parameter r(a) ocekavany vynos
/
A1       0.1187
A2       0.1396
A3       0.0501
/;


*Parameter rInp(a) ocekavany vynos (z text. souboru)
*$include "H:\VAO 2015\vynos.txt";


Table V(a,a) rozptylova matice
         A1      A2      A3
A1       42.18   20.18   10.88
A2       20.18   70.89   21.58
A3       10.88   21.58   25.51
;

* -----------------------------------------;

Free variables
obj objective function;

Positive variables
x(a) portfolio weights;

* -----------------------------------------;

Equations
of portfolio variance
er minimal expected return
bc budget constraint;

* NE: of.. obj =e= sum(a, sum (a, x(a)*V(a,a)*x(a) ) ) ;
* of.. obj =e= sum(a, sum (b, x(a)*V(a,b)*x(b) ) ) ;
of.. obj =e= sum((a, b), x(a)*V(a,b)*x(b) ) ;
er.. sum(a, r(a)*x(a)) =g= r0;
bc.. sum(a, x(a)) =e= 1;

* -----------------------------------------;

Model MV mean-variance model / all / ;
* Model MV0 mean-variance model / of, bc / ;

Solve MV using NLP minimizing obj;
* Solve MV0 using NLP minimizing obj;

Display obj.l, x.l;