Mean Variance Portfolio Selection

    {  Exmpl13.7-1_QPPortfolio.mpl  }

    {  Applications of Optimization with Xpress-MP  }

    {  Chapter 13.7, Mean Variance Portfolio Selection,  Size: 2x4,  Page 281 }

!#define model2

Option
    Modeltype=Quadratic

TITLE
    QPPortfolio;

INDEX
    sec := 1..4;
    sec2 := sec;

DATA
    Ret[sec] := (108%,109%,112%,107%);
    Vari[sec,sec2] := ( 4, 3,-1, 0,
                        3, 6, 1, 0,
                       -1, 1,10, 0,
                        0, 0, 0, 0);
    Target := 100% + 8.5%;
#ifdef model2
    Maxassets := 2;
#endif


VARIABLE
    Fract[sec];
    Buy[sec];

MODEL

    MIN Variance = SUM(sec,sec2: Vari * Fract * Fract[sec:=sec2]);

SUBJECT TO

    SpendAllCapital -> ACAP:
        SUM(sec: Fract) = 1;

    TargetYield -> TYLD:
        SUM(sec: Ret * Fract) >= Target;

#ifdef model2
    AssetLimit -> ASL:
        SUM(sec: Buy) <= Maxassets;
#endif

BINARY
    Buy;

END