!Keyword: Downside Risk / Financial / Markowitz / Portfolio / Stocks / Transaction Costs;
MIN ATT + GMC + USX + BA + SA + BG + SG + BU + SU
+ PBUD + PRET + PTA + PTG + PTU
SUBJECT TO
! First order conditions on the amount invested in each asset;
FATT) 0.021615 ATT + 0.0248144 GMC + 0.0261502 USX
+ PBUD - 1.089083 PRET + PTA >= 0
FGMC) 0.0248144 ATT + 0.1167834 GMC + 0.1108528 USX
+ PBUD - 1.213667 PRET + PTG >= 0
FUSX) 0.0261502 ATT + 0.1108528 GMC + 0.1884536 USX
+ PBUD - 1.234583 PRET + PTU >= 0
! First order condition on amount bought of ATT;
FBA) 0.01 PBUD - PTA >= 0
! First order condition on amount sold of ATT;
FSA) 0.01 PBUD + PTA >= 0
! First order condtion on amount bought of GMC, etc.
FBG) 0.01 PBUD - PTG >= 0
FSG) 0.01 PBUD + PTG >= 0
FBU) 0.01 PBUD - PTU >= 0
FSU) 0.01 PBUD + PTU >= 0
! Budget constraint at beginning of period;
BUD) ATT + GMC + USX + 0.01 BA + 0.01 SA
+ 0.01 BG + 0.01 SG + 0.01 BU + 0.01 SU = 1
! Constraint on required expected return at end;
RET) 1.089083 ATT + 1.213667 GMC + 1.234583 USX >= 1.15
! Invested in ATT - bought + sold = initial holding;
TA) ATT - BA + SA = 0.5
! Ditto for GMC, and USX;
TG) GMC - BG + SG = 0.35
TU) USX - BU + SU = 0.15
END
QCP= 11
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