! Keywords: Accounting / Banking / Break Even Point / Downside Risk / Financial / Forecasting / Marketing / Markowitz / Portfolio / Stocks / Uncertainty;
MIN Y1 + Y2 + Y3 + Y4 + ATT + GMC + USX + MEAN
+ PS1 + PS2 + PS3 + PS4 + PBUD + PDEF + PRET
SUBJECT TO
! The first order conditions on the Y's
FY1) 0.5 Y1 + PS1 = 0
FY2) 0.5 Y2 + PS2 = 0
FY3) 0.5 Y3 + PS3 = 0
FY4) 0.5 Y4 + PS4 = 0
! First order conditions on the investments
FATT) - 0.9851237 PS1 - 1.193042 PS2 - 0.9851237 PS3
- 1.193042 PS4 + PBUD + 1.089083 PDEF >= 0
FGMC) - 1.304437 PS1 - 1.543131 PS2 - 0.8842088 PS3
- 1.122902 PS4 + PBUD + 1.213667 PDEF >= 0
FUSX) - 1.097669 PS1 - 1.756196 PS2 - 1.119948 PS3
- 0.9645076 PS4 + PBUD + 1.234583 PDEF >= 0
! First order conditions on the mean;
FMEAN) PS1 + PS2 + PS3 + PS4 - PDEF - PRET >= 0
! Here are the real constraints;
! Compute the return under each of 4 scenarios;
S1) Y1 - 0.9851237 ATT - 1.304437 GMC - 1.097669 USX
+ MEAN = 0
S2) Y2 - 1.193042 ATT - 1.543131 GMC - 1.756196 USX
+ MEAN = 0
S3) Y3 - 0.9851237 ATT - 0.8842088 GMC - 1.119948 USX
+ MEAN = 0
S4) Y4 - 1.193042 ATT - 1.122902 GMC - 0.9645076 USX
+ MEAN = 0
! The Budget constraint;
BUD) ATT + GMC + USX = 1
! Define or compute the mean;
DEF) 1.089083 ATT + 1.213667 GMC + 1.234583 USX
- MEAN = 0
! Target return;
RET) MEAN >= 1.15
END
! The first real constraint starts with row 10;
QCP= 10
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