! Keywords: Accounting / Banking / Bonds / Break Even Point / Downside Risk / Financial / Forecasting / Marketing / Portfolio / Uncertainty;
! The MIN row simply gives the order of the
! primal variables...;
MIN Y1 + Y2 + Y3 + Y4 + Y5 + Y6 + Y7 + Y8 + Y9 + Y10 + Y11 + Y12
+ ATT + GMC + USX + MEAN
! and the dual/price variables;
+ PS1 + PS2 + PS3 + PS4 + PS5 + PS6 + PS7 + PS8 + PS9 + PS10
+ PS11 + PS12 + PBUD + PDEF + PRET
Subject to
! The first order conditions on the Y's
FY1) .1666666 Y1 + PS1 = 0
FY2) .1666666 Y2 + PS2 = 0
FY3) .1666666 Y3 + PS3 = 0
FY4) .1666666 Y4 + PS4 = 0
FY5) .1666666 Y5 + PS5 = 0
FY6) .1666666 Y6 + PS6 = 0
FY7) .1666666 Y7 + PS7 = 0
FY8) .1666666 Y8 + PS8 = 0
FY9) .1666666 Y9 + PS9 = 0
FY10) .1666666 Y10 + PS10 = 0
FY11) .1666666 Y11 + PS11 = 0
FY12) .1666666 Y12 + PS12 = 0
! First order conditions on the investments;
FATT) + 1.3 PS1 + 1.103 PS2 + 1.216 PS3 + 0.954 PS4 + 0.929 PS5
+ 1.056 PS6 + 1.038 PS7 + 1.089 PS8 + 1.09 PS9 + 1.083 PS10
+ 1.035 PS11 + 1.176 PS12 + PBUD + 1.089083 PDEF >= 0
FGMC) + 1.225 PS1 + 1.29 PS2 + 1.216 PS3 + 0.728 PS4 + 1.144 PS5
+ 1.107 PS6 + 1.321 PS7 + 1.305 PS8 + 1.195 PS9 + 1.39 PS10
+ 0.928 PS11 + 1.715 PS12 + PBUD + 1.213667 PDEF >= 0
FUSX) + 1.149 PS1 + 1.26 PS2 + 1.419 PS3 + 0.922 PS4 + 1.169 PS5
+ 0.965 PS6 + 1.133 PS7 + 1.732 PS8 + 1.021 PS9 + 1.131 PS10
+ 1.006 PS11 + 1.908 PS12 + PBUD + 1.234583 PDEF >= 0
! First order conditions on the mean;
FMEAN) - PS1 - PS2 - PS3 - PS4 - PS5 - PS6 - PS7 - PS8
- PS9 - PS10 - PS11 - PS12 - PDEF - PRET >= 0
! Here are the real constraints, compute Y for each scenario;
S1) Y1 + 1.3 ATT + 1.225 GMC + 1.149 USX - MEAN = 0
S2) Y2 + 1.103 ATT + 1.29 GMC + 1.26 USX - MEAN = 0
S3) Y3 + 1.216 ATT + 1.216 GMC + 1.419 USX - MEAN = 0
S4) Y4 + 0.954 ATT + 0.728 GMC + 0.922 USX - MEAN = 0
S5) Y5 + 0.929 ATT + 1.144 GMC + 1.169 USX - MEAN = 0
S6) Y6 + 1.056 ATT + 1.107 GMC + 0.965 USX - MEAN = 0
S7) Y7 + 1.038 ATT + 1.321 GMC + 1.133 USX - MEAN = 0
S8) Y8 + 1.089 ATT + 1.305 GMC + 1.732 USX - MEAN = 0
S9) Y9 + 1.09 ATT + 1.195 GMC + 1.021 USX - MEAN = 0
S10) Y10 + 1.083 ATT + 1.39 GMC + 1.131 USX - MEAN = 0
S11) Y11 + 1.035 ATT + 0.928 GMC + 1.006 USX - MEAN = 0
S12) Y12 + 1.176 ATT + 1.715 GMC + 1.908 USX - MEAN = 0
! The Budget constraint;
BUD) ATT + GMC + USX = 1
! compute the mean;
DEF) 1.089083 ATT + 1.213667 GMC + 1.234583 USX - MEAN = 0
! The target Return constraint;
RET) MEAN >= 1.15
END
! Tell LINDO that this is a quadratic problem with
! first real constraint being row 18
QCP 18
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