Shayan
Reputation: 6375
Gekko seems to ignore the single equation
I've been using Gekko for the last three years for optimization purposes. As a matter of fact, I'm using Gekko version 1.0.4. Recently, I've been trying to solve an ESG-MVP problem developed by (Vo, He et al. 2019):
Considering sum(wesg) should be equal to 1 and 0 ≤ wesg_i ≤ 1 for iε[0, 1, 2,..., 23]. In this model, I'm trying to
find the best values of wesg_i for the model above. Hence, according to the information provided, I have to find the value of 24 variables through an optimization model. My code is available for you to test on your computer with all the vital data needed.
Libraries
from gekko import GEKKO
import numpy as np
import pandas as pd
Data Section
Make sure copy it all.
esg_scores_df = pd.DataFrame({'Score 2019': {'MSFT': 7,'PEP': 7,'TSLA': 4,'AMZN': 6,'LKQ': 3,'ABMD': 3,'MSI': 10,'PH': 8,'NKE': 6,'TM': 7,'EOG': 7,'GOOGL': 5,'NFLX': 4,'GS': 6,'EQIX': 9,'EA': 7,'AAP': 6,'TEL': 9,'DG': 6,'EXR': 5,'MDLZ': 6,'FIS': 8,'CRL': 8,'RCL': 9},
'Score 2020': {'MSFT': 6,'PEP': 11,'TSLA': 4,'AMZN': 6,'LKQ': 4,'ABMD': 4,'MSI': 8,'PH': 8,'NKE': 6,'TM': 7,'EOG': 7,'GOOGL': 5,'NFLX': 3,'GS': 6,'EQIX': 9,'EA': 6,'AAP': 7,'TEL': 9,'DG': 6,'EXR': 4,'MDLZ': 6,'FIS': 8,'CRL': 8,'RCL': 7}})
predicted_return_dataframe = pd.DataFrame({'MSFT': 1.0982472257593677e-15,'PEP': 4.567069595849647e-09,'TSLA': 7.439258841202596e-10,'AMZN': 3.176883309676764e-07,'LKQ': 4.825709334830293e-05,'ABMD': 2.0608058642685837e-05,'MSI': -3.1789250961959136e-12,'PH': -2.257237871892785e-07,'NKE': -4.737530217609426e-07,'TM': 9.951932427172896e-07,'EOG': 1.184074639824261e-08,'GOOGL': -1.7027206923083418e-10,'NFLX': 2.948344729885545e-05,'GS': 1.458862302453713e-07,'EQIX': 4.620207503091301e-07,'EA': -1.297137640100873e-06,'AAP': -3.493153382990658e-07,'TEL': 8.202463568291799e-08,'DG': 2.743802312024829e-05,'EXR': 1.971994818465128e-11,'MDLZ': 1.578772827915881e-08,'FIS': 1.3314663987166631e-08,'CRL': 4.112083587242872e-05,'RCL': -1.470829206425942e-09} , index = [0])
r = pd.DataFrame({'MSFT': -0.029838842874655123,'PEP': -0.012265555866403165,'TSLA': -0.053599428210690636,'AMZN': -0.02614876342440773,'LKQ': -0.026658034482507052,'ABMD': -0.017274321994365294,'MSI': -0.018624198080929168,'PH': -0.02871952268633362,'NKE': -0.028820168231794074,'TM': -0.011208781085200492,'EOG': -0.04606883798249617,'GOOGL': -0.027983366801701926,'NFLX': -0.0070609860042608165,'GS': -0.02429261616692462,'EQIX': -0.015181566244607758,'EA': -0.012009295653284258,'AAP': -0.011979871239295382,'TEL': -0.021782414925879602,'DG': -0.009820085124020328,'EXR': -0.012233190959318829,'MDLZ': -0.015917631061436933,'FIS': -0.023877815976094417,'CRL': -0.020169902356185498,'RCL': -0.06831607178882856} , index = [0])
sigma = pd.DataFrame(np.array([[ 1.02188994e-04, 3.16399586e-05, 8.54243667e-05,
7.14148287e-05, 3.55313650e-05, 5.44796564e-05,
3.39128448e-05, 6.65003271e-05, 5.42932808e-05,
2.29333906e-05, 4.26407605e-05, 7.92791756e-05,
9.28910574e-05, 6.36770764e-05, 3.75024646e-05,
5.13720672e-05, 1.33646720e-05, 6.21865710e-05,
4.72888751e-05, 2.35546749e-06, 2.49700413e-05,
6.74503236e-05, 7.08948785e-05, 5.55096135e-05],
[ 3.16399586e-05, 6.47824823e-05, -2.57461009e-05,
1.81931187e-05, 2.11795049e-05, 1.01708683e-05,
3.33739243e-05, 1.23893822e-05, 2.74825418e-05,
1.35954411e-05, 2.37108310e-06, 2.34208728e-05,
1.96972793e-05, 1.09335123e-05, 4.26042775e-05,
2.76849308e-05, 6.01821651e-06, 8.04387109e-06,
3.10892437e-05, 2.79970364e-05, 3.70572613e-05,
3.08215527e-05, 2.57244480e-05, 8.72002781e-06],
[ 8.54243667e-05, -2.57461009e-05, 8.84138653e-04,
6.16478906e-05, -1.78063009e-05, 3.62712388e-05,
-6.15200573e-05, 8.63597848e-05, 2.12571109e-05,
3.21749681e-05, 6.54693912e-05, 7.95298035e-05,
1.53917874e-04, 8.06306277e-05, -5.27893372e-06,
2.60899474e-05, 4.29017379e-05, 6.13689353e-05,
2.30097086e-06, -4.45963115e-05, -2.83669072e-06,
2.95395217e-05, 4.53889239e-05, 3.11615533e-05],
[ 7.14148287e-05, 1.81931187e-05, 6.16478906e-05,
1.19357840e-04, 5.48763301e-05, 5.55161292e-05,
2.77288469e-05, 6.25231790e-05, 5.19494452e-05,
1.93193913e-05, 4.28946368e-05, 7.00210371e-05,
9.92756795e-05, 6.54630027e-05, 1.73935405e-05,
4.46819063e-05, 2.94199398e-05, 5.76749375e-05,
3.75634244e-05, -5.53847280e-06, 9.72193169e-06,
4.42756733e-05, 4.21469376e-05, 4.35344231e-05],
[ 3.55313650e-05, 2.11795049e-05, -1.78063009e-05,
5.48763301e-05, 3.49607174e-04, 1.58156275e-04,
-1.64565378e-05, 5.95602984e-05, 3.36138721e-05,
2.25095973e-05, 4.90144491e-05, 5.60207136e-05,
3.73119885e-05, 8.65010497e-05, -1.68774498e-05,
1.06928038e-05, 3.53732120e-05, 8.46071106e-05,
3.89200328e-05, -1.10740797e-05, 4.20238479e-06,
2.07371361e-05, 2.27640364e-05, 7.39017715e-05],
[ 5.44796564e-05, 1.01708683e-05, 3.62712388e-05,
5.55161292e-05, 1.58156275e-04, 1.12266763e-03,
2.49786917e-05, 5.60053839e-05, -2.57686022e-05,
3.00855419e-05, 2.09079416e-04, 1.21797841e-04,
3.80689080e-06, 1.17305259e-04, -4.95192897e-05,
5.56059321e-05, 2.87765760e-06, 1.13640096e-04,
-2.73690072e-05, 2.17458024e-05, -1.24009254e-05,
6.11287657e-05, 1.12849096e-04, 1.17234141e-04],
[ 3.39128448e-05, 3.33739243e-05, -6.15200573e-05,
2.77288469e-05, -1.64565378e-05, 2.49786917e-05,
1.84271573e-04, -2.99455473e-06, 3.56885701e-05,
1.53451236e-05, 3.20222217e-06, 3.00619247e-05,
5.17902613e-05, 1.69851832e-05, 7.75007583e-05,
7.49839347e-06, -3.78485373e-05, -1.28942631e-05,
4.36657573e-05, 3.97590833e-05, 4.04704969e-05,
4.05201790e-05, 4.01384618e-05, 4.82818631e-06],
[ 6.65003271e-05, 1.23893822e-05, 8.63597848e-05,
6.25231790e-05, 5.95602984e-05, 5.60053839e-05,
-2.99455473e-06, 2.86568704e-04, 6.55278686e-05,
4.08938883e-05, 1.18822482e-04, 9.32577766e-05,
7.92498191e-05, 1.38967662e-04, -1.64128182e-05,
4.16393158e-05, 1.06300676e-04, 1.31672888e-04,
6.64839109e-05, -5.14108669e-05, -1.03044572e-05,
1.59107041e-05, 7.65457600e-05, 1.31611693e-04],
[ 5.42932808e-05, 2.74825418e-05, 2.12571109e-05,
5.19494452e-05, 3.36138721e-05, -2.57686022e-05,
3.56885701e-05, 6.55278686e-05, 1.36374334e-04,
1.36781102e-05, 2.38544176e-05, 5.90104054e-05,
6.20754315e-05, 5.84082445e-05, 3.96422393e-05,
2.96064418e-05, 5.54456912e-05, 5.69396332e-05,
7.28867485e-05, 7.92870807e-06, 3.79528145e-05,
3.38036564e-05, 3.47015652e-05, 3.86545249e-05],
[ 2.29333906e-05, 1.35954411e-05, 3.21749681e-05,
1.93193913e-05, 2.25095973e-05, 3.00855419e-05,
1.53451236e-05, 4.08938883e-05, 1.36781102e-05,
5.30619573e-05, 4.42693706e-05, 2.92937393e-05,
1.15184525e-05, 3.04141154e-05, 1.11981894e-06,
1.29388215e-05, 1.41913521e-05, 2.37704063e-05,
1.27983719e-05, -3.53963791e-06, 5.41505031e-06,
1.21874870e-05, 2.04099948e-05, 2.89151466e-05],
[ 4.26407605e-05, 2.37108310e-06, 6.54693912e-05,
4.28946368e-05, 4.90144491e-05, 2.09079416e-04,
3.20222217e-06, 1.18822482e-04, 2.38544176e-05,
4.42693706e-05, 5.01946804e-04, 7.79572195e-05,
7.61563242e-05, 1.31597522e-04, -2.43789107e-05,
6.77962026e-05, 5.39745318e-05, 9.05223133e-05,
-1.88433584e-06, -1.63784490e-05, -1.04001201e-05,
1.79450881e-05, 5.33951974e-05, 1.07102393e-04],
[ 7.92791756e-05, 2.34208728e-05, 7.95298035e-05,
7.00210371e-05, 5.60207136e-05, 1.21797841e-04,
3.00619247e-05, 9.32577766e-05, 5.90104054e-05,
2.92937393e-05, 7.79572195e-05, 1.10688236e-04,
8.13294795e-05, 8.72981821e-05, 2.13737337e-05,
4.33439061e-05, 3.06090710e-05, 7.60853329e-05,
4.44363057e-05, 3.33458671e-06, 1.60908360e-05,
4.09067616e-05, 5.72051871e-05, 6.05239478e-05],
[ 9.28910574e-05, 1.96972793e-05, 1.53917874e-04,
9.92756795e-05, 3.73119885e-05, 3.80689080e-06,
5.17902613e-05, 7.92498191e-05, 6.20754315e-05,
1.15184525e-05, 7.61563242e-05, 8.13294795e-05,
3.77348891e-04, 8.99709029e-05, 2.58732673e-05,
8.24015922e-05, 2.77333081e-05, 4.74146019e-05,
3.76467363e-05, -5.60031564e-06, 2.25653918e-05,
6.22679966e-05, 3.92394407e-05, 6.47067147e-05],
[ 6.36770764e-05, 1.09335123e-05, 8.06306277e-05,
6.54630027e-05, 8.65010497e-05, 1.17305259e-04,
1.69851832e-05, 1.38967662e-04, 5.84082445e-05,
3.04141154e-05, 1.31597522e-04, 8.72981821e-05,
8.99709029e-05, 1.54802097e-04, -1.57072336e-05,
3.58129141e-05, 5.52667399e-05, 1.02065825e-04,
4.96942712e-05, -2.44193897e-05, -5.66188177e-06,
2.35884764e-05, 5.15584350e-05, 9.98376706e-05],
[ 3.75024646e-05, 4.26042775e-05, -5.27893372e-06,
1.73935405e-05, -1.68774498e-05, -4.95192897e-05,
7.75007583e-05, -1.64128182e-05, 3.96422393e-05,
1.11981894e-06, -2.43789107e-05, 2.13737337e-05,
2.58732673e-05, -1.57072336e-05, 1.54605175e-04,
1.07085192e-05, -1.14274871e-05, -1.26204468e-05,
2.50810750e-05, 5.60340845e-05, 4.60520336e-05,
4.29696767e-05, 5.33004299e-05, -1.56063893e-05],
[ 5.13720672e-05, 2.76849308e-05, 2.60899474e-05,
4.46819063e-05, 1.06928038e-05, 5.56059321e-05,
7.49839347e-06, 4.16393158e-05, 2.96064418e-05,
1.29388215e-05, 6.77962026e-05, 4.33439061e-05,
8.24015922e-05, 3.58129141e-05, 1.07085192e-05,
1.32544808e-04, 3.15561503e-05, 3.62681876e-05,
1.76503394e-05, 1.90982407e-07, 1.02992114e-05,
2.81341342e-05, 2.81970597e-05, 3.94413355e-05],
[ 1.33646720e-05, 6.01821651e-06, 4.29017379e-05,
2.94199398e-05, 3.53732120e-05, 2.87765760e-06,
-3.78485373e-05, 1.06300676e-04, 5.54456912e-05,
1.41913521e-05, 5.39745318e-05, 3.06090710e-05,
2.77333081e-05, 5.52667399e-05, -1.14274871e-05,
3.15561503e-05, 2.71861487e-04, 6.04272650e-05,
3.55256428e-05, -2.37123843e-05, -1.99844011e-05,
-2.02943319e-07, -4.12746174e-07, 6.80701129e-05],
[ 6.21865710e-05, 8.04387109e-06, 6.13689353e-05,
5.76749375e-05, 8.46071106e-05, 1.13640096e-04,
-1.28942631e-05, 1.31672888e-04, 5.69396332e-05,
2.37704063e-05, 9.05223133e-05, 7.60853329e-05,
4.74146019e-05, 1.02065825e-04, -1.26204468e-05,
3.62681876e-05, 6.04272650e-05, 1.67171047e-04,
5.06392219e-05, -1.02673299e-05, 1.64715372e-05,
2.50897861e-05, 5.81836032e-05, 1.00294572e-04],
[ 4.72888751e-05, 3.10892437e-05, 2.30097086e-06,
3.75634244e-05, 3.89200328e-05, -2.73690072e-05,
4.36657573e-05, 6.64839109e-05, 7.28867485e-05,
1.27983719e-05, -1.88433584e-06, 4.44363057e-05,
3.76467363e-05, 4.96942712e-05, 2.50810750e-05,
1.76503394e-05, 3.55256428e-05, 5.06392219e-05,
1.99771178e-04, 4.70710752e-06, 3.76160380e-05,
2.30014580e-05, 3.12554634e-05, 5.94948441e-06],
[ 2.35546749e-06, 2.79970364e-05, -4.45963115e-05,
-5.53847280e-06, -1.10740797e-05, 2.17458024e-05,
3.97590833e-05, -5.14108669e-05, 7.92870807e-06,
-3.53963791e-06, -1.63784490e-05, 3.33458671e-06,
-5.60031564e-06, -2.44193897e-05, 5.60340845e-05,
1.90982407e-07, -2.37123843e-05, -1.02673299e-05,
4.70710752e-06, 8.86508330e-05, 4.02039134e-05,
2.39025489e-05, -5.94660474e-06, -1.92301274e-05],
[ 2.49700413e-05, 3.70572613e-05, -2.83669072e-06,
9.72193169e-06, 4.20238479e-06, -1.24009254e-05,
4.04704969e-05, -1.03044572e-05, 3.79528145e-05,
5.41505031e-06, -1.04001201e-05, 1.60908360e-05,
2.25653918e-05, -5.66188177e-06, 4.60520336e-05,
1.02992114e-05, -1.99844011e-05, 1.64715372e-05,
3.76160380e-05, 4.02039134e-05, 8.23927778e-05,
3.21948208e-05, 3.50482953e-05, -1.97971783e-07],
[ 6.74503236e-05, 3.08215527e-05, 2.95395217e-05,
4.42756733e-05, 2.07371361e-05, 6.11287657e-05,
4.05201790e-05, 1.59107041e-05, 3.38036564e-05,
1.21874870e-05, 1.79450881e-05, 4.09067616e-05,
6.22679966e-05, 2.35884764e-05, 4.29696767e-05,
2.81341342e-05, -2.02943319e-07, 2.50897861e-05,
2.30014580e-05, 2.39025489e-05, 3.21948208e-05,
1.20680211e-04, 5.96710279e-05, 3.14411495e-05],
[ 7.08948785e-05, 2.57244480e-05, 4.53889239e-05,
4.21469376e-05, 2.27640364e-05, 1.12849096e-04,
4.01384618e-05, 7.65457600e-05, 3.47015652e-05,
2.04099948e-05, 5.33951974e-05, 5.72051871e-05,
3.92394407e-05, 5.15584350e-05, 5.33004299e-05,
2.81970597e-05, -4.12746174e-07, 5.81836032e-05,
3.12554634e-05, -5.94660474e-06, 3.50482953e-05,
5.96710279e-05, 1.65974972e-04, 5.42453625e-05],
[ 5.55096135e-05, 8.72002781e-06, 3.11615533e-05,
4.35344231e-05, 7.39017715e-05, 1.17234141e-04,
4.82818631e-06, 1.31611693e-04, 3.86545249e-05,
2.89151466e-05, 1.07102393e-04, 6.05239478e-05,
6.47067147e-05, 9.98376706e-05, -1.56063893e-05,
3.94413355e-05, 6.80701129e-05, 1.00294572e-04,
5.94948441e-06, -1.92301274e-05, -1.97971783e-07,
3.14411495e-05, 5.42453625e-05, 1.92061080e-04]]))
sigma_bar = pd.DataFrame(np.array([[ 1.26820873e-09, 9.99357360e-01, 9.96834344e-01,
9.99572167e-01, 9.42281243e-01, 9.97900189e-01,
9.99540337e-01, 9.98601652e-01, 9.99273813e-01,
9.97018616e-01, -9.73801139e-01, 9.99572102e-01,
9.99493833e-01, 9.98516049e-01, 9.99016459e-01,
9.99032878e-01, -9.44718270e-01, 9.99102498e-01,
9.99273586e-01, 9.97964072e-01, 9.98809893e-01,
9.99306302e-01, 9.98670142e-01, 9.89075401e-01],
[ 9.99357360e-01, 8.85756152e-04, 9.96279483e-01,
9.99197947e-01, 9.41407791e-01, 9.97899466e-01,
9.99417552e-01, 9.98836192e-01, 9.99109838e-01,
9.97212584e-01, -9.74070678e-01, 9.99506469e-01,
9.99304970e-01, 9.98532839e-01, 9.99435799e-01,
9.99191149e-01, -9.45834544e-01, 9.99087732e-01,
9.99237110e-01, 9.98261304e-01, 9.98920402e-01,
9.99254574e-01, 9.98828941e-01, 9.88935866e-01],
[ 9.96834344e-01, 9.96279483e-01, 4.28636430e-07,
9.96600181e-01, 9.47870932e-01, 9.95399154e-01,
9.96381458e-01, 9.96592822e-01, 9.96914826e-01,
9.93862938e-01, -9.68327765e-01, 9.96760950e-01,
9.96379221e-01, 9.96672585e-01, 9.96674621e-01,
9.95069722e-01, -9.40676110e-01, 9.96340223e-01,
9.96354345e-01, 9.94003174e-01, 9.96112855e-01,
9.96745892e-01, 9.95997518e-01, 9.89905446e-01],
[ 9.99572167e-01, 9.99197947e-01, 9.96600181e-01,
1.21966822e-09, 9.43053169e-01, 9.97880532e-01,
9.99500369e-01, 9.98410401e-01, 9.99173244e-01,
9.96775797e-01, -9.74367127e-01, 9.99362203e-01,
9.99367414e-01, 9.98297331e-01, 9.98880383e-01,
9.98663753e-01, -9.44650667e-01, 9.98960337e-01,
9.99311633e-01, 9.97876202e-01, 9.98462419e-01,
9.99263944e-01, 9.98810150e-01, 9.89492504e-01],
[ 9.42281243e-01, 9.41407791e-01, 9.47870932e-01,
9.43053169e-01, 5.87433525e-09, 9.47101615e-01,
9.43035090e-01, 9.51819965e-01, 9.46546373e-01,
9.35729856e-01, -8.83958006e-01, 9.43231419e-01,
9.39614529e-01, 9.50658526e-01, 9.44337124e-01,
9.41768971e-01, -8.57348147e-01, 9.46361648e-01,
9.43788045e-01, 9.35138095e-01, 9.43924294e-01,
9.46696871e-01, 9.46932752e-01, 9.74895278e-01],
[ 9.97900189e-01, 9.97899466e-01, 9.95399154e-01,
9.97880532e-01, 9.47101615e-01, 8.52516849e-08,
9.98162029e-01, 9.97693085e-01, 9.97494890e-01,
9.94870487e-01, -9.71281207e-01, 9.97825507e-01,
9.97609029e-01, 9.97078699e-01, 9.97937996e-01,
9.97886353e-01, -9.39807793e-01, 9.97323488e-01,
9.98086971e-01, 9.96890683e-01, 9.97306126e-01,
9.98328683e-01, 9.98019225e-01, 9.90401184e-01],
[ 9.99540337e-01, 9.99417552e-01, 9.96381458e-01,
9.99500369e-01, 9.43035090e-01, 9.98162029e-01,
1.97026096e-09, 9.98697236e-01, 9.99167466e-01,
9.96534267e-01, -9.74797106e-01, 9.99405117e-01,
9.99312797e-01, 9.98338095e-01, 9.99222108e-01,
9.99012700e-01, -9.45433385e-01, 9.99002384e-01,
9.99391574e-01, 9.98227196e-01, 9.98655866e-01,
9.99450287e-01, 9.98871183e-01, 9.89348747e-01],
[ 9.98601652e-01, 9.98836192e-01, 9.96592822e-01,
9.98410401e-01, 9.51819965e-01, 9.97693085e-01,
9.98697236e-01, 3.81563526e-10, 9.98687080e-01,
9.97121814e-01, -9.69119242e-01, 9.98787443e-01,
9.98289054e-01, 9.98866436e-01, 9.98833399e-01,
9.98412389e-01, -9.40737501e-01, 9.99081172e-01,
9.98609560e-01, 9.96732620e-01, 9.98290946e-01,
9.98808945e-01, 9.98467379e-01, 9.92893798e-01],
[ 9.99273813e-01, 9.99109838e-01, 9.96914826e-01,
9.99173244e-01, 9.46546373e-01, 9.97494890e-01,
9.99167466e-01, 9.98687080e-01, 1.63952743e-09,
9.97076275e-01, -9.71833154e-01, 9.99346179e-01,
9.99129781e-01, 9.98683650e-01, 9.99143749e-01,
9.98628992e-01, -9.42716179e-01, 9.99193054e-01,
9.99051762e-01, 9.97592295e-01, 9.98279757e-01,
9.99206541e-01, 9.98709951e-01, 9.91294961e-01],
[ 9.97018616e-01, 9.97212584e-01, 9.93862938e-01,
9.96775797e-01, 9.35729856e-01, 9.94870487e-01,
9.96534267e-01, 9.97121814e-01, 9.97076275e-01,
4.14508406e-09, -9.69602110e-01, 9.97209084e-01,
9.97269710e-01, 9.96130871e-01, 9.96598901e-01,
9.96945711e-01, -9.41737281e-01, 9.97547921e-01,
9.96623630e-01, 9.95604803e-01, 9.96053414e-01,
9.96252977e-01, 9.96293594e-01, 9.87014134e-01],
[-9.73801139e-01, -9.74070678e-01, -9.68327765e-01,
-9.74367127e-01, -8.83958006e-01, -9.71281207e-01,
-9.74797106e-01, -9.69119242e-01, -9.71833154e-01,
-9.69602110e-01, 7.91579754e-08, -9.72627284e-01,
-9.74397877e-01, -9.66816215e-01, -9.74055921e-01,
-9.72152413e-01, 9.49931280e-01, -9.70349967e-01,
-9.74543996e-01, -9.77042256e-01, -9.72510826e-01,
-9.72753685e-01, -9.70977647e-01, -9.49332577e-01],
[ 9.99572102e-01, 9.99506469e-01, 9.96760950e-01,
9.99362203e-01, 9.43231419e-01, 9.97825507e-01,
9.99405117e-01, 9.98787443e-01, 9.99346179e-01,
9.97209084e-01, -9.72627284e-01, 9.49759898e-10,
9.99396168e-01, 9.98616747e-01, 9.99231469e-01,
9.99092707e-01, -9.43690714e-01, 9.99236560e-01,
9.99125265e-01, 9.97720253e-01, 9.98657360e-01,
9.99322811e-01, 9.98924819e-01, 9.89982094e-01],
[ 9.99493833e-01, 9.99304970e-01, 9.96379221e-01,
9.99367414e-01, 9.39614529e-01, 9.97609029e-01,
9.99312797e-01, 9.98289054e-01, 9.99129781e-01,
9.97269710e-01, -9.74397877e-01, 9.99396168e-01,
6.10314496e-08, 9.98282510e-01, 9.98908676e-01,
9.99022688e-01, -9.44584256e-01, 9.99076968e-01,
9.99242844e-01, 9.98014936e-01, 9.98393894e-01,
9.99093343e-01, 9.98535127e-01, 9.88011557e-01],
[ 9.98516049e-01, 9.98532839e-01, 9.96672585e-01,
9.98297331e-01, 9.50658526e-01, 9.97078699e-01,
9.98338095e-01, 9.98866436e-01, 9.98683650e-01,
9.96130871e-01, -9.66816215e-01, 9.98616747e-01,
9.98282510e-01, 1.39566686e-09, 9.98517176e-01,
9.98377797e-01, -9.41181012e-01, 9.99085880e-01,
9.98417332e-01, 9.95895305e-01, 9.98089538e-01,
9.98786233e-01, 9.98273278e-01, 9.92133050e-01],
[ 9.99016459e-01, 9.99435799e-01, 9.96674621e-01,
9.98880383e-01, 9.44337124e-01, 9.97937996e-01,
9.99222108e-01, 9.98833399e-01, 9.99143749e-01,
9.96598901e-01, -9.74055921e-01, 9.99231469e-01,
9.98908676e-01, 9.98517176e-01, 3.91145914e-09,
9.98762801e-01, -9.44712685e-01, 9.98882295e-01,
9.99167722e-01, 9.98365735e-01, 9.98539526e-01,
9.99349674e-01, 9.98682774e-01, 9.90282263e-01],
[ 9.99032878e-01, 9.99191149e-01, 9.95069722e-01,
9.98663753e-01, 9.41768971e-01, 9.97886353e-01,
9.99012700e-01, 9.98412389e-01, 9.98628992e-01,
9.96945711e-01, -9.72152413e-01, 9.99092707e-01,
9.99022688e-01, 9.98377797e-01, 9.98762801e-01,
6.12438062e-09, -9.43278583e-01, 9.98714615e-01,
9.98765094e-01, 9.97518255e-01, 9.98234814e-01,
9.98833239e-01, 9.98556185e-01, 9.88600916e-01],
[-9.44718270e-01, -9.45834544e-01, -9.40676110e-01,
-9.44650667e-01, -8.57348147e-01, -9.39807793e-01,
-9.45433385e-01, -9.40737501e-01, -9.42716179e-01,
-9.41737281e-01, 9.49931280e-01, -9.43690714e-01,
-9.44584256e-01, -9.41181012e-01, -9.44712685e-01,
-9.43278583e-01, 1.85097555e-08, -9.42274581e-01,
-9.43930225e-01, -9.44416759e-01, -9.44123084e-01,
-9.43611879e-01, -9.43058469e-01, -9.20277725e-01],
[ 9.99102498e-01, 9.99087732e-01, 9.96340223e-01,
9.98960337e-01, 9.46361648e-01, 9.97323488e-01,
9.99002384e-01, 9.99081172e-01, 9.99193054e-01,
9.97547921e-01, -9.70349967e-01, 9.99236560e-01,
9.99076968e-01, 9.99085880e-01, 9.98882295e-01,
9.98714615e-01, -9.42274581e-01, 4.63172335e-10,
9.99055447e-01, 9.96678367e-01, 9.97947641e-01,
9.99023756e-01, 9.98655609e-01, 9.90680163e-01],
[ 9.99273586e-01, 9.99237110e-01, 9.96354345e-01,
9.99311633e-01, 9.43788045e-01, 9.98086971e-01,
9.99391574e-01, 9.98609560e-01, 9.99051762e-01,
9.96623630e-01, -9.74543996e-01, 9.99125265e-01,
9.99242844e-01, 9.98417332e-01, 9.99167722e-01,
9.98765094e-01, -9.43930225e-01, 9.99055447e-01,
1.49968419e-08, 9.98019738e-01, 9.98407433e-01,
9.99222857e-01, 9.98652394e-01, 9.89226980e-01],
[ 9.97964072e-01, 9.98261304e-01, 9.94003174e-01,
9.97876202e-01, 9.35138095e-01, 9.96890683e-01,
9.98227196e-01, 9.96732620e-01, 9.97592295e-01,
9.95604803e-01, -9.77042256e-01, 9.97720253e-01,
9.98014936e-01, 9.95895305e-01, 9.98365735e-01,
9.97518255e-01, -9.44416759e-01, 9.96678367e-01,
9.98019738e-01, 7.47650147e-10, 9.97617693e-01,
9.97870740e-01, 9.97367170e-01, 9.86577350e-01],
[ 9.98809893e-01, 9.98920402e-01, 9.96112855e-01,
9.98462419e-01, 9.43924294e-01, 9.97306126e-01,
9.98655866e-01, 9.98290946e-01, 9.98279757e-01,
9.96053414e-01, -9.72510826e-01, 9.98657360e-01,
9.98393894e-01, 9.98089538e-01, 9.98539526e-01,
9.98234814e-01, -9.44123084e-01, 9.97947641e-01,
9.98407433e-01, 9.97617693e-01, 9.94482237e-10,
9.98596112e-01, 9.98000736e-01, 9.89489744e-01],
[ 9.99306302e-01, 9.99254574e-01, 9.96745892e-01,
9.99263944e-01, 9.46696871e-01, 9.98328683e-01,
9.99450287e-01, 9.98808945e-01, 9.99206541e-01,
9.96252977e-01, -9.72753685e-01, 9.99322811e-01,
9.99093343e-01, 9.98786233e-01, 9.99349674e-01,
9.98833239e-01, -9.43611879e-01, 9.99023756e-01,
9.99222857e-01, 9.97870740e-01, 9.98596112e-01,
7.44695142e-09, 9.99016834e-01, 9.90734007e-01],
[ 9.98670142e-01, 9.98828941e-01, 9.95997518e-01,
9.98810150e-01, 9.46932752e-01, 9.98019225e-01,
9.98871183e-01, 9.98467379e-01, 9.98709951e-01,
9.96293594e-01, -9.70977647e-01, 9.98924819e-01,
9.98535127e-01, 9.98273278e-01, 9.98682774e-01,
9.98556185e-01, -9.43058469e-01, 9.98655609e-01,
9.98652394e-01, 9.97367170e-01, 9.98000736e-01,
9.99016834e-01, 1.79765233e-09, 9.91199840e-01],
[ 9.89075401e-01, 9.88935866e-01, 9.89905446e-01,
9.89492504e-01, 9.74895278e-01, 9.90401184e-01,
9.89348747e-01, 9.92893798e-01, 9.91294961e-01,
9.87014134e-01, -9.49332577e-01, 9.89982094e-01,
9.88011557e-01, 9.92133050e-01, 9.90282263e-01,
9.88600916e-01, -9.20277725e-01, 9.90680163e-01,
9.89226980e-01, 9.86577350e-01, 9.89489744e-01,
9.90734007e-01, 9.91199840e-01, 9.41720628e-08]]))
Algorithm Section
N = 24
model = GEKKO(remote=False)
wesg = model.Array(model.Var , N , value = 1/N , lb=0 , ub=1)
model.Equation = (sum(wesg) == 1)
def obj(rf = 0.02):
esg_portfo = 0
for i in range(N):
esg_portfo += model.Intermediate(wesg[i] * ((esg_scores_df["Score 2019"][i] + esg_scores_df["Score 2020"][i])/2))
return_portfo = 0
for i in range(N):
return_portfo += model.Intermediate(wesg[i]*((predicted_return_dataframe.iloc[0 , i] + r.iloc[0 ,i])/2))
sigma_portfo = 0
for i in range(N):
for j in range(N):
sigma_portfo += model.Intermediate(wesg[i] * ((sigma.iloc[i,j] + sigma_bar.iloc[i,j])/2) * wesg[j])
return -esg_portfo * ((return_portfo - rf)/sigma_portfo)
model.Minimize(obj())
model.solve(disp=False)
wesg = np.array( [item[0] for item in wesg], dtype=float)
print(wesg)
Result
The code results in:
[0.00000000e+00 1.31172076e-07 0.00000000e+00 0.00000000e+00
1.88847768e-01 1.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 1.00000000e+00 0.00000000e+00 0.00000000e+00
1.00000000e+00 0.00000000e+00 0.00000000e+00 1.00000000e+00
0.00000000e+00 0.00000000e+00 1.00000000e+00 1.00000000e+00
9.07168980e-01 0.00000000e+00 0.00000000e+00 0.00000000e+00]
But, there are many ones in the result!! I have a constraint of sum(wesg) == 1! But the result indicates that somehow, Gekko doesn't consider the constraint. If you try print(wesg.sum()), then it will result:
7.096016879722077
Which I expected to be exact 1!
How can I fix this issue, and where is the problem? Any help would be appreciated.
Upvotes: 2
Views: 68
Answers (1)
John Hedengren
Reputation: 14376
The error is with model.Equation = (sum(wesg) == 1) that redefines the model.Equation function as False. Use this instead:
model.Equation(sum(wesg) == 1)
The new result enforces the constraint to add to one with sum(wesg)=1.000000000001.
[0. 0. 0. 0. 0.1425506 0.24959448
0. 0. 0. 0. 0. 0.0281217
0.32053308 0. 0. 0. 0. 0.
0.05860444 0.18554967 0.01504603 0. 0. 0. ]
Here are a couple additional suggestions and options:
- For larger portfolios use
model.sum()instead for better performance. - To select the top 3 stocks as integers (
purchaseordon't purchase) then useinteger=Truewith the APOPT solver.
wesg = model.Array(model.Var, N, value = 1/N, lb=0, ub=1, integer=True)
model.Equation(model.sum(wesg) == 3)
model.options.SOLVER=1
Here is the complete code.
from gekko import GEKKO
import numpy as np
import pandas as pd
esg_scores_df = pd.DataFrame({'Score 2019': {'MSFT': 7,'PEP': 7,'TSLA': 4,'AMZN': 6,'LKQ': 3,'ABMD': 3,'MSI': 10,'PH': 8,'NKE': 6,'TM': 7,'EOG': 7,'GOOGL': 5,'NFLX': 4,'GS': 6,'EQIX': 9,'EA': 7,'AAP': 6,'TEL': 9,'DG': 6,'EXR': 5,'MDLZ': 6,'FIS': 8,'CRL': 8,'RCL': 9},
'Score 2020': {'MSFT': 6,'PEP': 11,'TSLA': 4,'AMZN': 6,'LKQ': 4,'ABMD': 4,'MSI': 8,'PH': 8,'NKE': 6,'TM': 7,'EOG': 7,'GOOGL': 5,'NFLX': 3,'GS': 6,'EQIX': 9,'EA': 6,'AAP': 7,'TEL': 9,'DG': 6,'EXR': 4,'MDLZ': 6,'FIS': 8,'CRL': 8,'RCL': 7}})
predicted_return_dataframe = pd.DataFrame({'MSFT': 1.0982472257593677e-15,'PEP': 4.567069595849647e-09,'TSLA': 7.439258841202596e-10,'AMZN': 3.176883309676764e-07,'LKQ': 4.825709334830293e-05,'ABMD': 2.0608058642685837e-05,'MSI': -3.1789250961959136e-12,'PH': -2.257237871892785e-07,'NKE': -4.737530217609426e-07,'TM': 9.951932427172896e-07,'EOG': 1.184074639824261e-08,'GOOGL': -1.7027206923083418e-10,'NFLX': 2.948344729885545e-05,'GS': 1.458862302453713e-07,'EQIX': 4.620207503091301e-07,'EA': -1.297137640100873e-06,'AAP': -3.493153382990658e-07,'TEL': 8.202463568291799e-08,'DG': 2.743802312024829e-05,'EXR': 1.971994818465128e-11,'MDLZ': 1.578772827915881e-08,'FIS': 1.3314663987166631e-08,'CRL': 4.112083587242872e-05,'RCL': -1.470829206425942e-09} , index = [0])
r = pd.DataFrame({'MSFT': -0.029838842874655123,'PEP': -0.012265555866403165,'TSLA': -0.053599428210690636,'AMZN': -0.02614876342440773,'LKQ': -0.026658034482507052,'ABMD': -0.017274321994365294,'MSI': -0.018624198080929168,'PH': -0.02871952268633362,'NKE': -0.028820168231794074,'TM': -0.011208781085200492,'EOG': -0.04606883798249617,'GOOGL': -0.027983366801701926,'NFLX': -0.0070609860042608165,'GS': -0.02429261616692462,'EQIX': -0.015181566244607758,'EA': -0.012009295653284258,'AAP': -0.011979871239295382,'TEL': -0.021782414925879602,'DG': -0.009820085124020328,'EXR': -0.012233190959318829,'MDLZ': -0.015917631061436933,'FIS': -0.023877815976094417,'CRL': -0.020169902356185498,'RCL': -0.06831607178882856} , index = [0])
sigma = pd.DataFrame(np.array([[ 1.02188994e-04, 3.16399586e-05, 8.54243667e-05,
7.14148287e-05, 3.55313650e-05, 5.44796564e-05,
3.39128448e-05, 6.65003271e-05, 5.42932808e-05,
2.29333906e-05, 4.26407605e-05, 7.92791756e-05,
9.28910574e-05, 6.36770764e-05, 3.75024646e-05,
5.13720672e-05, 1.33646720e-05, 6.21865710e-05,
4.72888751e-05, 2.35546749e-06, 2.49700413e-05,
6.74503236e-05, 7.08948785e-05, 5.55096135e-05],
[ 3.16399586e-05, 6.47824823e-05, -2.57461009e-05,
1.81931187e-05, 2.11795049e-05, 1.01708683e-05,
3.33739243e-05, 1.23893822e-05, 2.74825418e-05,
1.35954411e-05, 2.37108310e-06, 2.34208728e-05,
1.96972793e-05, 1.09335123e-05, 4.26042775e-05,
2.76849308e-05, 6.01821651e-06, 8.04387109e-06,
3.10892437e-05, 2.79970364e-05, 3.70572613e-05,
3.08215527e-05, 2.57244480e-05, 8.72002781e-06],
[ 8.54243667e-05, -2.57461009e-05, 8.84138653e-04,
6.16478906e-05, -1.78063009e-05, 3.62712388e-05,
-6.15200573e-05, 8.63597848e-05, 2.12571109e-05,
3.21749681e-05, 6.54693912e-05, 7.95298035e-05,
1.53917874e-04, 8.06306277e-05, -5.27893372e-06,
2.60899474e-05, 4.29017379e-05, 6.13689353e-05,
2.30097086e-06, -4.45963115e-05, -2.83669072e-06,
2.95395217e-05, 4.53889239e-05, 3.11615533e-05],
[ 7.14148287e-05, 1.81931187e-05, 6.16478906e-05,
1.19357840e-04, 5.48763301e-05, 5.55161292e-05,
2.77288469e-05, 6.25231790e-05, 5.19494452e-05,
1.93193913e-05, 4.28946368e-05, 7.00210371e-05,
9.92756795e-05, 6.54630027e-05, 1.73935405e-05,
4.46819063e-05, 2.94199398e-05, 5.76749375e-05,
3.75634244e-05, -5.53847280e-06, 9.72193169e-06,
4.42756733e-05, 4.21469376e-05, 4.35344231e-05],
[ 3.55313650e-05, 2.11795049e-05, -1.78063009e-05,
5.48763301e-05, 3.49607174e-04, 1.58156275e-04,
-1.64565378e-05, 5.95602984e-05, 3.36138721e-05,
2.25095973e-05, 4.90144491e-05, 5.60207136e-05,
3.73119885e-05, 8.65010497e-05, -1.68774498e-05,
1.06928038e-05, 3.53732120e-05, 8.46071106e-05,
3.89200328e-05, -1.10740797e-05, 4.20238479e-06,
2.07371361e-05, 2.27640364e-05, 7.39017715e-05],
[ 5.44796564e-05, 1.01708683e-05, 3.62712388e-05,
5.55161292e-05, 1.58156275e-04, 1.12266763e-03,
2.49786917e-05, 5.60053839e-05, -2.57686022e-05,
3.00855419e-05, 2.09079416e-04, 1.21797841e-04,
3.80689080e-06, 1.17305259e-04, -4.95192897e-05,
5.56059321e-05, 2.87765760e-06, 1.13640096e-04,
-2.73690072e-05, 2.17458024e-05, -1.24009254e-05,
6.11287657e-05, 1.12849096e-04, 1.17234141e-04],
[ 3.39128448e-05, 3.33739243e-05, -6.15200573e-05,
2.77288469e-05, -1.64565378e-05, 2.49786917e-05,
1.84271573e-04, -2.99455473e-06, 3.56885701e-05,
1.53451236e-05, 3.20222217e-06, 3.00619247e-05,
5.17902613e-05, 1.69851832e-05, 7.75007583e-05,
7.49839347e-06, -3.78485373e-05, -1.28942631e-05,
4.36657573e-05, 3.97590833e-05, 4.04704969e-05,
4.05201790e-05, 4.01384618e-05, 4.82818631e-06],
[ 6.65003271e-05, 1.23893822e-05, 8.63597848e-05,
6.25231790e-05, 5.95602984e-05, 5.60053839e-05,
-2.99455473e-06, 2.86568704e-04, 6.55278686e-05,
4.08938883e-05, 1.18822482e-04, 9.32577766e-05,
7.92498191e-05, 1.38967662e-04, -1.64128182e-05,
4.16393158e-05, 1.06300676e-04, 1.31672888e-04,
6.64839109e-05, -5.14108669e-05, -1.03044572e-05,
1.59107041e-05, 7.65457600e-05, 1.31611693e-04],
[ 5.42932808e-05, 2.74825418e-05, 2.12571109e-05,
5.19494452e-05, 3.36138721e-05, -2.57686022e-05,
3.56885701e-05, 6.55278686e-05, 1.36374334e-04,
1.36781102e-05, 2.38544176e-05, 5.90104054e-05,
6.20754315e-05, 5.84082445e-05, 3.96422393e-05,
2.96064418e-05, 5.54456912e-05, 5.69396332e-05,
7.28867485e-05, 7.92870807e-06, 3.79528145e-05,
3.38036564e-05, 3.47015652e-05, 3.86545249e-05],
[ 2.29333906e-05, 1.35954411e-05, 3.21749681e-05,
1.93193913e-05, 2.25095973e-05, 3.00855419e-05,
1.53451236e-05, 4.08938883e-05, 1.36781102e-05,
5.30619573e-05, 4.42693706e-05, 2.92937393e-05,
1.15184525e-05, 3.04141154e-05, 1.11981894e-06,
1.29388215e-05, 1.41913521e-05, 2.37704063e-05,
1.27983719e-05, -3.53963791e-06, 5.41505031e-06,
1.21874870e-05, 2.04099948e-05, 2.89151466e-05],
[ 4.26407605e-05, 2.37108310e-06, 6.54693912e-05,
4.28946368e-05, 4.90144491e-05, 2.09079416e-04,
3.20222217e-06, 1.18822482e-04, 2.38544176e-05,
4.42693706e-05, 5.01946804e-04, 7.79572195e-05,
7.61563242e-05, 1.31597522e-04, -2.43789107e-05,
6.77962026e-05, 5.39745318e-05, 9.05223133e-05,
-1.88433584e-06, -1.63784490e-05, -1.04001201e-05,
1.79450881e-05, 5.33951974e-05, 1.07102393e-04],
[ 7.92791756e-05, 2.34208728e-05, 7.95298035e-05,
7.00210371e-05, 5.60207136e-05, 1.21797841e-04,
3.00619247e-05, 9.32577766e-05, 5.90104054e-05,
2.92937393e-05, 7.79572195e-05, 1.10688236e-04,
8.13294795e-05, 8.72981821e-05, 2.13737337e-05,
4.33439061e-05, 3.06090710e-05, 7.60853329e-05,
4.44363057e-05, 3.33458671e-06, 1.60908360e-05,
4.09067616e-05, 5.72051871e-05, 6.05239478e-05],
[ 9.28910574e-05, 1.96972793e-05, 1.53917874e-04,
9.92756795e-05, 3.73119885e-05, 3.80689080e-06,
5.17902613e-05, 7.92498191e-05, 6.20754315e-05,
1.15184525e-05, 7.61563242e-05, 8.13294795e-05,
3.77348891e-04, 8.99709029e-05, 2.58732673e-05,
8.24015922e-05, 2.77333081e-05, 4.74146019e-05,
3.76467363e-05, -5.60031564e-06, 2.25653918e-05,
6.22679966e-05, 3.92394407e-05, 6.47067147e-05],
[ 6.36770764e-05, 1.09335123e-05, 8.06306277e-05,
6.54630027e-05, 8.65010497e-05, 1.17305259e-04,
1.69851832e-05, 1.38967662e-04, 5.84082445e-05,
3.04141154e-05, 1.31597522e-04, 8.72981821e-05,
8.99709029e-05, 1.54802097e-04, -1.57072336e-05,
3.58129141e-05, 5.52667399e-05, 1.02065825e-04,
4.96942712e-05, -2.44193897e-05, -5.66188177e-06,
2.35884764e-05, 5.15584350e-05, 9.98376706e-05],
[ 3.75024646e-05, 4.26042775e-05, -5.27893372e-06,
1.73935405e-05, -1.68774498e-05, -4.95192897e-05,
7.75007583e-05, -1.64128182e-05, 3.96422393e-05,
1.11981894e-06, -2.43789107e-05, 2.13737337e-05,
2.58732673e-05, -1.57072336e-05, 1.54605175e-04,
1.07085192e-05, -1.14274871e-05, -1.26204468e-05,
2.50810750e-05, 5.60340845e-05, 4.60520336e-05,
4.29696767e-05, 5.33004299e-05, -1.56063893e-05],
[ 5.13720672e-05, 2.76849308e-05, 2.60899474e-05,
4.46819063e-05, 1.06928038e-05, 5.56059321e-05,
7.49839347e-06, 4.16393158e-05, 2.96064418e-05,
1.29388215e-05, 6.77962026e-05, 4.33439061e-05,
8.24015922e-05, 3.58129141e-05, 1.07085192e-05,
1.32544808e-04, 3.15561503e-05, 3.62681876e-05,
1.76503394e-05, 1.90982407e-07, 1.02992114e-05,
2.81341342e-05, 2.81970597e-05, 3.94413355e-05],
[ 1.33646720e-05, 6.01821651e-06, 4.29017379e-05,
2.94199398e-05, 3.53732120e-05, 2.87765760e-06,
-3.78485373e-05, 1.06300676e-04, 5.54456912e-05,
1.41913521e-05, 5.39745318e-05, 3.06090710e-05,
2.77333081e-05, 5.52667399e-05, -1.14274871e-05,
3.15561503e-05, 2.71861487e-04, 6.04272650e-05,
3.55256428e-05, -2.37123843e-05, -1.99844011e-05,
-2.02943319e-07, -4.12746174e-07, 6.80701129e-05],
[ 6.21865710e-05, 8.04387109e-06, 6.13689353e-05,
5.76749375e-05, 8.46071106e-05, 1.13640096e-04,
-1.28942631e-05, 1.31672888e-04, 5.69396332e-05,
2.37704063e-05, 9.05223133e-05, 7.60853329e-05,
4.74146019e-05, 1.02065825e-04, -1.26204468e-05,
3.62681876e-05, 6.04272650e-05, 1.67171047e-04,
5.06392219e-05, -1.02673299e-05, 1.64715372e-05,
2.50897861e-05, 5.81836032e-05, 1.00294572e-04],
[ 4.72888751e-05, 3.10892437e-05, 2.30097086e-06,
3.75634244e-05, 3.89200328e-05, -2.73690072e-05,
4.36657573e-05, 6.64839109e-05, 7.28867485e-05,
1.27983719e-05, -1.88433584e-06, 4.44363057e-05,
3.76467363e-05, 4.96942712e-05, 2.50810750e-05,
1.76503394e-05, 3.55256428e-05, 5.06392219e-05,
1.99771178e-04, 4.70710752e-06, 3.76160380e-05,
2.30014580e-05, 3.12554634e-05, 5.94948441e-06],
[ 2.35546749e-06, 2.79970364e-05, -4.45963115e-05,
-5.53847280e-06, -1.10740797e-05, 2.17458024e-05,
3.97590833e-05, -5.14108669e-05, 7.92870807e-06,
-3.53963791e-06, -1.63784490e-05, 3.33458671e-06,
-5.60031564e-06, -2.44193897e-05, 5.60340845e-05,
1.90982407e-07, -2.37123843e-05, -1.02673299e-05,
4.70710752e-06, 8.86508330e-05, 4.02039134e-05,
2.39025489e-05, -5.94660474e-06, -1.92301274e-05],
[ 2.49700413e-05, 3.70572613e-05, -2.83669072e-06,
9.72193169e-06, 4.20238479e-06, -1.24009254e-05,
4.04704969e-05, -1.03044572e-05, 3.79528145e-05,
5.41505031e-06, -1.04001201e-05, 1.60908360e-05,
2.25653918e-05, -5.66188177e-06, 4.60520336e-05,
1.02992114e-05, -1.99844011e-05, 1.64715372e-05,
3.76160380e-05, 4.02039134e-05, 8.23927778e-05,
3.21948208e-05, 3.50482953e-05, -1.97971783e-07],
[ 6.74503236e-05, 3.08215527e-05, 2.95395217e-05,
4.42756733e-05, 2.07371361e-05, 6.11287657e-05,
4.05201790e-05, 1.59107041e-05, 3.38036564e-05,
1.21874870e-05, 1.79450881e-05, 4.09067616e-05,
6.22679966e-05, 2.35884764e-05, 4.29696767e-05,
2.81341342e-05, -2.02943319e-07, 2.50897861e-05,
2.30014580e-05, 2.39025489e-05, 3.21948208e-05,
1.20680211e-04, 5.96710279e-05, 3.14411495e-05],
[ 7.08948785e-05, 2.57244480e-05, 4.53889239e-05,
4.21469376e-05, 2.27640364e-05, 1.12849096e-04,
4.01384618e-05, 7.65457600e-05, 3.47015652e-05,
2.04099948e-05, 5.33951974e-05, 5.72051871e-05,
3.92394407e-05, 5.15584350e-05, 5.33004299e-05,
2.81970597e-05, -4.12746174e-07, 5.81836032e-05,
3.12554634e-05, -5.94660474e-06, 3.50482953e-05,
5.96710279e-05, 1.65974972e-04, 5.42453625e-05],
[ 5.55096135e-05, 8.72002781e-06, 3.11615533e-05,
4.35344231e-05, 7.39017715e-05, 1.17234141e-04,
4.82818631e-06, 1.31611693e-04, 3.86545249e-05,
2.89151466e-05, 1.07102393e-04, 6.05239478e-05,
6.47067147e-05, 9.98376706e-05, -1.56063893e-05,
3.94413355e-05, 6.80701129e-05, 1.00294572e-04,
5.94948441e-06, -1.92301274e-05, -1.97971783e-07,
3.14411495e-05, 5.42453625e-05, 1.92061080e-04]]))
sigma_bar = pd.DataFrame(np.array([[ 1.26820873e-09, 9.99357360e-01, 9.96834344e-01,
9.99572167e-01, 9.42281243e-01, 9.97900189e-01,
9.99540337e-01, 9.98601652e-01, 9.99273813e-01,
9.97018616e-01, -9.73801139e-01, 9.99572102e-01,
9.99493833e-01, 9.98516049e-01, 9.99016459e-01,
9.99032878e-01, -9.44718270e-01, 9.99102498e-01,
9.99273586e-01, 9.97964072e-01, 9.98809893e-01,
9.99306302e-01, 9.98670142e-01, 9.89075401e-01],
[ 9.99357360e-01, 8.85756152e-04, 9.96279483e-01,
9.99197947e-01, 9.41407791e-01, 9.97899466e-01,
9.99417552e-01, 9.98836192e-01, 9.99109838e-01,
9.97212584e-01, -9.74070678e-01, 9.99506469e-01,
9.99304970e-01, 9.98532839e-01, 9.99435799e-01,
9.99191149e-01, -9.45834544e-01, 9.99087732e-01,
9.99237110e-01, 9.98261304e-01, 9.98920402e-01,
9.99254574e-01, 9.98828941e-01, 9.88935866e-01],
[ 9.96834344e-01, 9.96279483e-01, 4.28636430e-07,
9.96600181e-01, 9.47870932e-01, 9.95399154e-01,
9.96381458e-01, 9.96592822e-01, 9.96914826e-01,
9.93862938e-01, -9.68327765e-01, 9.96760950e-01,
9.96379221e-01, 9.96672585e-01, 9.96674621e-01,
9.95069722e-01, -9.40676110e-01, 9.96340223e-01,
9.96354345e-01, 9.94003174e-01, 9.96112855e-01,
9.96745892e-01, 9.95997518e-01, 9.89905446e-01],
[ 9.99572167e-01, 9.99197947e-01, 9.96600181e-01,
1.21966822e-09, 9.43053169e-01, 9.97880532e-01,
9.99500369e-01, 9.98410401e-01, 9.99173244e-01,
9.96775797e-01, -9.74367127e-01, 9.99362203e-01,
9.99367414e-01, 9.98297331e-01, 9.98880383e-01,
9.98663753e-01, -9.44650667e-01, 9.98960337e-01,
9.99311633e-01, 9.97876202e-01, 9.98462419e-01,
9.99263944e-01, 9.98810150e-01, 9.89492504e-01],
[ 9.42281243e-01, 9.41407791e-01, 9.47870932e-01,
9.43053169e-01, 5.87433525e-09, 9.47101615e-01,
9.43035090e-01, 9.51819965e-01, 9.46546373e-01,
9.35729856e-01, -8.83958006e-01, 9.43231419e-01,
9.39614529e-01, 9.50658526e-01, 9.44337124e-01,
9.41768971e-01, -8.57348147e-01, 9.46361648e-01,
9.43788045e-01, 9.35138095e-01, 9.43924294e-01,
9.46696871e-01, 9.46932752e-01, 9.74895278e-01],
[ 9.97900189e-01, 9.97899466e-01, 9.95399154e-01,
9.97880532e-01, 9.47101615e-01, 8.52516849e-08,
9.98162029e-01, 9.97693085e-01, 9.97494890e-01,
9.94870487e-01, -9.71281207e-01, 9.97825507e-01,
9.97609029e-01, 9.97078699e-01, 9.97937996e-01,
9.97886353e-01, -9.39807793e-01, 9.97323488e-01,
9.98086971e-01, 9.96890683e-01, 9.97306126e-01,
9.98328683e-01, 9.98019225e-01, 9.90401184e-01],
[ 9.99540337e-01, 9.99417552e-01, 9.96381458e-01,
9.99500369e-01, 9.43035090e-01, 9.98162029e-01,
1.97026096e-09, 9.98697236e-01, 9.99167466e-01,
9.96534267e-01, -9.74797106e-01, 9.99405117e-01,
9.99312797e-01, 9.98338095e-01, 9.99222108e-01,
9.99012700e-01, -9.45433385e-01, 9.99002384e-01,
9.99391574e-01, 9.98227196e-01, 9.98655866e-01,
9.99450287e-01, 9.98871183e-01, 9.89348747e-01],
[ 9.98601652e-01, 9.98836192e-01, 9.96592822e-01,
9.98410401e-01, 9.51819965e-01, 9.97693085e-01,
9.98697236e-01, 3.81563526e-10, 9.98687080e-01,
9.97121814e-01, -9.69119242e-01, 9.98787443e-01,
9.98289054e-01, 9.98866436e-01, 9.98833399e-01,
9.98412389e-01, -9.40737501e-01, 9.99081172e-01,
9.98609560e-01, 9.96732620e-01, 9.98290946e-01,
9.98808945e-01, 9.98467379e-01, 9.92893798e-01],
[ 9.99273813e-01, 9.99109838e-01, 9.96914826e-01,
9.99173244e-01, 9.46546373e-01, 9.97494890e-01,
9.99167466e-01, 9.98687080e-01, 1.63952743e-09,
9.97076275e-01, -9.71833154e-01, 9.99346179e-01,
9.99129781e-01, 9.98683650e-01, 9.99143749e-01,
9.98628992e-01, -9.42716179e-01, 9.99193054e-01,
9.99051762e-01, 9.97592295e-01, 9.98279757e-01,
9.99206541e-01, 9.98709951e-01, 9.91294961e-01],
[ 9.97018616e-01, 9.97212584e-01, 9.93862938e-01,
9.96775797e-01, 9.35729856e-01, 9.94870487e-01,
9.96534267e-01, 9.97121814e-01, 9.97076275e-01,
4.14508406e-09, -9.69602110e-01, 9.97209084e-01,
9.97269710e-01, 9.96130871e-01, 9.96598901e-01,
9.96945711e-01, -9.41737281e-01, 9.97547921e-01,
9.96623630e-01, 9.95604803e-01, 9.96053414e-01,
9.96252977e-01, 9.96293594e-01, 9.87014134e-01],
[-9.73801139e-01, -9.74070678e-01, -9.68327765e-01,
-9.74367127e-01, -8.83958006e-01, -9.71281207e-01,
-9.74797106e-01, -9.69119242e-01, -9.71833154e-01,
-9.69602110e-01, 7.91579754e-08, -9.72627284e-01,
-9.74397877e-01, -9.66816215e-01, -9.74055921e-01,
-9.72152413e-01, 9.49931280e-01, -9.70349967e-01,
-9.74543996e-01, -9.77042256e-01, -9.72510826e-01,
-9.72753685e-01, -9.70977647e-01, -9.49332577e-01],
[ 9.99572102e-01, 9.99506469e-01, 9.96760950e-01,
9.99362203e-01, 9.43231419e-01, 9.97825507e-01,
9.99405117e-01, 9.98787443e-01, 9.99346179e-01,
9.97209084e-01, -9.72627284e-01, 9.49759898e-10,
9.99396168e-01, 9.98616747e-01, 9.99231469e-01,
9.99092707e-01, -9.43690714e-01, 9.99236560e-01,
9.99125265e-01, 9.97720253e-01, 9.98657360e-01,
9.99322811e-01, 9.98924819e-01, 9.89982094e-01],
[ 9.99493833e-01, 9.99304970e-01, 9.96379221e-01,
9.99367414e-01, 9.39614529e-01, 9.97609029e-01,
9.99312797e-01, 9.98289054e-01, 9.99129781e-01,
9.97269710e-01, -9.74397877e-01, 9.99396168e-01,
6.10314496e-08, 9.98282510e-01, 9.98908676e-01,
9.99022688e-01, -9.44584256e-01, 9.99076968e-01,
9.99242844e-01, 9.98014936e-01, 9.98393894e-01,
9.99093343e-01, 9.98535127e-01, 9.88011557e-01],
[ 9.98516049e-01, 9.98532839e-01, 9.96672585e-01,
9.98297331e-01, 9.50658526e-01, 9.97078699e-01,
9.98338095e-01, 9.98866436e-01, 9.98683650e-01,
9.96130871e-01, -9.66816215e-01, 9.98616747e-01,
9.98282510e-01, 1.39566686e-09, 9.98517176e-01,
9.98377797e-01, -9.41181012e-01, 9.99085880e-01,
9.98417332e-01, 9.95895305e-01, 9.98089538e-01,
9.98786233e-01, 9.98273278e-01, 9.92133050e-01],
[ 9.99016459e-01, 9.99435799e-01, 9.96674621e-01,
9.98880383e-01, 9.44337124e-01, 9.97937996e-01,
9.99222108e-01, 9.98833399e-01, 9.99143749e-01,
9.96598901e-01, -9.74055921e-01, 9.99231469e-01,
9.98908676e-01, 9.98517176e-01, 3.91145914e-09,
9.98762801e-01, -9.44712685e-01, 9.98882295e-01,
9.99167722e-01, 9.98365735e-01, 9.98539526e-01,
9.99349674e-01, 9.98682774e-01, 9.90282263e-01],
[ 9.99032878e-01, 9.99191149e-01, 9.95069722e-01,
9.98663753e-01, 9.41768971e-01, 9.97886353e-01,
9.99012700e-01, 9.98412389e-01, 9.98628992e-01,
9.96945711e-01, -9.72152413e-01, 9.99092707e-01,
9.99022688e-01, 9.98377797e-01, 9.98762801e-01,
6.12438062e-09, -9.43278583e-01, 9.98714615e-01,
9.98765094e-01, 9.97518255e-01, 9.98234814e-01,
9.98833239e-01, 9.98556185e-01, 9.88600916e-01],
[-9.44718270e-01, -9.45834544e-01, -9.40676110e-01,
-9.44650667e-01, -8.57348147e-01, -9.39807793e-01,
-9.45433385e-01, -9.40737501e-01, -9.42716179e-01,
-9.41737281e-01, 9.49931280e-01, -9.43690714e-01,
-9.44584256e-01, -9.41181012e-01, -9.44712685e-01,
-9.43278583e-01, 1.85097555e-08, -9.42274581e-01,
-9.43930225e-01, -9.44416759e-01, -9.44123084e-01,
-9.43611879e-01, -9.43058469e-01, -9.20277725e-01],
[ 9.99102498e-01, 9.99087732e-01, 9.96340223e-01,
9.98960337e-01, 9.46361648e-01, 9.97323488e-01,
9.99002384e-01, 9.99081172e-01, 9.99193054e-01,
9.97547921e-01, -9.70349967e-01, 9.99236560e-01,
9.99076968e-01, 9.99085880e-01, 9.98882295e-01,
9.98714615e-01, -9.42274581e-01, 4.63172335e-10,
9.99055447e-01, 9.96678367e-01, 9.97947641e-01,
9.99023756e-01, 9.98655609e-01, 9.90680163e-01],
[ 9.99273586e-01, 9.99237110e-01, 9.96354345e-01,
9.99311633e-01, 9.43788045e-01, 9.98086971e-01,
9.99391574e-01, 9.98609560e-01, 9.99051762e-01,
9.96623630e-01, -9.74543996e-01, 9.99125265e-01,
9.99242844e-01, 9.98417332e-01, 9.99167722e-01,
9.98765094e-01, -9.43930225e-01, 9.99055447e-01,
1.49968419e-08, 9.98019738e-01, 9.98407433e-01,
9.99222857e-01, 9.98652394e-01, 9.89226980e-01],
[ 9.97964072e-01, 9.98261304e-01, 9.94003174e-01,
9.97876202e-01, 9.35138095e-01, 9.96890683e-01,
9.98227196e-01, 9.96732620e-01, 9.97592295e-01,
9.95604803e-01, -9.77042256e-01, 9.97720253e-01,
9.98014936e-01, 9.95895305e-01, 9.98365735e-01,
9.97518255e-01, -9.44416759e-01, 9.96678367e-01,
9.98019738e-01, 7.47650147e-10, 9.97617693e-01,
9.97870740e-01, 9.97367170e-01, 9.86577350e-01],
[ 9.98809893e-01, 9.98920402e-01, 9.96112855e-01,
9.98462419e-01, 9.43924294e-01, 9.97306126e-01,
9.98655866e-01, 9.98290946e-01, 9.98279757e-01,
9.96053414e-01, -9.72510826e-01, 9.98657360e-01,
9.98393894e-01, 9.98089538e-01, 9.98539526e-01,
9.98234814e-01, -9.44123084e-01, 9.97947641e-01,
9.98407433e-01, 9.97617693e-01, 9.94482237e-10,
9.98596112e-01, 9.98000736e-01, 9.89489744e-01],
[ 9.99306302e-01, 9.99254574e-01, 9.96745892e-01,
9.99263944e-01, 9.46696871e-01, 9.98328683e-01,
9.99450287e-01, 9.98808945e-01, 9.99206541e-01,
9.96252977e-01, -9.72753685e-01, 9.99322811e-01,
9.99093343e-01, 9.98786233e-01, 9.99349674e-01,
9.98833239e-01, -9.43611879e-01, 9.99023756e-01,
9.99222857e-01, 9.97870740e-01, 9.98596112e-01,
7.44695142e-09, 9.99016834e-01, 9.90734007e-01],
[ 9.98670142e-01, 9.98828941e-01, 9.95997518e-01,
9.98810150e-01, 9.46932752e-01, 9.98019225e-01,
9.98871183e-01, 9.98467379e-01, 9.98709951e-01,
9.96293594e-01, -9.70977647e-01, 9.98924819e-01,
9.98535127e-01, 9.98273278e-01, 9.98682774e-01,
9.98556185e-01, -9.43058469e-01, 9.98655609e-01,
9.98652394e-01, 9.97367170e-01, 9.98000736e-01,
9.99016834e-01, 1.79765233e-09, 9.91199840e-01],
[ 9.89075401e-01, 9.88935866e-01, 9.89905446e-01,
9.89492504e-01, 9.74895278e-01, 9.90401184e-01,
9.89348747e-01, 9.92893798e-01, 9.91294961e-01,
9.87014134e-01, -9.49332577e-01, 9.89982094e-01,
9.88011557e-01, 9.92133050e-01, 9.90282263e-01,
9.88600916e-01, -9.20277725e-01, 9.90680163e-01,
9.89226980e-01, 9.86577350e-01, 9.89489744e-01,
9.90734007e-01, 9.91199840e-01, 9.41720628e-08]]))
N = 24
model = GEKKO(remote=False)
wesg = model.Array(model.Var, N, value = 1/N, lb=0, ub=1)
model.Equation(m.sum(wesg) == 1)
def obj(rf = 0.02):
esg_portfo = 0
for i in range(N):
esg_portfo += model.Intermediate(wesg[i] * ((esg_scores_df["Score 2019"][i] + esg_scores_df["Score 2020"][i])/2))
return_portfo = 0
for i in range(N):
return_portfo += model.Intermediate(wesg[i]*((predicted_return_dataframe.iloc[0 , i] + r.iloc[0 ,i])/2))
sigma_portfo = 0
for i in range(N):
for j in range(N):
sigma_portfo += model.Intermediate(wesg[i] * ((sigma.iloc[i,j] + sigma_bar.iloc[i,j])/2) * wesg[j])
return -esg_portfo * ((return_portfo - rf)/sigma_portfo)
model.Minimize(obj())
model.solve(disp=True)
wesg = np.array( [item[0] for item in wesg], dtype=float)
print(wesg)
print(sum(wesg))
Thanks for the well-written question and for sharing the application.
Upvotes: 1
Related Questions
- How to fix Python Gekko equation error “m.solve(disp=False)”?
- Solving Functions with Gekko in Python
- Gekko Intermediate Variable,error: equation without equality or inequality
- Gekko is not respecting the restrictions of the variables
- Gekko incorrectly finding no integer solution
- Gekko returning incorrect successful solution
- Gekko: Problem with the obtained solution
- Equation Definition Error (Equation without an equality or inequality) while using GEKKO MHE
- Gekko Python3. System of equations
- Gekko can't find solution of a small problem