robertmartin8 / PyPortfolioOpt

Financial portfolio optimisation in python, including classical efficient frontier, Black-Litterman, Hierarchical Risk Parity
https://pyportfolioopt.readthedocs.io/
MIT License
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Negative weigths returned using Efficient Frontier optimizer when expected returns are computed using ema_historical_return() #226

Closed Pjuske closed 3 years ago

Pjuske commented 3 years ago

I'm not sure if I missed something in the documentation, but I suppose that the efficient frontier shouldn't output negative weighted assets. (It works fine if returns are computed using _mean_historicalreturn()). What could be the possible cause of this?

Thanks in advance

cov_matrix = risk_models.sample_cov(Closeprices) mu_vector = expected_returns.ema_historical_return(Closeprices)

Console-output of EfficientFrontier(mu_vector, cov_matrix, verbose=True), .portfolio_performance(verbose=True) followed by some assets contained in .clean_weights() printed:

-----------------------------------------------------------------
           OSQP v0.6.0  -  Operator Splitting QP Solver
              (c) Bartolomeo Stellato,  Goran Banjac
        University of Oxford  -  Stanford University 2019
-----------------------------------------------------------------
problem:  variables n = 152, constraints m = 329
          nnz(P) + nnz(A) = 12547
settings: linear system solver = qdldl,
          eps_abs = 1.0e-05, eps_rel = 1.0e-05,
          eps_prim_inf = 1.0e-04, eps_dual_inf = 1.0e-04,
          rho = 1.00e-01 (adaptive),
          sigma = 1.00e-06, alpha = 1.60, max_iter = 10000
          check_termination: on (interval 25),
          scaling: on, scaled_termination: off
          warm start: on, polish: on, time_limit: off

iter   objective    pri res    dua res    rho        time
   1   0.0000e+00   1.00e+00   1.00e+02   1.00e-01   2.40e-03s
 200   1.6072e-04   1.23e-04   1.05e-05   1.57e-02   9.51e-03s
 400   1.6507e-04   4.70e-05   4.81e-06   1.57e-02   1.55e-02s
 600   1.6683e-04   1.84e-05   2.14e-08   1.57e-02   2.17e-02s

status:               solved
solution polish:      unsuccessful
number of iterations: 600
optimal objective:    0.0002
run time:             2.28e-02s
optimal rho estimate: 1.26e-01

Expected annual return: 4004.1%
Annual volatility: 51.7%
Sharpe Ratio: 77.42
MAERSK-B.CO -0.00025
ALMB.CO -0.00012
AMBU-B.CO 0.02501
COLO-B.CO 0.01646
[...]

with mu_vector = expected_returns.mean_historical_return(Closeprices)

-----------------------------------------------------------------
           OSQP v0.6.0  -  Operator Splitting QP Solver
              (c) Bartolomeo Stellato,  Goran Banjac
        University of Oxford  -  Stanford University 2019
-----------------------------------------------------------------
problem:  variables n = 152, constraints m = 329
          nnz(P) + nnz(A) = 12547
settings: linear system solver = qdldl,
          eps_abs = 1.0e-05, eps_rel = 1.0e-05,
          eps_prim_inf = 1.0e-04, eps_dual_inf = 1.0e-04,
          rho = 1.00e-01 (adaptive),
          sigma = 1.00e-06, alpha = 1.60, max_iter = 10000
          check_termination: on (interval 25),
          scaling: on, scaled_termination: off
          warm start: on, polish: on, time_limit: off

iter   objective    pri res    dua res    rho        time
   1   0.0000e+00   1.00e+00   1.00e+02   1.00e-01   2.38e-03s
 200   4.2729e-02   3.74e-03   7.49e-03   1.80e-02   9.39e-03s
 400   4.0332e-02   1.91e-03   1.05e-03   1.80e-02   1.53e-02s
 600   4.2968e-02   6.61e-04   1.28e-04   1.80e-02   2.14e-02s
 800   4.4131e-02   3.45e-04   6.60e-05   1.80e-02   2.76e-02s
1000   4.4723e-02   1.79e-04   3.90e-05   1.80e-02   3.35e-02s
1200   4.5037e-02   9.34e-05   1.96e-05   1.80e-02   3.97e-02s
1400   4.5202e-02   4.88e-05   1.03e-05   1.80e-02   4.57e-02s
1600   4.5288e-02   2.55e-05   5.38e-06   1.80e-02   5.16e-02s
1675   4.5308e-02   2.00e-05   4.22e-06   1.80e-02   5.39e-02s

status:               solved
solution polish:      unsuccessful
number of iterations: 1675
optimal objective:    0.0453
run time:             5.51e-02s
optimal rho estimate: 1.55e-02

Expected annual return: 117.1%
Annual volatility: 24.5%
Sharpe Ratio: 4.70
AMBU-B.CO 0.03266
PNDORA.CO 0.13627
ORSTED.CO 0.05422
HART.CO 0.20111
AGF-B.CO 0.06952
BOLIGA.CO 0.05799
CBRAIN.CO 0.10093
FLUG-B.CO 0.05887
NEWCAP.CO 0.00018
NORTHM.CO 0.09822
PSNRDC-A.CO 0.02521
SBS.CO 0.02326
ENALYZ.CO 0.03234
KONSOL.CO 0.03748
WIRTEK.CO 0.07268
phschiele commented 3 years ago

@Pjuske Would you mind sharing cov_matrix and mu_vector to make the error reproducible? Also, which function did you call on the EfficientFrontier object (efficient_return(), ...)?

The default bound values are weight_bounds=(0, 1), so negative weights are not expected.

The output "Expected annual return: 4004.1%" suggests that the optimization problem might be ill-conditioned.

On a more general note though, @robertmartin8, I think when defining the weight variables here

# Optimisation variables
self._w = cp.Variable(n_assets)

one could add the keyword "nonneg=True" if all lower bounds are >=0. Source In my experience, this makes the optimization a bit more robust to problems such as the one described here. However, as the bounds might get changed later, this likely requires a bigger change.

Pjuske commented 3 years ago

Thanks alot for looking into this, yes, I made as small as I could a reproduceable sample:

Download-link for _mu_vector and cov_matrix_ (they are also a part of this post): https://gofile.io/d/qLFU4O

These are the methods I'm using from the library:

Closeprice = pandas.DataFrame()

[...]

mu_vector = expected_returns.ema_historical_return(Closeprice)
cov_matrix = risk_models.sample_cov(Closeprice)
EfficientFrontierObject = EfficientFrontier(mu_vector, cov_matrix, verbose=True)
-----------------------------------------------------------------
           OSQP v0.6.0  -  Operator Splitting QP Solver
              (c) Bartolomeo Stellato,  Goran Banjac
        University of Oxford  -  Stanford University 2019
-----------------------------------------------------------------
problem:  variables n = 64, constraints m = 153
          nnz(P) + nnz(A) = 2471
settings: linear system solver = qdldl,
          eps_abs = 1.0e-05, eps_rel = 1.0e-05,
          eps_prim_inf = 1.0e-04, eps_dual_inf = 1.0e-04,
          rho = 1.00e-01 (adaptive),
          sigma = 1.00e-06, alpha = 1.60, max_iter = 10000
          check_termination: on (interval 25),
          scaling: on, scaled_termination: off
          warm start: on, polish: on, time_limit: off

iter   objective    pri res    dua res    rho        time
   1   0.0000e+00   1.00e+00   1.00e+02   1.00e-01   1.10e-03s
 200   2.7798e-04   9.79e-05   5.03e-07   1.88e-02   3.15e-03s
 300   2.8031e-04   1.05e-05   1.68e-06   1.92e-02   4.04e-03s

status:               solved
solution polish:      unsuccessful
number of iterations: 300
optimal objective:    0.0003
run time:             4.30e-03s
optimal rho estimate: 1.70e-02

[...]

EfficientFrontierObject.add_sector_constraints(ticker_sector_mapper, efficient_frontier_sector_constraints_lower_ratio, efficient_frontier_sector_constraints_upper_ratio)
raw_weights = EfficientFrontierObject.max_sharpe()
cleaned_weights = EfficientFrontierObject.clean_weights()
EfficientFrontierObject.portfolio_performance(verbose=True)
Expected annual return: 5130.4%
Annual volatility: 85.9%
Sharpe Ratio: 59.73

[...]

for key, value in cleaned_weights.items():
        if value != 0:
            print(key, value)
ALK-B.CO 0.00017
ALMB.CO 0.00019
AMBU-B.CO 0.05603
CHR.CO 0.00017
COLO-B.CO 0.11568
DANSKE.CO 0.0001
DSV.CO 0.00058
FLS.CO -0.00012
G4S.CO -0.00027
GMAB.CO 0.07671
GN.CO 0.25947
ISS.CO 0.00011
JDAN.CO -0.00019
JYSK.CO 0.00029
KBHL.CO 0.00021
NETC.CO 0.00019
NOVO-B.CO 0.00024
NZYM-B.CO 0.11705
PNDORA.CO -0.00022
RILBA.CO 0.00034
ROCK-B.CO -0.00025
RBREW.CO -0.00026
STG.CO 0.0007
SIM.CO 0.00022
SPNO.CO 0.00029
SYDB.CO 0.00026
TOP.CO 0.00016
TRYG.CO 0.00016
OSSR.CO 0.00038
ORSTED.CO 0.00014
ASTGRP.CO -0.00027
CONFRZ.CO 0.23548
DAC.CO 0.00032
EGNETY.CO 0.00073
ENALYZ.CO 0.02285
ERRIA.CO -0.00012
FASTPC.CO 0.00039
GREENM.CO 0.00011
HAPPY.CO -0.00014
JOBNDX.CO 0.00025
NPINV.CO 0.04212
ODICO.CO -0.00031
VIRO.CO 0.02238
WATURU.CO 0.00086
WIRTEK.CO 0.00051
KMI 0.00021
MSFT 0.0462

These are the arguments I use for sector_constraints: _ticker_sectormapper: {'MAERSK-B.CO': 'Industrials', 'ALK-B.CO': 'Health Care', 'ALMB.CO': 'Financials', 'AMBU-B.CO': 'Health Care', 'CARL-B.CO': 'Consumer Staples', 'CHR.CO': 'Health Care', 'COLO-B.CO': 'Health Care', 'DANSKE.CO': 'Financials', 'DEMANT.CO': 'Health Care', 'DFDS.CO': 'Industrials', 'DRLCO.CO': 'Energy', 'DSV.CO': 'Industrials', 'FLS.CO': 'Industrials', 'G4S.CO': 'Industrials', 'GMAB.CO': 'Health Care', 'GN.CO': 'Health Care', 'ISS.CO': 'Industrials', 'JDAN.CO': 'Real Estate', 'JYSK.CO': 'Financials', 'KBHL.CO': 'Industrials', 'LUN.CO': 'Health Care', 'NETC.CO': 'Information Technology', 'NDA-DK.CO': 'Financials', 'NOVO-B.CO': 'Health Care', 'NZYM-B.CO': 'Health Care', 'PNDORA.CO': 'Consumer Cyclicals', 'RILBA.CO': 'Financials', 'ROCK-B.CO': 'Industrials', 'RBREW.CO': 'Consumer Staples', 'STG.CO': 'Consumer Staples', 'SCHO.CO': 'Industrials', 'SIM.CO': 'Information Technology', 'SPNO.CO': 'Financials', 'SYDB.CO': 'Financials', 'TOP.CO': 'Financials', 'TRYG.CO': 'Financials', 'VWS.CO': 'Energy', 'OSSR.CO': 'Health Care', 'ORSTED.CO': 'Utilities', 'BO.CO': 'Consumer Cyclicals', 'BNORDIK-CSE.CO': 'Financials', 'BAVA.CO': 'Health Care', 'HART.CO': 'Industrials', 'CHEMM.CO': 'Health Care', 'COLUM.CO': 'Information Technology', 'DNORD.CO': 'Industrials', 'HH.CO': 'Industrials', 'JUTBK.CO': 'Financials', 'LASP.CO': 'Financials', 'MATAS.CO': 'Consumer Cyclicals', 'NLFSK.CO': 'Industrials', 'NKT.CO': 'Industrials', 'NNIT.CO': 'Information Technology', 'NTG.CO': 'Industrials', 'ORPHA.CO': 'Health Care', 'PAAL-B.CO': 'Industrials', 'RTX.CO': 'Communication Services', 'SAS-DKK.CO': 'Consumer Cyclicals', 'SOLAR-B.CO': 'Industrials', 'SPG.CO': 'Industrials', 'SPKSJF.CO': 'Financials', 'TIV.CO': 'Consumer Cyclicals', 'TRMD-A.CO': 'Industrials', 'UIE.CO': 'Consumer Staples', 'VJBA.CO': 'Financials', 'ZEAL.CO': 'Health Care', 'AAB.CO': 'Consumer Cyclicals', 'AGAT.CO': 'Real Estate', 'AGF-B.CO': 'Consumer Cyclicals', 'AM-B.CO': 'Consumer Cyclicals', 'ATHENA.CO': 'Utilities', 'ATLA-DKK.CO': 'Energy', 'BIOPOR.CO': 'Health Care', 'BLVIS-A.CO': 'Real Estate', 'BOLIGA.CO': 'Consumer Cyclicals', 'KLEE-B.CO': 'Industrials', 'AOJ-P.CO': 'Industrials', 'BIF.CO': 'Consumer Cyclicals', 'CBRAIN.CO': 'Information Technology', 'CEMAT.CO': 'Information Technology', 'CPHCAP-PREF.CO': 'Real Estate', 'CPHCAP-ST.CO': 'Real Estate', 'DAB.CO': 'Financials', 'DANT.CO': 'Consumer Cyclicals', 'DJS.CO': 'Financials', 'DJUR.CO': 'Financials', 'BORD-B.CO': 'Industrials', 'FED.CO': 'Real Estate', 'FFARMS.CO': 'Consumer Staples', 'FLUG-B.CO': 'Industrials', 'FYNBK.CO': 'Financials', 'GABR.CO': 'Consumer Cyclicals', 'GERHSP.CO': 'Real Estate', 'GJ.CO': 'Industrials', 'GRLA.CO': 'Financials', 'GYLD-B.CO': 'Consumer Cyclicals', 'HARB-B.CO': 'Consumer Staples', 'HVID.CO': 'Financials', 'IMAIL.CO': 'Industrials', 'KRE.CO': 'Financials', 'LOLB.CO': 'Financials', 'LUXOR-B.CO': 'Financials', 'MIGA-B.CO': 'Industrials', 'MTHH.CO': 'Industrials', 'MNBA.CO': 'Financials', 'NEWCAP.CO': 'Financials', 'NRDF.CO': 'Financials', 'NORDIC.CO': 'Energy', 'NORTHM.CO': 'Consumer Cyclicals', 'NTR-B.CO': 'Industrials', 'ONXEO.CO': 'Health Care', 'PSNRDC-A.CO': 'Real Estate', 'PARKEN.CO': 'Consumer Cyclicals', 'PRIMOF.CO': 'Real Estate', 'RIAS-B.CO': 'Industrials', 'RBLN-B.CO': 'Industrials', 'ROV.CO': 'Industrials', 'SALB.CO': 'Financials', 'SANI.CO': 'Consumer Cyclicals', 'SBS.CO': 'Consumer Cyclicals', 'SIG.CO': 'Industrials', 'SIF.CO': 'Consumer Cyclicals', 'SKAKO.CO': 'Industrials', 'SKJE.CO': 'Financials', 'SCD.CO': 'Financials', 'STRINV.CO': 'Financials', 'TCM.CO': 'Consumer Cyclicals', 'TOTA.CO': 'Financials', 'VIPRO.CO': 'Real Estate', 'AGILC.CO': 'Information Technology', 'ASTGRP.CO': 'Consumer Cyclicals', 'CONFRZ.CO': 'Information Technology', 'DAC.CO': 'Industrials', 'EGNETY.CO': 'Real Estate', 'ENALYZ.CO': 'Information Technology', 'ERRIA.CO': 'Industrials', 'ESOFT.CO': 'Consumer Cyclicals', 'FASTPC.CO': 'Information Technology', 'FOM.CO': 'Industrials', 'GREENM.CO': 'Consumer Cyclicals', 'HAPPY.CO': 'Consumer Cyclicals', 'HYPE.CO': 'Information Technology', 'JOBNDX.CO': 'Industrials', 'KONSOL.CO': 'Information Technology', 'LEDIBOND.CO': 'Industrials', 'MDUNDO.CO': 'Information Technology', 'MONSO.CO': 'Health Care', 'NPINV.CO': 'Financials', 'ODICO.CO': 'Industrials', 'PENNEO.CO': 'Information Technology', 'SCAPE.CO': 'Industrials', 'SLXIT.CO': 'Information Technology', 'SHAPE.CO': 'Information Technology', 'STENO.CO': 'Health Care', 'VIRO.CO': 'Health Care', 'WATURU.CO': 'Consumer Cyclicals', 'WIRTEK.CO': 'Information Technology', 'NAS.OL': 'Unknown', 'KMI': 'Unknown', 'MSFT': 'Unknown', 'SPG': 'Unknown'}

_efficient_frontier_sector_constraints_lower_ratio:_ {'Consumer Cyclicals': 0.0, 'Information Technology': 0.0, 'Industrials': 0.0, 'Basic Materials': 0.0, 'Energy': 0.0, 'Consumer Staples': 0.0, 'Health Care': 0.0, 'Utilities': 0.0, 'Financials': 0.0, 'Real Estate': 0.0, 'Communication Services': 0.0, 'Unknown': 0.0}

_efficient_frontier_sector_constraints_upper_ratio:_ {'Consumer Cyclicals': 1.0, 'Information Technology': 1.0, 'Industrials': 1.0, 'Basic Materials': 1.0, 'Energy': 1.0, 'Consumer Staples': 1.0, 'Health Care': 1.0, 'Utilities': 1.0, 'Financials': 1.0, 'Real Estate': 1.0, 'Communication Services': 1.0, 'Unknown': 1.0}

_mu_vector:_

MAERSK-B.CO | 0.907777337
ALK-B.CO | 0.485939377
ALMB.CO | 0.546754921
AMBU-B.CO | 0.673690045
CARL-B.CO | 0.110170304
CHR.CO | 0.132453193
COLO-B.CO | 0.050540616
DANSKE.CO | 0.469149799
DEMANT.CO | 0.278357033
DFDS.CO | 0.33790475
DRLCO.CO | -0.141084593
DSV.CO | 0.597125401
FLS.CO | 0.149102877
G4S.CO | 0.804201605
GMAB.CO | 0.515462812
GN.CO | 0.708123677
ISS.CO | 0.131036047
JDAN.CO | -0.453442542
JYSK.CO | 0.260503205
KBHL.CO | 0.143897721
LUN.CO | -0.236537122
NETC.CO | 0.955412877
NDA-DK.CO | 0.320422608
NOVO-B.CO | 0.087540155
NZYM-B.CO | 0.075394735
PNDORA.CO | 2.238814418
RILBA.CO | 0.256267544
ROCK-B.CO | 0.953971893
RBREW.CO | 0.318498739
STG.CO | 0.35489276
SCHO.CO | 0.267836069
SIM.CO | 0.197893829
SPNO.CO | 0.250748774
SYDB.CO | 0.323472455
TOP.CO | -0.038106969
TRYG.CO | -0.015084109
VWS.CO | 1.316684003
OSSR.CO | 0.004166429
ORSTED.CO | 1.007563123
AGILC.CO | -0.271249927
ASTGRP.CO | -0.520322672
CONFRZ.CO | 216.2736784
DAC.CO | 0.213814762
EGNETY.CO | 0.18543608
ENALYZ.CO | 1.217935927
ERRIA.CO | 1.112734305
FASTPC.CO | 0.261238189
GREENM.CO | 1.291803564
HAPPY.CO | 0.452500341
HYPE.CO | 0.773967628
JOBNDX.CO | 0.424448987
KONSOL.CO | 1.154212014
NPINV.CO | 0.149113835
ODICO.CO | 0.148555791
SCAPE.CO | -0.505910337
SLXIT.CO | 0.52635828
VIRO.CO | 1.835246516
WATURU.CO | -0.880662775
WIRTEK.CO | 1.446589138
NAS.OL | -0.975011559
KMI | 0.052293229
MSFT | 0.519070155
SPG | 0.380407558

_covmatrix:

  | MAERSK-B.CO | ALK-B.CO | ALMB.CO | AMBU-B.CO | CARL-B.CO | CHR.CO | COLO-B.CO | DANSKE.CO | DEMANT.CO | DFDS.CO | DRLCO.CO | DSV.CO | FLS.CO | G4S.CO | GMAB.CO | GN.CO | ISS.CO | JDAN.CO | JYSK.CO | KBHL.CO | LUN.CO | NETC.CO | NDA-DK.CO | NOVO-B.CO | NZYM-B.CO | PNDORA.CO | RILBA.CO | ROCK-B.CO | RBREW.CO | STG.CO | SCHO.CO | SIM.CO | SPNO.CO | SYDB.CO | TOP.CO | TRYG.CO | VWS.CO | OSSR.CO | ORSTED.CO | AGILC.CO | ASTGRP.CO | CONFRZ.CO | DAC.CO | EGNETY.CO | ENALYZ.CO | ERRIA.CO | FASTPC.CO | GREENM.CO | HAPPY.CO | HYPE.CO | JOBNDX.CO | KONSOL.CO | NPINV.CO | ODICO.CO | SCAPE.CO | SLXIT.CO | VIRO.CO | WATURU.CO | WIRTEK.CO | NAS.OL | KMI | MSFT | SPG
-- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | --
MAERSK-B.CO | 0.224360003 | 0.05866456 | 0.057029438 | 0.029701722 | 0.068523405 | 0.033551996 | -0.007626925 | 0.090344373 | 0.059062248 | 0.104598809 | 0.150314121 | 0.104356807 | 0.137675041 | 0.115922294 | 0.049228102 | 0.070089413 | 0.132720585 | 0.094202924 | 0.072145201 | 0.033964563 | 0.059647867 | 0.054776955 | 0.100548982 | 0.026827912 | 0.01387464 | 0.094494052 | 0.061117076 | 0.111532187 | 0.096595766 | 0.039071233 | 0.075358407 | 0.071752712 | 0.07876722 | 0.09029064 | 0.066015437 | 0.057476443 | 0.103307153 | 0.050605525 | 0.057861489 | 0.062742237 | 0.056185369 | -0.029406208 | 0.005258211 | 0.003660194 | 0.013881389 | 0.078860732 | 0.02812496 | 0.057953199 | 0.040307382 | 0.029450451 | 0.022464417 | 0.063528782 | 0.066335833 | 0.121107646 | 0.080856395 | 0.068635527 | 0.050712633 | 0.061711113 | -0.016078881 | 0.117912192 | 0.1296483 | 0.08160594 | 0.152739216
ALK-B.CO | 0.05866456 | 0.167880686 | 0.058702447 | 0.02913735 | 0.03709651 | 0.046149613 | 0.024414851 | 0.052090945 | 0.078337301 | 0.062843831 | 0.05294722 | 0.078345683 | 0.051862499 | 0.089406862 | 0.08600893 | 0.100603954 | 0.063205823 | 0.055021157 | 0.054326034 | 0.024967623 | 0.064888043 | 0.064766367 | 0.066332402 | 0.046262706 | 0.030782867 | 0.056173721 | 0.045670191 | 0.076126502 | 0.072193167 | 0.037041093 | 0.067355587 | 0.052849939 | 0.050637127 | 0.044520818 | 0.04450317 | 0.044296081 | 0.063685039 | 0.036568091 | 0.04033922 | 0.056536358 | 0.068036892 | -0.116036534 | 0.013014712 | 0.010438385 | -0.009367783 | 0.014620985 | 0.019619518 | 0.031294897 | 0.0332257 | 0.078312794 | 0.017492347 | 0.065422776 | 0.034634025 | 0.095170934 | 0.061459356 | 0.041882845 | 0.063984649 | 0.089895306 | 0.014214852 | 0.048559776 | 0.075203902 | 0.060470976 | 0.102946939
ALMB.CO | 0.057029438 | 0.058702447 | 0.103387586 | 0.01862 | 0.038203494 | 0.015379518 | 0.016111219 | 0.050761283 | 0.040774749 | 0.050652633 | 0.079371248 | 0.056592758 | 0.055782356 | 0.085158072 | 0.058563402 | 0.055849337 | 0.052872595 | 0.031723137 | 0.044842653 | 0.019040375 | 0.050329564 | 0.051108971 | 0.068190659 | 0.019923906 | 0.026925366 | 0.0491173 | 0.048407666 | 0.069023949 | 0.057826702 | 0.027409256 | 0.048929421 | 0.037079049 | 0.048302809 | 0.061012424 | 0.061099805 | 0.046624681 | 0.056571089 | 0.033990762 | 0.042074299 | 0.058831523 | 0.059485512 | 0.034812205 | 0.01182528 | 0.010747627 | 0.017561379 | 0.036146093 | 0.031484797 | 0.028975756 | 0.042556875 | 0.049296032 | 0.017167644 | 0.064998946 | 0.043946308 | 0.067184992 | 0.063690323 | 0.05919154 | 0.055240859 | 0.064541862 | 0.011087503 | 0.098805477 | 0.075770573 | 0.052649762 | 0.099878158
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DSV.CO | 0.104356807 | 0.078345683 | 0.056592758 | 0.008876498 | 0.053814764 | 0.018427575 | 0.014045441 | 0.047396146 | 0.051073895 | 0.071042266 | 0.105278564 | 0.152746603 | 0.089544868 | 0.086639704 | 0.075415693 | 0.086030149 | 0.070789675 | 0.047279874 | 0.048923579 | 0.017856163 | 0.046137591 | 0.089545365 | 0.071571914 | 0.047218834 | 0.017936728 | 0.064597884 | 0.053022918 | 0.11432806 | 0.083693763 | 0.044139587 | 0.064765262 | 0.069913268 | 0.055284718 | 0.062392203 | 0.043918046 | 0.041360055 | 0.103722547 | 0.036384784 | 0.059302874 | 0.062954885 | 0.061265613 | -0.137045636 | 0.012688883 | 0.009293095 | 0.006867686 | 0.044245236 | 0.012282732 | 0.036889731 | 0.030336994 | 0.050402858 | 0.013526145 | 0.088198707 | 0.091217754 | 0.077518701 | 0.048086242 | 0.0476088 | 0.062921258 | 0.083216354 | 0.009943129 | 0.015204427 | 0.112916178 | 0.070910627 | 0.100678814
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JOBNDX.CO | 0.022464417 | 0.017492347 | 0.017167644 | 0.008485152 | 0.018745257 | 0.007482322 | 0.005772164 | 0.019513243 | 0.018236299 | 0.026410336 | 0.033010391 | 0.013526145 | 0.029853221 | 0.037317958 | 0.017016448 | 0.018744407 | 0.016552 | 0.043112934 | 0.013280792 | 0.013624635 | 0.022512631 | 0.011485135 | 0.026187704 | 0.011910381 | 0.011432594 | 0.034776996 | 0.013537355 | 0.030486719 | 0.024760505 | 0.020955853 | 0.020656834 | 0.020623675 | 0.02206515 | 0.008851255 | 0.019561882 | 0.015770245 | 0.0120366 | 0.017142692 | 0.01762678 | 0.020803458 | 0.013780033 | 0.095084192 | 0.014498762 | 0.00340176 | -0.007988524 | 0.024668558 | 0.015468655 | 0.007169785 | 0.030952262 | 0.034102198 | 0.089113984 | 0.0415135 | 0.017037624 | 0.025541559 | 0.034994792 | 0.02311981 | 0.047967642 | 0.022335245 | -0.003163304 | 0.016190544 | 0.022919199 | 0.015016639 | 0.031826386
KONSOL.CO | 0.063528782 | 0.065422776 | 0.064998946 | 0.084203096 | 0.068564304 | 0.032822104 | 0.033349236 | 0.069747464 | 0.076141358 | 0.039389414 | 0.100883644 | 0.088198707 | 0.097802546 | 0.055659538 | 0.095717263 | 0.085986947 | 0.044864773 | 0.052521239 | 0.051034598 | 0.030851797 | 0.08116948 | 0.04223651 | 0.068208487 | 0.048730852 | 0.02598589 | 0.059340002 | 0.051986652 | 0.09754816 | 0.097448937 | 0.069265199 | 0.064288652 | 0.085922764 | 0.059617121 | 0.044739069 | 0.068080774 | 0.055044292 | 0.075446666 | 0.057146778 | 0.057815538 | 0.08885484 | 0.085759849 | -0.122527229 | 0.024793533 | 0.015571084 | -0.042517582 | 0.114095975 | 0.054388925 | 0.011491454 | 0.088051142 | 0.018301928 | 0.0415135 | 0.874534733 | 0.068850057 | 0.069053707 | 0.049305486 | 0.058927207 | 0.077509293 | 0.147502987 | -0.000620533 | 0.088195168 | 0.098416045 | 0.083621623 | 0.087268517
NPINV.CO | 0.066335833 | 0.034634025 | 0.043946308 | 0.000789249 | 0.04177141 | 0.009024336 | 0.000420743 | 0.034880654 | 0.029602938 | 0.047089008 | 0.10784381 | 0.091217754 | 0.057456659 | 0.035054511 | 0.061355439 | 0.046763112 | 0.071059204 | 0.018951528 | 0.07449484 | 0.042169102 | 0.03434668 | 0.076604848 | 0.099643313 | 0.044939825 | 0.034108564 | 0.039562162 | 0.070842601 | 0.079441216 | 0.057959132 | 0.043589345 | 0.052510891 | 0.043776426 | 0.054990776 | 0.098552651 | 0.053722823 | 0.05467558 | 0.045987011 | 0.023217629 | 0.035839392 | 0.087015875 | 0.086539945 | -0.249170608 | 0.0406669 | 0.014582736 | -0.019378248 | 0.085563139 | 0.03973376 | 0.05707539 | 0.123174305 | 0.060584125 | 0.017037624 | 0.068850057 | 0.851494194 | 0.062659456 | 0.019774506 | 0.069781612 | 0.072553299 | 0.198436129 | -0.017070733 | 0.107841277 | 0.09947218 | 0.046519342 | 0.057539772
ODICO.CO | 0.121107646 | 0.095170934 | 0.067184992 | 0.07027213 | 0.073637828 | 0.04853141 | 0.004397364 | 0.113792505 | 0.079111439 | 0.078100296 | 0.107834874 | 0.077518701 | 0.120237854 | 0.122837612 | 0.058965368 | 0.082291312 | 0.114883267 | 0.07634191 | 0.079020903 | 0.044551801 | 0.080154343 | 0.042660925 | 0.100480022 | 0.039351173 | 0.041991835 | 0.075820612 | 0.064645327 | 0.099354 | 0.097563397 | 0.052596554 | 0.0772864 | 0.066425863 | 0.078544175 | 0.084359674 | 0.072946403 | 0.080666937 | 0.066555205 | 0.077214699 | 0.055058039 | 0.080081278 | 0.090842826 | 0.115336573 | 0.024487236 | 0.012526781 | 0.013019618 | 0.032785251 | 0.022000706 | 0.062122317 | 0.042427384 | 0.066701467 | 0.025541559 | 0.069053707 | 0.062659456 | 0.396417704 | 0.139883382 | 0.080525413 | 0.105336404 | 0.063127914 | -0.005267973 | 0.204786892 | 0.101024974 | 0.07902014 | 0.199025419
SCAPE.CO | 0.080856395 | 0.061459356 | 0.063690323 | 0.040389682 | 0.048708151 | 0.036469727 | 0.0057679 | 0.062607584 | 0.044304218 | 0.047789802 | 0.091177538 | 0.048086242 | 0.074915157 | 0.085602972 | 0.052761702 | 0.068272128 | 0.059804129 | 0.081753417 | 0.048723242 | 0.026248299 | 0.05172747 | 0.064867096 | 0.064655072 | 0.027490616 | 0.032542041 | 0.048727505 | 0.048733628 | 0.064572962 | 0.079006055 | 0.039797696 | 0.044979037 | 0.048293074 | 0.057406334 | 0.067130005 | 0.061248425 | 0.047742121 | 0.058924002 | 0.043501369 | 0.055847347 | 0.067332349 | 0.067043811 | 0.421804115 | 0.010380054 | 0.02073679 | -0.029013841 | 0.034905798 | 0.028282234 | 0.034587585 | 0.026655876 | 0.095685561 | 0.034994792 | 0.049305486 | 0.019774506 | 0.139883382 | 0.382169591 | 0.086025553 | 0.058789366 | 0.11096002 | 0.038929037 | 0.141836575 | 0.082258506 | 0.065437081 | 0.125749457
SLXIT.CO | 0.068635527 | 0.041882845 | 0.05919154 | 0.024261029 | 0.042257003 | 0.040385364 | 0.007716064 | 0.089056892 | 0.05627418 | 0.044506903 | 0.118486764 | 0.0476088 | 0.072297557 | 0.05197472 | 0.050100248 | 0.061672174 | 0.063074983 | 0.053332249 | 0.03757102 | 0.034672338 | 0.028512773 | 0.068102939 | 0.087862895 | 0.029080635 | 0.029162515 | 0.030823054 | 0.048992255 | 0.082033947 | 0.084924836 | 0.019125561 | 0.065480511 | 0.047324318 | 0.05908223 | 0.063133513 | 0.059114323 | 0.052747858 | 0.057672881 | 0.027617798 | 0.04856342 | 0.079648109 | 0.077472575 | 0.175317396 | 0.003915079 | 0.013299707 | 0.020281257 | 0.070737831 | 0.061510846 | 0.017481083 | 0.060003552 | 0.086958402 | 0.02311981 | 0.058927207 | 0.069781612 | 0.080525413 | 0.086025553 | 0.521616012 | 0.095359539 | 0.255180215 | 0.04023586 | 0.11704948 | 0.122780139 | 0.105793048 | 0.140596552
VIRO.CO | 0.050712633 | 0.063984649 | 0.055240859 | 0.080347842 | 0.049240557 | 0.027804649 | 0.024761334 | 0.065500454 | 0.042358395 | 0.04602596 | 0.072869583 | 0.062921258 | 0.053207134 | 0.084037178 | 0.055226499 | 0.041035872 | 0.029580208 | -0.07435456 | 0.046946918 | 0.033826584 | 0.075804498 | 0.031171604 | 0.063506215 | 0.035067067 | 0.029747191 | 0.052764134 | 0.047805871 | 0.042434524 | 0.060980243 | 0.02469746 | 0.047718407 | 0.043583066 | 0.074458294 | 0.054629874 | 0.072230723 | 0.069638928 | 0.054262204 | 0.039932003 | 0.035716009 | 0.105165919 | 0.0792144 | -0.094533314 | 0.016096176 | 0.019647663 | -0.014405564 | 0.140438302 | 0.057655945 | 0.004830616 | 0.040027853 | 0.197374223 | 0.047967642 | 0.077509293 | 0.072553299 | 0.105336404 | 0.058789366 | 0.095359539 | 0.735835754 | 0.130911158 | -0.048664788 | 0.063168626 | 0.074977138 | 0.067530776 | 0.109910064
WATURU.CO | 0.061711113 | 0.089895306 | 0.064541862 | 0.027077873 | 0.05645917 | 0.052272849 | 0.012482044 | 0.106562612 | 0.033704704 | 0.10296903 | 0.096609017 | 0.083216354 | 0.066385771 | 0.028946464 | 0.077339744 | 0.087977966 | 0.065961639 | 0.015027496 | 0.054590911 | 0.013763736 | 0.045229863 | 0.110146352 | 0.107869044 | 0.03837256 | 0.059636186 | 0.032649915 | 0.051343241 | 0.084173887 | 0.104624483 | 0.044464168 | 0.066363823 | 0.044518582 | 0.080191029 | 0.093330734 | 0.053466645 | 0.055690333 | 0.074750485 | 0.00671341 | 0.04654269 | 0.072854016 | 0.225990861 | -0.178269284 | 0.034727352 | 0.043854002 | 0.067904574 | 0.093216618 | 0.061194791 | 0.011189585 | 0.016226518 | 0.061218 | 0.022335245 | 0.147502987 | 0.198436129 | 0.063127914 | 0.11096002 | 0.255180215 | 0.130911158 | 1.51279791 | 0.047342916 | 0.109996947 | 0.160967268 | 0.09488785 | 0.102045179
WIRTEK.CO | -0.016078881 | 0.014214852 | 0.011087503 | 0.01989089 | 0.004136647 | 0.010288034 | 0.009045784 | -0.009064491 | 0.000335337 | 0.010857617 | -0.016400953 | 0.009943129 | 0.011182641 | 0.022415604 | 0.024576226 | 0.020922537 | 0.002480121 | 0.020662335 | 0.002629855 | -0.005757605 | 0.012793505 | 0.038049522 | -0.002486867 | 0.016334818 | 0.006905193 | 0.020105101 | 0.00543859 | 0.032702665 | 0.010822034 | 0.01473896 | 0.017299612 | -0.001736154 | 0.010506219 | 0.011138062 | -0.000649941 | 0.005775328 | 0.014666943 | -0.006519175 | 0.013734379 | -0.003584996 | 0.019158548 | 0.071912852 | -0.002203148 | -0.002167037 | -0.001806627 | 0.005560668 | 0.03733579 | -0.020192682 | -0.037615786 | -0.005655723 | -0.003163304 | -0.000620533 | -0.017070733 | -0.005267973 | 0.038929037 | 0.04023586 | -0.048664788 | 0.047342916 | 0.35886412 | -0.005544534 | 0.013171373 | 0.009288321 | 0.002398284
NAS.OL | 0.117912192 | 0.048559776 | 0.098805477 | 0.146430865 | 0.073900456 | 0.106296023 | 0.016792474 | 0.179392938 | 0.071681152 | 0.089240426 | 0.175388787 | 0.015204427 | 0.068234477 | 0.105193083 | 0.089072483 | 0.058271448 | 0.054190953 | -0.058927314 | 0.13018204 | 0.122927028 | 0.147882663 | 0.013782941 | 0.110060889 | 0.039071691 | 0.067746707 | 0.03221763 | 0.09049511 | 0.038736812 | 0.107667683 | 0.022440752 | 0.025354987 | 0.078642422 | 0.083625858 | 0.159824982 | 0.119088716 | 0.119635827 | 0.096079014 | 0.060571735 | 0.0223259 | 0.045037165 | 0.11177653 | -0.127096766 | -0.005220309 | 0.013709971 | -0.034105168 | 0.038017031 | 0.04178037 | -0.019646104 | 0.132941669 | 0.155702979 | 0.016190544 | 0.088195168 | 0.107841277 | 0.204786892 | 0.141836575 | 0.11704948 | 0.063168626 | 0.109996947 | -0.005544534 | 1.858300507 | 0.053099186 | 0.077339481 | 0.066815825
KMI | 0.1296483 | 0.075203902 | 0.075770573 | -0.03644594 | 0.083842958 | -6.09719E-05 | -0.007799027 | 0.100593685 | 0.056513334 | 0.093665998 | 0.213795834 | 0.112916178 | 0.112163054 | 0.133699759 | 0.079576095 | 0.070353445 | 0.132161164 | 0.090950831 | 0.089003986 | 0.04432375 | 0.063487215 | 0.090304582 | 0.129494111 | 0.015323168 | 0.002193321 | 0.077129282 | 0.085790981 | 0.119279384 | 0.092927811 | 0.05134425 | 0.086724117 | 0.034783468 | 0.092886984 | 0.127536207 | 0.063584632 | 0.056426969 | 0.105562457 | 0.044346206 | 0.066267646 | 0.081516127 | 0.129824649 | 0.287644083 | 0.035574298 | 0.012321189 | -0.024067128 | 0.059694403 | 0.047192453 | 0.06238634 | 0.073574125 | 0.100663064 | 0.022919199 | 0.098416045 | 0.09947218 | 0.101024974 | 0.082258506 | 0.122780139 | 0.074977138 | 0.160967268 | 0.013171373 | 0.053099186 | 0.315317257 | 0.123488109 | 0.350876004
MSFT | 0.08160594 | 0.060470976 | 0.052649762 | 0.016873747 | 0.037966928 | 0.041137728 | 0.028819488 | 0.042518692 | 0.058511287 | 0.041884721 | 0.072387138 | 0.070910627 | 0.059722371 | 0.058427181 | 0.073239368 | 0.049610366 | 0.030892458 | 0.017835495 | 0.032000082 | 0.014993034 | 0.049871488 | 0.053323204 | 0.05581794 | 0.034169898 | 0.020842185 | 0.049960344 | 0.036819721 | 0.079243629 | 0.068071468 | 0.024504397 | 0.050650438 | 0.05069385 | 0.05630433 | 0.047217935 | 0.06512678 | 0.062912172 | 0.051501445 | 0.02880983 | 0.051085842 | 0.04770696 | 0.06845334 | -0.127786254 | 0.006945984 | 0.011294294 | -0.030544817 | 0.038847885 | 0.019091967 | 0.026870975 | 0.044768112 | 0.041262281 | 0.015016639 | 0.083621623 | 0.046519342 | 0.07902014 | 0.065437081 | 0.105793048 | 0.067530776 | 0.09488785 | 0.009288321 | 0.077339481 | 0.123488109 | 0.195292031 | 0.145032731
SPG | 0.152739216 | 0.102946939 | 0.099878158 | -0.052999178 | 0.125846053 | -0.050293058 | -0.028427736 | 0.167020448 | 0.094722171 | 0.169698937 | 0.249966119 | 0.100678814 | 0.164089217 | 0.242881164 | 0.064338817 | 0.073613252 | 0.236152813 | 0.110970051 | 0.142896995 | 0.029027515 | 0.090384903 | 0.052969928 | 0.222039326 | -0.00868344 | -0.0073714 | 0.107628876 | 0.113993787 | 0.136756338 | 0.112486305 | 0.047010184 | 0.110960134 | -0.001341067 | 0.129818915 | 0.16496706 | 0.083837982 | 0.085967083 | 0.104895855 | 0.045899154 | 0.046491961 | 0.090044608 | 0.095978177 | 0.390040177 | 0.016361121 | 0.027451811 | 0.019681023 | 0.180179608 | -0.001592364 | 0.082838276 | 0.132491211 | 0.172065162 | 0.031826386 | 0.087268517 | 0.057539772 | 0.199025419 | 0.125749457 | 0.140596552 | 0.109910064 | 0.102045179 | 0.002398284 | 0.066815825 | 0.350876004 | 0.145032731 | 0.87490544

Please let me know if I can help further.

phschiele commented 3 years ago

@Pjuske I was able to reproduce the output.

Some observations:

Pjuske commented 3 years ago

Thanks for the follow-up

>>> asset = d["CONFRZ.CO"]
>>> asset
0      0.7000
1      0.7400
2      0.7280
3      0.7060
4      0.7380
5      0.6860
6      0.7080
7      0.7080
8      0.7100
9      0.7280
10     0.7220
11     0.7480
12     0.7480
13     0.7100
14     0.6840
15     0.7200
16     0.7180
17     0.6900
18     0.6980
19     0.7140
20     0.6980
21     0.6800
22     0.6400
23     0.6960
24     0.6500
25     0.6480
26     0.6880
27     0.6860
28     0.6980
29     0.6980
30     0.6920
31     0.6940
32     0.6940
33     0.6880
34     0.6880
35     0.6960
36     0.6880
37     0.6780
38     0.6680
39     0.6760
40     0.6660
41     0.6580
42     0.6320
43     0.6260
44     0.6060
45     0.6360
46     0.6340
47     0.6800
48     0.6800
49     0.6800
50     0.6760
51     0.6800
52     0.6800
53     0.6800
54     0.6800
55     0.6800
56     0.6680
57     0.6580
58     0.6680
59     0.6600
60     0.6360
61     0.6340
62     0.6200
63     0.5500
64     0.5300
65     0.5300
66     0.5100
67     0.5400
68     0.5980
69     0.6000
70     0.5740
71     0.5060
72     0.5800
73     0.5380
74     0.5400
75     0.4990
76     0.4990
77     0.5480
78     0.5460
79     0.5180
80     0.5000
81     0.4980
82     0.5200
83     0.5200
84     0.5100
85     0.5100
86     0.5480
87     0.5480
88     0.5460
89     0.5380
90     0.4940
91     0.5000
92     0.5000
93     0.5280
94     0.4850
95     0.4700
96     0.4560
97     0.4350
98     0.4350
99     0.4400
100    0.4600
101    0.4550
102    0.5380
103    0.5580
104    0.5400
105    0.5080
106    0.5000
107    0.5000
108    0.4730
109    0.5800
110    0.5000
111    0.5480
112    0.5360
113    0.5360
114    0.5200
115    0.5200
116    0.5380
117    0.5400
118    0.6400
119    0.7000
120    0.9560
121    1.7200
122    1.2450
123    1.0900
124    1.1400
125    1.1700
126    1.1350
127    1.1200
128    1.0500
129    0.9600
130    0.9000
131    0.8700
132    0.8300
133    0.8800
134    0.9220
135    0.9580
136    0.9900
137    0.9800
138    1.0350
139    0.9620
140    1.0150
141    0.9700
142    0.9480
143    0.9000
144    0.8980
145    0.9300
146    0.8960
147    0.9220
148    0.9000
149    0.8800
150    0.8400
151    0.9180
152    0.9040
153    0.9180
154    0.9200
155    0.9780
156    1.0100
157    1.3300
158    1.5050
159    1.4350
160    1.3400
161    1.3100
162    1.3200
163    1.1300
164    1.1350
165    1.0800
166    1.1050
167    1.1700
168    1.1450
169    1.1100
170    1.1250
171    1.1800
172    1.1200
173    1.1000
174    1.1350
175    1.1300
176    1.0650
177    1.0100
178    0.9200
179    0.8700
180    0.9880
181    0.9260
182    0.9900
183    0.9440
184    0.9800
185    0.8300
186    0.8000
187    0.8320
188    0.8160
189    0.8300
190    0.7900
191    0.7900
192    0.8280
193    0.7720
194    0.7500
195    0.7220
196    0.7220
197    0.7000
198    0.6840
199    0.7900
200    0.7600
201    0.7360
202    0.7120
203    0.7280
204    0.7140
205    0.7100
206    0.6900
207    0.6800
208    0.6700
209    0.6800
210    0.6820
211    0.6980
212    0.7000
213    0.6860
214    0.6620
215    0.7000
216    0.6820
217    0.6760
218    0.6500
219    0.6760
220    0.6800
221    0.6960
222    0.6580
223    0.6760
224    0.6460
225    0.6300
226    0.6300
227    0.5700
228    0.0700
229    0.0530
230    0.0708
231    0.0680
232    0.0550
233    0.0512
234    0.0604
235    0.1200
236    0.4910
237    0.6580
238    0.4500
239    0.4090
240    0.4410
241    0.4700
242    0.4510
243    0.6000
244    0.5600
245    0.4970
246    0.4510
247    0.4750
Name: CONFRZ.CO, dtype: float64
>>> expected_returns.mean_historical_return(asset)
CONFRZ.CO   -0.326734
dtype: float64
>>> expected_returns.ema_historical_return(asset)
CONFRZ.CO    216.273678
Name: 247, dtype: float64
>>>

Something to note however is that the stock took a huge loss at 228-235 (which also happened in real life).

Thanks again for looking into this

phschiele commented 3 years ago

Looking at the time series, I think you will have a hard time modeling this adequately in this framework. The returns appear to be distributed with very heavy tails, such that using a mean-framework might not be ideal. Here is one way to visualize it: The daily mean of the returns is 0.0153, with a standard deviation of 0.2338. Assuming a normal distribution with these moments, the probability of observing the max return (>300%) is so small that scipy just returns 0. This would be a "13 sigma" event.

With regards to the sector constraints, the way you defined them was fine from a technical point of view. I was just making the point that even non-binding constraints can have an effect on your optimization results.

As mentioned above, the nonneg keyword is not yet implemented in PyPortfolioOpt. If you don't plan on having any short positions and the negative weights are the main problem, you can make the following change to base_optimizer.py.

# Optimisation variables
self._w = cp.Variable(n_assets)

to

self._w = cp.Variable(n_assets, nonneg=True)

Indeed, this problem seems not to be related to PyPortfolioOpt itself.

Pjuske commented 3 years ago

I see, thank you once again, I will close this issue.