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New-Portfolio-Optimization-Menu

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Dany
2022-04-13 01:48:40 -05:00
parent def003d50f
commit b4b7169cfb
14 changed files with 13746 additions and 20 deletions
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20
openbb_terminal/portfolio/portfolio_optimization/optimizer_model.py
View File

@@ -9,11 +9,15 @@ from typing import List, Tuple
import numpy as np
import pandas as pd
import yfinance as yf
import riskfolio as rp
from openbb_terminal.decorators import log_start_end
from openbb_terminal.portfolio.portfolio_optimization import yahoo_finance_model
from openbb_terminal.rich_config import console
from openbb_terminal.portfolio.portfolio_optimization.riskfolio import (
Portfolio,
HCPortfolio,
AuxFunctions,
)
logger = logging.getLogger(__name__)
@@ -330,7 +334,7 @@ def get_mean_risk_portfolio(
risk_free_rate = risk_free_rate / time_factor[freq.upper()]
# Building the portfolio object
port = rp.Portfolio(returns=stock_returns, alpha=alpha)
port = Portfolio.Portfolio(returns=stock_returns, alpha=alpha)
# Estimate input parameters:
port.assets_stats(method_mu=mean, method_cov=covariance, d=d_ewma)
@@ -462,7 +466,7 @@ def get_max_diversification_portfolio(
)
# Building the portfolio object
port = rp.Portfolio(returns=stock_returns)
port = Portfolio.Portfolio(returns=stock_returns)
# Estimate input parameters:
port.assets_stats(method_mu="hist", method_cov=covariance, d=d_ewma)
@@ -572,11 +576,11 @@ def get_max_decorrelation_portfolio(
)
# Building the portfolio object
port = rp.Portfolio(returns=stock_returns)
port = Portfolio.Portfolio(returns=stock_returns)
# Estimate input parameters:
port.assets_stats(method_mu="hist", method_cov=covariance, d=d_ewma)
port.cov = rp.cov2corr(port.cov)
port.cov = AuxFunctions.cov2corr(port.cov)
# Budget constraints
port.upperlng = value
@@ -726,7 +730,7 @@ def get_risk_parity_portfolio(
risk_free_rate = risk_free_rate / time_factor[freq.upper()]
# Building the portfolio object
port = rp.Portfolio(returns=stock_returns, alpha=alpha)
port = Portfolio.Portfolio(returns=stock_returns, alpha=alpha)
# Calculating optimal portfolio
port.assets_stats(method_mu=mean, method_cov=covariance, d=d_ewma)
@@ -872,7 +876,7 @@ def get_rel_risk_parity_portfolio(
)
# Building the portfolio object
port = rp.Portfolio(returns=stock_returns)
port = Portfolio.Portfolio(returns=stock_returns)
# Calculating optimal portfolio
port.assets_stats(method_mu=mean, method_cov=covariance, d=d_ewma)
@@ -1129,7 +1133,7 @@ def get_hcp_portfolio(
risk_free_rate = risk_free_rate / time_factor[freq.upper()]
# Building the portfolio object
port = rp.HCPortfolio(
port = HCPortfolio.HCPortfolio(
returns=stock_returns,
alpha=alpha,
a_sim=a_sim,

45
openbb_terminal/portfolio/portfolio_optimization/optimizer_view.py
View File

@@ -12,7 +12,6 @@ from datetime import date
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import riskfolio as rp
from matplotlib.lines import Line2D
from matplotlib.gridspec import GridSpec
@@ -26,6 +25,12 @@ from openbb_terminal.portfolio.portfolio_optimization import (
optimizer_model,
yahoo_finance_model,
)
from openbb_terminal.portfolio.portfolio_optimization.riskfolio import (
Portfolio,
PlotFunctions,
RiskFunctions,
)
from openbb_terminal.rich_config import console
from openbb_terminal.config_terminal import theme
@@ -105,6 +110,7 @@ time_factor = {
"M": 12.0,
}
@log_start_end(log=logger)
def d_period(period: str, start: str, end: str):
"""
@@ -149,6 +155,7 @@ def d_period(period: str, start: str, end: str):
return p
@log_start_end(log=logger)
def portfolio_performance(
weights: dict,
@@ -236,7 +243,7 @@ def portfolio_performance(
print(f"Sharpe ratio: {sharpe:.4f}")
if risk_measure != "MV":
risk = rp.Sharpe_Risk(
risk = RiskFunctions.Sharpe_Risk(
weights,
cov=stock_returns.cov(),
returns=stock_returns,
@@ -285,6 +292,7 @@ def portfolio_performance(
"Return / " + risk_names[risk_measure.lower()] + f" ratio: {sharpe_2:.4f}"
)
@log_start_end(log=logger)
def display_weights(weights: dict, market_neutral: bool = False):
"""
@@ -320,6 +328,7 @@ def display_weights(weights: dict, market_neutral: bool = False):
header = "Value ($)" if tot_value > 1.01 else "Value (%)"
print_rich_table(weight_df, headers=[header], show_index=True, title="Weights")
@log_start_end(log=logger)
def display_equal_weight(
stocks: List[str],
@@ -425,6 +434,7 @@ def display_equal_weight(
console.print("")
return weights
@log_start_end(log=logger)
def display_property_weighting(
stocks: List[str],
@@ -533,6 +543,7 @@ def display_property_weighting(
console.print("")
return weights
@log_start_end(log=logger)
def display_mean_risk(
stocks: List[str],
@@ -719,6 +730,7 @@ def display_mean_risk(
console.print("")
return weights
@log_start_end(log=logger)
def display_max_sharpe(
stocks: List[str],
@@ -860,6 +872,7 @@ def display_max_sharpe(
)
return weights
@log_start_end(log=logger)
def display_min_risk(
stocks: List[str],
@@ -1001,6 +1014,7 @@ def display_min_risk(
)
return weights
@log_start_end(log=logger)
def display_max_util(
stocks: List[str],
@@ -1147,6 +1161,7 @@ def display_max_util(
)
return weights
@log_start_end(log=logger)
def display_max_ret(
stocks: List[str],
@@ -1288,6 +1303,7 @@ def display_max_ret(
)
return weights
@log_start_end(log=logger)
def display_max_div(
stocks: List[str],
@@ -1400,6 +1416,7 @@ def display_max_div(
console.print("")
return weights
@log_start_end(log=logger)
def display_max_decorr(
stocks: List[str],
@@ -1513,6 +1530,7 @@ def display_max_decorr(
console.print("")
return weights
@log_start_end(log=logger)
def display_ef(
stocks: List[str],
@@ -1616,7 +1634,7 @@ def display_ef(
risk_free_rate = risk_free_rate / time_factor[freq.upper()]
# Building the portfolio object
port = rp.Portfolio(returns=stock_returns, alpha=alpha)
port = Portfolio.Portfolio(returns=stock_returns, alpha=alpha)
# Estimate input parameters:
port.assets_stats(method_mu="hist", method_cov="hist")
@@ -1662,7 +1680,7 @@ def display_ef(
for i in range(frontier.shape[1]):
w = np.array(frontier.iloc[:, i], ndmin=2).T
risk = rp.Sharpe_Risk(
risk = RiskFunctions.Sharpe_Risk(
w,
cov=cov,
returns=stock_returns,
@@ -1687,7 +1705,7 @@ def display_ef(
ax = external_axes[0]
frontier = pd.concat([frontier, random_weights], axis=1)
ax = rp.plot_frontier(
ax = PlotFunctions.plot_frontier(
w_frontier=frontier,
mu=mu,
cov=cov,
@@ -1708,7 +1726,7 @@ def display_ef(
# Add risk free line
if tangency:
ret_sharpe = (mu @ weights).to_numpy().item() * time_factor[freq.upper()]
risk_sharpe = rp.Sharpe_Risk(
risk_sharpe = RiskFunctions.Sharpe_Risk(
weights,
cov=cov,
returns=stock_returns,
@@ -1745,6 +1763,7 @@ def display_ef(
if external_axes is None:
theme.visualize_output(force_tight_layout=False)
@log_start_end(log=logger)
def display_risk_parity(
stocks: List[str],
@@ -1898,6 +1917,7 @@ def display_risk_parity(
console.print("")
return weights
@log_start_end(log=logger)
def display_rel_risk_parity(
stocks: List[str],
@@ -2038,6 +2058,7 @@ def display_rel_risk_parity(
console.print("")
return weights
@log_start_end(log=logger)
def display_hcp(
stocks: List[str],
@@ -2311,6 +2332,7 @@ def display_hcp(
console.print("")
return weights
@log_start_end(log=logger)
def display_hrp(
stocks: List[str],
@@ -2528,6 +2550,7 @@ def display_hrp(
)
return weights
@log_start_end(log=logger)
def display_herc(
stocks: List[str],
@@ -2753,6 +2776,7 @@ def display_herc(
)
return weights
@log_start_end(log=logger)
def display_nco(
stocks: List[str],
@@ -3092,6 +3116,7 @@ def pie_chart_weights(
if external_axes is None:
theme.visualize_output()
@log_start_end(log=logger)
def additional_plots(
weights: Dict,
@@ -3196,7 +3221,7 @@ def additional_plots(
else:
ax = external_axes[0]
ax = rp.plot_hist(
ax = PlotFunctions.plot_hist(
stock_returns, w=pd.Series(weights).to_frame(), alpha=alpha, ax=ax
)
ax.legend(fontsize="x-small", loc="best")
@@ -3215,7 +3240,7 @@ def additional_plots(
ax = external_axes[0]
nav = stock_returns.cumsum()
ax = rp.plot_drawdown(
ax = PlotFunctions.plot_drawdown(
nav=nav, w=pd.Series(weights).to_frame(), alpha=alpha, ax=ax
)
@@ -3239,7 +3264,7 @@ def additional_plots(
else:
ax = external_axes[0]
ax = rp.plot_risk_con(
ax = PlotFunctions.plot_risk_con(
w=pd.Series(weights).to_frame(),
cov=stock_returns.cov(),
returns=stock_returns,
@@ -3267,7 +3292,7 @@ def additional_plots(
else:
ax = external_axes[0]
ax = rp.plot_clusters(
ax = PlotFunctions.plot_clusters(
returns=stock_returns,
codependence="pearson",
linkage="ward",

1258
openbb_terminal/portfolio/portfolio_optimization/riskfolio/AuxFunctions.py Normal file
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964
openbb_terminal/portfolio/portfolio_optimization/riskfolio/ConstraintsFunctions.py Normal file
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@@ -0,0 +1,964 @@
"""""" #
"""
Copyright (c) 2020-2022, Dany Cajas
All rights reserved.
This work is licensed under BSD 3-Clause "New" or "Revised" License.
License available at https://github.com/dcajasn/Riskfolio-Lib/blob/master/LICENSE.txt
"""
import numpy as np
import pandas as pd
import scipy.cluster.hierarchy as hr
from scipy.spatial.distance import squareform
import openbb_terminal.portfolio.portfolio_optimization.riskfolio.AuxFunctions as af
import openbb_terminal.portfolio.portfolio_optimization.riskfolio.DBHT as db
def assets_constraints(constraints, asset_classes):
r"""
Create the linear constraints matrixes A and B of the constraint
:math:`Aw \geq B`.
Parameters
----------
constraints : DataFrame of shape (n_constraints, n_fields)
Constraints matrix, where n_constraints is the number of constraints
and n_fields is the number of fields of constraints matrix, the fields
are:
- Disabled: (bool) indicates if the constraint is enable.
- Type: (str) can be: 'Assets', 'Classes', 'All Assets', 'Each asset in a class' and 'All Classes'.
- Set: (str) if Type is 'Classes', 'Each asset in a class' or 'All Classes'specified the name of the asset's classes set.
- Position: (str) the name of the asset or asset class of the constraint.
- Sign: (str) can be '>=' or '<='.
- Weight: (scalar) is the maximum or minimum weight of the absolute constraint.
- Type Relative: (str) can be: 'Assets' or 'Classes'.
- Relative Set: (str) if Type Relative is 'Classes' specified the name of the set of asset classes.
- Relative: (str) the name of the asset or asset class of the relative constraint.
- Factor: (scalar) is the factor of the relative constraint.
asset_classes : DataFrame of shape (n_assets, n_cols)
Asset's classes matrix, where n_assets is the number of assets and
n_cols is the number of columns of the matrix where the first column
is the asset list and the next columns are the different asset's
classes sets.
Returns
-------
A : nd-array
The matrix A of :math:`Aw \geq B`.
B : nd-array
The matrix B of :math:`Aw \geq B`.
Raises
------
ValueError when the value cannot be calculated.
Examples
--------
::
import riskfolio as rp
asset_classes = {'Assets': ['FB', 'GOOGL', 'NTFX', 'BAC', 'WFC', 'TLT', 'SHV'],
'Class 1': ['Equity', 'Equity', 'Equity', 'Equity', 'Equity',
'Fixed Income', 'Fixed Income'],
'Class 2': ['Technology', 'Technology', 'Technology',
'Financial', 'Financial', 'Treasury', 'Treasury'],}
asset_classes = pd.DataFrame(asset_classes)
asset_classes = asset_classes.sort_values(by=['Assets'])
constraints = {'Disabled': [False, False, False, False, False, False, False],
'Type': ['Classes', 'Classes', 'Assets', 'Assets', 'Classes',
'All Assets', 'Each asset in a class'],
'Set': ['Class 1', 'Class 1', '', '', 'Class 2', '', 'Class 1'],
'Position': ['Equity', 'Fixed Income', 'BAC', 'WFC', 'Financial',
'', 'Equity'],
'Sign': ['<=', '<=', '<=', '<=', '>=', '>=', '>='],
'Weight': [0.6, 0.5, 0.1, '', '', 0.02, ''],
'Type Relative': ['', '', '', 'Assets', 'Classes', '', 'Assets'],
'Relative Set': ['', '', '', '', 'Class 1', '', ''],
'Relative': ['', '', '', 'FB', 'Fixed Income', '', 'TLT'],
'Factor': ['', '', '', 1.2, 0.5, '', 0.4]}
constraints = pd.DataFrame(constraints)
The constraint looks like this:
.. image:: images/Constraints.png
It is easier to construct the constraints in excel and then upload to a
dataframe.
To create the matrixes A and B we use the following command:
::
A, B = rp.assets_constraints(constraints, asset_classes)
The matrixes A and B looks like this (all constraints were converted to a linear
constraint):
.. image:: images/AxB.png
"""
if not isinstance(constraints, pd.DataFrame) and not isinstance(
asset_classes, pd.DataFrame
):
raise ValueError("constraints and asset_classes must be DataFrames")
if constraints.shape[1] != 10:
raise ValueError("constraints must have ten columns")
n = len(constraints)
m = len(asset_classes)
data = constraints.fillna("")
data = data.values.tolist()
assetslist = asset_classes.iloc[:, 0].values.tolist()
A = []
B = []
for i in range(0, n):
if data[i][0] == False:
if data[i][1] == "Assets":
item = assetslist.index(data[i][3])
if data[i][4] == ">=":
d = 1
elif data[i][4] == "<=":
d = -1
if data[i][5] != "":
A1 = [0] * m
A1[item] = d
A.append(A1)
B.append([data[i][5] * d])
else:
A1 = [0] * m
A1[item] = 1
if data[i][6] == "Assets":
item2 = assetslist.index(data[i][8])
A2 = [0] * m
A2[item2] = 1
elif data[i][6] == "Classes":
A2 = np.where(
asset_classes[data[i][7]].values == data[i][8], 1, 0
)
A1 = ((np.array(A1) + np.array(A2) * data[i][9] * -1) * d).tolist()
A.append(A1)
B.append([0])
elif data[i][1] == "All Assets":
item = len(assetslist)
if data[i][4] == ">=":
d = 1
elif data[i][4] == "<=":
d = -1
if data[i][5] != "":
A1 = np.identity(item) * d
A1 = A1.tolist()
B1 = np.ones((item, 1)) * d * data[i][5]
for i in range(0, item):
A.append(A1[i])
B.append(B1.tolist()[0])
else:
A1 = np.identity(item)
if data[i][6] == "Assets":
item2 = assetslist.index(data[i][8])
A2 = np.zeros((item, item - 1))
A2 = np.insert(A2, item2 - 1, 1, axis=1)
elif data[i][6] == "Classes":
A1 = np.identity(item)
A2 = np.where(
asset_classes[data[i][7]].values == data[i][8], 1, 0
)
A2 = np.ones((item, item)) * np.array(A2)
A1 = ((np.array(A1) + np.array(A2) * data[i][9] * -1) * d).tolist()
for i in range(0, item):
A.append(A1[i])
B.append([0])
elif data[i][1] == "Classes":
if data[i][4] == ">=":
d = 1
elif data[i][4] == "<=":
d = -1
if data[i][5] != "":
A1 = np.where(asset_classes[data[i][2]].values == data[i][3], 1, 0)
A1 = np.array(A1) * d
A1 = A1.tolist()
A.append(A1)
B.append([data[i][5] * d])
else:
A1 = np.where(asset_classes[data[i][2]].values == data[i][3], 1, 0)
if data[i][6] == "Assets":
item2 = assetslist.index(data[i][8])
A2 = [0] * m
A2[item2] = 1
elif data[i][6] == "Classes":
A2 = np.where(
asset_classes[data[i][7]].values == data[i][8], 1, 0
)
A1 = ((np.array(A1) + np.array(A2) * data[i][9] * -1) * d).tolist()
A.append(A1)
B.append([0])
elif data[i][1] == "Each asset in a class":
if data[i][4] == ">=":
d = 1
elif data[i][4] == "<=":
d = -1
if data[i][5] != "":
A1 = np.where(asset_classes[data[i][2]].values == data[i][3], 1, 0)
l = 0
for k in A1:
if k == 1:
A3 = [0] * m
A3[l] = 1 * d
A.append(A3)
B.append([data[i][5] * d])
l = l + 1
else:
A1 = np.where(asset_classes[data[i][2]].values == data[i][3], 1, 0)
l = 0
for k in A1:
if k == 1:
A3 = [0] * m
A3[l] = 1
if data[i][6] == "Assets":
item2 = assetslist.index(data[i][8])
A2 = [0] * m
A2[item2] = 1
elif data[i][6] == "Classes":
A2 = np.where(
asset_classes[data[i][7]].values == data[i][8], 1, 0
)
A3 = (
(np.array(A3) + np.array(A2) * data[i][9] * -1) * d
).tolist()
A.append(A3)
B.append([0])
l = l + 1
elif data[i][1] == "All Classes":
if data[i][4] == ">=":
d = 1
elif data[i][4] == "<=":
d = -1
if data[i][5] != "":
for k in np.unique(asset_classes[data[i][2]].values):
A1 = np.where(asset_classes[data[i][2]].values == k, 1, 0) * d
A1 = A1.tolist()
A.append(A1)
B.append([data[i][5] * d])
else:
for k in np.unique(asset_classes[data[i][2]].values):
A1 = np.where(asset_classes[data[i][2]].values == k, 1, 0)
if data[i][6] == "Assets":
item2 = assetslist.index(data[i][8])
A2 = [0] * m
A2[item2] = 1
elif data[i][6] == "Classes":
A2 = np.where(
asset_classes[data[i][7]].values == data[i][8], 1, 0
)
A3 = (
(np.array(A1) + np.array(A2) * data[i][9] * -1) * d
).tolist()
A.append(A3)
B.append([0])
A = np.array(A, ndmin=2)
B = np.array(B, ndmin=2)
return A, B
def factors_constraints(constraints, loadings):
r"""
Create the factors constraints matrixes C and D of the constraint
:math:`Cw \geq D`.
Parameters
----------
constraints : DataFrame of shape (n_constraints, n_fields)
Constraints matrix, where n_constraints is the number of constraints
and n_fields is the number of fields of constraints matrix, the fields
are:
- Disabled: (bool) indicates if the constraint is enable.
- Factor: (str) the name of the factor of the constraint.
- Sign: (str) can be '>=' or '<='.
- Value: (scalar) is the maximum or minimum value of the factor.
loadings : DataFrame of shape (n_assets, n_features)
The loadings matrix.
Returns
-------
C : nd-array
The matrix C of :math:`Cw \geq D`.
D : nd-array
The matrix D of :math:`Cw \geq D`.
Raises
------
ValueError when the value cannot be calculated.
Examples
--------
::
loadings = {'const': [0.0004, 0.0002, 0.0000, 0.0006, 0.0001, 0.0003, -0.0003],
'MTUM': [0.1916, 1.0061, 0.8695, 1.9996, 0.0000, 0.0000, 0.0000],
'QUAL': [0.0000, 2.0129, 1.4301, 0.0000, 0.0000, 0.0000, 0.0000],
'SIZE': [0.0000, 0.0000, 0.0000, 0.4717, 0.0000, -0.1857, 0.0000],
'USMV': [-0.7838, -1.6439, -1.0176, -1.4407, 0.0055, 0.5781, 0.0000],
'VLUE': [1.4772, -0.7590, -0.4090, 0.0000, -0.0054, -0.4844, 0.9435]}
loadings = pd.DataFrame(loadings)
constraints = {'Disabled': [False, False, False],
'Factor': ['MTUM', 'USMV', 'VLUE'],
'Sign': ['<=', '<=', '>='],
'Value': [0.9, -1.2, 0.3],
'Relative Factor': ['USMV', '', '']}
constraints = pd.DataFrame(constraints)
The constraint looks like this:
.. image:: images/Constraints2.png
It is easier to construct the constraints in excel and then upload to a
dataframe.
To create the matrixes C and D we use the following command:
::
C, D = rp.factors_constraints(constraints, loadings)
The matrixes C and D looks like this (all constraints were converted to a linear
constraint):
.. image:: images/CxD.png
"""
if not isinstance(constraints, pd.DataFrame) and not isinstance(
loadings, pd.DataFrame
):
raise ValueError("constraints and loadings must be DataFrames")
if constraints.shape[1] != 5:
raise ValueError("constraints must have five columns")
n = len(constraints)
data = constraints.fillna("")
data = data.values.tolist()
C = []
D = []
for i in range(0, n):
if data[i][0] == False:
if data[i][2] == ">=":
d = 1
elif data[i][2] == "<=":
d = -1
C1 = loadings[data[i][1]].values
if data[i][4] != "":
C2 = loadings[data[i][4]].values
C1 = C1 - C2
C.append(C1 * d)
D.append([data[i][3] * d])
C = np.array(C, ndmin=2)
D = np.array(D, ndmin=2)
return C, D
def assets_views(views, asset_classes):
r"""
Create the assets views matrixes P and Q of the views :math:`Pw = Q`.
Parameters
----------
views : DataFrame of shape (n_views, n_fields)
Constraints matrix, where n_views is the number of views
and n_fields is the number of fields of views matrix, the fields
are:
- Disabled: (bool) indicates if the constraint is enable.
- Type: (str) can be: 'Assets' or 'Classes'.
- Set: (str) if Type is 'Classes' specified the name of the set of asset classes.
- Position: (str) the name of the asset or asset class of the view.
- Sign: (str) can be '>=' or '<='.
- Return: (scalar) is the return of the view.
- Type Relative: (str) can be: 'Assets' or 'Classes'.
- Relative Set: (str) if Type Relative is 'Classes' specified the name of the set of asset classes.
- Relative: (str) the name of the asset or asset class of the relative view.
asset_classes : DataFrame of shape (n_assets, n_cols)
Asset's classes matrix, where n_assets is the number of assets and
n_cols is the number of columns of the matrix where the first column
is the asset list and the next columns are the different asset's
classes sets.
Returns
-------
P : nd-array
The matrix P that shows the relation among assets in each view.
Q : nd-array
The matrix Q that shows the expected return of each view.
Raises
------
ValueError when the value cannot be calculated.
Examples
--------
::
asset_classes = {'Assets': ['FB', 'GOOGL', 'NTFX', 'BAC', 'WFC', 'TLT', 'SHV'],
'Class 1': ['Equity', 'Equity', 'Equity', 'Equity', 'Equity',
'Fixed Income', 'Fixed Income'],
'Class 2': ['Technology', 'Technology', 'Technology',
'Financial', 'Financial', 'Treasury', 'Treasury'],}
asset_classes = pd.DataFrame(asset_classes)
asset_classes = asset_classes.sort_values(by=['Assets'])
views = {'Disabled': [False, False, False, False],
'Type': ['Assets', 'Classes', 'Classes', 'Assets'],
'Set': ['', 'Class 2','Class 1', ''],
'Position': ['WFC', 'Financial', 'Equity', 'FB'],
'Sign': ['<=', '>=', '>=', '>='],
'Return': [ 0.3, 0.1, 0.05, 0.03 ],
'Type Relative': [ 'Assets', 'Classes', 'Assets', ''],
'Relative Set': [ '', 'Class 1', '', ''],
'Relative': ['FB', 'Fixed Income', 'TLT', '']}
views = pd.DataFrame(views)
The constraint looks like this:
.. image:: images/Views.png
It is easier to construct the constraints in excel and then upload to a
dataframe.
To create the matrixes P and Q we use the following command:
::
P, Q = rp.assets_views(views, asset_classes)
The matrixes P and Q looks like this:
.. image:: images/PxQ.png
"""
if not isinstance(views, pd.DataFrame) and not isinstance(
asset_classes, pd.DataFrame
):
raise ValueError("constraints and asset_classes must be DataFrames")
if views.shape[1] != 9:
raise ValueError("constraints must have nine columns")
n = len(views)
m = len(asset_classes)
data = views.fillna("")
data = data.values.tolist()
assetslist = asset_classes.iloc[:, 0].values.tolist()
P = []
Q = []
for i in range(0, n):
valid = False
if data[i][0] == False:
if data[i][1] == "Assets":
item = assetslist.index(data[i][3])
if data[i][4] == ">=":
d = 1
elif data[i][4] == "<=":
d = -1
if data[i][5] != "":
P1 = [0] * m
P1[item] = 1
if data[i][6] == "Assets" and data[i][8] != "":
item2 = assetslist.index(data[i][8])
P2 = [0] * m
P2[item2] = 1
valid = True
elif (
data[i][6] == "Classes"
and data[i][7] != ""
and data[i][8] != ""
):
P2 = np.where(
asset_classes[data[i][7]].values == data[i][8], 1, 0
)
P2 = P2 / np.sum(P2)
valid = True
elif data[i][6] == "" and data[i][7] == "" and data[i][8] == "":
P2 = [0] * m
valid = True
if valid == True:
P1 = ((np.array(P1) - np.array(P2)) * d).tolist()
P.append(P1)
Q.append([data[i][5] * d])
elif data[i][1] == "Classes":
if data[i][4] == ">=":
d = 1
else:
d = -1
if data[i][5] != "":
P1 = np.where(asset_classes[data[i][2]].values == data[i][3], 1, 0)
P1 = P1 / np.sum(P1)
if data[i][6] == "Assets" and data[i][8] != "":
item2 = assetslist.index(data[i][8])
P2 = [0] * m
P2[item2] = 1
valid = True
elif (
data[i][6] == "Classes"
and data[i][7] != ""
and data[i][8] != ""
):
P2 = np.where(
asset_classes[data[i][7]].values == data[i][8], 1, 0
)
P2 = P2 / np.sum(P2)
valid = True
elif data[i][6] == "" and data[i][7] == "" and data[i][8] == "":
P2 = [0] * m
valid = True
if valid == True:
P1 = ((np.array(P1) - np.array(P2)) * d).tolist()
P.append(P1)
Q.append([data[i][5] * d])
P = np.array(P, ndmin=2)
Q = np.array(Q, ndmin=2)
for i in range(len(Q)):
if Q[i, 0] < 0:
P[i, :] = -1 * P[i, :]
Q[i, :] = -1 * Q[i, :]
return P, Q
def factors_views(views, loadings, const=True):
r"""
Create the factors constraints matrixes C and D of the constraint
:math:`Cw \geq D`.
Parameters
----------
constraints : DataFrame of shape (n_constraints, n_fields)
Constraints matrix, where n_constraints is the number of constraints
and n_fields is the number of fields of constraints matrix, the fields
are:
- Disabled: (bool) indicates if the constraint is enable.
- Factor: (str) the name of the factor of the constraint.
- Sign: (str) can be '>=' or '<='.
- Value: (scalar) is the maximum or minimum value of the factor.
loadings : DataFrame of shape (n_assets, n_features)
The loadings matrix.
Returns
-------
P : nd-array
The matrix P that shows the relation among factors in each factor view.
Q : nd-array
The matrix Q that shows the expected return of each factor view.
Raises
------
ValueError when the value cannot be calculated.
Examples
--------
::
loadings = {'const': [0.0004, 0.0002, 0.0000, 0.0006, 0.0001, 0.0003, -0.0003],
'MTUM': [0.1916, 1.0061, 0.8695, 1.9996, 0.0000, 0.0000, 0.0000],
'QUAL': [0.0000, 2.0129, 1.4301, 0.0000, 0.0000, 0.0000, 0.0000],
'SIZE': [0.0000, 0.0000, 0.0000, 0.4717, 0.0000, -0.1857, 0.0000],
'USMV': [-0.7838, -1.6439, -1.0176, -1.4407, 0.0055, 0.5781, 0.0000],
'VLUE': [1.4772, -0.7590, -0.4090, 0.0000, -0.0054, -0.4844, 0.9435]}
loadings = pd.DataFrame(loadings)
factorsviews = {'Disabled': [False, False, False],
'Factor': ['MTUM', 'USMV', 'VLUE'],
'Sign': ['<=', '<=', '>='],
'Value': [0.9, -1.2, 0.3],
'Relative Factor': ['USMV', '', '']}
factorsviews = pd.DataFrame(factorsviews)
The constraint looks like this:
.. image:: images/factorsviews.png
It is easier to construct the constraints in excel and then upload to a
dataframe.
To create the matrixes P and Q we use the following command:
::
P, Q = rp.factors_views(factorsviews, loadings, const=True)
The matrixes P and Q looks like this:
.. image:: images/P_fxQ_f.png
"""
if not isinstance(views, pd.DataFrame) and not isinstance(loadings, pd.DataFrame):
raise ValueError("constraints and loadings must be DataFrames")
if views.shape[1] != 5:
raise ValueError("constraints must have five columns")
n = len(views)
data = views.fillna("")
data = data.values.tolist()
factorslist = loadings.columns.tolist()
if const == True:
factorslist = factorslist[1:]
m = len(factorslist)
P = []
Q = []
for i in range(0, n):
if data[i][0] == False:
item = factorslist.index(data[i][1])
if data[i][2] == ">=":
d = 1
elif data[i][2] == "<=":
d = -1
P1 = [0] * m
P1[item] = d
if data[i][4] != "":
item = factorslist.index(data[i][4])
P1[item] = -d
P.append(P1)
Q.append([data[i][3] * d])
P = np.array(P, ndmin=2)
Q = np.array(Q, ndmin=2)
return P, Q
def assets_clusters(
returns,
codependence="pearson",
linkage="ward",
k=None,
max_k=10,
bins_info="KN",
alpha_tail=0.05,
leaf_order=True,
):
r"""
Create asset classes based on hierarchical clustering.
Parameters
----------
returns : DataFrame
Assets returns.
codependence : str, can be {'pearson', 'spearman', 'abs_pearson', 'abs_spearman', 'distance', 'mutual_info' or 'tail'}
The codependence or similarity matrix used to build the distance
metric and clusters. The default is 'pearson'. Posible values are:
- 'pearson': pearson correlation matrix. Distance formula: :math:`D_{i,j} = \sqrt{0.5(1-\rho^{pearson}_{i,j})}`.
- 'spearman': spearman correlation matrix. Distance formula: :math:`D_{i,j} = \sqrt{0.5(1-\rho^{spearman}_{i,j})}`.
- 'abs_pearson': absolute value pearson correlation matrix. Distance formula: :math:`D_{i,j} = \sqrt{(1-|\rho^{pearson}_{i,j}|)}`.
- 'abs_spearman': absolute value spearman correlation matrix. Distance formula: :math:`D_{i,j} = \sqrt{(1-|\rho^{spearman}_{i,j}|)}`.
- 'distance': distance correlation matrix. Distance formula :math:`D_{i,j} = \sqrt{(1-\rho^{distance}_{i,j})}`.
- 'mutual_info': mutual information matrix. Distance used is variation information matrix.
- 'tail': lower tail dependence index matrix. Dissimilarity formula :math:`D_{i,j} = -\log{\lambda_{i,j}}`.
linkage : string, optional
Linkage method of hierarchical clustering, see `linkage <https://docs.scipy.org/doc/scipy/reference/generated/scipy.cluster.hierarchy.linkage.html?highlight=linkage#scipy.cluster.hierarchy.linkage>`_ for more details.
The default is 'ward'. Posible values are:
- 'single'.
- 'complete'.
- 'average'.
- 'weighted'.
- 'centroid'.
- 'median'.
- 'ward'.
- 'DBHT'. Direct Bubble Hierarchical Tree.
k : int, optional
Number of clusters. This value is took instead of the optimal number
of clusters calculated with the two difference gap statistic.
The default is None.
max_k : int, optional
Max number of clusters used by the two difference gap statistic
to find the optimal number of clusters. The default is 10.
bins_info: int or str
Number of bins used to calculate variation of information. The default
value is 'KN'. Posible values are:
- 'KN': Knuth's choice method. See more in `knuth_bin_width <https://docs.astropy.org/en/stable/api/astropy.stats.knuth_bin_width.html>`_.
- 'FD': Freedman–Diaconis' choice method. See more in `freedman_bin_width <https://docs.astropy.org/en/stable/api/astropy.stats.freedman_bin_width.html>`_.
- 'SC': Scotts' choice method. See more in `scott_bin_width <https://docs.astropy.org/en/stable/api/astropy.stats.scott_bin_width.html>`_.
- 'HGR': Hacine-Gharbi and Ravier' choice method.
- int: integer value choice by user.
alpha_tail : float, optional
Significance level for lower tail dependence index. The default is 0.05.
leaf_order : bool, optional
Indicates if the cluster are ordered so that the distance between
successive leaves is minimal. The default is True.
Returns
-------
clusters : DataFrame
A dataframe with asset classes based on hierarchical clustering.
Raises
------
ValueError when the value cannot be calculated.
Examples
--------
::
clusters = rp.assets_clusters(returns, codependence='pearson',
linkage='ward', k=None, max_k=10,
alpha_tail=0.05, leaf_order=True)
The clusters dataframe looks like this:
.. image:: images/clusters_df.png
"""
if not isinstance(returns, pd.DataFrame):
raise ValueError("returns must be a DataFrame")
# Calculating codependence matrix and distance metric
if codependence in {"pearson", "spearman"}:
codep = returns.corr(method=codependence)
dist = np.sqrt(np.clip((1 - codep) / 2, a_min=0.0, a_max=1.0))
elif codependence in {"abs_pearson", "abs_spearman"}:
codep = np.abs(returns.corr(method=codependence[4:]))
dist = np.sqrt(np.clip((1 - codep), a_min=0.0, a_max=1.0))
elif codependence in {"distance"}:
codep = af.dcorr_matrix(returns).astype(float)
dist = np.sqrt(np.clip((1 - codep), a_min=0.0, a_max=1.0))
elif codependence in {"mutual_info"}:
codep = af.mutual_info_matrix(returns, bins_info).astype(float)
dist = af.var_info_matrix(returns, bins_info).astype(float)
elif codependence in {"tail"}:
codep = af.ltdi_matrix(returns, alpha_tail).astype(float)
dist = -np.log(codep)
# Hierarchcial clustering
dist = dist.to_numpy()
dist = pd.DataFrame(dist, columns=codep.columns, index=codep.index)
if linkage == "DBHT":
# different choices for D, S give different outputs!
D = dist.to_numpy() # dissimilatity matrix
if codependence in {"pearson", "spearman"}:
S = (1 - dist**2).to_numpy()
else:
S = codep.copy().to_numpy() # similarity matrix
(_, _, _, _, _, clustering) = db.DBHTs(
D, S, leaf_order=leaf_order
) # DBHT clustering
else:
p_dist = squareform(dist, checks=False)
clustering = hr.linkage(p_dist, method=linkage, optimal_ordering=leaf_order)
# Optimal number of clusters
if k is None:
k = af.two_diff_gap_stat(codep, dist, clustering, max_k)
# Building clusters
clusters_inds = hr.fcluster(clustering, k, criterion="maxclust")
labels = np.array(returns.columns.tolist())
clusters = {"Assets": [], "Clusters": []}
for i, v in enumerate(clusters_inds):
clusters["Assets"].append(labels[i])
clusters["Clusters"].append("Cluster " + str(v))
clusters = pd.DataFrame(clusters)
clusters = clusters.sort_values(by=["Assets"])
return clusters
def hrp_constraints(constraints, asset_classes):
r"""
Create the upper and lower bounds constraints for hierarchical risk parity
model.
Parameters
----------
constraints : DataFrame of shape (n_constraints, n_fields)
Constraints matrix, where n_constraints is the number of constraints
and n_fields is the number of fields of constraints matrix, the fields
are:
- Disabled: (bool) indicates if the constraint is enable.
- Type: (str) can be: 'Assets', All Assets' and 'Each asset in a class'.
- Position: (str) the name of the asset or asset class of the constraint.
- Sign: (str) can be '>=' or '<='.
- Weight: (scalar) is the maximum or minimum weight of the absolute constraint.
asset_classes : DataFrame of shape (n_assets, n_cols)
Asset's classes matrix, where n_assets is the number of assets and
n_cols is the number of columns of the matrix where the first column
is the asset list and the next columns are the different asset's
classes sets.
Returns
-------
w_max : pd.Series
The upper bound of hierarchical risk parity weights constraints.
w_min : pd.Series
The lower bound of hierarchical risk parity weights constraints.
Raises
------
ValueError when the value cannot be calculated.
Examples
--------
::
asset_classes = {'Assets': ['FB', 'GOOGL', 'NTFX', 'BAC', 'WFC', 'TLT', 'SHV'],
'Class 1': ['Equity', 'Equity', 'Equity', 'Equity', 'Equity',
'Fixed Income', 'Fixed Income'],
'Class 2': ['Technology', 'Technology', 'Technology',
'Financial', 'Financial', 'Treasury', 'Treasury'],}
asset_classes = pd.DataFrame(asset_classes)
asset_classes = asset_classes.sort_values(by=['Assets'])
constraints = {'Disabled': [False, False, False, False, False, False],
'Type': ['Assets', 'Assets', 'All Assets', 'All Assets',
'Each asset in a class', 'Each asset in a class'],
'Set': ['', '', '', '','Class 1', 'Class 2'],
'Position': ['BAC', 'FB', '', '', 'Equity', 'Treasury'],
'Sign': ['>=', '<=', '<=', '>=', '<=', '<='],
'Weight': [0.02, 0.085, 0.09, 0.01, 0.07, 0.06]}
constraints = pd.DataFrame(constraints)
The constraint looks like this:
.. image:: images/HRPConstraints.png
It is easier to construct the constraints in excel and then upload to a
dataframe.
To create the pd.Series w_max and w_min we use the following command:
::
w_max, w_min = rp.hrp_constraints(constraints, asset_classes)
The pd.Series w_max and w_min looks like this (all constraints were
merged to a single upper bound for each asset):
.. image:: images/HRP_Bounds.png
"""
if not isinstance(constraints, pd.DataFrame) and not isinstance(
asset_classes, pd.DataFrame
):
raise ValueError("constraints and asset_classes must be DataFrames")
if constraints.shape[1] != 6:
raise ValueError("constraints must have ten columns")
n = len(constraints)
data = constraints.fillna("").copy()
assetslist = asset_classes.iloc[:, 0].values.tolist()
w_max = pd.Series(1, index=assetslist)
w_min = pd.Series(0, index=assetslist)
for i in range(0, n):
if data.loc[i, "Disabled"] == False:
if data.loc[i, "Type"] == "Assets":
assets = data.loc[i, "Position"]
if data.loc[i, "Sign"] == ">=":
if w_min.loc[assets] <= data.loc[i, "Weight"]:
w_min.loc[assets] = data.loc[i, "Weight"]
elif data.loc[i, "Sign"] == "<=":
if w_max.loc[assets] >= data.loc[i, "Weight"]:
w_max.loc[assets] = data.loc[i, "Weight"]
elif data.loc[i, "Type"] == "All Assets":
if data.loc[i, "Sign"] == ">=":
if w_min[w_min <= data.loc[i, "Weight"]].shape[0] != 0:
w_min[w_min <= data.loc[i, "Weight"]] = data.loc[i, "Weight"]
elif data.loc[i, "Sign"] == "<=":
if w_max[w_max >= data.loc[i, "Weight"]].shape[0] != 0:
w_max[w_max >= data.loc[i, "Weight"]] = data.loc[i, "Weight"]
elif data.loc[i, "Type"] == "Each asset in a class":
label_0 = asset_classes.columns.tolist()[0]
label_1 = data.loc[i, "Set"]
label_2 = data.loc[i, "Position"]
assets = asset_classes[[label_0, label_1]][
asset_classes[label_1] == label_2
]
assets = assets["Assets"].tolist()
if data.loc[i, "Sign"] == ">=":
if (
w_min.loc[assets][
w_min.loc[assets] <= data.loc[i, "Weight"]
].shape[0]
!= 0
):
w_min.loc[assets] = np.where(
w_min.loc[assets] <= data.loc[i, "Weight"],
data.loc[i, "Weight"],
w_min.loc[assets],
)
elif data.loc[i, "Sign"] == "<=":
if (
w_max.loc[assets][
w_max.loc[assets] >= data.loc[i, "Weight"]
].shape[0]
!= 0
):
w_max.loc[assets] = np.where(
w_max.loc[assets] >= data.loc[i, "Weight"],
data.loc[i, "Weight"],
w_max.loc[assets],
)
return w_max, w_min

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"""""" #
"""
Copyright (c) 2020-2022, Dany Cajas
All rights reserved.
This work is licensed under BSD 3-Clause "New" or "Revised" License.
License available at https://github.com/dcajasn/Riskfolio-Lib/blob/master/LICENSE.txt
"""
import numpy as np
import pandas as pd
import scipy.cluster.hierarchy as hr
from scipy.spatial.distance import squareform
import openbb_terminal.portfolio.portfolio_optimization.riskfolio.Portfolio as pf
import openbb_terminal.portfolio.portfolio_optimization.riskfolio.RiskFunctions as rk
import openbb_terminal.portfolio.portfolio_optimization.riskfolio.AuxFunctions as af
import openbb_terminal.portfolio.portfolio_optimization.riskfolio.ParamsEstimation as pe
import openbb_terminal.portfolio.portfolio_optimization.riskfolio.DBHT as db
class HCPortfolio(object):
r"""
Class that creates a portfolio object with all properties needed to
calculate optimal portfolios.
Parameters
----------
returns : DataFrame, optional
A dataframe that containts the returns of the assets.
The default is None.
alpha : float, optional
Significance level of VaR, CVaR, EVaR, DaR, CDaR, EDaR and Tail Gini of losses.
The default is 0.05.
a_sim : float, optional
Number of CVaRs used to approximate Tail Gini of losses. The default is 100.
beta : float, optional
Significance level of CVaR and Tail Gini of gains. If None it duplicates alpha value.
The default is None.
b_sim : float, optional
Number of CVaRs used to approximate Tail Gini of gains. If None it duplicates a_sim value.
The default is None.
w_max : Series, optional
Upper bound constraint for hierarchical risk parity weights :cite:`c-Pfitzinger`.
w_min : Series, optional
Lower bound constraint for hierarchical risk parity weights :cite:`c-Pfitzinger`.
"""
def __init__(
self,
returns=None,
alpha=0.05,
a_sim=100,
beta=None,
b_sim=None,
w_max=None,
w_min=None,
alpha_tail=0.05,
bins_info=None,
):
self._returns = returns
self.alpha = alpha
self.a_sim = a_sim
self.beta = beta
self.b_sim = b_sim
self.alpha_tail = alpha_tail
self.bins_info = bins_info
self.asset_order = None
self.clusters = None
self.cov = None
self.mu = None
self.codep = None
self.codep_sorted = None
self.w_max = w_max
self.w_min = w_min
@property
def returns(self):
if self._returns is not None and isinstance(self._returns, pd.DataFrame):
return self._returns
else:
raise NameError("returns must be a DataFrame")
@returns.setter
def returns(self, value):
if value is not None and isinstance(value, pd.DataFrame):
self._returns = value
else:
raise NameError("returns must be a DataFrame")
@property
def assetslist(self):
if self._returns is not None and isinstance(self._returns, pd.DataFrame):
return self._returns.columns.tolist()
# get naive-risk weights
def _naive_risk(self, returns, cov, rm="MV", rf=0):
assets = returns.columns.tolist()
n = len(assets)
if rm == "equal":
weight = np.ones((n, 1)) * 1 / n
else:
inv_risk = np.zeros((n, 1))
for i in assets:
k = assets.index(i)
w = np.zeros((n, 1))
w[k, 0] = 1
w = pd.DataFrame(w, columns=["weights"], index=assets)
if rm == "vol":
risk = rk.Sharpe_Risk(
w,
cov=cov,
returns=returns,
rm="MV",
rf=rf,
alpha=self.alpha,
a_sim=self.a_sim,
beta=self.beta,
b_sim=self.b_sim,
)
else:
risk = rk.Sharpe_Risk(
w,
cov=cov,
returns=returns,
rm=rm,
rf=rf,
alpha=self.alpha,
a_sim=self.a_sim,
beta=self.beta,
b_sim=self.b_sim,
)
inv_risk[k, 0] = risk
if rm == "MV":
inv_risk = 1 / np.power(inv_risk, 2)
else:
inv_risk = 1 / inv_risk
weight = inv_risk * (1 / np.sum(inv_risk))
weight = weight.reshape(-1, 1)
return weight
# get optimal weights
def _opt_w(self, returns, mu, cov, obj="MinRisk", rm="MV", rf=0, l=2):
if returns.shape[1] == 1:
weight = np.array([1]).reshape(-1, 1)
else:
if obj in {"MinRisk", "Utility", "Sharpe"}:
port = pf.Portfolio(returns=returns)
port.assets_stats(method_mu="hist", method_cov="hist", d=0.94)
port.cov = cov
if mu is not None:
port.mu = mu
weight = port.optimization(
model="Classic", rm=rm, obj=obj, rf=rf, l=l, hist=True
).to_numpy()
elif obj in {"ERC"}:
port = pf.Portfolio(returns=returns)
port.assets_stats(method_mu="hist", method_cov="hist", d=0.94)
port.cov = cov
weight = port.rp_optimization(
model="Classic", rm=rm, rf=rf, b=None, hist=True
).to_numpy()
weight = weight.reshape(-1, 1)
return weight
# Create hierarchical clustering
def _hierarchical_clustering(
self,
model="HRP",
linkage="ward",
codependence="pearson",
max_k=10,
leaf_order=True,
):
# Calculating distance
if codependence in {"pearson", "spearman", "custom_cov"}:
dist = np.sqrt(np.clip((1 - self.codep) / 2, a_min=0.0, a_max=1.0))
elif codependence in {"abs_pearson", "abs_spearman", "distance"}:
dist = np.sqrt(np.clip((1 - self.codep), a_min=0.0, a_max=1.0))
elif codependence in {"mutual_info"}:
dist = af.var_info_matrix(self.returns, self.bins_info).astype(float)
elif codependence in {"tail"}:
dist = -np.log(self.codep).astype(float)
# Hierarchcial clustering
dist = dist.to_numpy()
dist = pd.DataFrame(dist, columns=self.codep.columns, index=self.codep.index)
if linkage == "DBHT":
# different choices for D, S give different outputs!
D = dist.to_numpy() # dissimilatity matrix
if codependence in {"pearson", "spearman", "custom_cov"}:
codep = 1 - dist**2
S = codep.to_numpy() # similarity matrix
else:
S = self.codep.to_numpy() # similarity matrix
(_, _, _, _, _, clustering) = db.DBHTs(
D, S, leaf_order=leaf_order
) # DBHT clustering
else:
p_dist = squareform(dist, checks=False)
clustering = hr.linkage(p_dist, method=linkage, optimal_ordering=leaf_order)
if model in {"HERC", "HERC2", "NCO"}:
# optimal number of clusters
k = af.two_diff_gap_stat(self.codep, dist, clustering, max_k)
else:
k = None
return clustering, k
# sort clustered items by distance
def _seriation(self, clusters):
return hr.leaves_list(clusters)
# compute HRP weight allocation through recursive bisection
def _recursive_bisection(self, sort_order, rm="MV", rf=0):
if isinstance(self.w_max, pd.Series) and isinstance(self.w_min, pd.Series):
if (self.w_max.all() >= self.w_min.all()).item():
flag = True
else:
raise NameError("All upper bounds must be higher than lower bounds")
else:
flag = False
weight = pd.Series(1, index=sort_order) # set initial weights to 1
items = [sort_order]
while len(items) > 0: # loop while weights is under 100%
items = [
i[j:k]
for i in items
for j, k in (
(0, len(i) // 2),
(len(i) // 2, len(i)),
) # get cluster indi
if len(i) > 1
]
# allocate weight to left and right cluster
for i in range(0, len(items), 2):
left_cluster = items[i]
right_cluster = items[i + 1]
# Left cluster
left_cov = self.cov.iloc[left_cluster, left_cluster]
left_returns = self.returns.iloc[:, left_cluster]
left_weight = self._naive_risk(left_returns, left_cov, rm=rm, rf=rf)
if rm == "vol":
left_risk = rk.Sharpe_Risk(
left_weight,
cov=left_cov,
returns=left_returns,
rm="MV",
rf=rf,
alpha=self.alpha,
a_sim=self.a_sim,
beta=self.beta,
b_sim=self.b_sim,
)
else:
left_risk = rk.Sharpe_Risk(
left_weight,
cov=left_cov,
returns=left_returns,
rm=rm,
rf=rf,
alpha=self.alpha,
a_sim=self.a_sim,
beta=self.beta,
b_sim=self.b_sim,
)
if rm == "MV":
left_risk = np.power(left_risk, 2)
# Right cluster
right_cov = self.cov.iloc[right_cluster, right_cluster]
right_returns = self.returns.iloc[:, right_cluster]
right_weight = self._naive_risk(right_returns, right_cov, rm=rm, rf=rf)
if rm == "vol":
right_risk = rk.Sharpe_Risk(
right_weight,
cov=right_cov,
returns=right_returns,
rm="MV",
rf=rf,
alpha=self.alpha,
a_sim=self.a_sim,
beta=self.beta,
b_sim=self.b_sim,
)
else:
right_risk = rk.Sharpe_Risk(
right_weight,
cov=right_cov,
returns=right_returns,
rm=rm,
rf=rf,
alpha=self.alpha,
a_sim=self.a_sim,
beta=self.beta,
b_sim=self.b_sim,
)
if rm == "MV":
right_risk = np.power(right_risk, 2)
# Allocate weight to clusters
alpha_1 = 1 - left_risk / (left_risk + right_risk)
# Weights constraints
if flag:
a1 = np.sum(self.w_max[left_cluster]) / weight[left_cluster[0]]
a2 = np.max(
[
np.sum(self.w_min[left_cluster]) / weight[left_cluster[0]],
alpha_1,
]
)
alpha_1 = np.min([a1, a2])
a1 = np.sum(self.w_max[right_cluster]) / weight[right_cluster[0]]
a2 = np.max(
[
np.sum(self.w_min[right_cluster])
/ weight[right_cluster[0]],
1 - alpha_1,
]
)
alpha_1 = 1 - np.min([a1, a2])
weight[left_cluster] *= alpha_1 # weight 1
weight[right_cluster] *= 1 - alpha_1 # weight 2
weight.index = self.asset_order
return weight
# compute HRP weight allocation through cluster-based bisection
def _hierarchical_recursive_bisection(
self, Z, rm="MV", rf=0, linkage="ward", model="HERC"
):
# Transform linkage to tree and reverse order
root, nodes = hr.to_tree(Z, rd=True)
nodes = np.array(nodes)
nodes_1 = np.array([i.dist for i in nodes])
idx = np.argsort(nodes_1)
nodes = nodes[idx][::-1].tolist()
weight = pd.Series(1, index=self.cov.index) # Set initial weights to 1
clustering_inds = hr.fcluster(Z, self.k, criterion="maxclust")
clusters = {
i: [] for i in range(min(clustering_inds), max(clustering_inds) + 1)
}
for i, v in enumerate(clustering_inds):
clusters[v].append(i)
# Loop through k clusters
for i in nodes[: self.k - 1]:
if i.is_leaf() == False: # skip leaf-nodes
left = i.get_left().pre_order() # lambda i: i.id) # get left cluster
right = i.get_right().pre_order() # lambda i: i.id) # get right cluster
left_set = set(left)
right_set = set(right)
left_risk = 0
right_risk = 0
# Allocate weight to clusters
if rm == "equal":
alpha_1 = 0.5
else:
for j in clusters.keys():
if set(clusters[j]).issubset(left_set):
# Left cluster
left_cov = self.cov.iloc[clusters[j], clusters[j]]
left_returns = self.returns.iloc[:, clusters[j]]
left_weight = self._naive_risk(
left_returns, left_cov, rm=rm, rf=rf
)
if rm == "vol":
left_risk_ = rk.Sharpe_Risk(
left_weight,
cov=left_cov,
returns=left_returns,
rm="MV",
rf=rf,
alpha=self.alpha,
a_sim=self.a_sim,
beta=self.beta,
b_sim=self.b_sim,
)
else:
left_risk_ = rk.Sharpe_Risk(
left_weight,
cov=left_cov,
returns=left_returns,
rm=rm,
rf=rf,
alpha=self.alpha,
a_sim=self.a_sim,
beta=self.beta,
b_sim=self.b_sim,
)
if rm == "MV":
left_risk_ = np.power(left_risk_, 2)
left_risk += left_risk_
elif set(clusters[j]).issubset(right_set):
# Right cluster
right_cov = self.cov.iloc[clusters[j], clusters[j]]
right_returns = self.returns.iloc[:, clusters[j]]
right_weight = self._naive_risk(
right_returns, right_cov, rm=rm, rf=rf
)
if rm == "vol":
right_risk_ = rk.Sharpe_Risk(
right_weight,
cov=right_cov,
returns=right_returns,
rm="MV",
rf=rf,
alpha=self.alpha,
a_sim=self.a_sim,
beta=self.beta,
b_sim=self.b_sim,
)
else:
right_risk_ = rk.Sharpe_Risk(
right_weight,
cov=right_cov,
returns=right_returns,
rm=rm,
rf=rf,
alpha=self.alpha,
a_sim=self.a_sim,
beta=self.beta,
b_sim=self.b_sim,
)
if rm == "MV":
right_risk_ = np.power(right_risk_, 2)
right_risk += right_risk_
alpha_1 = 1 - left_risk / (left_risk + right_risk)
weight[left] *= alpha_1 # weight 1
weight[right] *= 1 - alpha_1 # weight 2
# Get constituents of k clusters
clustered_assets = pd.Series(
hr.cut_tree(Z, n_clusters=self.k).flatten(), index=self.cov.index
)
# Multiply within-cluster weight with inter-cluster weight
for i in range(self.k):
cluster = clustered_assets.loc[clustered_assets == i]
cluster_cov = self.cov.loc[cluster.index, cluster.index]
cluster_returns = self.returns.loc[:, cluster.index]
if model == "HERC":
cluster_weights = pd.Series(
self._naive_risk(
cluster_returns, cluster_cov, rm=rm, rf=rf
).flatten(),
index=cluster_cov.index,
)
elif model == "HERC2":
cluster_weights = pd.Series(
self._naive_risk(
cluster_returns, cluster_cov, rm="equal", rf=rf
).flatten(),
index=cluster_cov.index,
)
weight.loc[cluster_weights.index] *= cluster_weights
return weight
# compute intra-cluster weights
def _intra_weights(self, Z, obj="MinRisk", rm="MV", rf=0, l=2):
# Get constituents of k clusters
clustered_assets = pd.Series(
hr.cut_tree(Z, n_clusters=self.k).flatten(), index=self.cov.index
)
# get covariance matrices for each cluster
intra_weights = pd.DataFrame(index=clustered_assets.index)
for i in range(self.k):
cluster = clustered_assets.loc[clustered_assets == i]
if self.mu is not None:
cluster_mu = self.mu.loc[:, cluster.index]
else:
cluster_mu = None
cluster_cov = self.cov.loc[cluster.index, cluster.index]
cluster_returns = self.returns.loc[:, cluster.index]
weights = pd.Series(
self._opt_w(
cluster_returns, cluster_mu, cluster_cov, obj=obj, rm=rm, rf=rf, l=l
).flatten(),
index=cluster_cov.index,
)
intra_weights[i] = weights
intra_weights = intra_weights.fillna(0)
return intra_weights
def _inter_weights(self, intra_weights, obj="MinRisk", rm="MV", rf=0, l=2):
# inter-cluster mean vector
if self.mu is not None:
tot_mu = self.mu @ intra_weights
else:
tot_mu = None
# inter-cluster covariance matrix
tot_cov = intra_weights.T.dot(np.dot(self.cov, intra_weights))
# inter-cluster returns matrix
tot_ret = self.returns @ intra_weights
# inter-cluster weights
inter_weights = pd.Series(
self._opt_w(tot_ret, tot_mu, tot_cov, obj=obj, rm=rm, rf=rf, l=l).flatten(),
index=intra_weights.columns,
)
# determine the weight on each cluster by multiplying the intra-cluster weight with the inter-cluster weight
weights = intra_weights.mul(inter_weights, axis=1).sum(axis=1).sort_index()
return weights
# Allocate weights
def optimization(
self,
model="HRP",
codependence="pearson",
covariance="hist",
obj="MinRisk",
rm="MV",
rf=0,
l=2,
custom_cov=None,
custom_mu=None,
linkage="single",
k=None,
max_k=10,
bins_info="KN",
alpha_tail=0.05,
leaf_order=True,
d=0.94,
**kwargs,
):
r"""
This method calculates the optimal portfolio according to the
optimization model selected by the user.
Parameters
----------
model : str, can be {'HRP', 'HERC' or 'HERC2'}
The hierarchical cluster portfolio model used for optimize the
portfolio. The default is 'HRP'. Posible values are:
- 'HRP': Hierarchical Risk Parity.
- 'HERC': Hierarchical Equal Risk Contribution.
- 'HERC2': HERC but splitting weights equally within clusters.
- 'NCO': Nested Clustered Optimization.
codependence : str, optional
The codependence or similarity matrix used to build the distance
metric and clusters. The default is 'pearson'. Posible values are:
- 'pearson': pearson correlation matrix. Distance formula: :math:`D_{i,j} = \sqrt{0.5(1-\rho^{pearson}_{i,j})}`.
- 'spearman': spearman correlation matrix. Distance formula: :math:`D_{i,j} = \sqrt{0.5(1-\rho^{spearman}_{i,j})}`.
- 'abs_pearson': absolute value pearson correlation matrix. Distance formula: :math:`D_{i,j} = \sqrt{(1-|\rho^{pearson}_{i,j}|)}`.
- 'abs_spearman': absolute value spearman correlation matrix. Distance formula: :math:`D_{i,j} = \sqrt{(1-|\rho^{spearman}_{i,j}|)}`.
- 'distance': distance correlation matrix. Distance formula :math:`D_{i,j} = \sqrt{(1-\rho^{distance}_{i,j})}`.
- 'mutual_info': mutual information matrix. Distance used is variation information matrix.
- 'tail': lower tail dependence index matrix. Dissimilarity formula :math:`D_{i,j} = -\log{\lambda_{i,j}}`.
- 'custom_cov': use custom correlation matrix based on the custom_cov parameter. Distance formula: :math:`D_{i,j} = \sqrt{0.5(1-\rho^{pearson}_{i,j})}`.
covariance : str, optional
The method used to estimate the covariance matrix:
The default is 'hist'. Posible values are:
- 'hist': use historical estimates.
- 'ewma1': use ewma with adjust=True. For more information see `EWM <https://pandas.pydata.org/pandas-docs/stable/user_guide/window.html#exponentially-weighted-window>`_.
- 'ewma2': use ewma with adjust=False. For more information see `EWM <https://pandas.pydata.org/pandas-docs/stable/user_guide/window.html#exponentially-weighted-window>`_.
- 'ledoit': use the Ledoit and Wolf Shrinkage method.
- 'oas': use the Oracle Approximation Shrinkage method.
- 'shrunk': use the basic Shrunk Covariance method.
- 'gl': use the basic Graphical Lasso Covariance method.
- 'jlogo': use the j-LoGo Covariance method. For more information see: :cite:`c-jLogo`.
- 'fixed': denoise using fixed method. For more information see chapter 2 of :cite:`c-MLforAM`.
- 'spectral': denoise using spectral method. For more information see chapter 2 of :cite:`c-MLforAM`.
- 'shrink': denoise using shrink method. For more information see chapter 2 of :cite:`c-MLforAM`.
- 'custom_cov': use custom covariance matrix.
obj : str can be {'MinRisk', 'Utility', 'Sharpe' or 'ERC'}.
Objective function used by the NCO model.
The default is 'MinRisk'. Posible values are:
- 'MinRisk': Minimize the selected risk measure.
- 'Utility': Maximize the Utility function :math:`\mu w - l \phi_{i}(w)`.
- 'Sharpe': Maximize the risk adjusted return ratio based on the selected risk measure.
- 'ERC': Equally risk contribution portfolio of the selected risk measure.
rm : str, optional
The risk measure used to optimze the portfolio. If model is 'NCO',
the risk measures available depends on the objective functon.
The default is 'MV'. Posible values are:
- 'equal': Equally weighted.
- 'vol': Standard Deviation.
- 'MV': Variance.
- 'MAD': Mean Absolute Deviation.
- 'MSV': Semi Standard Deviation.
- 'FLPM': First Lower Partial Moment (Omega Ratio).
- 'SLPM': Second Lower Partial Moment (Sortino Ratio).
- 'VaR': Value at Risk.
- 'CVaR': Conditional Value at Risk.
- 'TG': Tail Gini.
- 'EVaR': Entropic Value at Risk.
- 'WR': Worst Realization (Minimax).
- 'RG': Range of returns.
- 'CVRG': CVaR range of returns.
- 'TGRG': Tail Gini range of returns.
- 'MDD': Maximum Drawdown of uncompounded cumulative returns (Calmar Ratio).
- 'ADD': Average Drawdown of uncompounded cumulative returns.
- 'DaR': Drawdown at Risk of uncompounded cumulative returns.
- 'CDaR': Conditional Drawdown at Risk of uncompounded cumulative returns.
- 'EDaR': Entropic Drawdown at Risk of uncompounded cumulative returns.
- 'UCI': Ulcer Index of uncompounded cumulative returns.
- 'MDD_Rel': Maximum Drawdown of compounded cumulative returns (Calmar Ratio).
- 'ADD_Rel': Average Drawdown of compounded cumulative returns.
- 'DaR_Rel': Drawdown at Risk of compounded cumulative returns.
- 'CDaR_Rel': Conditional Drawdown at Risk of compounded cumulative returns.
- 'EDaR_Rel': Entropic Drawdown at Risk of compounded cumulative returns.
- 'UCI_Rel': Ulcer Index of compounded cumulative returns.
rf : float, optional
Risk free rate, must be in the same period of assets returns.
The default is 0.
l : scalar, optional
Risk aversion factor of the 'Utility' objective function.
The default is 2.
custom_cov : DataFrame or None, optional
Custom covariance matrix, used when codependence or covariance
parameters have value 'custom_cov'. The default is None.
custom_mu : DataFrame or None, optional
Custom mean vector when NCO objective is 'Utility' or 'Sharpe'.
The default is None.
linkage : string, optional
Linkage method of hierarchical clustering. For more information see `linkage <https://docs.scipy.org/doc/scipy/reference/generated/scipy.cluster.hierarchy.linkage.html>`_.
The default is 'single'. Posible values are:
- 'single'.
- 'complete'.
- 'average'.
- 'weighted'.
- 'centroid'.
- 'median'.
- 'ward'.
- 'DBHT': Direct Bubble Hierarchical Tree.
k : int, optional
Number of clusters. This value is took instead of the optimal number
of clusters calculated with the two difference gap statistic.
The default is None.
max_k : int, optional
Max number of clusters used by the two difference gap statistic
to find the optimal number of clusters. The default is 10.
bins_info: int or str
Number of bins used to calculate variation of information. The default
value is 'KN'. Posible values are:
- 'KN': Knuth's choice method. See more in `knuth_bin_width <https://docs.astropy.org/en/stable/api/astropy.stats.knuth_bin_width.html>`_.
- 'FD': Freedman–Diaconis' choice method. See more in `freedman_bin_width <https://docs.astropy.org/en/stable/api/astropy.stats.freedman_bin_width.html>`_.
- 'SC': Scotts' choice method. See more in `scott_bin_width <https://docs.astropy.org/en/stable/api/astropy.stats.scott_bin_width.html>`_.
- 'HGR': Hacine-Gharbi and Ravier' choice method.
- int: integer value choice by user.
alpha_tail : float, optional
Significance level for lower tail dependence index. The default is 0.05.
leaf_order : bool, optional
Indicates if the cluster are ordered so that the distance between
successive leaves is minimal. The default is True.
d : scalar
The smoothing factor of ewma methods.
The default is 0.94.
**kwargs:
Other variables related to covariance estimation. See
`Scikit Learn <https://scikit-learn.org/stable/modules/covariance.html>`_
and chapter 2 of :cite:`d-MLforAM` for more details.
Returns
-------
w : DataFrame
The weights of optimal portfolio.
"""
# Covariance matrix
if covariance == "custom_cov":
self.cov = custom_cov.copy()
else:
self.cov = pe.covar_matrix(
self.returns, method=covariance, d=0.94, **kwargs
)
# Custom mean vector
if custom_mu is not None:
if isinstance(custom_mu, pd.Series) == True:
self.mu = custom_mu.to_frame().T
elif isinstance(custom_mu, pd.DataFrame) == True:
if custom_mu.shape[0] > 1 and custom_mu.shape[1] == 1:
self.mu = custom_mu.T
elif custom_mu.shape[0] == 1 and custom_mu.shape[1] > 1:
self.mu = custom_mu
else:
raise NameError("custom_mu must be a column DataFrame")
else:
raise NameError("custom_mu must be a column DataFrame or Series")
self.alpha_tail = alpha_tail
self.bins_info = bins_info
# Codependence matrix
if codependence in {"pearson", "spearman"}:
self.codep = self.returns.corr(method=codependence).astype(float)
elif codependence in {"abs_pearson", "abs_spearman"}:
self.codep = np.abs(self.returns.corr(method=codependence[4:])).astype(
float
)
elif codependence in {"distance"}:
self.codep = af.dcorr_matrix(self.returns).astype(float)
elif codependence in {"mutual_info"}:
self.codep = af.mutual_info_matrix(self.returns, self.bins_info).astype(
float
)
elif codependence in {"tail"}:
self.codep = af.ltdi_matrix(self.returns, alpha=self.alpha_tail).astype(
float
)
elif codependence in {"custom_cov"}:
self.codep = af.cov2corr(custom_cov).astype(float)
# Step-1: Tree clustering
self.clusters, self.k = self._hierarchical_clustering(
model, linkage, codependence, max_k, leaf_order=leaf_order
)
if k is not None:
self.k = int(k)
# Step-2: Seriation (Quasi-Diagnalization)
self.sort_order = self._seriation(self.clusters)
asset_order = self.assetslist
asset_order[:] = [self.assetslist[i] for i in self.sort_order]
self.asset_order = asset_order.copy()
self.codep_sorted = self.codep.reindex(
index=self.asset_order, columns=self.asset_order
)
if isinstance(self.w_max, pd.Series) and isinstance(self.w_min, pd.Series):
self.w_max = self.w_max.reindex(index=self.asset_order)
self.w_max.index = self.sort_order
self.w_min = self.w_min.reindex(index=self.asset_order)
self.w_min.index = self.sort_order
# Step-3: Recursive bisection
if model == "HRP":
# Recursive bisection
weights = self._recursive_bisection(self.sort_order, rm=rm, rf=rf)
elif model in ["HERC", "HERC2"]:
# Cluster-based Recursive bisection
weights = self._hierarchical_recursive_bisection(
self.clusters, rm=rm, rf=rf, linkage=linkage, model=model
)
elif model == "NCO":
# Step-3.1: Determine intra-cluster weights
intra_weights = self._intra_weights(
self.clusters, obj=obj, rm=rm, rf=rf, l=l
)
# Step-3.2: Determine inter-cluster weights and multiply with 􏰁→ intra-cluster weights
weights = self._inter_weights(intra_weights, obj=obj, rm=rm, rf=rf, l=l)
if isinstance(self.w_max, pd.Series) and isinstance(self.w_min, pd.Series):
self.w_max = self.w_max.sort_index()
self.w_max.index = self.assetslist
self.w_min = self.w_min.sort_index()
self.w_max.index = self.assetslist
weights = weights.loc[self.assetslist].to_frame()
weights.columns = ["weights"]
return weights

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@@ -0,0 +1,257 @@
"""""" #
"""
Copyright (c) 2020-2022, Dany Cajas
All rights reserved.
This work is licensed under BSD 3-Clause "New" or "Revised" License.
License available at https://github.com/dcajasn/Riskfolio-Lib/blob/master/LICENSE.txt
"""
import numpy as np
def owa_gmd(T):
r"""
Calculate the OWA weights to calculate the Gini mean difference (GMD)
of a returns series.
Parameters
----------
T : int
Number of observations of the returns series.
Returns
-------
value : 1d-array
An OWA weights vector of size Tx1.
"""
w_ = []
for i in range(1, T + 1):
w_.append(2 * i - 1 - T)
w_ = 2 * np.array(w_) / (T * (T - 1))
w_ = w_.reshape(-1, 1)
return w_
def owa_cvar(T, alpha=0.05):
r"""
Calculate the OWA weights to calculate the Conditional Value at Risk (CVaR)
of a returns series.
Parameters
----------
T : int
Number of observations of the returns series.
alpha : float, optional
Significance level of CVaR. The default is 0.05.
Returns
-------
value : 1d-array
An OWA weights vector of size Tx1.
"""
k = int(np.ceil(T * alpha)) - 1
w_ = np.zeros((T, 1))
w_[:k, :] = -1 / (T * alpha)
w_[k, :] = -1 - np.sum(w_[:k, :])
return w_
def owa_wcvar(T, alphas, weights):
r"""
Calculate the OWA weights to calculate the Weighted Conditional Value at
Risk (WCVaR) of a returns series.
Parameters
----------
T : int
Number of observations of the returns series.
alphas : list
List of significance levels of each CVaR model.
weights : list
List of weights of each CVaR model.
Returns
-------
value : 1d-array
An OWA weights vector of size Tx1.
"""
w_ = 0
for i, j in zip(alphas, weights):
w_ += owa_cvar(T, i) * j
return w_
def owa_tg(T, alpha=0.05, a_sim=100):
r"""
Calculate the OWA weights to calculate the Tail Gini of a returns series.
Parameters
----------
T : int
Number of observations of the returns series.
alpha : float, optional
Significance level of TaiL Gini. The default is 0.05.
a_sim : float, optional
Number of CVaRs used to approximate the Tail Gini. The default is 100.
Returns
-------
value : 1d-array
A OWA weights vector of size Tx1.
"""
alphas = np.linspace(alpha, 0.0001, a_sim)[::-1]
w_ = [(alphas[1] - 0) * alphas[0] / alphas[-1] ** 2]
for i in range(1, len(alphas) - 1):
w_.append((alphas[i + 1] - alphas[i - 1]) * alphas[i] / alphas[-1] ** 2)
w_.append((alphas[-1] - alphas[-2]) / alphas[-1])
w_ = owa_wcvar(T, alphas, w_)
return w_
def owa_wr(T):
r"""
Calculate the OWA weights to calculate the Worst realization (minimum) of a returns series.
Parameters
----------
T : int
Number of observations of the returns series.
Returns
-------
value : 1d-array
A OWA weights vector of size Tx1.
"""
w_ = np.zeros((T, 1))
w_[0, :] = -1
return w_
def owa_rg(T):
r"""
Calculate the OWA weights to calculate the range of a returns series.
Parameters
----------
T : int
Number of observations of the returns series.
Returns
-------
value : 1d-array
A OWA weights vector of size Tx1.
"""
w_ = np.zeros((T, 1))
w_[0, :] = -1
w_[-1, :] = 1
return w_
def owa_cvrg(T, alpha=0.05, beta=None):
r"""
Calculate the OWA weights to calculate the CVaR range of a returns series.
Parameters
----------
T : int
Number of observations of the returns series.
alpha : float, optional
Significance level of CVaR of losses. The default is 0.05.
beta : float, optional
Significance level of CVaR of gains. If None it duplicates alpha.
The default is None.
Returns
-------
value : 1d-array
A OWA weights vector of size Tx1.
"""
if beta is None:
beta = alpha
w_ = owa_cvar(T, alpha) - owa_cvar(T, beta)[::-1]
return w_
def owa_wcvrg(T, alphas, weights_a, betas=None, weights_b=None):
r"""
Calculate the OWA weights to calculate the WCVaR range of a returns series.
Parameters
----------
T : int
Number of observations of the returns series.
alphas : list
List of significance levels of each CVaR of losses model.
weights_a : list
List of weights of each CVaR of losses model.
betas : list, optional
List of significance levels of each CVaR of gains model. If None it duplicates alpha.
The default is None.
weights_b : list, optional
List of weights of each CVaR of gains model. If None it duplicates weights_a.
The default is None.
Returns
-------
value : 1d-array
A OWA weights vector of size Tx1.
"""
if betas is None or weights_b is None:
betas = alphas
weights_b = weights_a
w_ = owa_wcvar(T, alphas, weights_a) - owa_wcvar(T, betas, weights_b)[::-1]
return w_
def owa_tgrg(T, alpha=0.05, a_sim=100, beta=None, b_sim=None):
r"""
Calculate the OWA weights to calculate the Tail Gini range of a returns
series.
Parameters
----------
T : int
Number of observations of the returns series.
alpha : float, optional
Significance level of Tail Gini of losses. The default is 0.05.
a_sim : float, optional
Number of CVaRs used to approximate Tail Gini of losses. The default is 100.
beta : float, optional
Significance level of Tail Gini of gains. If None it duplicates alpha value.
The default is None.
b_sim : float, optional
Number of CVaRs used to approximate Tail Gini of gains. If None it duplicates a_sim value.
The default is None.
Returns
-------
value : 1d-array
A OWA weights vector of size Tx1.
"""
if beta is None:
beta = alpha
if b_sim is None:
b_sim = a_sim
w_ = owa_tg(T, alpha, a_sim) - owa_tg(T, beta, b_sim)[::-1]
return w_

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requirements-full.txt vendored
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@@ -238,7 +238,6 @@ reportlab==3.6.9; python_version >= "3.7" and python_version < "4"
requests-oauthlib==1.3.1; python_version >= "3.6" and python_full_version < "3.0.0" or python_full_version >= "3.4.0" and python_version >= "3.6"
requests==2.27.1; (python_version >= "2.7" and python_full_version < "3.0.0") or (python_full_version >= "3.6.0")
rich==10.16.2; python_full_version >= "3.6.2" and python_full_version < "4.0.0"
riskfolio-lib==3.0.2; python_full_version >= "3.7"
robin-stocks==2.1.0; python_version >= "3"
rsa==4.8; python_version >= "3.6" and python_version < "4" and (python_version >= "3.6" and python_full_version < "3.0.0" or python_full_version >= "3.6.0" and python_version >= "3.6")
scikit-learn==1.0.2; python_version >= "3.7" and python_full_version < "3.0.0" or python_full_version >= "3.6.0" and python_version >= "3.7"

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@@ -190,7 +190,6 @@ reportlab==3.6.9; python_version >= "3.7" and python_version < "4"
requests-oauthlib==1.3.1; python_version >= "2.7" and python_full_version < "3.0.0" or python_full_version >= "3.4.0"
requests==2.27.1; (python_version >= "2.7" and python_full_version < "3.0.0") or (python_full_version >= "3.6.0")
rich==10.16.2; python_full_version >= "3.6.2" and python_full_version < "4.0.0"
riskfolio-lib==3.0.2; python_full_version >= "3.7"
robin-stocks==2.1.0; python_version >= "3"
scikit-learn==1.0.2; python_version >= "3.7" and python_full_version < "3.0.0" or python_full_version >= "3.6.0" and python_version >= "3.7"
scipy==1.8.0; python_version >= "3.8" and python_version < "3.11" and python_full_version >= "3.7.1" and python_full_version < "4.0.0" and (python_version >= "2.7" and python_full_version < "3.0.0" or python_full_version >= "3.6.0") and (python_version >= "3.7" and python_full_version < "3.0.0" or python_full_version >= "3.6.0" and python_version >= "3.7")