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sector constraints #10

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robertmartin8
2020-04-28 16:02:11 +08:00
parent fa0cadfb68
commit 2bda7e5dd9
5 changed files with 389 additions and 27 deletions
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26
docs/EfficientFrontier.rst
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@@ -97,11 +97,26 @@ Basic Usage
risk-aversion parameter, which gives a useful estimate in the absence of other
information!
.. caution::
.. automethod:: efficient_risk
If you pass an unreasonable target into :py:meth:`efficient_risk` or
:py:meth:`efficient_return`, the optimiser will fail silently and return
weird weights. *Caveat emptor* applies!
.. caution::
If you pass an unreasonable target into :py:meth:`efficient_risk` or
:py:meth:`efficient_return`, the optimiser will fail silently and return
weird weights. *Caveat emptor* applies!
.. automethod:: portfolio_performance
.. tip::
If you would like to use the ``portfolio_performance`` function independently of any
optimiser (e.g for debugging purposes), you can use::
from pypfopt import base_optimizer
base_optimizer.portfolio_performance(
weights, expected_returns, cov_matrix, verbose=True, risk_free_rate=0.02
)
Adding objectives and constraints
=================================
@@ -114,6 +129,8 @@ add constraints and objectives are documented below:
.. automethod:: add_constraint
.. automethod:: add_sector_constraints
.. automethod:: add_objective
@@ -164,6 +181,7 @@ used to make them larger).
universes, or if you want more non-negligible weights in the final portfolio,
increase ``gamma``.
.. _custom-optimisation:
Custom optimisation problems

43
pypfopt/base_optimizer.py
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@@ -8,6 +8,7 @@ evaluate return and risk for a given set of portfolio weights.
"""
import json
import warnings
import numpy as np
import pandas as pd
import cvxpy as cp
@@ -138,7 +139,6 @@ class BaseConvexOptimizer(BaseOptimizer):
self._w = cp.Variable(n_assets)
self._objective = None
self._additional_objectives = []
self._additional_constraints_raw = []
self._constraints = []
self._lower_bounds = None
self._upper_bounds = None
@@ -233,12 +233,45 @@ class BaseConvexOptimizer(BaseOptimizer):
"""
if not callable(new_constraint):
raise TypeError("New constraint must be provided as a lambda function")
# Save raw constraint (needed for e.g max_sharpe)
self._additional_constraints_raw.append(new_constraint)
# Add constraint
self._constraints.append(new_constraint(self._w))
def add_sector_constraints(self, sector_mapper, sector_lower, sector_upper):
"""
Add sector constraints, e.g portfolio's exposure to tech must be less than x%::
sector_mapper = {
"GOOG": "tech",
"FB": "tech",,
"XOM": "Oil/Gas",
"RRC": "Oil/Gas",
"MA": "Financials",
"JPM": "Financials",
}
sector_lower = {"tech": 0.1} # at least 10% to tech
sector_upper = {
"tech": 0.4, # less than 40% tech
"Oil/Gas: 0.1 # less than 10% oil and gas
}
:param sector_mapper: dict that maps tickers to sectors
:type sector_mapper: {str: str} dict
:param sector_lower: lower bounds for each sector
:type sector_lower: {str: float} dict
:param sector_upper: upper bounds for each sector
:type sector_upper: {str:float} dict
"""
if np.any(self._lower_bounds < 0):
warnings.warn(
"Sector constraints may not produce reasonable results if shorts are allowed."
)
for sector in sector_upper:
is_sector = [v == sector for k, v in sector_mapper.items()]
self._constraints.append(cp.sum(self._w[is_sector]) <= sector_upper[sector])
for sector in sector_lower:
is_sector = [v == sector for k, v in sector_mapper.items()]
self._constraints.append(cp.sum(self._w[is_sector]) >= sector_lower[sector])
def convex_objective(self, custom_objective, weights_sum_to_one=True, **kwargs):
"""
Optimise a custom convex objective function. Constraints should be added with

32
pypfopt/efficient_frontier.py
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@@ -185,22 +185,30 @@ class EfficientFrontier(base_optimizer.BaseConvexOptimizer):
for obj in self._additional_objectives:
self._objective += obj
# Overwrite original constraints with suitable constraints
# for the transformed max_sharpe problem
new_constraints = []
# Must rebuild the constraints
for constr in self._constraints:
if isinstance(constr, cp.constraints.nonpos.Inequality):
# Either the first or second item is the expression
if isinstance(
constr.args[0], cp.expressions.constants.constant.Constant
):
new_constraints.append(constr.args[1] >= constr.args[0] * k)
else:
new_constraints.append(constr.args[0] <= constr.args[1] * k)
elif isinstance(constr, cp.constraints.zero.Equality):
new_constraints.append(constr.args[0] == constr.args[1] * k)
else:
raise TypeError(
"Please check that your constraints are in a suitable format"
)
# Transformed max_sharpe convex problem:
self._constraints = [
(self.expected_returns - risk_free_rate).T * self._w == 1,
cp.sum(self._w) == k,
k >= 0,
]
#  Rebuild original constraints with scaling factor
for raw_constr in self._additional_constraints_raw:
self._constraints.append(raw_constr(self._w / k))
# Sharpe ratio is invariant w.r.t scaled weights, so we must
# replace infinities and negative infinities
# new_lower_bound = np.nan_to_num(self._lower_bounds, neginf=-1)
# new_upper_bound = np.nan_to_num(self._upper_bounds, posinf=1)
self._constraints.append(self._w >= k * self._lower_bounds)
self._constraints.append(self._w <= k * self._upper_bounds)
] + new_constraints
self._solve_cvxpy_opt_problem()
# Inverse-transform

14
tests/test_custom_objectives.py
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@@ -17,6 +17,20 @@ def test_custom_convex_equal_weights():
np.testing.assert_allclose(ef.weights, np.array([1 / 20] * 20))
def test_custom_convex_abs_exposure():
ef = EfficientFrontier(
*setup_efficient_frontier(data_only=True), weight_bounds=(None, None)
)
ef.add_constraint(lambda x: cp.norm(x, 1) <= 2)
ef.min_volatility()
ef.convex_objective(
objective_functions.portfolio_variance,
cov_matrix=ef.cov_matrix,
weights_sum_to_one=False,
)
def test_custom_convex_min_var():
ef = setup_efficient_frontier()
ef.min_volatility()

301
tests/test_efficient_frontier.py
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@@ -118,7 +118,7 @@ def test_min_volatility_short():
def test_min_volatility_L2_reg():
ef = setup_efficient_frontier()
ef.add_objective(objective_functions.L2_reg, gamma=5)
ef.add_objective(objective_functions.L2_reg, gamma=1)
weights = ef.min_volatility()
assert isinstance(weights, dict)
assert set(weights.keys()) == set(ef.tickers)
@@ -137,7 +137,7 @@ def test_min_volatility_L2_reg():
np.testing.assert_allclose(
ef.portfolio_performance(),
(0.2382083649754719, 0.20795460936504614, 1.049307662098637),
(0.23129890623344232, 0.1955254118258614, 1.080672349748733),
)
@@ -214,6 +214,57 @@ def test_min_volatility_cvxpy_vs_scipy():
assert cvxpy_var <= scipy_var
def test_min_volatility_sector_constraints():
sector_mapper = {
"GOOG": "tech",
"AAPL": "tech",
"FB": "tech",
"AMZN": "tech",
"BABA": "tech",
"GE": "utility",
"AMD": "tech",
"WMT": "retail",
"BAC": "fig",
"GM": "auto",
"T": "auto",
"UAA": "airline",
"SHLD": "retail",
"XOM": "energy",
"RRC": "energy",
"BBY": "retail",
"MA": "fig",
"PFE": "pharma",
"JPM": "fig",
"SBUX": "retail",
}
sector_upper = {
"tech": 0.2,
"utility": 0.1,
"retail": 0.2,
"fig": 0.4,
"airline": 0.05,
"energy": 0.2,
}
sector_lower = {"utility": 0.01, "fig": 0.02, "airline": 0.01}
# ef = setup_efficient_frontier()
ef = EfficientFrontier(
*setup_efficient_frontier(data_only=True), weight_bounds=(None, None)
)
ef.add_sector_constraints(sector_mapper, sector_lower, sector_upper)
weights = ef.min_volatility()
for sector in list(set().union(sector_upper, sector_lower)):
sector_sum = 0
for t, v in weights.items():
if sector_mapper[t] == sector:
sector_sum += v
assert sector_sum <= sector_upper.get(sector, 1) + 1e-5
assert sector_sum >= sector_lower.get(sector, 0) - 1e-5
def test_min_volatility_vs_max_sharpe():
# Test based on issue #75
expected_returns_daily = pd.Series(
@@ -287,6 +338,19 @@ def test_max_sharpe_long_weight_bounds():
assert (0.02 <= ef.weights[1::2]).all() and (ef.weights[1::2] <= 0.11).all()
def test_max_sharpe_explicit_bound():
ef = setup_efficient_frontier()
ef.add_constraint(lambda w: w[0] >= 0.2)
ef.add_constraint(lambda w: w[2] == 0.15)
ef.add_constraint(lambda w: w[3] + w[4] <= 0.10)
ef.max_sharpe()
np.testing.assert_almost_equal(ef.weights.sum(), 1)
assert ef.weights[0] >= 0.2 - 1e-5
np.testing.assert_almost_equal(ef.weights[2], 0.15)
assert ef.weights[3] + ef.weights[4] <= 0.10 + 1e-5
def test_max_sharpe_short():
ef = EfficientFrontier(
*setup_efficient_frontier(data_only=True), weight_bounds=(None, None)
@@ -337,13 +401,15 @@ def test_max_sharpe_L2_reg():
def test_max_sharpe_L2_reg_many_values():
warnings.filterwarnings("ignore")
ef = setup_efficient_frontier()
ef.max_sharpe()
# Count the number of weights more 1%
initial_number = sum(ef.weights > 0.01)
for _ in range(10):
print(initial_number)
ef.add_objective(objective_functions.L2_reg, gamma=0.05)
for i in range(1, 20, 2):
ef = setup_efficient_frontier()
ef.add_objective(objective_functions.L2_reg, gamma=0.05 * i)
ef.max_sharpe()
np.testing.assert_almost_equal(ef.weights.sum(), 1)
new_number = sum(ef.weights > 0.01)
@@ -406,15 +472,239 @@ def test_max_sharpe_risk_free_rate():
ef = setup_efficient_frontier()
ef.max_sharpe()
_, _, initial_sharpe = ef.portfolio_performance()
ef = setup_efficient_frontier()
ef.max_sharpe(risk_free_rate=0.10)
_, _, new_sharpe = ef.portfolio_performance(risk_free_rate=0.10)
assert new_sharpe <= initial_sharpe
ef = setup_efficient_frontier()
ef.max_sharpe(risk_free_rate=0)
_, _, new_sharpe = ef.portfolio_performance(risk_free_rate=0)
assert new_sharpe >= initial_sharpe
def test_min_vol_pair_constraint():
ef = setup_efficient_frontier()
ef.min_volatility()
old_sum = ef.weights[:2].sum()
ef = setup_efficient_frontier()
ef.add_constraint(lambda w: (w[1] + w[0] <= old_sum / 2))
ef.min_volatility()
new_sum = ef.weights[:2].sum()
assert new_sum <= old_sum / 2 + 1e-4
def test_max_sharpe_pair_constraint():
ef = setup_efficient_frontier()
ef.max_sharpe()
old_sum = ef.weights[:2].sum()
ef = setup_efficient_frontier()
ef.add_constraint(lambda w: (w[1] + w[0] <= old_sum / 2))
ef.max_sharpe()
new_sum = ef.weights[:2].sum()
assert new_sum <= old_sum / 2 + 1e-4
def test_max_sharpe_sector_constraints_manual():
sector_mapper = {
"GOOG": "tech",
"AAPL": "tech",
"FB": "tech",
"AMZN": "tech",
"BABA": "tech",
"GE": "utility",
"AMD": "tech",
"WMT": "retail",
"BAC": "fig",
"GM": "auto",
"T": "auto",
"UAA": "airline",
"SHLD": "retail",
"XOM": "energy",
"RRC": "energy",
"BBY": "retail",
"MA": "fig",
"PFE": "pharma",
"JPM": "fig",
"SBUX": "retail",
}
sector_upper = {
"tech": 0.2,
"utility": 0.1,
"retail": 0.2,
"fig": 0.4,
"airline": 0.05,
"energy": 0.2,
}
sector_lower = {"utility": 0.01, "fig": 0.02, "airline": 0.01}
ef = setup_efficient_frontier()
for sector in sector_upper:
is_sector = [v == sector for k, v in sector_mapper.items()]
ef.add_constraint(lambda w: cp.sum(w[is_sector]) <= sector_upper[sector])
for sector in sector_lower:
is_sector = [v == sector for k, v in sector_mapper.items()]
ef.add_constraint(lambda w: cp.sum(w[is_sector]) >= sector_lower[sector])
weights = ef.max_sharpe()
for sector in list(set().union(sector_upper, sector_lower)):
sector_sum = 0
for t, v in weights.items():
if sector_mapper[t] == sector:
sector_sum += v
assert sector_sum <= sector_upper.get(sector, 1) + 1e-5
assert sector_sum >= sector_lower.get(sector, 0) - 1e-5
def test_max_sharpe_sector_constraints_auto():
sector_mapper = {
"GOOG": "tech",
"AAPL": "tech",
"FB": "tech",
"AMZN": "tech",
"BABA": "tech",
"GE": "utility",
"AMD": "tech",
"WMT": "retail",
"BAC": "fig",
"GM": "auto",
"T": "auto",
"UAA": "airline",
"SHLD": "retail",
"XOM": "energy",
"RRC": "energy",
"BBY": "retail",
"MA": "fig",
"PFE": "pharma",
"JPM": "fig",
"SBUX": "retail",
}
sector_upper = {
"tech": 0.2,
"utility": 0.1,
"retail": 0.2,
"fig": 0.4,
"airline": 0.05,
"energy": 0.2,
}
sector_lower = {"utility": 0.01, "fig": 0.02, "airline": 0.01}
ef = setup_efficient_frontier()
ef.add_sector_constraints(sector_mapper, sector_lower, sector_upper)
weights = ef.max_sharpe()
for sector in list(set().union(sector_upper, sector_lower)):
sector_sum = 0
for t, v in weights.items():
if sector_mapper[t] == sector:
sector_sum += v
assert sector_sum <= sector_upper.get(sector, 1) + 1e-5
assert sector_sum >= sector_lower.get(sector, 0) - 1e-5
def test_efficient_risk_sector_constraints_manual():
sector_mapper = {
"GOOG": "tech",
"AAPL": "tech",
"FB": "tech",
"AMZN": "tech",
"BABA": "tech",
"GE": "utility",
"AMD": "tech",
"WMT": "retail",
"BAC": "fig",
"GM": "auto",
"T": "auto",
"UAA": "airline",
"SHLD": "retail",
"XOM": "energy",
"RRC": "energy",
"BBY": "retail",
"MA": "fig",
"PFE": "pharma",
"JPM": "fig",
"SBUX": "retail",
}
sector_upper = {
"tech": 0.2,
"utility": 0.1,
"retail": 0.2,
"fig": 0.4,
"airline": 0.05,
"energy": 0.2,
}
sector_lower = {"utility": 0.01, "fig": 0.02, "airline": 0.01}
ef = setup_efficient_frontier()
for sector in sector_upper:
is_sector = [v == sector for k, v in sector_mapper.items()]
ef.add_constraint(lambda w: cp.sum(w[is_sector]) <= sector_upper[sector])
for sector in sector_lower:
is_sector = [v == sector for k, v in sector_mapper.items()]
ef.add_constraint(lambda w: cp.sum(w[is_sector]) >= sector_lower[sector])
weights = ef.efficient_risk(0.19)
for sector in list(set().union(sector_upper, sector_lower)):
sector_sum = 0
for t, v in weights.items():
if sector_mapper[t] == sector:
sector_sum += v
assert sector_sum <= sector_upper.get(sector, 1) + 1e-5
assert sector_sum >= sector_lower.get(sector, 0) - 1e-5
def test_efficient_risk_sector_constraints_auto():
sector_mapper = {
"GOOG": "tech",
"AAPL": "tech",
"FB": "tech",
"AMZN": "tech",
"BABA": "tech",
"GE": "utility",
"AMD": "tech",
"WMT": "retail",
"BAC": "fig",
"GM": "auto",
"T": "auto",
"UAA": "airline",
"SHLD": "retail",
"XOM": "energy",
"RRC": "energy",
"BBY": "retail",
"MA": "fig",
"PFE": "pharma",
"JPM": "fig",
"SBUX": "retail",
}
sector_upper = {
"tech": 0.2,
"utility": 0.1,
"retail": 0.2,
"fig": 0.4,
"airline": 0.05,
"energy": 0.2,
}
sector_lower = {"utility": 0.01, "fig": 0.02, "airline": 0.01}
ef = setup_efficient_frontier()
ef.add_sector_constraints(sector_mapper, sector_lower, sector_upper)
weights = ef.efficient_risk(0.19)
for sector in list(set().union(sector_upper, sector_lower)):
sector_sum = 0
for t, v in weights.items():
if sector_mapper[t] == sector:
sector_sum += v
assert sector_sum <= sector_upper.get(sector, 1) + 1e-5
assert sector_sum >= sector_lower.get(sector, 0) - 1e-5
def test_max_quadratic_utility():
ef = setup_efficient_frontier()
w = ef.max_quadratic_utility(risk_aversion=2)
@@ -536,7 +826,6 @@ def test_efficient_risk_many_values():
ef.efficient_risk(target_risk)
np.testing.assert_almost_equal(ef.weights.sum(), 1)
volatility = ef.portfolio_performance()[1]
print(volatility)
assert abs(target_risk - volatility) < 1e-5