def benchmark_build_linear(n_samples: int, n_risks: int, n_loop: int) -> None:
print("-" * 60)
print("Starting portfolio construction by linear programming")
print("Parameters(n_samples: {0}, n_risks: {1}, n_loop: {2})".format(
n_samples, n_risks, n_loop))
er = np.random.randn(n_samples)
risk_exp = np.random.randn(n_samples, n_risks)
bm = np.random.rand(n_samples)
bm /= bm.sum()
lbound = -0.04
ubound = 0.05
risk_lbound = bm @ risk_exp
risk_ubound = bm @ risk_exp
start = dt.datetime.now()
for _ in range(n_loop):
status, v, x = linear_builder(er,
lbound,
ubound,
risk_exp,
risk_target=(risk_lbound, risk_ubound))
impl_model_time = dt.datetime.now() - start
print('{0:20s}: {1}'.format('Implemented model (ECOS)', impl_model_time))
c = -er
bounds = [(lbound, ubound) for _ in range(n_samples)]
a_eq = np.ones((1, n_samples))
a_eq = np.vstack((a_eq, risk_exp.T))
b_eq = np.hstack((np.array([1.]), risk_exp.T @ bm))
start = dt.datetime.now()
for _ in range(n_loop):
res = linprog(c,
A_eq=a_eq,
b_eq=b_eq,
bounds=bounds,
options={'maxiter': 10000})
benchmark_model_time = dt.datetime.now() - start
print('{0:20s}: {1}'.format('Benchmark model (scipy)',
benchmark_model_time))
np.testing.assert_array_almost_equal(x, res['x'])
c = matrix(-er)
aneq = matrix(a_eq)
b = matrix(b_eq)
g = matrix(
np.vstack((np.diag(np.ones(n_samples)), -np.diag(np.ones(n_samples)))))
h = matrix(
np.hstack((ubound * np.ones(n_samples), -lbound * np.ones(n_samples))))
solvers.lp(c, g, h, solver='glpk')
start = dt.datetime.now()
for _ in range(n_loop):
res2 = solvers.lp(c, g, h, aneq, b, solver='glpk')
benchmark_model_time = dt.datetime.now() - start
print('{0:20s}: {1}'.format('Benchmark model (glpk)',
benchmark_model_time))
np.testing.assert_array_almost_equal(x, np.array(res2['x']).flatten())
def test_linear_build_with_to_constraint(self):
bm = self.bm / self.bm.sum()
eplson = 1e-6
turn_over_target = 0.1
risk_lbound = bm @ self.risk_exp
risk_ubound = bm @ self.risk_exp
risk_tolerance = 0.01 * np.abs(risk_lbound[:-1])
risk_lbound[:-1] = risk_lbound[:-1] - risk_tolerance
risk_ubound[:-1] = risk_ubound[:-1] + risk_tolerance
status, _, w = linear_builder(self.er,
0.,
0.01,
self.risk_exp,
risk_target=(risk_lbound, risk_ubound),
turn_over_target=turn_over_target,
current_position=self.current_pos)
self.assertEqual(status, 'optimal')
self.assertAlmostEqual(np.sum(w), 1.)
self.assertTrue(np.all(w <= 0.01 + eplson))
self.assertTrue(np.all(w >= -eplson))
self.assertAlmostEqual(
np.abs(w - self.current_pos).sum(), turn_over_target)
calc_risk = (w - bm) @ self.risk_exp / np.abs(bm @ self.risk_exp)
self.assertTrue(np.all(np.abs(calc_risk) <= 1.0001e-2))
def test_linear_build(self):
bm = self.bm / self.bm.sum()
eplson = 1e-6
status, _, w = linear_builder(self.er, 0., 0.01, self.risk_exp,
(bm @ self.risk_exp, bm @ self.risk_exp))
self.assertEqual(status, 'optimal')
self.assertAlmostEqual(np.sum(w), 1.)
self.assertTrue(np.all(w <= 0.01 + eplson))
self.assertTrue(np.all(w >= -eplson))
calc_risk = (w - bm) @ self.risk_exp
expected_risk = np.zeros(self.risk_exp.shape[1])
np.testing.assert_array_almost_equal(calc_risk, expected_risk)
def test_linear_build_with_inequality_constraints(self):
bm = self.bm / self.bm.sum()
eplson = 1e-6
risk_lbound = bm @ self.risk_exp
risk_ubound = bm @ self.risk_exp
risk_tolerance = 0.01 * np.abs(risk_lbound[:-1])
risk_lbound[:-1] = risk_lbound[:-1] - risk_tolerance
risk_ubound[:-1] = risk_ubound[:-1] + risk_tolerance
status, _, w = linear_builder(self.er,
0.,
0.01,
self.risk_exp,
risk_target=(risk_lbound, risk_ubound))
self.assertEqual(status, 'optimal')
self.assertAlmostEqual(np.sum(w), 1.)
self.assertTrue(np.all(w <= 0.01 + eplson))
self.assertTrue(np.all(w >= -eplson))
calc_risk = (w - bm) @ self.risk_exp / np.abs(bm @ self.risk_exp)
self.assertTrue(np.all(np.abs(calc_risk) <= 1.01e-2))
def er_portfolio_analysis(
er: np.ndarray,
industry: np.ndarray,
dx_return: np.ndarray,
constraints: Optional[Union[LinearConstraints, Constraints]] = None,
detail_analysis=True,
benchmark: Optional[np.ndarray] = None,
is_tradable: Optional[np.ndarray] = None,
method='risk_neutral',
**kwargs) -> Tuple[pd.DataFrame, Optional[pd.DataFrame]]:
er = er.flatten()
def create_constraints(benchmark, **kwargs):
if 'lbound' in kwargs:
lbound = kwargs['lbound'].copy()
del kwargs['lbound']
else:
lbound = np.maximum(0., benchmark - 0.01)
if 'ubound' in kwargs:
ubound = kwargs['ubound'].copy()
del kwargs['ubound']
else:
ubound = 0.01 + benchmark
if is_tradable is not None:
ubound[~is_tradable] = np.minimum(lbound, ubound)[~is_tradable]
risk_lbound, risk_ubound = constraints.risk_targets()
cons_exp = constraints.risk_exp
return lbound, ubound, cons_exp, risk_lbound, risk_ubound
if method == 'risk_neutral':
lbound, ubound, cons_exp, risk_lbound, risk_ubound = create_constraints(
benchmark, **kwargs)
turn_over_target = kwargs.get('turn_over_target')
current_position = kwargs.get('current_position')
status, _, weights = linear_builder(er,
risk_constraints=cons_exp,
lbound=lbound,
ubound=ubound,
risk_target=(risk_lbound,
risk_ubound),
turn_over_target=turn_over_target,
current_position=current_position)
if status != 'optimal':
raise ValueError(
'linear programming optimizer in status: {0}'.format(status))
elif method == 'rank':
weights = rank_build(
er, use_rank=kwargs['use_rank'],
masks=is_tradable).flatten() * benchmark.sum() / kwargs['use_rank']
elif method == 'ls' or method == 'long_short':
weights = long_short_builder(er).flatten()
elif method == 'mv' or method == 'mean_variance':
lbound, ubound, cons_exp, risk_lbound, risk_ubound = create_constraints(
benchmark, **kwargs)
cov = kwargs['cov']
if 'lam' in kwargs:
lam = kwargs['lam']
else:
lam = 1.
status, _, weights = mean_variance_builder(er,
cov=cov,
bm=benchmark,
lbound=lbound,
ubound=ubound,
risk_exposure=cons_exp,
risk_target=(risk_lbound,
risk_ubound),
lam=lam)
if status != 'optimal':
raise ValueError(
'mean variance optimizer in status: {0}'.format(status))
elif method == 'tv' or method == 'target_vol':
lbound, ubound, cons_exp, risk_lbound, risk_ubound = create_constraints(
benchmark, **kwargs)
cov = kwargs['cov']
if 'target_vol' in kwargs:
target_vol = kwargs['target_vol']
else:
target_vol = 1.
status, _, weights = target_vol_builder(er,
cov=cov,
bm=benchmark,
lbound=lbound,
ubound=ubound,
risk_exposure=cons_exp,
risk_target=(risk_lbound,
risk_ubound),
vol_low=0,
vol_high=target_vol)
else:
raise ValueError("Unknown building type ({0})".format(method))
if detail_analysis:
analysis = simple_settle(weights, dx_return, industry, benchmark)
else:
analysis = None
return pd.DataFrame({'weight': weights,
'industry': industry,
'er': er}), \
analysis
