def test_lpoptimizer(self):
objective = np.array([1., 2.])
lower_bound = np.array([0., 0.2])
upper_bound = np.array([1., 0.8])
optimizer = LPOptimizer(np.array([[1., 1., 1., 1.]]), lower_bound,
upper_bound, objective)
self.assertAlmostEqual(optimizer.feval(), 1.2)
np.testing.assert_array_almost_equal(optimizer.x_value(), [0.8, 0.2])
def linear_builder(er: np.ndarray,
lbound: Union[np.ndarray, float],
ubound: Union[np.ndarray, float],
risk_constraints: np.ndarray,
risk_target: Tuple[np.ndarray, np.ndarray],
turn_over_target: float = None,
current_position: np.ndarray = None,
method: str = 'ecos') -> Tuple[str, np.ndarray, np.ndarray]:
er = er.flatten()
n, m = risk_constraints.shape
if not risk_target:
risk_lbound = -np.inf * np.ones((m, 1))
risk_ubound = np.inf * np.ones((m, 1))
else:
risk_lbound = risk_target[0].reshape((-1, 1))
risk_ubound = risk_target[1].reshape((-1, 1))
if isinstance(lbound, float):
lbound = np.ones(n) * lbound
if isinstance(ubound, float):
ubound = np.ones(n) * ubound
if not turn_over_target or current_position is None:
cons_matrix = np.concatenate(
(risk_constraints.T, risk_lbound, risk_ubound), axis=1)
prob = LPOptimizer(cons_matrix, lbound, ubound, -er, method)
if prob.status() == 0:
return 'optimal', prob.feval(), prob.x_value()
else:
raise PortfolioBuilderException(prob.status())
else:
if method in ("simplex", "interior"):
# we need to expand bounded condition and constraint matrix to handle L1 bound
w_u_bound = np.minimum(
np.maximum(np.abs(current_position - lbound),
np.abs(current_position - ubound)),
turn_over_target).reshape((-1, 1))
current_position = current_position.reshape((-1, 1))
lbound = np.concatenate((lbound, np.zeros(n)), axis=0)
ubound = np.concatenate((ubound, w_u_bound.flatten()), axis=0)
risk_lbound = np.concatenate((risk_lbound, [[0.]]), axis=0)
risk_ubound = np.concatenate((risk_ubound, [[turn_over_target]]),
axis=0)
risk_constraints = np.concatenate(
(risk_constraints.T, np.zeros((m, n))), axis=1)
er = np.concatenate((er, np.zeros(n)), axis=0)
turn_over_row = np.zeros(2 * n)
turn_over_row[n:] = 1.
risk_constraints = np.concatenate(
(risk_constraints, [turn_over_row]), axis=0)
turn_over_matrix = np.zeros((2 * n, 2 * n))
for i in range(n):
turn_over_matrix[i, i] = 1.
turn_over_matrix[i, i + n] = -1.
turn_over_matrix[i + n, i] = 1.
turn_over_matrix[i + n, i + n] = 1.
risk_constraints = np.concatenate(
(risk_constraints, turn_over_matrix), axis=0)
risk_lbound = np.concatenate((risk_lbound, -np.inf * np.ones(
(n, 1))),
axis=0)
risk_lbound = np.concatenate((risk_lbound, current_position),
axis=0)
risk_ubound = np.concatenate((risk_ubound, current_position),
axis=0)
risk_ubound = np.concatenate((risk_ubound, np.inf * np.ones(
(n, 1))),
axis=0)
cons_matrix = np.concatenate(
(risk_constraints, risk_lbound, risk_ubound), axis=1)
prob = LPOptimizer(cons_matrix, lbound, ubound, -er, method)
if prob.status() == 0:
return 'optimal', prob.feval(), prob.x_value()[:n]
else:
raise PortfolioBuilderException(prob.status())
elif method.lower() == 'ecos':
from cvxpy import Problem
from cvxpy import Variable
from cvxpy import multiply
from cvxpy import norm1
from cvxpy import Minimize
w = Variable(n)
current_risk_exposure = risk_constraints.T @ w
constraints = [
w >= lbound, w <= ubound,
current_risk_exposure >= risk_lbound.flatten(),
current_risk_exposure <= risk_ubound.flatten(),
norm1(w - current_position) <= turn_over_target
]
objective = Minimize(-w.T * er)
prob = Problem(objective, constraints)
prob.solve(solver='ECOS',
feastol=1e-10,
abstol=1e-10,
reltol=1e-10)
if prob.status == 'optimal' or prob.status == 'optimal_inaccurate':
return prob.status, prob.value, w.value.flatten()
else:
raise PortfolioBuilderException(prob.status)
else:
raise ValueError("{0} is not recognized".format(method))
def linear_build(er: np.ndarray,
lbound: Union[np.ndarray, float],
ubound: Union[np.ndarray, float],
risk_constraints: np.ndarray,
risk_target: Tuple[np.ndarray, np.ndarray],
turn_over_target: float = None,
current_position: np.ndarray = None) -> Tuple[str, np.ndarray, np.ndarray]:
er = er.flatten()
n, m = risk_constraints.shape
if not risk_target:
risk_lbound = -np.inf * np.ones((m, 1))
risk_ubound = np.inf * np.ones((m, 1))
else:
risk_lbound = risk_target[0].reshape((-1, 1))
risk_ubound = risk_target[1].reshape((-1, 1))
if isinstance(lbound, float):
lbound = np.ones(n) * lbound
if isinstance(ubound, float):
ubound = np.ones(n) * ubound
if not turn_over_target:
cons_matrix = np.concatenate((risk_constraints.T, risk_lbound, risk_ubound), axis=1)
opt = LPOptimizer(cons_matrix, lbound, ubound, -er)
status = opt.status()
if status == 0:
status = 'optimal'
return status, opt.feval(), opt.x_value()
else:
current_position = current_position.reshape((-1, 1))
# we need to expand bounded condition and constraint matrix to handle L1 bound
lbound = np.concatenate((lbound, np.zeros(n)), axis=0)
ubound = np.concatenate((ubound, np.inf * np.ones(n)), axis=0)
risk_lbound = np.concatenate((risk_lbound, [[0.]]), axis=0)
risk_ubound = np.concatenate((risk_ubound, [[turn_over_target]]), axis=0)
risk_constraints = np.concatenate((risk_constraints.T, np.zeros((m, n))), axis=1)
er = np.concatenate((er, np.zeros(n)), axis=0)
turn_over_row = np.zeros(2 * n)
turn_over_row[n:] = 1.
risk_constraints = np.concatenate((risk_constraints, [turn_over_row]), axis=0)
turn_over_matrix = np.zeros((2 * n, 2 * n))
for i in range(n):
turn_over_matrix[i, i] = 1.
turn_over_matrix[i, i + n] = -1.
turn_over_matrix[i + n, i] = 1.
turn_over_matrix[i + n, i + n] = 1.
risk_constraints = np.concatenate((risk_constraints, turn_over_matrix), axis=0)
risk_lbound = np.concatenate((risk_lbound, -np.inf * np.ones((n, 1))), axis=0)
risk_lbound = np.concatenate((risk_lbound, current_position), axis=0)
risk_ubound = np.concatenate((risk_ubound, current_position), axis=0)
risk_ubound = np.concatenate((risk_ubound, np.inf * np.ones((n, 1))), axis=0)
cons_matrix = np.concatenate((risk_constraints, risk_lbound, risk_ubound), axis=1)
opt = LPOptimizer(cons_matrix, lbound, ubound, -er)
status = opt.status()
if status == 0:
status = 'optimal'
return status, opt.feval(), opt.x_value()[:n]