def test_qpoptimizer_with_factor_model(self):
objective = np.array([0.1, 0.2, 0.3])
lbound = np.array([0.0, 0.0, 0.0])
ubound = np.array([1.0, 1.0, 1.0])
factor_var = np.array([[0.5, -0.3], [-0.3, 0.7]])
factor_load = np.array([[0.8, 0.2], [0.5, 0.5], [0.2, 0.8]])
idsync = np.array([0.1, 0.3, 0.2])
cons = np.array([[1., 1., 1.]])
clbound = np.array([1.])
cubound = np.array([1.])
optimizer = QPOptimizer(objective,
None,
lbound,
ubound,
cons,
clbound,
cubound,
1.,
factor_var,
factor_load,
idsync)
# check against cvxpy result
np.testing.assert_array_almost_equal(optimizer.x_value(),
[0.2866857, 0.21416417, 0.49915014],
4)
def test_qpoptimizer(self):
objective = np.array([0.01, 0.02, 0.03])
cov = np.array([[0.02, 0.01, 0.02],
[0.01, 0.02, 0.03],
[0.02, 0.03, 0.02]])
ids_var = np.diag([0.01, 0.02, 0.03])
cov += ids_var
lbound = np.array([0., 0., 0.])
ubound = np.array([0.4, 0.4, 0.5])
cons = np.array([[1., 1., 1.],
[1., 0., 1.]])
clbound = np.array([1., 0.3])
cubound = np.array([1., 0.7])
optimizer = QPOptimizer(objective,
cov,
lbound,
ubound,
cons,
clbound,
cubound)
# check against matlab result
np.testing.assert_array_almost_equal(optimizer.x_value(),
[0.1996, 0.3004, 0.5000],
4)
def test_qpoptimizer_with_identity_matrix(self):
objective = np.array([-0.02, 0.01, 0.03])
cov = np.diag([1., 1., 1.])
lbound = np.array([-np.inf, -np.inf, -np.inf])
ubound = np.array([np.inf, np.inf, np.inf])
optimizer = QPOptimizer(objective,
cov,
lbound,
ubound,
risk_aversion=1.)
np.testing.assert_array_almost_equal(optimizer.x_value(),
[-0.02, 0.01, 0.03], 8)
def mean_variance_builder(er: np.ndarray,
cov: np.ndarray,
bm: np.ndarray,
lbound: Union[np.ndarray, float],
ubound: Union[np.ndarray, float],
risk_exposure: np.ndarray,
risk_target: Tuple[np.ndarray, np.ndarray],
lam: float = 1.) -> Tuple[str, float, np.ndarray]:
lbound = lbound - bm
ubound = ubound - bm
bm_risk = risk_exposure.T @ bm
clbound = risk_target[0] - bm_risk
cubound = risk_target[1] - bm_risk
optimizer = QPOptimizer(er, cov, lbound, ubound, risk_exposure.T, clbound,
cubound, lam)
if optimizer.status() == 0 or optimizer.status() == 1:
status = 'optimal'
else:
status = optimizer.status()
return status, optimizer.feval(), optimizer.x_value() + bm
def mean_variance_builder(
er: np.ndarray,
risk_model: Dict[str, Union[None, np.ndarray]],
bm: np.ndarray,
lbound: Union[np.ndarray, float],
ubound: Union[np.ndarray, float],
risk_exposure: Optional[np.ndarray],
risk_target: Optional[Tuple[np.ndarray, np.ndarray]],
lam: float = 1.,
linear_solver: str = 'ma27') -> Tuple[str, float, np.ndarray]:
lbound, ubound, cons_mat, clbound, cubound = _create_bounds(
lbound, ubound, bm, risk_exposure, risk_target)
if np.all(lbound == -np.inf) and np.all(
ubound == np.inf) and cons_mat is None:
# using fast path cvxpy
n = len(er)
w = cvxpy.Variable(n)
cov = risk_model['cov']
special_risk = risk_model['idsync']
risk_cov = risk_model['factor_cov']
risk_exposure = risk_model['factor_loading']
if cov is None:
risk = cvxpy.sum_squares(cvxpy.multiply(cvxpy.sqrt(special_risk), w)) \
+ cvxpy.quad_form((w.T * risk_exposure).T, risk_cov)
else:
risk = cvxpy.quad_form(w, cov)
objective = cvxpy.Minimize(-w.T * er + 0.5 * lam * risk)
prob = cvxpy.Problem(objective)
prob.solve(solver='ECOS', feastol=1e-9, abstol=1e-9, reltol=1e-9)
if prob.status == 'optimal' or prob.status == 'optimal_inaccurate':
return 'optimal', prob.value, np.array(w.value).flatten() + bm
else:
raise PortfolioBuilderException(prob.status)
else:
optimizer = QPOptimizer(er,
risk_model['cov'],
lbound,
ubound,
cons_mat,
clbound,
cubound,
lam,
risk_model['factor_cov'],
risk_model['factor_loading'],
risk_model['idsync'],
linear_solver=linear_solver)
return _create_result(optimizer, bm)
def mean_variance_builder(er: np.ndarray,
cov: np.ndarray,
bm: np.ndarray,
lbound: Union[np.ndarray, float],
ubound: Union[np.ndarray, float],
risk_exposure: Optional[np.ndarray],
risk_target: Optional[Tuple[np.ndarray, np.ndarray]],
lam: float=1.) -> Tuple[str, float, np.ndarray]:
lbound, ubound, cons_mat, clbound, cubound = _create_bounds(lbound, ubound, bm, risk_exposure, risk_target)
optimizer = QPOptimizer(er,
cov,
lbound,
ubound,
cons_mat,
clbound,
cubound,
lam)
return _create_result(optimizer, bm)