def test_min_volatility_cvxpy_vs_scipy():
# cvxpy
ef = setup_efficient_frontier()
ef.min_volatility()
w1 = ef.weights
# scipy
args = (ef.cov_matrix, )
initial_guess = np.array([1 / ef.n_assets] * ef.n_assets)
result = sco.minimize(
objective_functions.portfolio_variance,
x0=initial_guess,
args=args,
method="SLSQP",
bounds=[(0, 1)] * 20,
constraints=[{
"type": "eq",
"fun": lambda x: np.sum(x) - 1
}],
)
w2 = result["x"]
cvxpy_var = objective_functions.portfolio_variance(w1, ef.cov_matrix)
scipy_var = objective_functions.portfolio_variance(w2, ef.cov_matrix)
assert cvxpy_var <= scipy_var
def test_efficient_return_short():
ef = EfficientFrontier(*setup_efficient_frontier(data_only=True),
weight_bounds=(None, None))
target_return = 0.25
weights_sum = 1.0 # Not market neutral, weights must sum to 1.
w = ef.efficient_return(target_return)
assert isinstance(w, dict)
assert set(w.keys()) == set(ef.tickers)
np.testing.assert_almost_equal(ef.weights.sum(), weights_sum)
w_expected = simple_ef_weights(ef.expected_returns, ef.cov_matrix,
target_return, weights_sum)
np.testing.assert_almost_equal(ef.weights, w_expected)
vol_expected = np.sqrt(
objective_functions.portfolio_variance(w_expected, ef.cov_matrix))
sharpe_expected = objective_functions.sharpe_ratio(w_expected,
ef.expected_returns,
ef.cov_matrix,
negative=False)
np.testing.assert_allclose(ef.portfolio_performance(),
(target_return, vol_expected, sharpe_expected))
sharpe = ef.portfolio_performance()[2]
ef_long_only = setup_efficient_frontier()
ef_long_only.efficient_return(target_return)
long_only_sharpe = ef_long_only.portfolio_performance()[2]
assert sharpe > long_only_sharpe
def test_quadratic_utility():
df = get_data()
e_rets = mean_historical_return(df)
S = sample_cov(df)
w = np.array([1 / len(e_rets)] * len(e_rets))
utility = objective_functions.quadratic_utility(w,
e_rets,
S,
risk_aversion=3)
assert isinstance(utility, float)
assert utility < 0
mu = objective_functions.portfolio_return(w, e_rets, negative=False)
variance = objective_functions.portfolio_variance(w, S)
np.testing.assert_almost_equal(-utility + 3 / 2 * variance, mu)
def test_volatility_dummy():
w = np.array([0.4, 0.4, 0.2])
data = np.diag([0.5, 0.8, 0.9])
test_var = objective_functions.portfolio_variance(w, data)
np.testing.assert_almost_equal(test_var, 0.244)
def test_volatility():
df = get_data()
S = sample_cov(df)
w = np.array([1 / df.shape[1]] * df.shape[1])
var = objective_functions.portfolio_variance(w, S)
np.testing.assert_almost_equal(var, 0.04498224489292057)
