def test_portfolio_return_dummy():
w = np.array([0.3, 0.1, 0.2, 0.25, 0.15])
e_rets = pd.Series([0.19, 0.08, 0.09, 0.23, 0.17])
mu = objective_functions.portfolio_return(w, e_rets, negative=False)
assert isinstance(mu, float)
assert mu > 0
np.testing.assert_almost_equal(mu, w.dot(e_rets))
np.testing.assert_almost_equal(mu, (w * e_rets).sum())
def test_portfolio_return_real():
df = get_data()
e_rets = mean_historical_return(df)
w = np.array([1 / len(e_rets)] * len(e_rets))
negative_mu = objective_functions.portfolio_return(w, e_rets)
assert isinstance(negative_mu, float)
assert negative_mu < 0
np.testing.assert_almost_equal(negative_mu, -w.dot(e_rets))
np.testing.assert_almost_equal(negative_mu, -(w * e_rets).sum())
np.testing.assert_almost_equal(-e_rets.sum() / len(e_rets), negative_mu)
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_sharpe_ratio():
df = get_data()
e_rets = mean_historical_return(df)
S = sample_cov(df)
w = np.array([1 / len(e_rets)] * len(e_rets))
sharpe = objective_functions.sharpe_ratio(w, e_rets, S)
assert isinstance(sharpe, float)
assert sharpe < 0
sigma = np.sqrt(np.dot(w, np.dot(S, w.T)))
negative_mu = objective_functions.portfolio_return(w, e_rets)
np.testing.assert_almost_equal(sharpe * sigma - 0.02, negative_mu)
# Risk free rate increasing should lead to negative Sharpe increasing.
assert sharpe < objective_functions.sharpe_ratio(
w, e_rets, S, risk_free_rate=0.1)
