def test_passing_user_specified_omega():
"""
Test calculation of weights when passing a custom omega matrix.
"""
tickers = ['A', 'B']
covariance = pd.DataFrame([[46.0, 1.06], [1.06, 5.33]],
index=tickers,
columns=tickers) * 10e-4
market_cap_weights = [0.44, 0.56]
views = [0.02, 0.04]
pick_list = [{'A': 1}, {'B': 1}]
omega = np.array([[0.0023, 0], [0., 0.0002665]])
bl_model = VanillaBlackLitterman()
bl_model.allocate(covariance=covariance,
market_capitalised_weights=market_cap_weights,
investor_views=views,
pick_list=pick_list,
omega=omega,
asset_names=tickers)
weights = bl_model.weights.values[0]
assert len(weights) == 2
assert np.round(weights[0], 2) == 0.14
assert np.round(weights[1], 2) == 0.86
np.testing.assert_almost_equal(np.sum(weights), 1)
def test_idzorek_omega_method():
"""
Test the Idzorek method for calculating omega matrix.
"""
tickers = ['A', 'B']
covariance = pd.DataFrame([[46.0, 1.06], [1.06, 5.33]],
index=tickers,
columns=tickers) * 10e-4
market_cap_weights = [0.44, 0.56]
views = [0.02, 0.04]
pick_list = [{'A': 1}, {'B': 1}]
bl_model = VanillaBlackLitterman()
bl_model.allocate(covariance=covariance.values,
market_capitalised_weights=market_cap_weights,
investor_views=views,
pick_list=pick_list,
omega_method='user_confidences',
view_confidences=[0.1, 0.5],
asset_names=tickers)
weights = bl_model.weights.values[0]
assert np.round(weights[0], 2) == 0.39
assert np.round(weights[1], 2) == 0.61
assert len(weights) == 2
np.testing.assert_almost_equal(np.sum(weights), 1)
def test_value_error_on_unknown_omega_method(self):
"""
Test ValueError when passing an unknown omega method string.
"""
with self.assertRaises(ValueError):
tickers = ['A', 'B']
covariance = pd.DataFrame([[46.0, 1.06], [1.06, 5.33]],
index=tickers,
columns=tickers) * 10e-4
market_cap_weights = [0.44, 0.56]
views = [0.02, 0.04]
pick_list = [{'A': 1}, {'B': 1}]
bl_model = VanillaBlackLitterman()
bl_model.allocate(covariance=covariance,
market_capitalised_weights=market_cap_weights,
investor_views=views,
omega_method='unknown_string',
pick_list=pick_list)
def test_value_error_on_inconsistent_views_and_pick_list(self):
# pylint: disable=invalid-name
"""
Test ValueError when passing different lengths of views and pick list.
"""
with self.assertRaises(ValueError):
tickers = ['A', 'B']
covariance = pd.DataFrame([[46.0, 1.06], [1.06, 5.33]],
index=tickers,
columns=tickers) * 10e-4
market_cap_weights = [0.44, 0.56]
views = [0.02, 0.04]
pick_list = [{'A': 1}]
bl_model = VanillaBlackLitterman()
bl_model.allocate(covariance=covariance,
market_capitalised_weights=market_cap_weights,
investor_views=views,
pick_list=pick_list)
def test_value_error_for_no_user_confidences(self):
"""
Test ValueError when using Idzorek omega method and not passing any user confidences.
"""
with self.assertRaises(ValueError):
tickers = ['A', 'B']
covariance = pd.DataFrame([[46.0, 1.06], [1.06, 5.33]],
index=tickers,
columns=tickers) * 10e-4
market_cap_weights = [0.44, 0.56]
views = [0.02, 0.04]
pick_list = [{'A': 1}, {'B': 1}]
bl_model = VanillaBlackLitterman()
bl_model.allocate(covariance=covariance,
market_capitalised_weights=market_cap_weights,
investor_views=views,
pick_list=pick_list,
omega_method='user_confidences',
asset_names=tickers)
def test_black_litterman_with_relative_views():
"""
Test the weights calculated by the Black Litterman algorithm for relative investor views.
"""
tickers = ['A', 'B']
covariance = pd.DataFrame([[46.0, 1.06], [1.06, 5.33]],
index=tickers,
columns=tickers) * 10e-4
market_cap_weights = [0.44, 0.56]
views = [0.02]
pick_list = [{'A': 1, 'B': -1}]
bl_model = VanillaBlackLitterman()
bl_model.allocate(covariance=covariance,
market_capitalised_weights=market_cap_weights,
investor_views=views,
pick_list=pick_list)
weights = bl_model.weights.values[0]
assert len(weights) == 2
assert np.round(weights[0], 2) == 0.35
assert np.round(weights[1], 2) == 0.65
np.testing.assert_almost_equal(np.sum(weights), 1)
def test_black_litterman_on_no_asset_names():
"""
Test the weights calculated by the Black Litterman algorithm when no asset names are specified
"""
tickers = ['A', 'B']
covariance = pd.DataFrame([[46.0, 1.06], [1.06, 5.33]],
index=tickers,
columns=tickers) * 10e-4
market_cap_weights = [0.44, 0.56]
views = [0.02, 0.04]
pick_list = [{'0': 1}, {'1': 1}]
bl_model = VanillaBlackLitterman()
bl_model.allocate(covariance=covariance.values,
market_capitalised_weights=market_cap_weights,
investor_views=views,
pick_list=pick_list)
weights = bl_model.weights.values[0]
assert len(weights) == 2
assert np.round(weights[0], 2) == 0.14
assert np.round(weights[1], 2) == 0.86
np.testing.assert_almost_equal(np.sum(weights), 1)
def test_value_error_on_negative_view_confidences(self):
# pylint: disable=invalid-name
"""
Test ValueError when user specifies a negative view confidence.
"""
with self.assertRaises(ValueError):
tickers = ['A', 'B']
covariance = pd.DataFrame([[46.0, 1.06], [1.06, 5.33]],
index=tickers,
columns=tickers) * 10e-4
market_cap_weights = [0.44, 0.56]
views = [0.02, 0.04]
pick_list = [{'A': 1}, {'B': 1}]
bl_model = VanillaBlackLitterman()
bl_model.allocate(covariance=covariance,
market_capitalised_weights=market_cap_weights,
investor_views=views,
pick_list=pick_list,
omega_method='user_confidences',
view_confidences=[-0.1, 0.5],
asset_names=tickers)
def test_original_black_litterman_results_for_first_view():
#pylint: disable=invalid-name, protected-access, unsubscriptable-object
"""
Test and replicate the results of original Black Litterman paper for first view - Germany vs Rest of Europe.
"""
def calculate_weights(risk_aversion, covariance, expected_returns):
return (inv(covariance).dot(expected_returns.T)) / risk_aversion
countries = ['AU', 'CA', 'FR', 'DE', 'JP', 'UK', 'US']
# Table 1 of the He-Litterman paper: Correlation matrix
correlation = pd.DataFrame(
[[1.000, 0.488, 0.478, 0.515, 0.439, 0.512, 0.491],
[0.488, 1.000, 0.664, 0.655, 0.310, 0.608, 0.779],
[0.478, 0.664, 1.000, 0.861, 0.355, 0.783, 0.668],
[0.515, 0.655, 0.861, 1.000, 0.354, 0.777, 0.653],
[0.439, 0.310, 0.355, 0.354, 1.000, 0.405, 0.306],
[0.512, 0.608, 0.783, 0.777, 0.405, 1.000, 0.652],
[0.491, 0.779, 0.668, 0.653, 0.306, 0.652, 1.000]],
index=countries,
columns=countries)
# Table 2 of the He-Litterman paper: Volatilities
volatilities = pd.DataFrame(
[0.160, 0.203, 0.248, 0.271, 0.210, 0.200, 0.187],
index=countries,
columns=["vol"])
covariance = volatilities.dot(volatilities.T) * correlation
# Table 2 of the He-Litterman paper: Market-capitalised weights
market_weights = pd.DataFrame(
[0.016, 0.022, 0.052, 0.055, 0.116, 0.124, 0.615],
index=countries,
columns=["CapWeight"])
bl_model = VanillaBlackLitterman()
equilibrium_returns = bl_model._calculate_implied_equilibrium_returns(
2.5, covariance, market_weights)
equilibrium_returns = (equilibrium_returns * 100).round(1).T
assert list(equilibrium_returns.values[0]) == [
3.9, 6.9, 8.4, 9.0, 4.3, 6.8, 7.6
]
# View-1
bl_model = VanillaBlackLitterman()
views = [0.05]
pick_list = [{
"DE":
1.0,
"FR":
-market_weights.loc["FR"] /
(market_weights.loc["FR"] + market_weights.loc["UK"]),
"UK":
-market_weights.loc["UK"] /
(market_weights.loc["FR"] + market_weights.loc["UK"])
}]
bl_model.allocate(covariance=covariance,
market_capitalised_weights=market_weights,
investor_views=views,
pick_list=pick_list,
asset_names=covariance.columns,
tau=0.05,
risk_aversion=2.5)
expected_returns = (bl_model.posterior_expected_returns * 100).round(1)
assert list(expected_returns.values[0]) == [
4.3, 7.6, 9.3, 11.0, 4.5, 7.0, 8.1
]
weights = calculate_weights(2.5, bl_model.posterior_covariance,
bl_model.posterior_expected_returns)
weights = (weights * 100).round(1).T
assert list(weights[0]) == [1.5, 2.1, -4.0, 35.4, 11., -9.5, 58.6]
def test_original_black_litterman_results_for_third_view():
# pylint: disable=invalid-name, unsubscriptable-object
"""
Test and replicate the results of original Black Litterman paper for third view - bullish view on Canada vs US
"""
def calculate_weights(risk_aversion, covariance, expected_returns):
return (inv(covariance).dot(expected_returns.T)) / risk_aversion
countries = ['AU', 'CA', 'FR', 'DE', 'JP', 'UK', 'US']
# Table 1 of the He-Litterman paper: Correlation matrix
correlation = pd.DataFrame(
[[1.000, 0.488, 0.478, 0.515, 0.439, 0.512, 0.491],
[0.488, 1.000, 0.664, 0.655, 0.310, 0.608, 0.779],
[0.478, 0.664, 1.000, 0.861, 0.355, 0.783, 0.668],
[0.515, 0.655, 0.861, 1.000, 0.354, 0.777, 0.653],
[0.439, 0.310, 0.355, 0.354, 1.000, 0.405, 0.306],
[0.512, 0.608, 0.783, 0.777, 0.405, 1.000, 0.652],
[0.491, 0.779, 0.668, 0.653, 0.306, 0.652, 1.000]],
index=countries,
columns=countries)
# Table 2 of the He-Litterman paper: Volatilities
volatilities = pd.DataFrame(
[0.160, 0.203, 0.248, 0.271, 0.210, 0.200, 0.187],
index=countries,
columns=["vol"])
covariance = volatilities.dot(volatilities.T) * correlation
# Table 2 of the He-Litterman paper: Market-capitalised weights
market_weights = pd.DataFrame(
[0.016, 0.022, 0.052, 0.055, 0.116, 0.124, 0.615],
index=countries,
columns=["CapWeight"])
# View-2
bl_model = VanillaBlackLitterman()
views = [0.05, 0.04]
pick_list = [{
"DE":
1.0,
"FR":
-market_weights.loc["FR"] /
(market_weights.loc["FR"] + market_weights.loc["UK"]),
"UK":
-market_weights.loc["UK"] /
(market_weights.loc["FR"] + market_weights.loc["UK"])
}, {
"CA": 1,
"US": -1
}]
bl_model.allocate(covariance=covariance,
market_capitalised_weights=market_weights,
investor_views=views,
pick_list=pick_list,
asset_names=covariance.columns,
tau=0.05,
risk_aversion=2.5)
expected_returns = (bl_model.posterior_expected_returns * 100).round(1)
assert list(expected_returns.values[0]) == [
4.4, 9.1, 9.5, 11.3, 4.6, 7.0, 7.3
]
weights = calculate_weights(2.5, bl_model.posterior_covariance,
bl_model.posterior_expected_returns)
weights = (weights * 100).round(1).T
assert list(weights[0]) == [1.5, 53.3, -3.3, 33.1, 11.0, -7.8, 7.3]