def test_bayesian_allocation_for_asset_names(self):
# pylint: disable=invalid-name
"""
Test bayesian allocation when passing a list of custom asset names
"""
bayes_allocator = RobustBayesianAllocation(
discretisations=self.num_of_portfolios)
bayes_allocator.allocate(sample_mean=self.sample_mean,
sample_covariance=self.sample_covariance,
prior_mean=self.prior_mean,
prior_covariance=self.prior_covariance,
relative_confidence_in_prior_mean=3,
relative_confidence_in_prior_covariance=3,
max_volatility=0.8 * max(self.sample_mean),
asset_names=self.asset_names,
sample_size=self.num_observations)
weights = bayes_allocator.weights.values[0]
assert len(weights) == self.num_assets
assert round(weights[0], 3) == 0.733
assert round(weights[1], 3) == 0.146
assert round(weights[2], 3) == 0.094
assert round(weights[3], 3) == 0.019
assert round(weights[4], 3) == 0.008
np.testing.assert_almost_equal(np.sum(weights), 1)
def test_value_error_for_no_weights_found(self):
"""
Test ValueError when no robust portfolio is found.
"""
with self.assertRaises(ValueError):
bayes_allocator = RobustBayesianAllocation(
discretisations=self.num_of_portfolios)
bayes_allocator.allocate(sample_mean=self.sample_mean,
sample_covariance=self.sample_covariance,
prior_mean=self.prior_mean,
prior_covariance=self.prior_covariance,
relative_confidence_in_prior_mean=3,
relative_confidence_in_prior_covariance=3,
max_volatility=1e-5,
sample_size=self.num_observations)
def test_value_error_for_negative_confidence(self):
"""
Test ValueError when the investor specifies negative confidence in prior.
"""
with self.assertRaises(ValueError):
bayes_allocator = RobustBayesianAllocation(
discretisations=self.num_of_portfolios)
bayes_allocator.allocate(sample_mean=self.sample_mean,
sample_covariance=self.sample_covariance,
prior_mean=self.prior_mean,
prior_covariance=self.prior_covariance,
relative_confidence_in_prior_mean=-3,
relative_confidence_in_prior_covariance=3,
max_volatility=0.8 *
max(self.sample_mean),
sample_size=self.num_observations)
def test_value_error_for_diff_means_lengths(self):
"""
Test ValueError when the lengths of sample mean and prior mean do not match.
"""
with self.assertRaises(ValueError):
bayes_allocator = RobustBayesianAllocation(
discretisations=self.num_of_portfolios)
bayes_allocator.allocate(
sample_mean=self.sample_mean[:2],
sample_covariance=self.sample_covariance[:2, :2],
prior_mean=self.prior_mean[:3],
prior_covariance=self.prior_covariance[:3, :3],
relative_confidence_in_prior_mean=3,
relative_confidence_in_prior_covariance=3,
max_volatility=0.8 * max(self.sample_mean),
sample_size=self.num_observations)
def test_value_error_for_single_sample_size(self):
"""
Test ValueError when the investor specifies only sample size of 1.
"""
with self.assertRaises(ValueError):
bayes_allocator = RobustBayesianAllocation(
discretisations=self.num_of_portfolios)
bayes_allocator.allocate(
sample_mean=self.sample_mean,
sample_covariance=self.sample_covariance,
prior_mean=self.prior_mean,
prior_covariance=self.prior_covariance,
relative_confidence_in_prior_mean=3,
relative_confidence_in_prior_covariance=3,
posterior_covariance_estimation_risk_level=1,
max_volatility=0.8 * max(self.sample_mean),
sample_size=1)
def test_value_error_for_negative_max_volatility(self):
# pylint: disable=invalid-name
"""
Test ValueError when the investor specifies negative maximum volatility.
"""
with self.assertRaises(ValueError):
bayes_allocator = RobustBayesianAllocation(
discretisations=self.num_of_portfolios)
bayes_allocator.allocate(
sample_mean=self.sample_mean,
sample_covariance=self.sample_covariance,
prior_mean=self.prior_mean,
prior_covariance=self.prior_covariance,
relative_confidence_in_prior_mean=3,
relative_confidence_in_prior_covariance=3,
posterior_covariance_estimation_risk_level=1,
max_volatility=-2,
sample_size=self.num_observations)
def test_bayesian_allocation_for_low_confidence(self):
# pylint: disable=invalid-name, too-many-locals, broad-except
"""
Test the efficient frontiers generated by RBA when investor has low confidence in prior.
"""
sample_expected_returns = []
sample_volatilities = []
bayesian_expected_returns = []
bayesian_volatilities = []
robust_bayesian_expected_returns = []
robust_bayesian_volatilities = []
prior_expected_returns = []
prior_volatilities = []
for _ in range(self.num_simulations):
try:
returns = np.random.multivariate_normal(
mean=self.true_mean,
cov=self.true_covariance,
size=self.num_observations)
# Sample estimate
sample_mean = np.mean(returns, axis=0).reshape(
(self.num_assets, 1))
sample_covariance = np.cov(returns, rowvar=False)
# Bayesian prior
prior_covariance = np.diag(np.diag(sample_covariance))
prior_mean = 0.5 * sample_covariance.dot(
np.ones((self.num_assets, 1))) / self.num_assets
# Prior efficient frontier
_, volatilities, expected_returns = self._calculate_efficient_frontier(
prior_mean, prior_covariance, self.asset_names,
self.num_of_portfolios)
for i in range(self.num_of_portfolios):
prior_expected_returns.append(expected_returns[i])
prior_volatilities.append(volatilities[i])
# Sample efficient frontier (True market frontier)
_, volatilities, expected_returns = self._calculate_efficient_frontier(
sample_mean, sample_covariance, self.asset_names,
self.num_of_portfolios)
for i in range(self.num_of_portfolios):
sample_expected_returns.append(expected_returns[i])
sample_volatilities.append(volatilities[i])
# Do robust bayesian allocation
bayes_allocator = RobustBayesianAllocation(
discretisations=self.num_of_portfolios)
bayes_allocator.allocate(
sample_mean=sample_mean,
sample_covariance=sample_covariance,
prior_mean=prior_mean,
prior_covariance=prior_covariance,
relative_confidence_in_prior_mean=1e-4,
relative_confidence_in_prior_covariance=1e-4,
max_volatility=0.8 * max(sample_mean),
sample_size=self.num_observations)
# Bayesian efficient frontier
_, volatilities, expected_returns = self._calculate_efficient_frontier(
bayes_allocator.posterior_mean,
bayes_allocator.posterior_covariance, self.asset_names,
self.num_of_portfolios)
for i in range(self.num_of_portfolios):
bayesian_expected_returns.append(expected_returns[i])
bayesian_volatilities.append(volatilities[i])
# Robust bayesian portfolio
robust_bayesian_expected_returns.append(
bayes_allocator.portfolio_return)
robust_bayesian_volatilities.append(
bayes_allocator.portfolio_risk)
except Exception:
continue
assert np.mean(sample_expected_returns) >= np.mean(
robust_bayesian_expected_returns)
assert np.mean(robust_bayesian_expected_returns) >= np.mean(
prior_expected_returns)
assert np.abs(np.mean(sample_expected_returns) - np.mean(robust_bayesian_expected_returns)) < \
np.abs(np.mean(robust_bayesian_expected_returns) - np.mean(prior_expected_returns))