def get_annualised_risk_given_inputs(std_dev, cmatrix, weights):
weights = np.array(weights)
std_dev = np.array(std_dev)
std_dev, cmatrix, weights = clean_values(std_dev, cmatrix, weights)
sigma = sigma_from_corr_and_std(std_dev, cmatrix)
portfolio_variance = weights.dot(sigma).dot(weights.transpose())
portfolio_std = portfolio_variance**.5
return portfolio_std
def combine_list_of_correlations_and_stdev(rolling_correlations,
rolling_stdev):
corr_index_dates = rolling_correlations.fit_dates
std_index_dates = list(rolling_stdev.index)
sigma_list = []
for corr_index, index_date in enumerate(corr_index_dates):
std_dev = rolling_stdev.loc[index_date].values
std_dev[np.isnan(std_dev)] = 0.0
cmatrix = rolling_correlations.corr_list[corr_index]
cmatrix = pd.DataFrame(cmatrix)
cmatrix[cmatrix.isna()] = 1.0
cmatrix = np.array(cmatrix)
sigma = sigma_from_corr_and_std(std_dev, cmatrix)
sigma_list.append(sigma)
covariance_estimates = CorrelationList(sigma_list, rolling_stdev.columns,
corr_index_dates)
return covariance_estimates
def markosolver(period_subset_data,
moments_estimator,
cleaning,
must_haves,
equalise_SR=False,
equalise_vols=True,
**ignored_args):
"""
Returns the optimal portfolio for the returns data
If equalise_SR=True then assumes all assets have SR if False uses the asset natural SR
If equalise_vols=True then normalises returns to have same standard deviation; the weights returned
will be 'risk weightings'
:param subset_data: The data to optimise over
:type subset_data: pd.DataFrame TxN
:param cleaning: Should we clean correlations so can use incomplete data?
:type cleaning: bool
:param must_haves: The indices of things we must have weights for, used for cleaning
:type must_haves: list of bool
:param equalise_SR: Set all means equal before optimising (makes more stable)
:type equalise_SR: bool
:param equalise_vols: Set all vols equal before optimising (makes more stable)
:type equalise_vols: bool
Other arguments are kept so we can use **kwargs with other optimisation functions
*_params passed through to data estimation functions
:returns: float
"""
rawmoments = moments_estimator.moments(period_subset_data)
(mean_list, corrmatrix, stdev_list) = copy(rawmoments)
# equalise vols first
if equalise_vols:
(mean_list, stdev_list) = vol_equaliser(mean_list, stdev_list)
if equalise_SR:
# moments are annualised
ann_target_SR = moments_estimator.ann_target_SR
mean_list = SR_equaliser(stdev_list, ann_target_SR)
sigma = sigma_from_corr_and_std(stdev_list, corrmatrix)
unclean_weights = optimise(sigma, mean_list)
if cleaning:
weights = clean_weights(unclean_weights, must_haves)
else:
weights = unclean_weights
diag = dict(
raw=rawmoments,
sigma=sigma,
mean_list=mean_list,
unclean=unclean_weights,
weights=weights,
)
return (weights, diag)
def optimise_using_correlation(mean_list, avg_correlation, std):
corr_matrix = boring_corr_matrix(len(mean_list), offdiag=avg_correlation)
stdev_list = [std] * len(mean_list)
sigma = sigma_from_corr_and_std(stdev_list, corr_matrix)
return optimise(sigma, mean_list)
def opt_shrinkage(period_subset_data,
moments_estimator,
cleaning,
must_haves,
shrinkage_SR=0.9,
shrinkage_corr=0.5,
equalise_vols=False,
**ignored_args):
"""
Given dataframe of returns; returns_to_bs, performs a shrinkage optimisation
:param subset_data: The data to optimise over
:type subset_data: pd.DataFrame TxN
:param cleaning: Should we clean correlations so can use incomplete data?
:type cleaning: bool
:param equalise_vols: Set all vols equal before optimising (makes more stable)
:type equalise_vols: bool
:param shrinkage_SR: Shrinkage factor to use with SR. 1.0 = full shrinkage
:type shrinkage_SR: float
:param shrinkage_corr: Shrinkage factor to use with correlations. 1.0 = full shrinkage
:type shrinkage_corr: float
Other arguments are kept so we can use **kwargs with other optimisation functions
*_params passed through to data estimation functions
:returns: float
"""
# subset_data will be stacked up list, need to average
rawmoments = moments_estimator.moments(period_subset_data)
(mean_list, corrmatrix, stdev_list) = copy(rawmoments)
# equalise vols first
if equalise_vols:
(mean_list, stdev_list) = vol_equaliser(mean_list, stdev_list)
# shrinkage:
# everything is now annualised
ann_target_SR = moments_estimator.ann_target_SR
mean_list = shrink_SR(mean_list, stdev_list, shrinkage_SR, ann_target_SR)
corrmatrix = shrink_corr(corrmatrix, shrinkage_corr)
# get sigma matrix back
sigma = sigma_from_corr_and_std(stdev_list, corrmatrix)
unclean_weights = optimise(sigma, mean_list)
if cleaning:
weights = clean_weights(unclean_weights, must_haves)
else:
weights = unclean_weights
diag = dict(
raw=rawmoments,
sigma=sigma,
mean_list=mean_list,
unclean=unclean_weights,
weights=weights,
)
return (weights, diag)
