def optimisation_bayesian_riskweights(weekly_returns,
shrinkcorr=0.0,
shrinkSR=0.0,
priorcorroffdiag=0.5,
priorSR=0.25):
prior_corrmatrix = boring_corr_matrix(len(weekly_returns.columns),
priorcorroffdiag)
est_corrmatrix = weekly_returns.corr().values
shrink_corrmatrix = (prior_corrmatrix * shrinkcorr) + (est_corrmatrix *
(1 - shrinkcorr))
est_mean_list = list(annualised_mean(weekly_returns).values)
est_stdev_list = list(annualised_std(weekly_returns).values)
est_sr_list = [
each_return / each_std
for each_return, each_std in zip(est_mean_list, est_stdev_list)
]
prior_sr_list = [priorSR] * len(est_sr_list)
shrink_sr_list = [(prior * shrinkSR) + (est * (1 - shrinkSR))
for prior, est in zip(prior_sr_list, est_sr_list)]
shrunk_mean_list = [
each_std * shrunk_sr
for each_std, shrunk_sr in zip(est_stdev_list, shrink_sr_list)
]
## apply risk weights
avg_std = np.nanmean(est_stdev_list)
riskwt_mean_list = [
this_mean * avg_std / this_std
for this_mean, this_std in zip(shrunk_mean_list, est_stdev_list)
]
norm_stdev_list = [avg_std] * len(est_stdev_list)
return optimisation_with_data(shrink_corrmatrix, riskwt_mean_list,
norm_stdev_list)
def shrink_corr(corrmatrix, shrinkage_corr):
"""
>>> sigma=np.array([[1.0,0.0,0.5], [0.0, 1.0, 0.75],[0.5, 0.75, 1.0]])
>>> shrink_corr(sigma, 0.5)
array([[ 1. , 0.20833333, 0.45833333],
[ 0.20833333, 1. , 0.58333333],
[ 0.45833333, 0.58333333, 1. ]])
>>> shrink_corr(sigma, 0.0)
array([[ 1. , 0. , 0.5 ],
[ 0. , 1. , 0.75],
[ 0.5 , 0.75, 1. ]])
>>> shrink_corr(sigma, 1.0)
array([[ 1. , 0.41666667, 0.41666667],
[ 0.41666667, 1. , 0.41666667],
[ 0.41666667, 0.41666667, 1. ]])
"""
avg_corr=get_avg_corr(corrmatrix)
prior_corr=boring_corr_matrix(corrmatrix.shape[0], offdiag=avg_corr)
sigma_corr=shrinkage_corr*prior_corr+(1-shrinkage_corr)*corrmatrix
return sigma_corr
def shrink_corr(corrmatrix, shrinkage_corr):
"""
>>> sigma=np.array([[1.0,0.0,0.5], [0.0, 1.0, 0.75],[0.5, 0.75, 1.0]])
>>> shrink_corr(sigma, 0.5)
array([[ 1. , 0.20833333, 0.45833333],
[ 0.20833333, 1. , 0.58333333],
[ 0.45833333, 0.58333333, 1. ]])
>>> shrink_corr(sigma, 0.0)
array([[ 1. , 0. , 0.5 ],
[ 0. , 1. , 0.75],
[ 0.5 , 0.75, 1. ]])
>>> shrink_corr(sigma, 1.0)
array([[ 1. , 0.41666667, 0.41666667],
[ 0.41666667, 1. , 0.41666667],
[ 0.41666667, 0.41666667, 1. ]])
"""
avg_corr=get_avg_corr(corrmatrix)
prior_corr=boring_corr_matrix(corrmatrix.shape[0], offdiag=avg_corr)
sigma_corr=shrinkage_corr*prior_corr+(1-shrinkage_corr)*corrmatrix
return sigma_corr
def get_shocked_corr_matrix(list_of_instruments):
return boring_corr_matrix(len(list_of_instruments), offdiag=1.0)
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)
