Add Mean and covariance matrix.

[andrewcztrack]

Hi @Jackal08 @PanPip !

I hope your well.

I was wondering if it was possible to add the mean and covariance calculation based on the below reference -

https://github.com/twistedcubic/coin-press

I am trying to use it with Robust Bayesian allocation but i am getting errors.

[andrewcztrack]

import utils
import torch
import numpy as np
from algos import *
import pandas as pd

args = utils.parse_args()
args.d = 6
dist_mean = torch.zeros(args.d)
dist_cov = torch.eye(args.d)
args.u = 10*np.sqrt(args.d)
args.total_budget = .5
args.t = 3
args.rho = [(1.0/8.0)*args.total_budget, (1.0/8.0)*args.total_budget, (3.0/4.0)*args.total_budget]
args.n = 5000

rr=torch.from_numpy(data.to_numpy()).float()


Sigma_numpy = cov_est(rr, args)
#print(Sigma_numpy)
px = pd.DataFrame(Sigma_numpy).astype("float")
cov=np.array(px)
cov

import numpy as np
from mlfinlab.portfolio_optimization.bayesian import RobustBayesianAllocation

# Number of time series observations to use for the model.
returns = data.to_numpy()
num_assets=6
# Sample estimate
sample_mean = np.mean(returns, axis=0).reshape((num_assets, 1))
sample_covariance = np.cov(returns, rowvar=False)
sample_covariance = px

# Bayesian prior
prior_covariance = np.diag(np.diag(sample_covariance))
prior_mean = 0.5 * sample_covariance.dot(np.ones((num_assets, 1))) / num_assets

# Do robust bayesian allocation
bayes_allocator = RobustBayesianAllocation(discretisations=10)
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-5,
    relative_confidence_in_prior_covariance=1e-5,
    max_volatility=0.8 * max(sample_mean),
    sample_size=500
)

# Get the weights
portfolio_weights = bayes_allocator.weights
portfolio_weights


---------------------------------------------------------------------------
DCPError                                  Traceback (most recent call last)
<ipython-input-32-60b6de718f08> in <module>
     24     relative_confidence_in_prior_covariance=1e-5,
     25     max_volatility=0.8 * max(sample_mean),
---> 26     sample_size=500
     27 )
     28 

~/miniconda3/envs/mlfinll/lib/python3.7/site-packages/mlfinlab/portfolio_optimization/bayesian/robust_bayesian_allocation.py in allocate(self, prior_mean, prior_covariance, sample_mean, sample_covariance, sample_size, relative_confidence_in_prior_mean, relative_confidence_in_prior_covariance, posterior_mean_estimation_risk_level, posterior_covariance_estimation_risk_level, max_volatility, asset_names)
     90 
     91         # Get portfolios along Bayesian Efficient Frontier
---> 92         bayesian_portfolios, bayesian_portfolio_volatilities, bayesian_portfolio_returns = self._calculate_bayesian_frontier(asset_names)
     93 
     94         # Calculate gamma values

~/miniconda3/envs/mlfinll/lib/python3.7/site-packages/mlfinlab/portfolio_optimization/bayesian/robust_bayesian_allocation.py in _calculate_bayesian_frontier(self, asset_names)
    230                      covariance_matrix=self.posterior_covariance,
    231                      asset_names=asset_names,
--> 232                      solution='min_volatility')
    233         min_volatility_weights = mvo.weights.values
    234         min_volatility_return = mvo.portfolio_return

~/miniconda3/envs/mlfinll/lib/python3.7/site-packages/mlfinlab/portfolio_optimization/modern_portfolio_theory/mean_variance.py in allocate(self, asset_names, asset_prices, expected_asset_returns, covariance_matrix, solution, target_return, target_risk, risk_aversion, weight_bounds)
     89         elif solution == 'min_volatility':
     90             self._min_volatility(covariance=covariance,
---> 91                                  expected_returns=expected_asset_returns)
     92         elif solution == 'max_return_min_volatility':
     93             self._max_return_min_volatility(covariance=covariance,

~/miniconda3/envs/mlfinll/lib/python3.7/site-packages/mlfinlab/portfolio_optimization/modern_portfolio_theory/mean_variance.py in _min_volatility(self, covariance, expected_returns)
    385             constraints=allocation_constraints
    386         )
--> 387         problem.solve(warm_start=True)
    388         if weights.value is None:
    389             raise ValueError('No optimal set of weights found.')

~/miniconda3/envs/mlfinll/lib/python3.7/site-packages/cvxpy/problems/problem.py in solve(self, *args, **kwargs)
    393         else:
    394             solve_func = Problem._solve
--> 395         return solve_func(self, *args, **kwargs)
    396 
    397     @classmethod

~/miniconda3/envs/mlfinll/lib/python3.7/site-packages/cvxpy/problems/problem.py in _solve(self, solver, warm_start, verbose, gp, qcp, requires_grad, enforce_dpp, **kwargs)
    742 
    743         data, solving_chain, inverse_data = self.get_problem_data(
--> 744             solver, gp, enforce_dpp)
    745         solution = solving_chain.solve_via_data(
    746             self, data, warm_start, verbose, kwargs)

~/miniconda3/envs/mlfinll/lib/python3.7/site-packages/cvxpy/problems/problem.py in get_problem_data(self, solver, gp, enforce_dpp)
    497             self._cache.invalidate()
    498             solving_chain = self._construct_chain(
--> 499                 solver=solver, gp=gp, enforce_dpp=enforce_dpp)
    500             self._cache.key = key
    501             self._cache.solving_chain = solving_chain

~/miniconda3/envs/mlfinll/lib/python3.7/site-packages/cvxpy/problems/problem.py in _construct_chain(self, solver, gp, enforce_dpp)
    650         candidate_solvers = self._find_candidate_solvers(solver=solver, gp=gp)
    651         return construct_solving_chain(self, candidate_solvers, gp=gp,
--> 652                                        enforce_dpp=enforce_dpp)
    653 
    654     def _invalidate_cache(self):

~/miniconda3/envs/mlfinll/lib/python3.7/site-packages/cvxpy/reductions/solvers/solving_chain.py in construct_solving_chain(problem, candidates, gp, enforce_dpp)
    149     if len(problem.variables()) == 0:
    150         return SolvingChain(reductions=[ConstantSolver()])
--> 151     reductions = _reductions_for_problem_class(problem, candidates, gp)
    152 
    153     dpp_context = 'dcp' if not gp else 'dgp'

~/miniconda3/envs/mlfinll/lib/python3.7/site-packages/cvxpy/reductions/solvers/solving_chain.py in _reductions_for_problem_class(problem, candidates, gp)
     88                        "Consider calling solve() with `qcp=True`.")
     89         raise DCPError(
---> 90             "Problem does not follow DCP rules. Specifically:\n" + append)
     91     elif gp and not problem.is_dgp():
     92         append = build_non_disciplined_error_msg(problem, 'DGP')

DCPError: Problem does not follow DCP rules. Specifically:
The objective is not DCP. Its following subexpressions are not:
QuadForm(var1732, [[ 8.34021141e-04  3.08789520e-04  2.31343587e-04  5.05312825e-04
  -9.42613832e-05 -3.41530294e-04]
 [ 2.94395753e-04  1.25483692e-03  5.66166581e-04 -3.44443558e-04
   1.65212615e-05 -1.46168376e-04]
 [ 2.31597647e-04  5.84590227e-04  1.42932241e-03 -4.90658025e-04
   1.56349033e-04 -4.02760446e-04]
 [ 5.14689928e-04 -3.50829457e-04 -5.00810387e-04  1.82570622e-03
   4.31106599e-04 -8.51376009e-05]
 [-9.16821548e-05  3.87639180e-05  1.77022819e-04  4.07299234e-04
   4.15572259e-04  2.58098892e-04]
 [-2.98206154e-04 -1.34785050e-04 -3.61017472e-04 -7.23656363e-05
   2.55446861e-04  1.57409953e-03]])

[aditya1702]

@andrewcztrack Thanks for raising the issue. Seems like cvxpy encountered matrices which make the problem non-convex. I will look into this and update as soon as possible

[andrewcztrack]

@aditya1702 !!! hi! thank you :)!

I was just wondering if you could have a look at the matrix calculation.
i calculated the correlation matrix from the covariance matrix and got some strange results.

https://github.com/twistedcubic/coin-press
twistedcubic/coin-press#3

could you possibly have a look and if this covariance matrix and mean calculation adds value could you possibly add them to the library.

Kind regards and thanks,
Andrew

[aditya1702]

@andrewcztrack Sure. Will give it a look soon

[andrewcztrack]

Hi @aditya1702 !! thank you :). much appreciated :)