# In[77]:
# Import the CovarianceShrinkage object, it reduces/shrinks the errors/residuals while calculating the covariance matrix
# Create the CovarianceShrinkage instance variable
cs = CovarianceShrinkage(df4)
# In[78]:
# Difference in calculating covariance matrix through covariance shrinkage and through sample cov() method
# Compute the sample covariance matrix of returns
sample_cov = df4.pct_change().cov() * 252
# Compute the efficient covariance matrix of returns
e_cov = cs.ledoit_wolf()
# Display both the sample covariance_matrix and the efficient e_cov estimate
print("Sample Covariance Matrix\n", sample_cov, "\n")
print("Efficient Covariance Matrix\n", e_cov, "\n")
# In[79]:
# Although the differences between the sample covariance and the efficient covariance (found by shrinking errors)
# may seem small, they have a huge impact on estimation of the optimal portfolio weights and the generation of the efficient
# frontier. Practitioners generally use some form of efficient covariance for Modern Portfolio Theory.
# In[80]:
df4.head()
import pandas as pd
import numpy as np
from pypfopt.efficient_frontier import EfficientFrontier
from pypfopt.objective_functions import negative_cvar
from pypfopt.risk_models import CovarianceShrinkage
##Importar série de dados
df = pd.read_excel(r'C:\Users\Jhona\OneDrive\Área de Trabalho\PRBR11.xlsx', index_col='Data')
##Obter os retornos dos ativos
returns = pd.DataFrame()
for i in df:
returns[i] = df[i].pct_change().dropna()
##Criar a matrix de covariância eficiente
covMatrix = CovarianceShrinkage(df)
e_cov = covMatrix.ledoit_wolf()
##Fronteira
ef = EfficientFrontier(None, e_cov)
##Encontrando o CVaR 95% minimizando
optimal_weights = ef.custom_objective(negative_cvar, returns)
print(optimal_weights)