# Compute ERIs df_eri = compute_eri(total_return_index=df, funding_return=df_cdi['CDI']) df_returns = df_eri.pct_change(1).dropna() # Correlation emp_cov = empirical_covariance(df_returns) emp_corr, _ = cov2corr(emp_cov) # print(emp_corr, '\n') # Shirinkage shrunk_cov = shrink_cov(df_returns, alpha=0.5) shrunk_corr, _ = cov2corr(shrunk_cov) # print(shrunk_corr, '\n') # Marchenko-Pastur mp_cov, _, _ = marchenko_pastur(df_returns) mp_corr, _ = cov2corr(mp_cov) # print(mp_corr, '\n') # Targeted Shrinkage ts_cov, _, _ = targeted_shirinkage(df_returns, ts_alpha=0.5) # TODO deveria dar o MP? ts_corr, _ = cov2corr(ts_cov) # print(ts_corr, '\n') # Ledoit-Wolfe lw_cov = ledoitwolf_cov(df_returns) lw_corr, _ = cov2corr(lw_cov) # print(lw_corr, '\n') # Detoning detone_corr = detone_corr(emp_corr, n=1)
# Read Bloomberg Tickers for renaming
df_tickers = pd.read_excel(file_path + r'/Data - BBG Data Values.xlsx',
index_col=0, sheet_name='Tickers')
tr_dict = df_tickers['Total Return Index (UBS)'].to_dict()
tr_dict = {v: k for k, v in tr_dict.items()}
# Read Total Return Index
df_tr = pd.read_excel(file_path + r'/Data - BBG Data Values.xlsx',
index_col=0, sheet_name='Total Return')
data = df_tr.rename(tr_dict, axis=1)
data = data.pct_change(1).dropna()
# ===== compute different correlations matrices =====
corr = data.corr().values # empirical correlation
corr_denoised, _, _ = marchenko_pastur(corr_matrix=corr, T=data.shape[0], N=data.shape[1]) # denoised correlation
corr_ts, _, _ = targeted_shirinkage(corr_matrix=corr, T=data.shape[0], N=data.shape[1], ts_alpha=1) # target-shrinkage
# # ===== sorted eigenvalues of each method =====
eig_empirical = np.sort(np.linalg.eig(corr)[0])[::-1]
eig_denoised = np.sort(np.linalg.eig(corr_denoised)[0])[::-1]
eig_ts = np.sort(np.linalg.eig(corr_ts)[0])[::-1]
df_eig = pd.DataFrame(data={'Empirical Eigenvalues': eig_empirical,
'Denoised Eigenvalues': eig_denoised,
'Targeted Shirinkage': eig_ts},
index=[i + 1 for i in range(data.shape[1])])
# ===== chart =====
MyFont = {'fontname': 'Century Gothic'}
rcParams['font.family'] = 'sans-serif'
rcParams['font.sans-serif'] = ['Century Gothic']
# add value views
value_countries = df_value.loc[date].dropna().index
for ccy in value_countries:
try:
v.loc[f'{ccy} value'] = df_value.loc[date, ccy]
P.loc[f'{ccy} value', ccy] = 1
except KeyError: # If a currency does not have a value signal, skips this view.
continue
P = P.fillna(0)
v = v.to_frame('Views')
# denoise the covariance matrix
mp_corr, _, _ = marchenko_pastur(df_corr.loc[date],
T=21 * 3,
N=vols.shape[0])
mp_cov = pd.DataFrame(data=np.diag(vols) @ mp_corr @ np.diag(vols),
index=vols.index,
columns=vols.index)
# optimization
bl = BlackLitterman(
sigma=mp_cov,
estimation_error=1 / (21 * 3),
views_p=P,
views_v=v,
w_equilibrium=weights_iv.loc[date].to_frame(),
avg_risk_aversion=1.2,
mu_historical=df_mom.loc[date].to_frame('Historical'),
continue
# add value views
for ccy in df_tr.columns:
try:
v.loc[f'{ccy} value'] = df_value.loc[last_date, ccy]
P.loc[f'{ccy} value', ccy] = 1
except KeyError: # If a currency does not have a value signal, skips this view.
continue
P = P.fillna(0)
v = v.to_frame('Views')
# denoise the covariance
mp_corr, _, _ = marchenko_pastur(df_corr.loc[last_date],
T=21 * 3, N=df_tr.shape[1])
mp_cov = pd.DataFrame(data=np.diag(vols) @ mp_corr @ np.diag(vols),
index=vols.index, columns=vols.index)
bl = BlackLitterman(sigma=mp_cov,
estimation_error=1 / (21 * 3),
views_p=P,
views_v=v,
w_equilibrium=df_weights['Inverse Volatility'].to_frame(),
avg_risk_aversion=1.2,
mu_historical=df_mom.loc[last_date].to_frame('Historical'),
mu_shrink=0.99, # needs to be tuned
overall_confidence=100) # needs to be tuned
vol_bl = pd.Series(data=np.sqrt(np.diag(bl.sigma_bl)), index=bl.sigma_bl.index)