import numpy as np
import matplotlib.pyplot as plt
from sklearn.covariance import LedoitWolf
import seaborn as sns
import statsmodels.api as sm

# Cài thư viện lấy dữ liệu miễn phí
!curl -fsSLO https://raw.githubusercontent.com/algo-stocks/data/master/data.py

from data import get_prices

start = '2024-01-01'
end = '2025-01-01'

tickers = ['BID', 'CTG', 'ACB', 'HDG', 'VIC', 'VRE']
historical_prices = get_prices(*tickers, start_date=start, end_date=end).ffill()

rets = historical_prices.pct_change().fillna(0) # Calculate returns
lw_cov = LedoitWolf().fit(rets).covariance_ # Calculate Ledoit-Wolf estimator

def extract_corr_from_cov(cov_matrix):
    # Linear algebra result:
    # https://math.stackexchange.com/questions/186959/correlation-matrix-from-covariance-matrix
    d = np.linalg.inv(np.diag(np.sqrt(np.diag(cov_matrix))))
    corr = d.dot(cov_matrix).dot(d)
    return corr

fig, (ax1, ax2) = plt.subplots(ncols=2)
fig.tight_layout()

corr = extract_corr_from_cov(lw_cov)
# Plot prices
left = historical_prices.plot(ax=ax1)
# Plot covariance as a heat map
right = sns.heatmap(corr, ax=ax2, fmt='d', vmin=-1, vmax=1, xticklabels=tickers, yticklabels=tickers)

average_corr = np.mean(corr[np.triu_indices_from(corr, k=1)])
print('Average pairwise correlation: %.4f' % average_corr)

Average pairwise correlation: 0.2938

tickers = ['BID', 'CTG', 'ACB', 'HDG', 'VIC', 'VRE', 'VNINDEX']
historical_prices = get_prices(*tickers, start_date=start, end_date=end).ffill()

rets = historical_prices.pct_change().fillna(0) # Calculate returns

market = rets['VNINDEX']
stock_rets = rets.drop('VNINDEX', axis=1)
residuals = stock_rets.copy()*0

for stock in stock_rets.columns:
    model = sm.OLS(stock_rets[stock], market.values)
    results = model.fit()
    residuals[stock] = results.resid

lw_cov = LedoitWolf().fit(residuals).covariance_ # Calculate Ledoit-Wolf Estimator

fig, (ax1, ax2) = plt.subplots(ncols=2)
fig.tight_layout()

corr = extract_corr_from_cov(lw_cov)
left = (1+residuals).cumprod().plot(ax=ax1)
right = sns.heatmap(corr, ax=ax2, fmt='d', vmin=-1, vmax=1, xticklabels=stock_rets.columns, yticklabels=stock_rets.columns)

average_corr = np.mean(corr[np.triu_indices_from(corr, k=1)])
print('Average pairwise correlation: %.4f' % average_corr)

Average pairwise correlation: -0.0351

tickers = ['BID', 'CTG', 'ACB', 'HDG', 'VIC', 'VRE', 'VNINDEX', 'VCB', 'VHM']

# Obtain prices
historical_prices = get_prices(*tickers, start_date=start, end_date=end).ffill()

rets = historical_prices.pct_change().fillna(0) # Calculate returns

# Get market hedge ticker
mkt = 'VNINDEX'
# Get sector hedge tickers
sector_1_hedge = 'VCB'
sector_2_hedge = 'VHM'
# Identify securities for each sector
sector_1_stocks = ['BID', 'CTG', 'ACB']
sector_2_stocks = ['HDG', 'VIC', 'VRE']

market_rets = rets[mkt]
sector_1_rets = rets[sector_1_hedge]
sector_2_rets = rets[sector_2_hedge]

stock_rets = rets.drop(['VNINDEX', 'VCB', 'VHM'], axis=1)
residuals_market = stock_rets.copy()*0
residuals = stock_rets.copy()*0
# Calculate market beta of sector 1 benchmark
model = sm.OLS(sector_1_rets.values, market.values)
results = model.fit()
sector_1_excess = results.resid
# Calculate market beta of sector 2 benchmark
model = sm.OLS(sector_2_rets.values, market.values)
results = model.fit()
sector_2_excess = results.resid

for stock in sector_1_stocks:
    # Calculate market betas for sector 1 stocks
    model = sm.OLS(stock_rets[stock], market.values)
    results = model.fit()
    # Calculate residual of security + market hedge
    residuals_market[stock] = results.resid
    # Calculate sector beta for previous residuals
    model = sm.OLS(residuals_market[stock], sector_1_excess)
    results = model.fit()
    # Get final residual
    residuals[stock] = results.resid

for stock in sector_2_stocks:
    # Calculate market betas for sector 2 stocks
    model = sm.OLS(stock_rets[stock], market.values)
    results = model.fit()
    # Calculate residual of security + market hedge
    residuals_market[stock] = results.resid
    # Calculate sector beta for previous residuals
    model = sm.OLS(residuals_market[stock], sector_2_excess)
    results = model.fit()
    # Get final residual
    residuals[stock] = results.resid

# Get covariance of residuals
lw_cov = LedoitWolf().fit(residuals).covariance_

fig, (ax1, ax2) = plt.subplots(ncols=2)
fig.tight_layout()

corr = extract_corr_from_cov(lw_cov)
left = (1+residuals).cumprod().plot(ax=ax1)
labels = sector_1_stocks + sector_2_stocks
right = sns.heatmap(corr, ax=ax2, fmt='d', vmin=-1, vmax=1, xticklabels=labels, yticklabels=labels)

average_corr = np.mean(corr[np.triu_indices_from(corr, k=1)])
print('Average pairwise correlation: %.4f' % average_corr)

Average pairwise correlation: -0.0281

def buckle_BR_const(N, rho):
    return N/(1 + rho*(N - 1))

corr = np.linspace(start=0, stop=1.0, num=500)
plt.plot(corr, buckle_BR_const(6, corr))
plt.title('Effective Breadth as a function of Forecast Correlation (6 Stocks)')
plt.ylabel('Effective Breadth (Number of Bets)')
plt.xlabel('Forecast Correlation');

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