strategy-lab/to_explore/pyquantnews/96_SectorHedge.ipynb

This code performs financial analysis by downloading historical stock price data and calculating returns and correlations. It visualizes price movements and correlations, then calculates residuals between sector returns and market returns using OLS regression. Finally, it plots cumulative returns of residuals and evaluates the impact of forecast correlations on portfolio breadth. This is useful for risk management and portfolio optimization.

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import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
import seaborn as sns
import statsmodels.api as sm
import yfinance as yf
import warnings

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warnings.filterwarnings("ignore")

Define a list of stock tickers to download data for

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tickers = ["WFC", "JPM", "USB", "XOM", "VLO", "SLB"]

Download historical stock price data from Yahoo Finance for the specified tickers

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data = yf.download(tickers, start="2015-01-01", end="2023-12-31")["Close"]

Calculate daily percentage returns and drop any missing values

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returns = data.pct_change().dropna()

Create a figure with two subplots to plot stock prices and correlation heatmap

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

Calculate the correlation matrix of the returns

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corr = returns.corr()

Plot the historical stock prices on the first subplot

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left = data.plot(ax=ax1)

Plot the correlation heatmap on the second subplot

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right = sns.heatmap(
    corr, ax=ax2, vmin=-1, vmax=1,
    xticklabels=tickers, yticklabels=tickers
)

Calculate and print the average pairwise correlation among the stocks

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average_corr = np.mean(
    corr.values[np.triu_indices_from(corr.values, k=1)]
)
print(f"Average pairwise correlation: {average_corr}")

Define stock tickers for market indices and two sectors

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market_symbols = ["XLF", "SPY", "XLE"]
sector_1_stocks = ["WFC", "JPM", "USB"]
sector_2_stocks = ["XOM", "VLO", "SLB"]

Combine all tickers into one list

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tickers = market_symbols + sector_1_stocks + sector_2_stocks

Download historical price data for the combined list of tickers

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price = yf.download(tickers, start="2015-01-01", end="2023-12-31").Close

Calculate daily percentage returns and drop any missing values

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returns = price.pct_change().dropna()

Separate market returns and sector returns from the combined returns data

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market_returns = returns["SPY"]
sector_1_returns = returns["XLF"]
sector_2_returns = returns["XLE"]

Initialize DataFrames to store residuals after regression against market returns

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stock_returns = returns.drop(market_symbols, axis=1)
residuals_market = stock_returns.copy() * 0.0
residuals = stock_returns.copy() * 0.0

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def ols_residual(y, x):
    """Calculate OLS residuals between two series
    
    Parameters
    ----------
    y : pd.Series
        Dependent variable series
    x : pd.Series
        Independent variable series
    
    Returns
    -------
    residuals : pd.Series
        Residuals from OLS regression
    """
    
    results = sm.OLS(y, x).fit()
    return results.resid

Calculate residuals of sector returns after removing market returns influence

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sector_1_excess = ols_residual(sector_1_returns, market_returns)
sector_2_excess = ols_residual(sector_2_returns, market_returns)

Calculate residuals for each stock in sector 1 after removing market and sector influence

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for stock in sector_1_stocks:
    residuals_market[stock] = ols_residual(returns[stock], market_returns)
    residuals[stock] = ols_residual(residuals_market[stock], sector_1_excess)

Calculate residuals for each stock in sector 2 after removing market and sector influence

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for stock in sector_2_stocks:
    residuals_market[stock] = ols_residual(returns[stock], market_returns)
    residuals[stock] = ols_residual(residuals_market[stock], sector_2_excess)

Plot cumulative returns of residuals and the correlation heatmap of residuals

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

Plot cumulative returns of residuals

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left = (1 + residuals).cumprod().plot(ax=ax1)

Plot correlation heatmap of residuals

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right = sns.heatmap(
    corr,
    ax=ax2,
    fmt="d",
    vmin=-1,
    vmax=1,
    xticklabels=residuals.columns,
    yticklabels=residuals.columns,
)

Calculate and print the average pairwise correlation among the residuals

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average_corr = np.mean(corr.values[np.triu_indices_from(corr.values, k=1)])
print(f"Average pairwise correlation: {average_corr}")

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def buckle_BR_const(N, rho):
    """Calculate effective breadth based on correlation
    
    Parameters
    ----------
    N : int
        Number of assets
    rho : np.ndarray
        Array of correlation values
    
    Returns
    -------
    effective_breadth : np.ndarray
        Effective number of independent bets
    """
    
    return N / (1 + rho * (N - 1))

Generate a range of correlation values and plot the effective breadth

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

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