strategy-lab/to_explore/pyquantnews/24_FactorAnalysis.ipynb

This code performs a multifactor analysis on monthly stock returns, applying the Fama-French three-factor model for financial analysis. It fetches historical factor data, calculates active returns of selected stocks, and estimates their sensitivities to the Fama-French factors. The code also performs rolling regression to analyze the stability of factor exposures over time. Lastly, it calculates and prints the marginal contributions to risk from each factor.

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import numpy as np
import pandas as pd

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import pandas_datareader as pdr
import yfinance as yf

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import statsmodels.api as sm
from statsmodels import regression
from statsmodels.regression.rolling import RollingOLS

Fetch Fama-French factors data starting from 2000-01-01 and select the SMB and HML factors

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factors = pdr.get_data_famafrench(
    'F-F_Research_Data_Factors',
    start='2000-01-01'
)[0][1:]

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SMB = factors.SMB
HML = factors.HML

Download monthly adjusted close prices for specified stocks starting from 2000-01-01

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data = yf.download(
    ['SPY', 'MSFT', 'AAPL', 'INTC'], 
    start="2000-01-01", 
    interval="1mo"
)['Adj Close']

Calculate the monthly returns and convert them to period-based returns

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monthly_returns = data.pct_change().to_period("M")

Extract the benchmark returns (SPY) and calculate active returns against the benchmark

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bench = monthly_returns.pop("SPY")
R = monthly_returns.mean(axis=1)
active = R - bench

Create a DataFrame with active returns and Fama-French factors SMB and HML

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df = pd.DataFrame({
    'R': active,
    'F1': SMB,
    'F2': HML,
}).dropna()

Perform Ordinary Least Squares (OLS) regression to estimate sensitivities to the factors

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b1, b2 = regression.linear_model.OLS(
    df.R, 
    df[['F1', 'F2']]
).fit().params

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print(f'Sensitivities of active returns to factors:\nSMB: {b1}\nHML: {b2}')

Perform rolling OLS regression to estimate how factor sensitivities change over time

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exog_vars = ["SMB", "HML"]
exog = sm.add_constant(factors[exog_vars])
rols = RollingOLS(df.R, exog, window=12)
rres = rols.fit()
fig = rres.plot_recursive_coefficient(variables=exog_vars)

Calculate covariance between factors and marginal contributions to active risk (MCAR) for each factor

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F1 = df.F1
F2 = df.F2

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cov = np.cov(F1, F2)
ar_squared = (active.std())**2
mcar1 = (b1 * (b2 * cov[0,1] + b1 * cov[0,0])) / ar_squared
mcar2 = (b2 * (b1 * cov[0,1] + b2 * cov[1,1])) / ar_squared
print(f'SMB risk contribution: {mcar1}')
print(f'HML risk contribution: {mcar2}')
print(f'Unexplained risk contribution: {1 - (mcar1 + mcar2)}')

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