Factor models

Introduction to Portfolio Analysis in Python

Charlotte Werger

Data Scientist

Using factors to explain performance

Factors are used for risk management.
Factors are used to help explain performance.
Factor models help you relate factors to portfolio returns
Empirical factor models exist that have been tested on historic data.
Fama French 3 factor model is a well-known factor model.

Fama French Multi Factor model

$ $

$ R_{pf} = \alpha + \beta_m MKT + \beta_s SMB + \beta_h HML $
MKT is the excess return of the market, i.e. $R_m - R_f$
SMB (Small Minus Big) a size factor
HML (High Minus Low) a value factor

Regression model refresher

Fitting a line to data points using linear regression

Difference between beta and correlation

Table comparing beta to correlation

Regression model in Python

import statsmodels.api as sm

# Define the model
model = sm.OLS(factor_data['sp500'],
               factor_data[['momentum','value']]).fit()

# Get the model predictions
predictions = model.predict(factor_data[['momentum','value']])

b1, b2 = model.params

The regression summary output

# Print out the summary statistics
model.summary()

Linear regression model summary

Obtaining betas quickly

# Get just beta coefficients from linear regression model
b1, b2 = regression.linear_model.OLS(df['returns'], 
                          df[['F1', 'F2']]).fit().params

# Print the coefficients 
print 'Sensitivities of active returns to factors:
                \nF1: %f\nF2: %f' %  (b1, b2)

Sensitivities of active returns to factors:
F1: -0.0381
F2: 0.9858

Let's practice!

Introduction to Portfolio Analysis in Python