Python for Finance

Multifactor Models and Performance Measures
Introduction to the Fama-French
three-factor model
Before discussing the Fama-French three-factor model and other models, let's look at
a general equation for a three-factor linear model:
Here, y is the dependent variable, α is the intercept, x1, x2, and x3 are three
independent variables, β1, β2 and β3 are three coefficients, and ε is a random factor.
In other words, we try to use three independent variables to explain one dependent
variable. The same as a one-factor linear model, the graphical presentation of this
three-factor linear model is a straight line, in a four-dimensional space, and the
power of each independent variable is a unit as well. Here, we will use two simple
examples to show how to run multifactor linear regression. For the first example,
we have the following code. The values have no specific meaning and readers could
enter their own values as well:
from pandas.stats.api import ols
import pandas as pd
y = [0.065, 0.0265, -0.0593, -0.001,0.0346]
x1 = [0.055, -0.09, -0.041,0.045,0.022]
x2 = [0.025, 0.10, 0.021,0.145,0.012]
x3= [0.015, -0.08, 0.341,0.245,-0.022]
df=pd.DataFrame({"y":y,"x1":x1, 'x2':x2,'x3':x3})
result=ols(y=df['y'],x=df[['x1','x2','x3']])
print(result)
In the preceding program, the pandas.stats.api.ols() function is applied. OLS
stands for Ordinary Least Squares. For more information about the OLS model, we
could use the help() function; see the following two lines of code. For brevity, the
output is not shown here:
from pandas.stats.api import ols
help(ols)
[ 214 ]