Table of Contents
Some of the factors I computed during my internship. I list the formula for each factor, and the code computing it. Those codes are only a little portion of the whole project, which contains much more things such as data cleaning, data merging, speed optimization and so on. I will give an example of how the whole project looks like
Fama-French 3-factor
![\[r_{i}^e = \alpha + \beta_1 r_{m}^e + \beta_2 SMB + \beta_3 HML + \epsilon_{i}\]](https://zhangyuantong.com/wp-content/ql-cache/quicklatex.com-32dfbc029aa551cbfbbac0c3d02a395c_l3.png "Rendered by QuickLaTeX.com")
from sklearn.linear_model import LinearRegression
def get_ff3(df):
x = df[['mkt_rf', 'smb', 'hml']]
y = df['excess_return']
reg = LinearRegression().fit(x,y)
return [reg.intercept_, reg.coef_[0], reg.coef_[1], reg.coef_[2]]Fama-French 5-factor
![\[r_{i}^e = \alpha_{i} + \beta_1 r_{m}^e + \beta_2 SMB + \beta_3 HML+ \beta_4 RMW + \beta_5 CMA + \epsilon_{i}\]](https://zhangyuantong.com/wp-content/ql-cache/quicklatex.com-17a1b2aa4f1f524eef7e403f2ef70fc3_l3.png "Rendered by QuickLaTeX.com")
def get_ff5(df):
x = df[['mkt_rf', 'smb', 'hml', 'rmw', 'cma']]
y = df['excess_return']
if np.isnan(y).any():
return np.nan
else:
reg = LinearRegression().fit(x,y)
return [reg.intercept_, reg.coef_[0], reg.coef_[1], reg.coef_[2], reg.coef_[3], reg.coef_[4]]Treynor-Mazuy Model
![\[r_{i}^e = \alpha + \beta_1 r_m^e + \beta_2 (r_m^e)^2 + \epsilon_i\]](https://zhangyuantong.com/wp-content/ql-cache/quicklatex.com-10cc5900b9f505d392845e930a197464_l3.png "Rendered by QuickLaTeX.com")
def gen_new_vars_tm(data):
#get excess return
data['excess_return'] = data['return'] - data['rf']
#For TM model
data['mkt_rf_sq'] = data['mkt_rf']**2
return [data['excess_return'], data['mkt_rf_sq']]
def get_tm1(suibian):
x = suibian[['mkt_rf', 'mkt_rf_sq']]
y = suibian['excess_return']
reg = LinearRegression().fit(x,y)
return [reg.intercept_, reg.coef_[0], reg.coef_[1]]Henriksson-Merton Model
![\[r_i^e = \alpha + \beta_1 r_m^e + D\cdot \beta_2 (r_m^e)^2 \; where \; D = \mathbb{I}_{r_m^e > 0}\]](https://zhangyuantong.com/wp-content/ql-cache/quicklatex.com-4bd30004569c3ed831b9443803d20229_l3.png "Rendered by QuickLaTeX.com")
def gen_new_vars_hm(data):
#get excess return
data['excess_return'] = data['return'] - data['rf']
data['mkt_rf_sq'] = data['mkt_rf']**2
data['mkt_rf_dummy'] = np.where(data['mkt_rf'] < 0, 0, 1)
data['mkt_rf_sq_times_dummy'] = data['mkt_rf_sq'] * data['mkt_rf_dummy']
return [data['excess_return'], data['mkt_rf_sq_times_dummy']]
def get_hm1(data):
x = data[['mkt_rf', 'mkt_rf_sq_times_dummy']]
y = data['excess_return']
reg = LinearRegression().fit(x,y)
return [reg.intercept_, reg.coef_[0]]