I am trying to calculate the dual beta in python using a statsmodel regression. Unfortunately I am prompting an error message.
The regression equation for dual betas is given here
I am neglecting the risk free rate (rf) for now, but implementation should be similiar once I add it. For now my code looks as follows, where my 'spx.xlsx' file simple has two columns with returns, called 'SPXrets' and 'AAPLrets' (+ one column with dates):
import pandas as pd
from pandas import ExcelWriter
from pandas import ExcelFile
import statsmodels.api as sm
import statsmodels.formula.api as smf
import numpy as np
df = pd.read_excel('spx.xlsx')
print(df.columns)
mod = smf.ols(formula='AAPLrets ~ SPXrets', data=df)
res = mod.fit()
print(res.summary())
Prompting an patsy error:
PatsyError: intercept term cannot interact with anything else AAPLrets ~ SPXrets:c(D) + SPXrets:(1-c(D))
Grateful for any help - many thanks!
Edit:
After my initial suggestions, the OP has changed both the title and the provided code snippet. My suggestions have since been edited accordingly.
New suggestion:
I suspect you're experiencing some problems with your dataset. I suggest that you tell us a little more about the data source, how you've loaded the data, what it looks like (structure) and what type your columns have (string, float etc).
What I can tell you right now, is that your snippet runs fine with some sample data like this:
Code:
CONret DAXret:c(D) DAXret:(1-c(D)) AAPLrets SPXrets dummy
2017-01-08 109 107 122 101 100 0
2017-01-09 117 108 124 113 147 0
2017-01-10 142 108 130 107 103 1
2017-01-11 106 121 149 103 104 1
2017-01-12 124 149 143 112 126 0
Output:
OLS Regression Results
==============================================================================
Dep. Variable: AAPLrets R-squared: 0.095
Model: OLS Adj. R-squared: 0.004
Method: Least Squares F-statistic: 1.044
Date: Thu, 14 Feb 2019 Prob (F-statistic): 0.331
Time: 16:00:01 Log-Likelihood: -48.388
No. Observations: 12 AIC: 100.8
Df Residuals: 10 BIC: 101.7
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
Intercept 84.3198 31.143 2.708 0.022 14.929 153.711
SPXrets 0.2635 0.258 1.022 0.331 -0.311 0.838
==============================================================================
Omnibus: 5.649 Durbin-Watson: 1.882
Prob(Omnibus): 0.059 Jarque-Bera (JB): 2.933
Skew: 1.202 Prob(JB): 0.231
Kurtosis: 3.290 Cond. No. 872.
==============================================================================
Here's the whole thing:
# imports
import statsmodels.formula.api as smf
import pandas as pd
import numpy as np
import statsmodels.api as sm
# sample data
np.random.seed(1)
rows = 12
listVars= ['CONret','DAXret:c(D)', 'DAXret:(1-c(D))', 'AAPLrets', 'SPXrets']
rng = pd.date_range('1/1/2017', periods=rows, freq='D')
df = pd.DataFrame(np.random.randint(100,150,size=(rows, len(listVars))), columns=listVars)
df = df.set_index(rng)
df['dummy'] = np.random.randint(2, size=df.shape[0])
mod = smf.ols(formula='AAPLrets ~ SPXrets', data=df)
res = mod.fit()
res.summary()
Another suggestion:
Personally, I'd feel much more comfortable without patsy.
The snippet below will let you run a linear regression and select whether to return the model summary, or a dataframe with other details like coefficient p-values and r-squared.
# Imports
import pandas as pd
import numpy as np
import statsmodels.api as sm
# sample data
np.random.seed(1)
rows = 12
listVars= ['CONret','DAXret:c(D)', 'DAXret:(1-c(D))', 'AAPLrets', 'SPXrets']
rng = pd.date_range('1/1/2017', periods=rows, freq='D')
df = pd.DataFrame(np.random.randint(100,150,size=(rows, len(listVars))), columns=listVars)
df = df.set_index(rng)
df['dummy'] = np.random.randint(2, size=df.shape[0])
def LinReg(df, y, x, const, results):
betas = x.copy()
# Model with out without a constant
if const == True:
x = sm.add_constant(df[x])
model = sm.OLS(df[y], x).fit()
else:
model = sm.OLS(df[y], df[x]).fit()
# Estimates of R2 and p
res1 = {'Y': [y],
'R2': [format(model.rsquared, '.4f')],
'p': [model.pvalues.tolist()],
'start': [df.index[0]],
'stop': [df.index[-1]],
'obs' : [df.shape[0]],
'X': [betas]}
df_res1 = pd.DataFrame(data = res1)
# Regression Coefficients
theParams = model.params[0:]
coefs = theParams.to_frame()
df_coefs = pd.DataFrame(coefs.T)
xNames = list(df_coefs)
xValues = list(df_coefs.loc[0].values)
xValues2 = [ '%.2f' % elem for elem in xValues ]
res2 = {'Independent': [xNames],
'beta': [xValues2]}
df_res2 = pd.DataFrame(data = res2)
# All results
df_res = pd.concat([df_res1, df_res2], axis = 1)
df_res = df_res.T
df_res.columns = ['results']
if results == 'summary':
return(model.summary())
print(model.summary())
else:
return(df_res)
df_regression = LinReg(df = df, y = 'CONret', x = ['DAXret:c(D)', 'DAXret:(1-c(D))', 'dummy'], const = True, results = 'summary')
print(df_regression)
Test run 1:
df_regression = LinReg(df = df, y = 'CONret', x = ['DAXret:c(D)', 'DAXret:(1-c(D))'], const = True, results = '')
Output 1:
results
Y CONret
R2 0.0813
p [0.13194822614949883, 0.45726622261432304, 0.9...
start 2017-01-01 00:00:00
stop 2017-01-12 00:00:00
obs 12
X [DAXret:c(D), DAXret:(1-c(D)), dummy]
Independent [const, DAXret:c(D), DAXret:(1-c(D)), dummy]
beta [88.94, 0.24, -0.01, 2.20]
Test run 2:
df_regression = LinReg(df = df, y = 'CONret', x = ['DAXret:c(D)', 'DAXret:(1-c(D))', 'dummy'], const = True, results = 'summary')
Output 2:
OLS Regression Results
==============================================================================
Dep. Variable: CONret R-squared: 0.081
Model: OLS Adj. R-squared: -0.263
Method: Least Squares F-statistic: 0.2361
Date: Thu, 14 Feb 2019 Prob (F-statistic): 0.869
Time: 16:04:02 Log-Likelihood: -47.138
No. Observations: 12 AIC: 102.3
Df Residuals: 8 BIC: 104.2
Df Model: 3
Covariance Type: nonrobust
===================================================================================
coef std err t P>|t| [0.025 0.975]
-----------------------------------------------------------------------------------
const 88.9438 53.019 1.678 0.132 -33.318 211.205
DAXret:c(D) 0.2350 0.301 0.781 0.457 -0.459 0.929
DAXret:(1-c(D)) -0.0060 0.391 -0.015 0.988 -0.908 0.896
dummy 2.2005 8.973 0.245 0.812 -18.490 22.891
==============================================================================
Omnibus: 1.025 Durbin-Watson: 2.354
Prob(Omnibus): 0.599 Jarque-Bera (JB): 0.720
Skew: 0.540 Prob(JB): 0.698
Kurtosis: 2.477 Cond. No. 2.15e+03
==============================================================================
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