How to Form a Good Cointegrating (and Mean-Reverting) Pair of Stocks

In [1]:

    

import numpy as np


    

In [2]:

    

import pandas as pd


    

In [3]:

    

import matplotlib.pyplot as plt


    

In [20]:

    

from statsmodels.tsa.stattools import coint


    

In [21]:

    

from statsmodels.api import OLS


    

In [5]:

    

df1=pd.read_excel('GLD.xls')


    

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df2=pd.read_excel('GDX.xls')


    

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df=pd.merge(df1, df2, on='Date', suffixes=('_GLD', '_GDX'))


    

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df.set_index('Date', inplace=True)


    

In [9]:

    

df.sort_index(inplace=True)


    

In [18]:

    

coint_t, pvalue, crit_value=coint(df['Adj Close_GLD'], df['Adj Close_GDX'])


    

In [19]:

    

(coint_t, pvalue, crit_value) # abs(t-stat) > critical value at 95%. pvalue says probability of null hypothesis (of no cointegration) is only 1.8%


    

    
Out[19]:





(-3.6981160763300593,
 0.018427835409537425,
 array([-3.92518794, -3.35208799, -3.05551324]))

In [22]:

    

model=OLS(df['Adj Close_GLD'], df['Adj Close_GDX'])


    

In [23]:

    

results=model.fit()


    

In [24]:

    

hedgeRatio=results.params


    

In [25]:

    

hedgeRatio


    

    
Out[25]:





Adj Close_GDX    1.639523
dtype: float64

In [26]:

    

spread=df['Adj Close_GLD']-hedgeRatio[0]*df['Adj Close_GDX']


    

In [27]:

    

plt.plot(spread)


    

    
Out[27]:





[<matplotlib.lines.Line2D at 0x1ae016bccc0>]