Simple Mean-Reverting Model with and without Transaction Costs



In [1]:

    
import numpy as np



In [2]:

    
import pandas as pd



In [3]:

    
startDate=20060101



In [4]:

    
endDate=20061231



In [5]:

    
df=pd.read_table('SPX_20071123.txt')



In [6]:

    
df['Date']=df['Date'].astype('int')



In [7]:

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



In [8]:

    
df.sort_index(inplace=True)



In [9]:

    
dailyret=df.pct_change()



In [10]:

    
marketDailyret=dailyret.mean(axis=1)



In [11]:

    
weights=-(np.array(dailyret)-np.array(marketDailyret).reshape((dailyret.shape[0], 1)))



In [12]:

    
wtsum=np.nansum(abs(weights), axis=1)



In [13]:

    
weights[wtsum==0,]=0



In [14]:

    
wtsum[wtsum==0]=1



In [15]:

    
weights=weights/wtsum.reshape((dailyret.shape[0],1))



In [16]:

    
dailypnl=np.nansum(np.array(pd.DataFrame(weights).shift())*np.array(dailyret), axis=1)



In [17]:

    
dailypnl=dailypnl[np.logical_and(df.index >= startDate, df.index <= endDate)]



In [18]:

    
sharpeRatio=np.sqrt(252)*np.mean(dailypnl)/np.std(dailypnl)



In [19]:

    
sharpeRatio









    Out[19]:





0.957785681010386

With transaction costs



In [20]:

    
onewaytcost=0.0005



In [21]:

    
weights=weights[np.logical_and(df.index >= startDate, df.index <= endDate)]



In [22]:

    
dailypnlminustcost=dailypnl - (np.nansum(abs(weights-np.array(pd.DataFrame(weights).shift())), axis=1)*onewaytcost)



In [23]:

    
sharpeRatioMinusTcost=np.sqrt(252)*np.mean(dailypnlminustcost)/np.std(dailypnlminustcost)



In [24]:

    
sharpeRatioMinusTcost









    Out[24]:





-2.1617433718962276