Capital Asset Pricing Model (CAPM)

In [1]:

    

%matplotlib inline


    

In [2]:

    

# Make the plots larger
from IPython.core.pylabtools import figsize
figsize(15, 5)


    

In [3]:

    

import pandas as pd
import pandas.io.data as web
from matplotlib import pyplot as plt


    

In [4]:

    

prices = web.get_data_yahoo(['GOOGL', 'AAPL', 'MSFT', 'FB'], start='2013-01-01', end='2013-12-31')['Adj Close']
prices.head()


    

    
Out[4]:






  

    

      

      
AAPL
      
FB
      
GOOGL
      
MSFT
    
    

      
Date
      

      

      

      

    
  
  

    

      
2013-01-02
      
 529.43
      
 28.00
      
 361.99
      
 26.42
    
    

      
2013-01-03
      
 522.75
      
 27.77
      
 362.20
      
 26.07
    
    

      
2013-01-04
      
 508.19
      
 28.76
      
 369.35
      
 25.58
    
    

      
2013-01-07
      
 505.20
      
 29.42
      
 367.74
      
 25.53
    
    

      
2013-01-08
      
 506.56
      
 29.06
      
 367.02
      
 25.40
    
  

5 rows × 4 columns

In [5]:

    

prices.plot()


    

    
Out[5]:





<matplotlib.axes.AxesSubplot at 0x7fd2863b2510>






    

In [6]:

    

gspc = web.get_data_yahoo('^GSPC', start='2013-01-01', end='2013-12-31')['Adj Close']
gspc.name = '^GSPC'
gspc.head()


    

    
Out[6]:





Date
2013-01-02    1462.42
2013-01-03    1459.37
2013-01-04    1466.47
2013-01-07    1461.89
2013-01-08    1457.15
Name: ^GSPC, dtype: float64

In [7]:

    

risk_free_rate = web.get_quote_yahoo('^TNX')['last'][0] / 100
risk_free_rate


    

    
Out[7]:





0.02597

In [8]:

    

daily_risk_free_rate = (1 + risk_free_rate) ** (1 / len(gspc)) - 1
daily_risk_free_rate


    

    
Out[8]:





0.00010174528107698144

In [9]:

    

def capm_analysis(stock, index, risk_free_rate, window=None):    
    stock_ret = stock.pct_change().dropna()
    index_ret = index.pct_change().dropna()
    stock_premium = stock_ret - risk_free_rate
    index_premium = index_ret - risk_free_rate
    window = window or len(index_ret)
    betas =  pd.ols(y=stock_premium, x=index_premium, window=window).beta
    return betas.rename(columns={'x': 'beta', 'intercept': 'alpha'})


    

In [10]:

    

capm_analysis(prices['GOOGL'], gspc, daily_risk_free_rate).iloc[0]


    

    
Out[10]:





beta     0.950279
alpha    0.000923
Name: 2013-12-31 00:00:00, dtype: float64

In [11]:

    

pd.DataFrame({stock: capm_analysis(prices[stock], gspc, daily_risk_free_rate).iloc[0]
              for stock in prices})


    

    
Out[11]:






  

    

      

      
AAPL
      
FB
      
GOOGL
      
MSFT
    
  
  

    

      
beta
      
 0.592082
      
 0.913468
      
 0.950279
      
 0.870342
    
    

      
alpha
      
-0.000261
      
 0.002182
      
 0.000923
      
 0.000606
    
  

2 rows × 4 columns

In [12]:

    

capm_analysis(prices['GOOGL'], gspc, daily_risk_free_rate, 30)['beta'].plot()


    

    
Out[12]:





<matplotlib.axes.AxesSubplot at 0x7fd27d9d4650>






    

In [13]:

    

pd.DataFrame({stock: capm_analysis(prices[stock], gspc, daily_risk_free_rate, 30)['beta']
              for stock in prices}).plot()


    

    
Out[13]:





<matplotlib.axes.AxesSubplot at 0x7fd27d9bea50>






    

In [14]:

    

returns = prices.pct_change().dropna()
corr = returns.corr()
corr


    

    
Out[14]:






  

    

      

      
AAPL
      
FB
      
GOOGL
      
MSFT
    
  
  

    

      
AAPL
      
 1.000000
      
 0.110946
      
 0.107809
      
 0.077613
    
    

      
FB
      
 0.110946
      
 1.000000
      
 0.135778
      
 0.068464
    
    

      
GOOGL
      
 0.107809
      
 0.135778
      
 1.000000
      
 0.223968
    
    

      
MSFT
      
 0.077613
      
 0.068464
      
 0.223968
      
 1.000000
    
  

4 rows × 4 columns

In [15]:

    

from statsmodels.graphics.correlation import plot_corr
plot_corr(corr, cmap='hot')
None


    

In [16]:

    

pd.scatter_matrix(returns, diagonal='kde', figsize=(10, 10))


    

    
Out[16]:





array([[<matplotlib.axes.AxesSubplot object at 0x7fd27c021b50>,
        <matplotlib.axes.AxesSubplot object at 0x7fd277fdc590>,
        <matplotlib.axes.AxesSubplot object at 0x7fd277fa6e90>,
        <matplotlib.axes.AxesSubplot object at 0x7fd277f66710>],
       [<matplotlib.axes.AxesSubplot object at 0x7fd277f366d0>,
        <matplotlib.axes.AxesSubplot object at 0x7fd277ef5650>,
        <matplotlib.axes.AxesSubplot object at 0x7fd277e44850>,
        <matplotlib.axes.AxesSubplot object at 0x7fd277daf0d0>],
       [<matplotlib.axes.AxesSubplot object at 0x7fd277d7a6d0>,
        <matplotlib.axes.AxesSubplot object at 0x7fd277db92d0>,
        <matplotlib.axes.AxesSubplot object at 0x7fd277d076d0>,
        <matplotlib.axes.AxesSubplot object at 0x7fd277cd2fd0>],
       [<matplotlib.axes.AxesSubplot object at 0x7fd277c96290>,
        <matplotlib.axes.AxesSubplot object at 0x7fd277c67250>,
        <matplotlib.axes.AxesSubplot object at 0x7fd277c261d0>,
        <matplotlib.axes.AxesSubplot object at 0x7fd277b752d0>]], dtype=object)






    

In [17]:

    

plt.scatter(returns.mean(), returns.std())
plt.xlabel('Expected returns')
plt.ylabel('Risk')
for label, x, y in zip(returns.columns, returns.mean(), returns.std()):
    plt.annotate(
        label, 
        xy = (x, y), xytext = (20, -20),
        textcoords = 'offset points', ha = 'right', va = 'bottom',
        bbox = dict(boxstyle = 'round,pad=0.5', fc = 'yellow', alpha = 0.5),
        arrowprops = dict(arrowstyle = '->', connectionstyle = 'arc3,rad=0'))