CAPM - Capital Asset Pricing Model¶
In [1]:
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In [2]:
import yfinance as yf
import pandas as pd
import numpy as np
import statsmodels.api as sm
import datetime as dt
import urllib.request # handle online files
import zipfile
import os
import statsmodels.formula.api as smf
import statsmodels.api as sm
from scipy import stats
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression
import matplotlib.pyplot as plt
from pylab import mpl, plt
plt.style.use('seaborn')
mpl.rcParams['font.family'] = 'DejaVu Sans'
mpl.rcParams["savefig.dpi"] = 500
np.set_printoptions(precision=5, suppress=True, formatter={"float": lambda x: f"{x:6.3f}"})
%matplotlib inline
<ipython-input-2-4039a680b4e1>:20: MatplotlibDeprecationWarning: The seaborn styles shipped by Matplotlib are deprecated since 3.6, as they no longer correspond to the styles shipped by seaborn. However, they will remain available as 'seaborn-v0_8-<style>'. Alternatively, directly use the seaborn API instead.
plt.style.use('seaborn')
In [ ]:
#help(stats.linregress)
In [3]:
def get_prices(tickers, freq_p, st_day, end_day):
mystock = pd.DataFrame()
for t in tickers:
mystock[t] = yf.download(t, start=st_day, end=end_day, interval=freq_p)['Adj Close']
return mystock
In [4]:
tic=['TSLA', 'SPY']
prices= get_prices(tic, freq_p='1wk', st_day="2011-01-01", end_day="2022-05-31") # id , 1wk, 1mo
print(prices)
prices.rename(columns={"TSLA": "Your_Stock", "SPY":"INDEX"}, inplace=True)
prices.info()
prices.tail(20)
[*********************100%***********************] 1 of 1 completed
[*********************100%***********************] 1 of 1 completed
TSLA SPY
Date
2011-01-01 1.882667 101.180954
2011-01-08 1.716667 102.899910
2011-01-15 1.536000 102.159821
2011-01-22 1.600667 101.642517
2011-01-29 1.564000 104.372192
... ... ...
2022-04-30 288.549988 406.030701
2022-05-07 256.529999 396.534882
2022-05-14 221.300003 384.600952
2022-05-21 253.210007 409.900116
2022-05-28 252.753326 407.600189
[596 rows x 2 columns]
<class 'pandas.core.frame.DataFrame'>
DatetimeIndex: 596 entries, 2011-01-01 to 2022-05-28
Data columns (total 2 columns):
# Column Non-Null Count Dtype
--- ------ -------------- -----
0 Your_Stock 596 non-null float64
1 INDEX 596 non-null float64
dtypes: float64(2)
memory usage: 14.0 KB
Out[4]:
| Your_Stock | INDEX | |
|---|---|---|
| Date | ||
| 2022-01-15 | 314.633331 | 430.987976 |
| 2022-01-22 | 282.116669 | 434.894592 |
| 2022-01-29 | 307.773346 | 441.536835 |
| 2022-02-05 | 286.666656 | 433.428345 |
| 2022-02-12 | 285.660004 | 427.297791 |
| 2022-02-19 | 269.956665 | 430.761627 |
| 2022-02-26 | 279.429993 | 425.270691 |
| 2022-03-05 | 265.116669 | 413.363861 |
| 2022-03-12 | 301.796661 | 437.423523 |
| 2022-03-19 | 336.880005 | 446.846985 |
| 2022-03-26 | 361.529999 | 447.074036 |
| 2022-04-02 | 341.829987 | 441.793091 |
| 2022-04-09 | 328.333344 | 432.139313 |
| 2022-04-16 | 335.016663 | 420.540985 |
| 2022-04-23 | 290.253326 | 406.682190 |
| 2022-04-30 | 288.549988 | 406.030701 |
| 2022-05-07 | 256.529999 | 396.534882 |
| 2022-05-14 | 221.300003 | 384.600952 |
| 2022-05-21 | 253.210007 | 409.900116 |
| 2022-05-28 | 252.753326 | 407.600189 |
In [5]:
print(prices.isnull().sum())
prices.dropna(how='any', inplace=True)
print(prices.isnull().sum())
prices.info()
print(prices)
Your_Stock 0
INDEX 0
dtype: int64
Your_Stock 0
INDEX 0
dtype: int64
<class 'pandas.core.frame.DataFrame'>
DatetimeIndex: 596 entries, 2011-01-01 to 2022-05-28
Data columns (total 2 columns):
# Column Non-Null Count Dtype
--- ------ -------------- -----
0 Your_Stock 596 non-null float64
1 INDEX 596 non-null float64
dtypes: float64(2)
memory usage: 14.0 KB
Your_Stock INDEX
Date
2011-01-01 1.882667 101.180954
2011-01-08 1.716667 102.899910
2011-01-15 1.536000 102.159821
2011-01-22 1.600667 101.642517
2011-01-29 1.564000 104.372192
... ... ...
2022-04-30 288.549988 406.030701
2022-05-07 256.529999 396.534882
2022-05-14 221.300003 384.600952
2022-05-21 253.210007 409.900116
2022-05-28 252.753326 407.600189
[596 rows x 2 columns]
In [6]:
prices.plot(figsize=(10,6))
plt.legend()
Out[6]:
<matplotlib.legend.Legend at 0x7f6d43cc6100>
In [7]:
(prices / prices.iloc[0] * 1).plot(figsize=(10, 6), subplots=False) #cumulative returns
plt.title('Cumulative Return')
plt.tight_layout()
In [8]:
prices.pct_change(1).dropna()
plt.scatter(prices['Your_Stock'], prices['INDEX'], color = 'red', alpha=0.2)
Out[8]:
<matplotlib.collections.PathCollection at 0x7f6d0c53ff40>
In [9]:
returns = prices.pct_change(1).dropna()
plt.hist(returns['INDEX'], label='INDEX', bins=100)
plt.hist(returns['Your_Stock'], label='Stock', bins=100)
plt.legend(loc='upper right')
plt.title('Overlapping')
plt.show()
In [10]:
returns
Out[10]:
| Your_Stock | INDEX | |
|---|---|---|
| Date | ||
| 2011-01-08 | -0.088173 | 0.016989 |
| 2011-01-15 | -0.105243 | -0.007192 |
| 2011-01-22 | 0.042101 | -0.005064 |
| 2011-01-29 | -0.022907 | 0.026856 |
| 2011-02-05 | -0.008951 | 0.014945 |
| ... | ... | ... |
| 2022-04-30 | -0.005868 | -0.001602 |
| 2022-05-07 | -0.110969 | -0.023387 |
| 2022-05-14 | -0.137333 | -0.030096 |
| 2022-05-21 | 0.144193 | 0.065780 |
| 2022-05-28 | -0.001804 | -0.005611 |
595 rows × 2 columns
using scipy¶
In [11]:
beta,alpha,r_value,p_value,std_err = stats.linregress(returns['INDEX'],returns["Your_Stock"])
In [12]:
print(beta.round(4))
print(alpha.round(4))
print(r_value.round(2))
print(p_value.round(4))
1.5397 0.0071 0.45 0.0
using statsmodels¶
In [13]:
formula = 'Your_Stock ~ INDEX'
results = smf.ols(formula, returns).fit()
print(results.summary())
OLS Regression Results
==============================================================================
Dep. Variable: Your_Stock R-squared: 0.205
Model: OLS Adj. R-squared: 0.204
Method: Least Squares F-statistic: 152.8
Date: Thu, 16 Mar 2023 Prob (F-statistic): 2.18e-31
Time: 23:16:11 Log-Likelihood: 756.72
No. Observations: 595 AIC: -1509.
Df Residuals: 593 BIC: -1501.
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
Intercept 0.0071 0.003 2.527 0.012 0.002 0.013
INDEX 1.5397 0.125 12.360 0.000 1.295 1.784
==============================================================================
Omnibus: 110.210 Durbin-Watson: 1.918
Prob(Omnibus): 0.000 Jarque-Bera (JB): 341.677
Skew: 0.874 Prob(JB): 6.40e-75
Kurtosis: 6.275 Cond. No. 44.7
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
using scikit-learn¶
You need to take a look at the shape of the data you are feeding into .fit().
Here x.shape = (10,) but we need it to be (10, 1), see sklearn. Same goes for y. So we reshape:
In [14]:
X = returns.loc[:, ['INDEX']].values
In [15]:
y = returns.loc[:, ['Your_Stock']].values
In [16]:
X.shape
Out[16]:
(595, 1)
In [17]:
type(X)
Out[17]:
numpy.ndarray
In [18]:
X.dtype
Out[18]:
dtype('float64')
In [19]:
y.shape
Out[19]:
(595, 1)
In [20]:
reg = LinearRegression(fit_intercept=True).fit(X,y)
In [21]:
reg.predict(X[0].reshape(-1,1))
Out[21]:
array([[ 0.033]])
In [22]:
reg.predict(X[0:10])
Out[22]:
array([[ 0.033],
[-0.004],
[-0.001],
[ 0.048],
[ 0.030],
[ 0.024],
[-0.018],
[ 0.009],
[-0.012],
[-0.029]])
In [23]:
score = reg.score(X, y)
print(score)
0.2048562366630433
In [24]:
reg.coef_
Out[24]:
array([[ 1.540]])
In [25]:
reg.intercept_
Out[25]:
array([ 0.007])
In [26]:
m = reg.coef_[0,0]
b = reg.intercept_[0]
In [27]:
m
Out[27]:
1.5397127262862014
In [28]:
b
Out[28]:
0.007084853239936928
In [29]:
# following slope intercept form
print("formula: y = {:.4f}X + {:.4f}".format(m, b) )
formula: y = 1.5397X + 0.0071
In [30]:
from numpy.ma.core import flatten_structured_array
fig, ax = plt.subplots(nrows = 1, ncols = 1, figsize = (10,7));
ax.scatter(X, y, color='blue', s=10);
ax.plot(X, reg.predict(X), color='red',linewidth=2);
ax.grid(True,
axis = 'both',
zorder = 0,
linestyle = ':',
color = 'y')
ax.tick_params(labelsize = 20)
ax.set_xlabel('INDEX', fontsize = 24)
ax.set_ylabel('Your_Stock', fontsize = 24)
ax.set_title("Linear Regression Line with Intercept y = {:.4f} + {:.4f}x (R2 = {:.2f})".format(b, m, score), fontsize = 16 )
fig.tight_layout()
#fig.savefig('images/linearregression', dpi = 300)
