#!/usr/bin/env python
# coding: utf-8

# <a href="https://colab.research.google.com/github/cyrus723/my-first-binder/blob/main/OLS_beta.ipynb" target="_parent"><img src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open In Colab"/></a>

# # Running the First Regression in Python

# Suppose this is your first time to write the code. Perhaps, you want to run a simple regression using two series of asset prices to fin the equity beta. Let's use a step-by-step approach to complete the task.
# 
#     Step 1: Download two assets' prices from the web
#     Step 2: Put them onto a matrix form
#     Step 3: Run the OLS
#     Step 4: Plot data

# ### Step 1: Download data
# We will use yahoo finance package (https://pypi.org/project/yfinance/) to download Yahoo Finance data from the web. We need to (1) install and (2) import this package.

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get_ipython().system('pip install yfinance   # to install, remove # and run the cell')
import yfinance as yf    # to import


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# download
mystock = yf.download("TSLA", start="2011-01-01", end="2022-05-31", interval='1mo')['Adj Close'].rename('TSLA')
index = yf.download("SPY", start="2011-01-01", end="2022-05-31", interval='1mo')['Adj Close'].rename('SPY')


# ### Step 2: Put two time series onto a matrix
# We need pandas module, so let's install and import it. https://pandas.pydata.org/

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#!pip install pandas   # Actually, you have this alread when you isntalled Anaconda.
import pandas as pd


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# combine two asset prices onto one matrix called pandas dataframe
data = pd.concat([mystock, index], axis=1)

# drop missing observations
data2 = data.dropna()

# compute monthly returns and drop the first observation
data3 = data2.pct_change().dropna()
data3


# ### Let's plot data.

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# need to import matplotlib. You already have this in your Jupyter environment, so no need to install.
import matplotlib.pyplot as plt       

data3.plot(subplots=False, figsize=(10, 6))                                # plot returns to see volatility levels

(data2 / data2.iloc[0] * 100).plot(figsize = (10, 6), subplots=False)      # plot the wealth change of $100 investment over time 


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data3.plot.hist(bins=50, alpha=0.7, edgecolor='black', subplots=False, figsize=(10,6))
data3.plot.scatter(x='SPY', y='TSLA', c='blue',figsize=(10,6))


# ### Step 3: Run OLS
# We need to install and import statsmodels module. https://www.statsmodels.org/stable/index.html

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#!pip install statsmodels
import statsmodels.formula.api as smf
import statsmodels.api as sm


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# run OLS
formula = 'TSLA ~ SPY'                      # set dep var and indep var
results = smf.ols(formula, data3).fit()     # run OLS
print(results.summary())                    # print  


# ### beta of TSLA = 1.7553

# ### Step 4: Plot the result
# We need to install and import matplotlib module. https://matplotlib.org/

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#!pip install matplotlib                            #again, if you installed Anaconda, you have this already.
import matplotlib.pyplot as plt

fig, ax=plt.subplots(figsize=(10,6))
fig = sm.graphics.plot_partregress_grid(results, fig=fig)


# ### Extra 1: using scipy module, we can get the same beta!

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#!pip install scipy         # Again, you probabaly have this installed in your Jupyter environment already
from scipy import stats

beta,alpha,r_value,p_value,std_err = stats.linregress(data3['SPY'],data3["TSLA"])

print(beta.round(4))
print(alpha.round(4))
print(r_value.round(2))
print(p_value.round(4))


# ### Extra 2: using a beta formula, we can get the same beta.
# 
# $$ 
# \beta_{tsla} = \frac{\sigma_{tsla,spy}}{\sigma_{spy}^2}
# $$
# 

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#  find covariance matrix
cov = data3.cov() * 12
print(cov)
print('\n')     # to give a space 
print(round(cov.iloc[0,1]/cov.iloc[1,1], 4))


# ### Extra3: using linear algebra, we can get the same beta.
# Need to install numpy and import it. You probably have this alreay. So skip installation. Just import it. https://numpy.org/
# 
# $$
# b=\begin{bmatrix} b_0 \\ b_1 \\ \vdots \\ b_{k} \end{bmatrix}= (X^{'}X)^{-1}X^{'}Y
# $$
# 
# 
# So, a beta estimate form OLS is equal to X matrix transpose times X matrix and take an inverse times X transpose times  times Y vector.
# 

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# warnings are annoying, so I include below to supress them. You do not need to do this.
import warnings
warnings.simplefilter(action='ignore', category=FutureWarning)


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import numpy as np

X = data3['SPY']
y = data3['TSLA']
X_ols = sm.add_constant(X)   # add a constant vector 
#print(X_ols)

# compute beta using matrix operation
beta = np.linalg.inv(X_ols.T.dot(X_ols)).dot(X_ols.T.dot(y))
print(round(beta[1], 4))


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# #sklearn

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type(y)


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x = np.array(X).reshape((-1, 1))
x.shape


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y=np.array(y).reshape((-1,1))
y.shape


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from sklearn.linear_model import LinearRegression
model = LinearRegression().fit(x,y)


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r_sq = model.score(x, y)
print(f"coefficient of determination: {r_sq}")
print(f"intercept: {model.intercept_}")
print(f"slope: {model.coef_}")


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