Python for Finance

Chapter 6
Here, yi is the ith observation for dependent variable y, 1 is the intercept, 0.8 is the
slope (beta), xi is the ith observation for an independent variable of x, and is the
random value. For the preceding equation, after we have generated a set of y and x,
we could run a linear regression. For this purpose, a set of random numbers are used:
from scipy import stats
import scipy as sp
sp.random.seed(12456)
alpha=1
beta=0.8
n=100
x=sp.arange(n)
y=alpha+beta*x+sp.random.rand(n)
(beta,alpha,r_value,p_value,std_err)=stats.linregress(y,x)
print(alpha,beta)
print("R-squared=", r_value**2)
print("p-value =", p_value)
In the preceding code, the sp.random.rand() function would call a set of random
numbers. In order to get the same set of random numbers, the sp.random.
seed() function is applied. In other words, whenever the same seed is used, any
programmers would get the same set of random numbers. This will be discussed in
more detail in Chapter 12, Monte Carlo Simulation. The result is shown here:
%run "C:/yan/teaching/Python2/codes/c6_02_random_OLS.py"
(-1.9648401142472594,1.2521836174247121,)
('R-squared=', 0.99987143193925765)
('p-value =', 1.7896498998980323e-192)
Now let's look at how to estimate the beta (market risk) for Microsoft. Assume that
we are interested in the period from 1/1/2012 to 12/31/2016, for a total of five year's
data. The complete Python program is shown here:
from scipy import stats
from matplotlib.finance import quotes_historical_yahoo_ochl as getData
begdate=(2012,1,1)
enddate=(2016,12,31)
ticker='MSFT'
p =getData(ticker, begdate, enddate,asobject=True,adjusted=True)
retIBM = p.aclose[1:]/p.aclose[:1]-1
ticker='^GSPC'
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