In the following examples, the np.size() function from NumPy shows the number of data items of an array, and the np.std() function is used to calculate standard deviation:

>>>import numpy as np
>>>x= np.array([[1,2,3],[3,4,6]])     # 2 by 3 matrix
>>>np.size(x)                         # number of data items
6
>>>np.size(x,1)                       # show number of columns
3
>>>np.std(x)
1.5723301886761005
>>>np.std(x,1)
Array([ 0.81649658, 1.24721913]
>>>total=x.sum()                      # attention to the format
>>>z=np.random.rand(50)               #50 random obs from [0.0, 1)
>>>y=np.random.normal(size=100)       # from standard normal
>>>r=np.array(range(0,100),float)/100 # from 0, .01,to .99

Compared with a Python array, a NumPy array is a contiguous piece of memory that is passed directly to LAPACK, which is a software library for numerical linear algebra under the hood, so...

The following are a few examples based on the functions enclosed in the SciPy module. The sp.npv() function estimates the present values for a given set of cash flows with the first cash flow happening at time zero. The first input value is the discount rate, and the second input is an array of all cash flows.

The following is one example. Note that the sp.npv() function is different from the Excel npv() function. We will explain why this is so in Chapter 3, Time Value of Money:

>>>import scipy as sp
>>>cashflows=[-100,50,40,20,10,50]
>>>x=sp.npv(0.1,cashflows)
>>>round(x,2)
>>>31.41

The sp.pmt() function is used to answer the following question.

What is the monthly cash flow to pay off a mortgage of $250,000 over 30 years with an annual percentage rate (APR) of 4.5 percent, compounded monthly? The following code shows the answer:

>>>payment=sp.pmt(0.045/12,30*12,250000)
>>>round(payment,2)
-1266.71

Based on...

Graphs and other visual representations have become more important in explaining many complex financial concepts, trading strategies, and formulas.

In this section, we discuss the matplotlib module, which is used to create various types of graphs. In addition, the module will be used intensively in Chapter 10, Options and Futures, when we discuss the famous Black-Scholes-Merton option model and various trading strategies. The matplotlib module is designed to produce publication-quality figures and graphs. The matplotlib module depends on NumPy and SciPy, which were discussed in the previous sections. To save generated graphs, there are several output formats available, such as PDF, Postscript, SVG, and PNG.

statsmodels is a powerful Python package for many types of statistical analysis. Again, if Python was installed via Anaconda, then the module was installed at the same time. In statistics, ordinary least square (OLS) regression is a method for estimating the unknown parameters in a linear regression model. It minimizes the sum of squared vertical distances between the observed values and the values predicted by the linear approximation. The OLS method is used extensively in finance. Assume that we have the following equation, where y is an n by 1 vector (array), and x is an n by (m+1) matrix, a return matrix (n by m), plus a vector that contains 1 only. n is the number of observations, and m is the number of independent variables:

In the following program, after generating the x and y vectors, we run an OLS regression (a linear regression). The x and y are artificial data. The last line prints the parameters only (the intercept is 1.28571420 and the slope is...

The pandas module is a powerful tool used to process various types of data, including economics, financial, and accounting data. If Python was installed on your machine via Anaconda, then the pandas module was installed already. If you issue the following command without any error, it indicates that the pandas module was installed:

>>>import pandas as pd

In the following example, we generate two time series starting from January 1, 2013. The names of those two time series (columns) are A and B:

import numpy as np
import pandas as pd
dates=pd.date_range('20160101',periods=5)
np.random.seed(12345)
x=pd.DataFrame(np.random.rand(5,2),index=dates,columns=('A','B'))

First, we import both NumPy and pandas modules. The pd.date_range() function is used to generate an index array. The x variable is a pandas DataFrame with dates as its index. Later in this chapter, we will discuss the pd.DataFrame() function. The columns() function defines...

Since this book is applying Python to finance, the modules (packages) related to finance will be our first priority.

The following table presents about a dozen Python modules or submodules related to finance:

Via this module, users can download various economics and financial via Yahoo! Finance, Google Finance, Federal Reserve Economics Data (FRED), and Fama-French factors.

Assume that the pandas_reader module is installed. For detail on how to install this module, see the How to install a Python module section. First, let's look at the simplest example, just two lines to get IBM's trading data; see the following:

import pandas_datareader.data as web
df=web.get_data_google("ibm")

We could use a dot head and dot tail to show part of the results; see the following code:

>>> df.head()
>>> 
                  Open        High         Low       Close   Volume  
Date                                                                  
2010-01-04  131.179993  132.970001  130.850006  132.449997  6155300   
2010-01-05  131.679993  131.850006  130.100006  130.850006  6841400   
2010-01-06  130.679993  131.490005  129.809998  130.000000...

In the next chapter, many basic financial concepts and formulas will be introduced and discussed. Usually, when taking corporate finance or financial management, students rely on either Excel or a financial calculator to conduct their estimations. Since Python is the computational tool, a financial calculator written in Python would definitely enhance our understanding of both finance and Python.

Here is the first financial calculator, written in Python, from Numpy.lib.financial; see the following code:

>>> import numpy.lib.financial as fin
>>> dir(fin)
['__all__', '__builtins__', '__cached__', '__doc__', '__file__', '__loader__', '__name__', '__package__', '__spec__', '_convert_when', '_g_div_gp', '_rbl', '_when_to_num', 'absolute_import', 'division', 'fv', 'ipmt', 'irr&apos...

If Python was installed via Anaconda, there is a good chance that many of the modules discussed in this book have been installed together with Python. If Python was installed independently, users could use PyPi to install or update.

For example, we are interested in installing NumPy. On Windows, we have the following code:

python -m pip install -U pip numpy

If Python.exe is on the path, we could open a DOS window first, then issue the preceding line. If Python.exe is not on the path, we open a DOS window, then move to the location of the Python.exe file; for an example, see the following screenshot:

For a Mac, we have the following codes. Sometimes, after running the preceding command, you might receive the following message asking for an update of PiP:

The command line to update pip is given here:

python –m pip install –upgrade pip

See the result shown in the following screenshot:

To install NumPy independently, on Linux or OS X, we issue the following...

At the very beginning of this book, we argued that one of the advantages of using Python is that it is a rich source of hundreds of special packages called modules.

To avoid duplicated efforts and to save time in developing new modules, later modules choose to use functions developed on early modules; that is, they depend on early modules.

The advantage is obvious because developers can save lots of time and effort when building and testing a new module. However, one disadvantage is that installation becomes difficult.

There are two competing approaches:

In this chapter, we have discussed one of the most important properties of Python: modules. A module is a package written by an expert or any individual to serve a special purpose. The knowledge related to modules is essential in our understanding of Python and its application to finance. In particular, we have introduced and discussed the most important modules, such as NumPy, SciPy, matplotlib, statsmodels, pandas, and pandas_reader. In addition, we have briefly mentioned module dependency and other issues. Two financial calculators written in Python were also presented. In Chapter 3, Time Value of Money, we will discuss many basic concepts associated with finance, such as the present value of one future cash flow, present value of perpetuity, present value of growing perpetuity, present value of annuity, and formulas related to future values. In addition, we will discuss definitions of Net Present Value (NPV), Internal Rate of Return (IRR), and Payback period. After that, several...