First, for Python language, an empty space or spaces is very important. For example, if we accidently have a space before typing pv=100, we will see the following error message:

The name of the error is called IndentationError. The reason is that, for Python, indentation is important. Later in the chapter, we will learn that a proper indentation will regulate/define how we write a function or why a group of codes belongs to a specific topic, function, or loop.

Assume that we deposit $100 in the bank today. What will be the value 3 years later if the bank offers us an annual deposit rate of 1.5%? The related codes is shown here:

>>>pv=100
>>>pv
    100
>>>pv*(1+0.015)**3
    104.56783749999997
>>>

In the preceding codes, ** means a power function. For example, 2**3 has a value of 8. To view the value of a variable, we simply type its name; see the previous example. The formula used is given here:

Here, FV is the future value, PV is the present value, R is the period deposit rate while n is the number of periods. In this case, R is the annual rate of 0.015 while n is 3. At the moment, readers should focus on simple Python concepts and operations.

In Chapter 3, Time Value of Money, this formula will be explained in detail. Since Python is case-sensitive, an error message will pop up if we type PV instead of pv; see the following code:

>>>PV
NameError: name 'PV' is not defined
>>>Traceback (most recent call last):
  File "<stdin>", line 1, in <module>

Unlike some languages, such as C and FORTRAN, for Python a new variable does not need to be defined before a value is assigned to it. To show all variables or function, we use the dir() function:

>>>dir()
['__builtins__', '__doc__', '__loader__', '__name__', '__package__', '__spec__', 'pv']
>>>

To find out all built-in functions, we type dir(__builtings__). The output is shown here:

Assume that we are interested in writing a Python function for equation (1).

After launching Spyder, click File, then New File. We write the following two lines, as shown in the left panel. The keyword def is for function,fv_f is the function name, and the three values of pv, r , and n in the pair of parentheses are input variables.

The colon (:) indicates the function hasn't finished yet. After we hit the Enter key, the next line will be automatically indented.

After we enter return pv*(1+r)**n and hit the Enter key twice, this simple program is completed. Obviously, for the second line, ** represents a power function.

Assume that we save it under c:/temp/temp.py:

To run or debug the program, click the arrow key under Run on the menu bar; see the preceding top-right image. The compiling result is shown by the bottom image right (the second image on top right). Now, we can use this function easily by calling it with three input values:

>>>fv_f(100,0.1,2)
     121.00000000000001
>>>fv_f(100,0.02,20)
    148.59473959783548

If some comments are added by explaining the meanings of input variables, the formula used, plus a few examples, it will be extremely helpful for other users or programmers. Check the following program with comments:

def pv_f(fv,r,n):
    """Objective: estimate present value
                     fv
    formula  : pv=-------------
                   (1+r)^n
          fv: fture value
          r : discount periodic rate
          n : number of periods

    Example #1  >>>pv_f(100,0.1,1)
                   90.9090909090909
    
    Example #2: >>>pv_f(r=0.1,fv=100,n=1)
                    90.9090909090909
    """
    return fv/(1+r)**n

The comments or explanations are included in a pair of three double quotation marks (""" and """). The indentation within a comment is not consequential. When compiling, the underlying software will ignore all comments. The beauty of those comments is that we can use help(pv_f) to see them, as illustrated here:

In Chapter 2, Introduction to Python Modules, we will show how to upload a financial calculator written in Python, and in Chapter 3, Time Value of Money, we will explain how to generate such a financial calculator.

In this section, we discuss a very important concept: loop or loops. A loop is used to repeat the same task with slightly different input or other factors.

Python loops, if...else conditions

Let's look at a simple loop through all the data items in an array:

>>>import numpy as np
>>>cashFlows=np.array([-100,50,40,30])
>>>for cash in cashFlows:
...    print(cash)
... 
-100
50
40
30

One type of data is called a tuple, where we use a pair of parentheses, (), to include all input values. One feature of a tuple variable is that we cannot modify its value. This special property could be valuable if some our variables should never be changed.A tuple is different from a dictionary, which stores data with key-value pairs. It is not ordered and it requires that the keys are hashable. Unlike a tuple, the value for a dictionary can be modified.

Note that for Python, the subscription for a vector or tuple starts from 0. If x has a length of 3, the subscriptions will be 0, 1 and 2:

>>> x=[1,2,3]
>>>x[0]=2
>>>x
>>>
     [2, 2, 3]
>>> y=(7,8,9)
>>>y[0]=10
>>>
TypeError: 'tuple' object does not support item assignment
>>>Traceback (most recent call last):
  File "<stdin>", line 1, in <module>

>>>type(x)
>>>
<class'list'>
>>>type(y)
>>>
<class'tuple'>
>>>

Assuming that we invest $100 today and $30 next year, the future cash inflow will be $10, $40, $50, $45, and $20 at the end of each year for the next 5 years, starting at the end of the second year; see the following timeline and its corresponding cash flows:

-100    -30       10       40        50         45       20
|--------|---------|--------|---------|----------|--------|
0        1         2        3         4          5        6

What is the Net Present Value (NPV) if the discount rate is 3.5%? NPVis defined as the present values of all benefits minus the present values of all costs. If a cash inflow has a positive sign while a cash outflow has a negative sign, then NPV can be defined conveniently as the summation of the present values of all cash flows. The present value of one future value is estimated by applying the following formula:

Here,PV is the present value, FV is the future value,R is the period discount rate and n is the number of periods. In Chapter 3, Time Value of Money, the meaning of this formula will be explained in more detail. At the moment, we just want to write annpv_f() function which applies the preceding equation n times, where n is the number of cash flows. The complete NPV program is given here:

def npv_f(rate, cashflows):
       total = 0.0
       for i in range(0,len(cashflows)):
             total += cashflows[i] / (1 + rate)**i
       return total

In the program, we used a for loop. Again, the correct indentation is important for Python. Lines from 2 to 5 are all indented by one unit, thus they belong to the same function, called npv_f. Similarly, line 4 is indented two units, that is, after the second column (:), it belongs to the forloop. The command of total +=a is equivalent to total=total +a.

For the NPV function, we use a for loop. Note that the subscription of a vector in Python starts from zero, and the intermediate variable i starts from zero as well. We could call this function easily by entering two sets of input values. The output is shown here:

>>>r=0.035
>>>cashflows=[-100,-30,10,40,50,45,20]
>>>npv_f(r,cashflows)
14.158224763725372 

Here is another npv_f() function with a function called enumerate(). This function willgenerate a pair of indices, starting from0, and its corresponding value:

def npv_f(rate, cashflows):
      total = 0.0
      for i, cashflow in enumerate(cashflows):
               total += cashflow / (1 + rate)**i
      return total

Here is an example illustrating the usage of enumerate():

x=["a","b","z"]
for i, value in enumerate(x):
      print(i, value)

Unlike the npv_f function specified previously, the NPV function from Microsoft Excel is actually a PV function, meaning that it can be applied only to the future values. Its equivalent Python program, which is called npv_Excel, is shown here:

def npv_Excel(rate, cashflows):
       total = 0.0
       for i, cashflow in enumerate(cashflows):
                total += cashflow / (1 + rate)**(i+1)
       return total

The comparisons are shown in the following table. The result from the Python program is shown in the left panel while the result by calling the Excel NPV function is shown in the right panel. Please pay enough attention to the preceding program shown itself and how to call such a function:

By using a loop, we can repeat the same task with different inputs. For example, we plan to print a set of values. The following is such an example for a while loop:

i=1
while(i<10):
      print(i)
      i+=1

The following program will report a discount (or any number of discount rates), making its corresponding NPV equal zero. Assume the cash flow will be 550, -500, -500, -500, and 1000 at time 0, at the end of each year of the next 4 years. In Chapter 3, Time Value of Money, we will explain the concept of this exercise in more detail.

Write a Python program to find out which discount rate makes NPV equal zero. Since the direction of cash flows changes twice, we might have two different rates making NPV equal zero:

cashFlows=(550,-500,-500,-500,1000)
r=0
while(r<1.0):
     r+=0.000001
     npv=npv_f(r,cashFlows)
     if(abs(npv)<=0.0001):
            print(r)

The corresponding output is given here:

0.07163900000005098
0.33673299999790873

Later in the chapter, a forloop is used to estimate the NPV of a project.

When we need to use a few math functions, we can import the math module first:

>>>import math
>>>dir(math)
['__doc__', '__loader__', '__name__', '__package__', '__spec__', 'acos', 'acosh', 'asin', 'asinh', 'atan', 'atan2', 'atanh', 'ceil', 'copysign', 'cos', 'cosh', 'degrees', 'e', 'erf', 'erfc', 'exp', 'expm1', 'fabs', 'factorial', 'floor', 'fmod', 'frexp', 'fsum', 'gamma', 'gcd', 'hypot', 'inf', 'isclose', 'isfinite', 'isinf', 'isnan', 'ldexp', 'lgamma', 'log', 'log10', 'log1p', 'log2', 'modf', 'nan', 'pi', 'pow', 'radians', 'sin', 'sinh', 'sqrt', 'tan', 'tanh', 'trunc']
>>>math.pi
3.141592653589793
>>>

The sqrt(), square root, function is contained in the math module. Thus, to use the sqrt() function, we need to use math.sqrt(); see the following code:

>>>sqrt(2)
NameError: name 'sqrt' is not defined
>>>Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
math.sqrt(2)
1.4142135623730951
>>>

If we want to call those functions directly, we can use from math import *; see the following code:

>>>from math import *
>>>sqrt(3)
1.7320508075688772
>>>

To learn about individual embedded functions, we can use thehelp() function;see the following code:

>>>help(len)
Help on built-in function len in module builtins:
len(obj, /)
    Return the number of items in a container.
>>>

Let's generate a very simple input dataset first, as shown here. Its name and location is c:/temp/test.txt. The format of the dataset is text:

a b
1 2
3 4

The code is shown here:

>>>f=open("c:/temp/test.txt","r")
>>>x=f.read()
>>>f.close()

The print() function could be used to show the value of x:

>>>print(x)
a b
1 2
3 4
>>>

For the second example, let's download the daily historical price for IBM from Yahoo!Finance first. To do so, we visit http://finance.yahoo.com:

Enter IBM to find its related web page. Then click Historical Data, then click Download:

Assume that we save the daily data as ibm.csv under c:/temp/. The first five lines are shown here:

Date,Open,High,Low,Close,Volume,Adj Close
2016-11-04,152.399994,153.639999,151.869995,152.429993,2440700,152.429993
2016-11-03,152.509995,153.740005,151.800003,152.369995,2878800,152.369995
2016-11-02,152.479996,153.350006,151.669998,151.949997,3074400,151.949997
2016-11-01,153.50,153.910004,151.740005,152.789993,3191900,152.789993

The first line shows the variable names: date, open price, high price achieved during the trading day, low price achieved during the trading day, close price of the last transaction during the trading day, trading volume, and adjusted price for the trading day. The delimiter is a comma. There are several ways of loading the text file. Some methods are discussed here:

Alternatively, we could download the IBM daily price data directly from Yahoo!Finance; see the following code:

>>> import pandas as pd
>>>url=url='http://canisius.edu/~yany/data/ibm.csv'
>>> x=pd.read_csv(url)
>>>x[1:5]
         Date        Open        High         Low       Close   Volume  \
1  2016-11-03  152.509995  153.740005  151.800003  152.369995  2843600   
2  2016-11-02  152.479996  153.350006  151.669998  151.949997  3074400   
3  2016-11-01  153.500000  153.910004  151.740005  152.789993  3191900   
4  2016-10-31  152.759995  154.330002  152.759995  153.690002  3553200   

Adj Close  
1  152.369995
2  151.949997
3  152.789993
4  153.690002>>>

We could retrieve data from an Excel file by using the ExcelFile() function from thepandas module. First, we generate an Excel file with just a few observations; see the following screenshot:

Let's call this Excel file stockReturns.xlxs and assume that it is saved under c:/temp/. The Python code is given here:

>>>infile=pd.ExcelFile("c:/temp/stockReturns.xlsx")
>>> x=infile.parse("Sheet1")
>>>x
date  returnAreturnB
0  2001     0.10     0.12
1  2002     0.03     0.05
2  2003     0.12     0.15
3  2004     0.20     0.22
>>>

To retrieve Python datasets with an extension of .pkl or .pickle, we can use the following code. First, we download the Python dataset called ffMonthly.pkl from the author's web page at http://www3.canisius.edu/~yany/python/ffMonthly.pkl.

Assume that the dataset is saved under c:/temp/. The function called read_pickle() included in the pandas module can be used to load the dataset with an extension of .pkl or .pickle:

>>> import pandas as pd
>>> x=pd.read_pickle("c:/temp/ffMonthly.pkl")
>>>x[1:3]
>>>
Mkt_RfSMBHMLRf
196308  0.0507 -0.0085  0.0163  0.0042
196309 -0.0157 -0.0050  0.0019 -0.0080
>>>

The following is the simplest if function: when our interest rate is negative, print a warning message:

if(r<0):
    print("interest rate is less than zero")

Conditions related to logical AND and OR are shown here:

>>>if(a>0 and b>0):
  print("both positive")
>>>if(a>0 or b>0):
  print("at least one is positive")

For the multiple if...elif conditions, the following program illustrates its application by converting a number grade to a letter grade:

grade=74
if grade>=90:
    print('A')
elif grade >=85:
    print('A-')
elif grade >=80:
    print('B+')
elif grade >=75:
    print('B')
elif grade >=70:
    print('B-')
elif grade>=65:
    print('C+')
else:
    print('D')

Note that it is a good idea for such multiple if...elif functions to end with an else condition since we know exactly what the result is if none of those conditions are met.

There are many different types of data, such as integer, real number, or string. The following table offers a list of those data types:

In the following examples, we assign a value to r, which is a scalar, and several values to pv, which is an array (vector).The type() function is used to show their types:

>>> import numpy as np
>>> r=0.023
>>>pv=np.array([100,300,500])
>>>type(r)
<class'float'>
>>>type(pv)
<class'numpy.ndarray'>

To choose the appropriate decision, we use the round()function; see the following example:

>>> 7/3
2.3333333333333335
>>>round(7/3,5)
2.33333
>>>

For data manipulation, let's look at some simple operations:

>>>import numpy as np
>>>a=np.zeros(10)                      # array with 10 zeros 
>>>b=np.zeros((3,2),dtype=float)       # 3 by 2 with zeros 
>>>c=np.ones((4,3),float)              # 4 by 3 with all ones 
>>>d=np.array(range(10),float)         # 0,1, 2,3 .. up to 9 
>>>e1=np.identity(4)                   # identity 4 by 4 matrix 
>>>e2=np.eye(4)                        # same as above 
>>>e3=np.eye(4,k=1)                    # 1 start from k 
>>>f=np.arange(1,20,3,float)           # from 1 to 19 interval 3 
>>>g=np.array([[2,2,2],[3,3,3]])       # 2 by 3 
>>>h=np.zeros_like(g)                  # all zeros 
>>>i=np.ones_like(g)                   # all ones

Some so-called dot functions are quite handy and useful:

>>> import numpy as np
>>> x=np.array([10,20,30])
>>>x.sum()
60

Anything after the number sign of # will be a comment. Arrays are another important data type:

>>>import numpy as np
>>>x=np.array([[1,2],[5,6],[7,9]])      # a 3 by 2 array
>>>y=x.flatten()
>>>x2=np.reshape(y,[2,3]              ) # a 2 by 3 array

We could assign a string to a variable:

>>> t="This is great"
>>>t.upper()
'THIS IS GREAT'
>>>

To find out all string-related functions, we use dir(''); see the following code:

>>>dir('')
['__add__', '__class__', '__contains__', '__delattr__', '__dir__', '__doc__', '__eq__', '__format__', '__ge__', '__getattribute__', '__getitem__', '__getnewargs__', '__gt__', '__hash__', '__init__', '__iter__', '__le__', '__len__', '__lt__', '__mod__', '__mul__', '__ne__', '__new__', '__reduce__', '__reduce_ex__', '__repr__', '__rmod__', '__rmul__', '__setattr__', '__sizeof__', '__str__', '__subclasshook__', 'capitalize', 'casefold', 'center', 'count', 'encode', 'endswith', 'expandtabs', 'find', 'format', 'format_map', 'index', 'isalnum', 'isalpha', 'isdecimal', 'isdigit', 'isidentifier', 'islower', 'isnumeric', 'isprintable', 'isspace', 'istitle', 'isupper', 'join', 'ljust', 'lower', 'lstrip', 'maketrans', 'partition', 'replace', 'rfind', 'rindex', 'rjust', 'rpartition', 'rsplit', 'rstrip', 'split', 'splitlines', 'startswith', 'strip', 'swapcase', 'title', 'translate', 'upper', 'zfill']
>>>

For example, from the preceding list we see a function called split. After typinghelp(''.split), we will have related help information:

>>>help(''.split)
Help on built-in function split:

split(...) method of builtins.str instance
S.split(sep=None, maxsplit=-1) -> list of strings

    Return a list of the words in S, using sep as the
delimiter string. If maxsplit is given, at most maxsplit
splits are done. If sep is not specified or is None, any
whitespace string is a separator and empty strings are
removed from the result.
>>>

We could try the following example:

>>> x="this is great"
>>>x.split()
['this', 'is', 'great']
>>>

Matrix manipulation is important when we deal with various matrices:

The condition for equation (3) is that matrices A and B should have the same dimensions. For the product of two matrices, we have the following equation:

Here,A is an n by k matrix (n rows and k columns), while B is a k by m matrix. Remember that the second dimension of the first matrix should be the same as the first dimension of the second matrix. In this case, it is k. If we assume that the individual data items in C, A, and B are Ci,j (the ith row and the jth column), Ai,j, and Bi,j, we have the following relationship between them:

The dot() function from the NumPy module could be used to carry the preceding matrix multiplication:

>>>a=np.array([[1,2,3],[4,5,6]],float)    # 2 by 3
>>>b=np.array([[1,2],[3,3],[4,5]],float)  # 3 by 2
>>>np.dot(a,b)                            # 2 by 2
>>>print(np.dot(a,b))
array([[ 19.,  23.],
[ 43.,  53.]])
>>>

We could manually calculate c(1,1): 1*1 + 2*3 + 3*4=19.

After retrieving data or downloading data from the internet, we need to process it. Such a skill to process various types of raw data is vital to finance students and to professionals working in the finance industry. Here we will see how to download price data and then estimate returns.

Assume that we have n values of x1, x2, … and xn. There exist two types of means: arithmetic mean and geometric mean; see their genetic definitions here:

Assume that there exist three values of 2,3, and 4. Their arithmetic and geometric means are calculated here:

>>>(2+3+4)/3.
>>>3.0
>>>geo_mean=(2*3*4)**(1./3)
>>>round(geo_mean,4) 
2.8845

For returns, the arithmetic mean's definition remains the same, while the geometric mean of returns is defined differently; see the following equations:

In Chapter 3, Time Value of Money, we will discuss both means again.

We could say that NumPy is a basic module while SciPy is a more advanced one. NumPy tries to retain all features supported by either of its predecessors, while most new features belong in SciPy rather than NumPy. On the other hand, NumPy and SciPy have many overlapping features in terms of functions for finance. For those two types of definitions, see the following example:

>>> import scipy as sp
>>> ret=sp.array([0.1,0.05,-0.02])
>>>sp.mean(ret)
0.043333333333333342
>>>pow(sp.prod(ret+1),1./len(ret))-1 
0.042163887067679262

Our second example is related to processing theFama-French 3 factor time series. Since this example is more complex than the previous one, if a user feels it is difficult to understand, he/she could simply skip this example. First, a ZIP file called F-F_Research_Data_Factor_TXT.zip could be downloaded from Prof. French's Data Library. After unzipping and removing the first few lines and annual datasets, we will have a monthly Fama-French factor time series. The first few lines and last few lines are shown here:

DATE    MKT_RFSMBHMLRF
192607    2.96   -2.30   -2.87    0.22
192608    2.64   -1.40    4.19    0.25
192609    0.36   -1.32    0.01    0.23

201607    3.95    2.90   -0.98    0.02
201608    0.49    0.94    3.18    0.02
201609    0.25    2.00   -1.34    0.02

Assume that the final file is called ffMonthly.txt under c:/temp/. The following program is used to retrieve and process the data:

import numpy as np
import pandas as pd
file=open("c:/temp/ffMonthly.txt","r")
data=file.readlines()
f=[]
index=[]
for i in range(1,np.size(data)):
    t=data[i].split()
    index.append(int(t[0]))
    for j in range(1,5):
        k=float(t[j])
        f.append(k/100)
n=len(f) 
f1=np.reshape(f,[n/4,4])
ff=pd.DataFrame(f1,index=index,columns=['Mkt_Rf','SMB','HML','Rf'])

To view the first and last few observations for the dataset called ff, the functions of .head() and .tail()can be used:

The simplest example is given here:

>>>f=open("c:/temp/out.txt","w")
>>>x="This is great"
>>>f.write(x)
>>>f.close()

For the next example, we download historical stock price data first, then write data to an output file:

import re
from matplotlib.finance import quotes_historical_yahoo_ochl
ticker='dell'
outfile=open("c:/temp/dell.txt","w")
begdate=(2013,1,1)
enddate=(2016,11,9)
p=quotes_historical_yahoo_ochl
(ticker,begdate,enddate,asobject=True,adjusted=True)
outfile.write(str(p))
outfile.close()

To retrieve the file, we have the following code:

>>>infile=open("c:/temp/dell.txt","r")
>>>x=infile.read()

One issue is that the preceding saved text file contains many unnecessary characters, such as [ and]. We could apply a substitution function called sub() contained in the Python module;see the simplest example given here:

>>> import re
>>>re.sub("a","9","abc")
>>>
'9bc'
>>>

In the preceding example, we will replace the letter a with9. Interested readers could try the following two lines of code for the preceding program:

p2= re.sub('[\(\)\{\}\.<>a-zA-Z]','', p)
outfile.write(p2)

It is a good idea to generate Python datasets with an extension of .pickle since we can retrieve such data quite efficiently. The following is the complete Python code to generate ffMonthly.pickle. Here, we show how to download price data and then estimate returns:

import numpy as np
import pandas as pd
file=open("c:/temp/ffMonthly.txt","r")
data=file.readlines()
f=[]
index=[]
for i in range(1,np.size(data)):
    t=data[i].split()
    index.append(int(t[0]))
    for j in range(1,5):
        k=float(t[j])
        f.append(k/100)
n=len(f)
f1=np.reshape(f,[n/4,4])
ff=pd.DataFrame(f1,index=index,columns=['Mkt_Rf','SMB','HML','Rf'])
ff.to_pickle("c:/temp/ffMonthly.pickle")

In this chapter, many basic concepts and several widely used functions related to Python werediscussed. In Chapter 2, Introduction to Python Modules, we will discuss a key component of the Python language: Python modules and theirrelated issues. A module is a set of programs written by experts, professionals, or any person around a specific topic. A module could be viewed as a toolbox for a specific task. The chapter willfocus on the five most important modules: NumPy, SciPy, matplotlib, statsmodels, and pandas.