INTRODUCTION TO R FOR FINANCE Part I

R introduction

R studio http://www.rstudio.com

• R Studio
  • Editor
    
  • Console
  • Environment
• Create project
  • -> File -> New Project -> Existing Directory -> …directory… -> Create Project
  • Create new a new R script (Ctrl + Shift + N), Save current document (Ctrl + s)

R introduction

Packages

• Packages
  • Installing packages:
    • install.packages(“package_name”)
      
  • Library:
    • library(package_name)
• Editor
  • Execution of the code: Ctrl + Enter
    
• Good practice in writing a code: https://google.github.io/styleguide/Rguide.xml
• Rcommended book (if you plan to develop further as a data scientists): https://r4ds.had.co.nz/index.html
• Be careful of letters capital vs lowercase
• Commenting line: # (Ctrl + Shift + c)
• help: ?function_name

# install.packages("tidyverse")
# library(tidyverse)

Basic operations

• Basic arithmetics:
  • Addition: +
  • Subtraction: -
  • Multiplication: *
  • Division: /
  • Exponentiation: ^
  • Modulo: %%
  • Natural log: log(x)
  • log10, log2, log(x, base)
  • Sum: sum(x)
  • Exponential function : exp(x)
  • Square: sqrt(x)

Excercise 1
Calculate the following operations:

2 + 5
12 - 15
3 * 7
16 / 4
4 ^ 2
23 %% 7
log(2.81)
sum(2, 5)
exp(5)
sqrt(256)
log(exp(3))
log10(1e7)

Calculate: the square of natural logarithm from the 2 to the power of 16

sqrt(log(2 ^ 16))

Logical operations

• Logical operations:
  • < for less than
  • > for greater than
  • <= for less than or equal to
  • >= for greater than or equal to
  • == for equal to each other
  • != not equal to each other

Excercise 2

Check whether: +\(\frac{1}{(1+0.03)^2}\) is grater than \(\frac{1}{(1+0.03/4)^8}\)

Note
Note the likely problem when using == floating point numbers.

sqrt(2) ^ 2 == 2
1 / 49 * 49 == 1

It is often better to use near() instead of ==

near(sqrt(2) ^ 2,  2)
near(1 / 49 * 49, 1)

Basic objects in R

Variables

• Assigning values to variables(!!!): <-

var1 <- 144
var1
sqrt(var1)
var2 <- sqrt(var1)
var2
var3 <- sum(sqrt(var1), 8)
var3

Excercise 3

1. Creat veriable called df and assigne the value of \(\frac{1}{(1+5.7\%)^4}\). Print the variable.

df <- 1 / (1 + 0.057) ^ 4

2. Create variable ir with assigned value 5.7% and use this variable instead of explicitly declared value in point (b). Print the variable ir and df.
3. Change the value of ir to 6.8% then print the variable ir and df.

ir <- 0.057
df <- 1 / (1 + ir) ^ 4

Basic objects in R

Data types

• Data types:
  • Numeric: 12.4
    
  • Character: "Low"
    
  • Logical: TRUE, FALSE
• Check class of variable: class()

var1 <- 12.4
var1
position <- "Short"
var4 <- TRUE

Vector

Declaration

A vector is a sequence of data elements of the same basic type.

• numeric_vector: -50, 2, 3, 54

• character_vector: "a", "b", "c"

• boolean_vector: TRUE, FALSE, FALSE

• To declare a vector we use c function
  

• To assigne name to vector object use <-

c(-50, 2, 3, 54)
c("a", "b", "c")
c(TRUE, FALSE, FALSE)

vector_cf <- c(-50, 2, 3, 54)

• Assigning names of vector elements:

names(vector_cf) <- c("CF_1", "CF_2", "CF_3", "CF_4")

Vector

Operations

• Select element of a vector:

vector_cf[1]
vector_cf[4]
vector_cf[c(2, 4)]
vector_cf[c("CF_1", "CF_3")]

• Sum two or more vectors:

vector_cf_1 <- c(10, 10, 10, 12)
vector_cf_2 <- c(1, -2, 1, 0)
vector_cf + vector_cf_1 

Vector_cf_3 <- vector_cf + vector_cf_1 + vector_cf_2

• Other operations on multiple vectors:
  • Subtraction: -
  • Multiplication: *
  • log()
  • …

log(vector_cf_1)
vector_cf_1 ^ 2
vector_cf_2 / vector_cf_1

Vector

Operations on a single vector

• Functions
  • sum(): Calculate the sum of all the values in a data structure
  • mean(): Calculate the arithmetic mean
  • median(): Compute the sample median
  • sd(): Computes the standard deviation
  • max(): Returns the mximum
  • min(): Returns the minimum
  • abs(): Calculate the absolute value
  • rev(): Reverse the elements in a data structures for which reversal is defined
  • sort(): Sort a vector in ascending order
  • c(): Combine values into a vector or list
  • append(): Merge vectors or lists

Excercise 4

1. Claculate following statistics for the vector (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10):

• sum
• standard deviation
• minimum
• maximum

sum(c(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10))
# or declare a vector:
vector_1 <- c(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
sum(vector_1)
sd(vector_1)
min(vector_1)
max(vector_1)

2. Check which is higher: mean or median, for the vector, which is a sum of vector (1, 2, 3, 4, 5, 6, 7, 8, 9, 10) and its nalural logarithm?

vector_2 <- c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10) + log(c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10))
median(vector_2) > mean(vector_2)

Vector

Other usful operations

• seq(): Generate sequences, by specifying the from, to, and by arguments.
• rep(): Replicate elements of vectors and lists.

seq(from = 0, to = 10, by = 1) 
seq(0, 10, 1)
seq(-2, 12, 4)
seq(10, -10, -2)
rep(2, 12)

Excercise 5
1. Generate vector (10, 8, 6, 4, 2, 0, -2, -4, -6, -8, -10) using seq() function.

seq(10, -10, -2)

2. Create a vector cf of cash payments: 10$ per year for next 9 years and 100 for the end of 10th year.
   
3. Create a vector of years corresponding to cash flows in point 2.

cf <- c(rep(10, 9), 100)
year <- seq(1, 10, 1)
# year <- c(1:10)

Data frame

Data frame

Fundamental data structure, coupled collections of variables. How to create data frame containing our vectors?

data.frame(cf, year)
# create object data frame and assigne name cf_data
cf_data <- data.frame(cf, year)

Check the structure of data frame: str()
How to select data from data frame?

# 1st way
cf_data[1, 2]
cf_data[1, ]
cf_data[, 1]

# 2nd way
cf_data$cf
cf_data$year

cf_data$cf[10]

How to create new values in a data frame (table)?

# add vector cf_2 with values equal cf * 2:
cf_data$cf_2 <- 2 * cf_data$cf

Data frame

Excercise 6
Calculate present value of the cash flows: 8$ paid at the end of each year 1 till 10th, 12$ at the end of each year from 11 till 20th and additional 100$ at the end of year 20th. Discount rate is 6% for first 12 years and 7.5% for remaining period.

Hint:

• Create vectors:
  • cf containting cash flows
    
  • r containing rates
  • year containing consecutive period numbers from 1 till 20
• put these vectors into data frame called cf_data using data.frame function (print the cf_data to get familiar with the structure of the data)
  
• just add a new vector (column) to the cf_data that will contain present value of each cash flow cf_data$persent_value_cf <- ...here type the formula for PV... using the relevent vector names from cf_data like cf_data$cf instead of declaring values explicitly;)

\(PV = \frac{1}{(1 + r) ^ t}\)

• and sum the elements of the newly created vector
  hope you got something like 124.2177

Solution:

cf <- c(rep(8, 10), rep(12, 9), 112)
year <- seq(1, 20, 1)
r <- c(rep(0.06, 12), rep(0.075, 8))
cf_data <- data.frame(cf, year, r)

cf_data$pv_cf <- cf_data$cf / (1 + cf_data$r) ^ cf_data$year

sum(cf_data$pv_cf)