Functions

Introduction

We can write our own functions in R. This will be useful as it will prevent us having to re-write difficult code over and over again. Remember the return calculation that we did last week. I do not want to have to do that again.

A function is an object just like everything else and we use the function function to create a new function. For example,

mysquare <- function(x){
  mynumber <- x^2
  return(mynumber)
  }

Look at this carefully. Make sure that you know what is happening.

Exercise 1.0

• Write a function that will double the number that you input

• Write a function that will multiply any number by 5

• Update the function so that it will multiply one number by another

---

Future values

Remember that the equation for future values is

\[FV = PV * (1 + R)^n\]

where FV is the future value, R is the rate of return and n is the number of years into the future. Therefore, if I have $100 and there is an interest rate or rate of return of 5% (0.05), I will have:

\[100 * (1 + 0.05)^5\]

in 5 years.

Now we write a function to make this calculation.

futurevalue <- function(PV = 100, R = 0.05, n = 1){
FV = PV * (1 + R)^n
return(FV)
}
futurevalue()

## [1] 105

futurevalue(PV = 25.5, R = 0.055, n = 4)

## [1] 31.59003

}

Exercise 2.0

• You have five customers with, $100, $250, $355 and £400 in their accounts. Assuming that the interest rate is 7.25% for all the customers, what will they have in their account in 5 years time?

Present value

Re-arrange the future value into present value:

\[PV = \frac{FV}{(1 + R)^n}\]

Exercise 3.0

• Write the function for Present value.

• You have 3 bonds that will mature at 100 in 5, 3 and 2 years. If the rate of return for all the bonds is 3.5%, what should be the price of these bonds?

Advanced function

This is an advanced function that will calculate the key descriptive statistics for our series.

mystats <- function(x){
  if(NA %in% x){
    x <- x[!is.na(x)]
    warning("NA removed")
  }
  mynumber <- length(x)
  mymean <- mean(x)
  mymed <- median(x)
  mysd <- sd(x)
  myskew <- sum((x-mymean)^3/mysd^3)/mynumber
  mykurt <- sum((x - mymean)^4/mysd^4)/mynumber - 3
  mymax <- max(x)
  mymin <- min(x)
  return(c("Number" = round(mynumber, 0), 
           "Mean" = round(mymean, 4),
           "Median" = round(mymed, 4),
           "St Dev" = round(mysd, 4), 
           "Skew" = round(myskew, 2), 
           "Kurtosis" = round(mykurt, 2),
           "Min" = round(mymin, 4),
           "Max" = round(mymax, 4))) 

}
mydata <- rnorm(10000)
mystats(mydata)

##     Number       Mean     Median     St Dev       Skew   Kurtosis        Min 
## 10000.0000     0.0043     0.0012     1.0002    -0.0300    -0.0200    -3.5981 
##        Max 
##     4.1257

Exercise 4.0

• Re-run the code for Bank of America and the S&P 500 that we had last week and then calculate the descriptive statistics

• Turn the re-basing calculation that we did last week into a function

• Turn the return calculation into a function

• Put all the functions into a file that you can access. Load these functions using ``source(‘functionfilename’)```